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SUDAN, R. and P. KAW (1981). “STABILIZING EFFECT OF FINITE-GYRORADIUS BEAM PARTICLES ON THE TILTING MODE OF SPHEROMAKS.” PHYSICAL REVIEW LETTERS 47(8): 575-578.

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YAMADA, M., H. FURTH, et al. (1981). “QUASISTATIC FORMATION OF THE SPHEROMAK PLASMA CONFIGURATION.” PHYSICAL REVIEW LETTERS 46(3): 188-191.

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GOLDENBAUM, G. (1982). “THE PHYSICS OF SPHEROMAK.” PHYSICA SCRIPTA T2(SI): 359-366.

HEIDBRINK, W., S. JARDIN, et al. (1982). “TEARING-MODE STABILITY OF A FORMING SPHEROMAK PLASMA.” NUCLEAR FUSION 22(4): 459-464.

JARDIN, S. (1982). “IDEAL MAGNETO-HYDRODYNAMIC STABILITY OF THE SPHEROMAK CONFIGURATION.” NUCLEAR FUSION 22(5): 629-642.

KATSURAI, M. and M. YAMADA (1982). “STUDIES OF CONCEPTUAL SPHEROMAK FUSION-REACTORS.” NUCLEAR FUSION 22(11): 1407-1419.

MARCHAND, R. and P. GUZDAR (1982). “COLLISIONAL DRIFT WAVES IN A SPHEROMAK GEOMETRY.” PHYSICS OF FLUIDS 25(11): 2037-2044.

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REIMAN, A. (1982). “COALESCENCE OF SPHEROMAKS.” PHYSICS OF FLUIDS 25(10): 1885-1893.

BRUHNS, H., C. CHINFATT, et al. (1983). “EXPERIMENTAL STUDIES OF SPHEROMAK FORMATION.” PHYSICS OF FLUIDS 26(6): 1616-1625.

GOLDENBAUM, G., H. BRUHNS, et al. (1983). “EXPERIMENTAL SPHEROMAK MHD STABILITY STUDIES.” NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH 207(1-2): 129-133.

HAMMETT, G. and W. TANG (1983). “KINETIC AND RESISTIVE EFFECTS ON INTERCHANGE INSTABILITIES FOR A CYLINDRICAL MODEL SPHEROMAK.” NUCLEAR FUSION 23(11): 1503-1506.

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JARBOE, T., I. HENINS, et al. (1983). “SLOW FORMATION AND SUSTAINMENT OF SPHEROMAKS BY A CO-AXIAL MAGNETIZED PLASMA SOURCE.” PHYSICAL REVIEW LETTERS 51(1): 39-42.

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OLSON, R. and G. MILEY (1983). “COMPUTATIONAL SIMULATION OF SPHEROMAK PLASMA-HEATING.” NUCLEAR TECHNOLOGY-FUSION 4(2): 1459-1464.

PARK, W. and S. JARDIN (1983). “NON-LINEAR SATURATION OF NON-RESONANT INTERNAL INSTABILITIES IN A STRAIGHT SPHEROMAK.” PHYSICS OF FLUIDS 26(7): 1871-1873.

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QUINN, W. (1983). “COMPACT TOROID EXPERIMENTS - SPHEROMAKS AND FIELD-REVERSED CONFIGURATIONS.” NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH 207(1-2): 121-127.

SAOUTIC, B. and C. CHOI (1983). “FEASIBILITY WINDOWS FOR THE GYROSCOPIC STABILIZATION OF A SPHEROMAK CONFIGURATION.” TRANSACTIONS OF THE AMERICAN NUCLEAR SOCIETY 44: 126-127.

SATO, T. and T. HAYASHI (1983). “3-DIMENSIONAL SIMULATION OF SPHEROMAK CREATION AND TILTING DISRUPTION.” PHYSICAL REVIEW LETTERS 50(1): 38-40.

SATO, T., Y. ODA, et al. (1983). “NUMERICAL-SIMULATION OF AXISYMMETRIC SPHEROMAK MERGING.” PHYSICS OF FLUIDS 26(12): 3602-3611.

SATO, T., A. TODD, et al. (1983). “NUMERICAL-SIMULATION OF SLOW SPHEROMAK FORMATION - FLUX CONTROL BY FORMATION SPEED.” PHYSICS OF FLUIDS 26(3): 775-779.

BARNES, C., T. JARBOE, et al. (1984). “SPHEROMAK FORMATION AND OPERATION WITH BACKGROUND FILLING GAS AND A SOLID FLUX CONSERVER IN CTX.” NUCLEAR FUSION 24(3): 267-281.

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DELUCIA, J. and S. JARDIN (1984). “NONLINEAR EVOLUTION OF THE RESISTIVE INTERCHANGE MODE IN THE CYLINDRICAL SPHEROMAK.” PHYSICS OF FLUIDS 27(7): 1773-1784.

FINN, J. (1984). “TILT AND SHIFT MODE-STABILITY IN A SPHEROMAK WITH A FLUX CORE.” PHYSICS OF FLUIDS 27(12): 2973-2975.

GRANATSTEIN, V. and K. CHU (1984). “ELECTRON-CYCLOTRON RESONANCE HEATING (ECRH) OF A SPHEROMAK PLASMA.” IEEE TRANSACTIONS ON PLASMA SCIENCE 12(2): 144-149.

HAYASHI, T. and T. SATO (1984). “SIMULATION STUDIES ON LINE-TYING STABILIZATION OF SPHEROMAK TILTING INSTABILITY.” PHYSICS OF FLUIDS 27(4): 778-780.

HONMA, T., M. KITO, et al. (1984). “MHD STABILITY ANALYSIS OF AXISYMMETRIC SURFACE CURRENT MODEL TOKAMAKS CLOSE TO THE SPHEROMAK REGIME.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 53(5): 1737-1745.

JARBOE, T., C. BARNES, et al. (1984). “THE OHMIC HEATING OF A SPHEROMAK TO 100 EV.” PHYSICS OF FLUIDS 27(1): 13-15.

KANEKO, S., A. TAKIMOTO, et al. (1984). “MAGNETOHYDRODYNAMIC EQUILIBRIUM AND STABILITY OF SPHEROMAK PLASMA IN FLUX CONSERVER.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 53(1): 201-209.

LITWIN, C., R. SUDAN, et al. (1984). “STABILIZATION OF THE SPHEROMAK TILT INSTABILITY.” PHYSICS OF FLUIDS 27(12): 2791-2793.

MEYERHOFER, D. and F. PERKINS (1984). “CURRENT-DRIVEN INSTABILITIES OF THE KINETIC SHEAR ALFVEN-WAVE - APPLICATION TO REVERSED FIELD PINCHES AND SPHEROMAKS.” PHYSICS OF FLUIDS 27(10): 2483-2492.

MOORE, R., C. MACEY, et al. (1984). “SURFACE PREPARATION OF THE S-1-SPHEROMAK FLUX CORE LINER.” THIN SOLID FILMS 118(1): 15-21.

BARNES, C., T. JARBOE, et al. (1985). “ZERO-DIMENSIONAL ENERGY-BALANCE MODELING OF THE CTX SPHEROMAK EXPERIMENT.” NUCLEAR FUSION 25(11): 1657-1675.

BARNES, C., H. HOIDA, et al. (1985). “INCREASED PARTICLE CONFINEMENT OBSERVED WITH THE USE OF AN EXTERNAL DC BIAS FIELD IN A SPHEROMAK EXPERIMENT.” PHYSICS OF FLUIDS 28(12): 3443-3446.

FREIRE, E. and R. CLEMENTE (1985). “CRITICAL BETA FOR ANALYTICAL SPHEROMAK EQUILIBRIA.” PLASMA PHYSICS AND CONTROLLED FUSION 27(4): 389-394.

GUZDAR, P., J. FINN, et al. (1985). “THE ROLE OF MAGNETIC RECONNECTION AND DIFFERENTIAL ROTATION IN SPHEROMAK FORMATION.” PHYSICS OF FLUIDS 28(10): 3154-3166.

HAGENSON, R. and R. KRAKOWSKI (1985). “STEADY-STATE SPHEROMAK REACTOR STUDIES.” FUSION TECHNOLOGY 8(1): 1606-1612.

HAYASHI, T., T. SATO, et al. (1985). “SPHEROMAK TILTING INSTABILITY AND MAGNETIC RECONNECTION - SIMULATION AND EXPERIMENT.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 54(11): 4172-4177.

HAYASHI, T. and T. SATO (1985). “SPHEROMAK GLOBAL INSTABILITIES AND STABILIZATION BY NEARBY CONDUCTORS.” PHYSICS OF FLUIDS 28(12): 3654-3666.

IVANOV, K. and A. HARSHILADZE (1985). “INTERPLANETARY HYDROMAGNETIC CLOUDS AS FLARE-GENERATED SPHEROMAKS.” SOLAR PHYSICS 98(2): 379-386.

JANOS, A., G. HART, et al. (1985). “RELAXATION OF SPHEROMAK PLASMAS TOWARD A MINIMUM-ENERGY STATE AND GLOBAL MAGNETIC FLUCTUATIONS.” PHYSICAL REVIEW LETTERS 55(26): 2868-2871.

JANOS, A., G. HART, et al. (1985). “GLOBAL MAGNETIC FLUCTUATIONS IN SPHEROMAK PLASMAS AND RELAXATION TOWARD A MINIMUM-ENERGY STATE.” PHYSICS OF FLUIDS 28(12): 3667-3675.

KANEKO, S., H. TSUTSUI, et al. (1985). “MAGNETOHYDRODYNAMIC STABILITY OF SPHEROMAK PLASMA IN TOROIDAL FLUX CONSERVER WITH RECTANGULAR CROSS-SECTION .2. APPLICATION OF MERCIER CRITERION.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 54(12): 4570-4575.

KANEKO, S. and A. KAMITANI (1985). “MAGNETOHYDRODYNAMIC EQUILIBRIUM CONFIGURATION BY BODY-FITTED CURVILINEAR COORDINATE SYSTEM - APPLICATION TO SPHEROMAK.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 54(2): 458-461.

KANEKO, S., A. KAMITANI, et al. (1985). “MAGNETOHYDRODYNAMIC EQUILIBRIUM AND STABILITY OF SPHEROMAK WITH SPHEROIDAL PLASMA-VACUUM INTERFACE.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 54(9): 3347-3357.

KATSURAI, M. (1985). “SPHEROMAK AND ITS APPLICATION TO FUSION-REACTORS.” JOURNAL OF THE ATOMIC ENERGY SOCIETY OF JAPAN 27(10): 885-889.

KONDOH, Y. (1985). “AVAILABLE BETA-VALUE FOR TOKAMAK, SCREW-PINCH, SPHEROMAK, AND REVERSED-FIELD-PINCH IN PARTIALLY RELAXED STATES.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 54(6): 2065-2068.

MUNSON, C., A. JANOS, et al. (1985). “EXPERIMENTAL CONTROL OF THE SPHEROMAK TILTING INSTABILITY.” PHYSICS OF FLUIDS 28(5): 1525-1527.

ODA, Y. (1985). “3D MHD SIMULATION STUDY ON PRESSURE-DRIVEN INSTABILITY OF SPHEROMAK IN A FLUX CONSERVER.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 54(3): 958-966.

TAGUCHI, M., T. MIYAZAKI, et al. (1985). “MAGNETOHYDRODYNAMIC STABILITY OF SPHEROMAK PLASMA IN TOROIDAL FLUX CONSERVER WITH RECTANGULAR CROSS-SECTION.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 54(6): 2163-2167.

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YAMADA, M. (1985). “S-1 SPHEROMAK.” NUCLEAR FUSION 25(9): 1327-1330.

BARNES, C., J. FERNANDEZ, et al. (1986). “EXPERIMENTAL-DETERMINATION OF THE CONSERVATION OF MAGNETIC HELICITY FROM THE BALANCE BETWEEN SOURCE AND SPHEROMAK.” PHYSICS OF FLUIDS 29(10): 3415-3432.

BOYD, D. (1986). “NEW DIAGNOSTIC FOR SPHEROMAKS - WHAT ARE THE POSSIBILITIES.” REVIEW OF SCIENTIFIC INSTRUMENTS 57(8): 1962-1964.

GOLDENBAUM, G., R. HESS, et al. (1986). “CRITICAL-FIELD INDEX FOR PASSIVE COIL STABILIZATION OF THE SPHEROMAK SHIFT INSTABILITY.” REVIEW OF SCIENTIFIC INSTRUMENTS 57(12): 2961-2965.

HART, G., A. JANOS, et al. (1986). “VERIFICATION OF THE TAYLOR (MINIMUM ENERGY) STATE IN A SPHEROMAK.” PHYSICS OF FLUIDS 29(6): 1994-1997.

JANOS, A. and M. YAMADA (1986). “INDUCTIVE SUSTAINMENT OF SPHEROMAKS.” FUSION TECHNOLOGY 9(1): 58-68.

JANOS, A. (1986). “MAGNETIC-FLUX CONVERSION AND RELAXATION TOWARD A MINIMUM-ENERGY STATE IN SPHEROMAK PLASMAS.” PHYSICS OF FLUIDS 29(10): 3342-3355.

JARDIN, S., A. JANOS, et al. (1986). “THE EFFECT OF A COLUMN INDUCTIVE TRANSFORMER ON THE S-1 SPHEROMAK.” NUCLEAR FUSION 26(5): 647-655.

KANEKO, S. and A. KAMITANI (1986). “MAGNETOHYDRODYNAMIC STABILITY OF SPHEROMAK PLASMA IN SPHEROIDAL FLUX CONSERVER - APPLICATION OF MERCIER CRITERION.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 55(6): 1918-1924.

KATAYAMA, K. and M. KATSURAI (1986). “3-DIMENSIONAL NUMERICAL SIMULATIONS OF THE RELAXATION PROCESS IN SPHEROMAK PLASMAS.” PHYSICS OF FLUIDS 29(6): 1939-1947.

KNOX, S., C. BARNES, et al. (1986). “OBSERVATIONS OF SPHEROMAK EQUILIBRIA WHICH DIFFER FROM THE MINIMUM-ENERGY STATE AND HAVE INTERNAL KINK DISTORTIONS.” PHYSICAL REVIEW LETTERS 56(8): 842-845.

MEYERHOFER, D., R. HULSE, et al. (1986). “ZERO-DIMENSIONAL STUDY OF THE COMPRESSION OF LOW-TEMPERATURE SPHEROMAKS.” NUCLEAR FUSION 26(2): 235-241.

YAMADA, M. (1986). “REVIEW OF EXPERIMENTAL SPHEROMAK RESEARCH AND FUTURE-PROSPECTS.” FUSION TECHNOLOGY 9(1): 38-47.

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BENNETT, C. (1987). “SPHEROMAK MODEL OF PLANETARY-NEBULAE.” ASTROPHYSICAL JOURNAL 323(2): L 123-L 125.

BRUHNS, H., R. BRENDEL, et al. (1987). “STUDY OF THE LOW ASPECT RATIO LIMIT TOKAMAK IN THE HEIDELBERG SPHEROMAK EXPERIMENT.” NUCLEAR FUSION 27(12): 2178-2182.

HAYASHI, T. and T. SATO (1987). “A 3-DIMENSIONAL STUDY OF SPINNING SPHEROMAK.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 56(6): 2039-2045.

KAMITANI, A., S. KANEKO, et al. (1987). “MAGNETOHYDRODYNAMIC EQUILIBRIUM AND STABILITY OF SPHEROMAK BY BOUNDARY-FITTED CURVILINEAR COORDINATE SYSTEM - IMPROVEMENT OF PLASMA-CONFINEMENT BY EXTERNAL COIL.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 56(8): 2755-2764.

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SGRO, A., A. MIRIN, et al. (1987). “THE EVOLUTION OF A DECAYING SPHEROMAK.” PHYSICS OF FLUIDS 30(10): 3219-3236.

SHAW, R. and J. FINN (1987). “AXISYMMETRICAL EQUILIBRIA IN THE MARYLAND SPHEROMAK.” NUCLEAR FUSION 27(8): 1309-1317.

SHAW, R., J. BOOSKE, et al. (1987). “BROAD-BAND CALIBRATION FOR MAGNETIC PROBES FOR USE IN THE MARYLAND SPHEROMAK.” REVIEW OF SCIENTIFIC INSTRUMENTS 58(7): 1204-1210.

THROUMOULOPOULOS, G. and G. PANTIS (1987). “ANALYTIC, AXISYMMETRICAL MHD SPHEROMAK TYPE EQUILIBRIA IN PARABOLIC-COORDINATES.” PHYSICS LETTERS A 121(8-9): 423-426.

UYAMA, T., Y. HONDA, et al. (1987). “TEMPORAL EVOLUTION OF THE DECAYING SPHEROMAK IN THE CTCC-I EXPERIMENT.” NUCLEAR FUSION 27(5): 799-813.

WYSOCKI, F. (1987). “EXPERIMENTAL INVESTIGATION OF LINE-TYING EFFECTS ON THE SPHEROMAK TILT MODE.” JOURNAL OF NUCLEAR MATERIALS 147(EB): 480-486.

WYSOCKI, F. (1987). “EXPERIMENTAL INVESTIGATION OF LINE-TYING EFFECTS ON THE SPHEROMAK TILT MODE.” PHYSICS OF FLUIDS 30(2): 482-498.

BOOZER, A. (1988). “OSCILLATING FIELD CURRENT DRIVE IN SPHEROMAKS.” PHYSICS OF FLUIDS 31(11): 3338-3340.

FERNANDEZ, J., C. BARNES, et al. (1988). “ENERGY CONFINEMENT STUDIES IN SPHEROMAKS WITH MESH FLUX CONSERVERS.” NUCLEAR FUSION 28(9): 1555-1594.

HONDA, Y., Y. KATO, et al. (1988). “THE INSTABILITY OBSERVED IN THE CTCC-I SPHEROMAK PLASMA.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 57(4): 1273-1280.

KAMITANI, A. (1988). “STABILITY OF SPHEROMAK AGAINST CURRENT DRIVEN MODES - EFFECTS OF FLUX HOLE ON STABILITY.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 57(11): 3809-3819.

KANEKO, S. and H. TSUTSUI (1988). “STABILITY OF FORCE-FREE SPHEROMAK PLASMA IN SPHEROIDAL FLUX CONSERVER.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 57(1): 108-116.

LITWIN, C. and R. SUDAN (1988). “EFFECT OF A STRONG-CURRENT ION RING ON SPHEROMAK STABILITY.” PHYSICS OF FLUIDS 31(3): 423-426.

MAYO, R. and G. MARKLIN (1988). “NUMERICAL-CALCULATION OF MERCIER BETA-LIMITS IN SPHEROMAKS.” PHYSICS OF FLUIDS 31(6): 1812-1815.

MEHANIAN, C. and R. LOVELACE (1988). “SPHEROMAK TILT STABILIZATION WITH AN ENERGETIC PARTICLE COMPONENT.” PHYSICS OF FLUIDS 31(6): 1681-1689.

MEYERHOFER, D., F. LEVINTON, et al. (1988). “PARTICLE DIFFUSION IN A SPHEROMAK.” PHYSICAL REVIEW LETTERS 60(10): 933-936.

ONO, Y., R. ELLIS, et al. (1988). “RELAXATION PHENOMENA IN THE HIGH-TEMPERATURE S-1 SPHEROMAK.” PHYSICAL REVIEW LETTERS 61(25): 2847-2850.

PEYSER, T. and G. GOLDENBAUM (1988). “PLASMA ROTATION DURING SPHEROMAK FORMATION.” PHYSICAL REVIEW LETTERS 61(8): 955-958.

WYSOCKI, F., J. FERNANDEZ, et al. (1988). “EVIDENCE FOR A PRESSURE-DRIVEN INSTABILITY IN THE CTX SPHEROMAK.” PHYSICAL REVIEW LETTERS 61(21): 2457-2460.

AMEMIYA, N., K. TAKAICHI, et al. (1989). “MAGNETIC-STRUCTURE IN THE ENTRANCE REGION OF SPHEROMAKS SUSTAINED BY A MAGNETIZED COAXIAL PLASMA GUN UNDER LONG PULSE OPERATION.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 58(6): 2049-2061.

FERNANDEZ, J., B. WRIGHT, et al. (1989). “THE M=1 HELICITY SOURCE SPHEROMAK EXPERIMENT.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 1(6): 1254-1270.

MAYO, R., F. LEVINTON, et al. (1989). “MEASUREMENT OF THE LOCAL CARBON DIFFUSION-COEFFICIENT IN THE S-1 SPHEROMAK.” NUCLEAR FUSION 29(9): 1493-1504.

TUSZEWSKI, M. and B. WRIGHT (1989). “OBSERVATION OF FIELD-REVERSED CONFIGURATIONS WITH SPHEROMAK MAGNETIC-FIELD PROFILES.” PHYSICAL REVIEW LETTERS 63(20): 2236-2239.

BARNES, C., T. JARBOE, et al. (1990). “THE IMPEDANCE AND ENERGY EFFICIENCY OF A COAXIAL MAGNETIZED PLASMA SOURCE USED FOR SPHEROMAK FORMATION AND SUSTAINMENT.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 2(8): 1871-1888.

BARROW, B. and G. GOLDENBAUM (1990). “MECHANICAL INJECTION OF MAGNETIC HELICITY DURING SPHEROMAK FORMATION.” PHYSICAL REVIEW LETTERS 64(12): 1369-1372.

BROWN, M. and P. BELLAN (1990). “CURRENT DRIVE BY SPHEROMAK INJECTION INTO A TOKAMAK.” PHYSICAL REVIEW LETTERS 64(18): 2144-2147.

BROWN, M. and P. BELLAN (1990). “SPHEROMAK INJECTION INTO A TOKAMAK.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 2(6): 1306-1310.

DIXON, A., P. BROWNING, et al. (1990). “RELAXED STATES IN A SPHEROMAK WITH INHOMOGENEOUS BOUNDARY FIELDS.” JOURNAL OF PLASMA PHYSICS 43(UN): 357-383.

FERNANDEZ, J., T. JARBOE, et al. (1990). “ION HEATING AND CURRENT DRIVE FROM RELAXATION IN DECAYING SPHEROMAKS IN MESH FLUX CONSERVERS.” NUCLEAR FUSION 30(1): 67-80.

JARBOE, T., F. WYSOCKI, et al. (1990). “PROGRESS WITH ENERGY CONFINEMENT TIME IN THE CTX SPHEROMAK.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 2(6): 1342-1346.

KANEKO, S. and Y. WANG (1990). “EFFECTS OF CENTRAL CONDUCTING POLE AND CHOKING CURRENT ON CONFINEMENT OF SPHEROMAK WITH FLUX HOLE.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 59(2): 553-561.

KATO, Y., N. SATOMI, et al. (1990). “IMPURITY BEHAVIOR AND ENERGY-BALANCE ON CTCC-SPHEROMAK.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 59(3): 939-953.

KITSON, D. and P. BROWNING (1990). “PARTIALLY RELAXED MAGNETIC-FIELD EQUILIBRIA IN A GUN-INJECTED SPHEROMAK.” PLASMA PHYSICS AND CONTROLLED FUSION 32(14): 1265-1287.
The UMIST spheromak (SPHEX) is a gun-injected spheromak similar in design to the Los Alamos spheromak CTX. A numerical code was written to calculate the possible zero pressure gradient axisymmetric spheromak equilibria, which deviate from the minimum energy relaxed states (del x B = mu-B, mu # constant), by solving a non-linear Grad-Shafranov equation in SPHEX geometry. It is demonstrated mathematically that in certain circumstances there exist two equilibria for the same boundary conditions. We also show that if mu is not a constant then the energy increases to infinity as a specified weighted average approaches a critical value. The relevant parameters of these equilibria (e.g. helicity, magnetic energy etc.) are calculated and their interdependence studied.

LEVINTON, F., D. MEYERHOFER, et al. (1990). “CONFINEMENT AND POWER BALANCE IN THE S-1 SPHEROMAK.” NUCLEAR FUSION 30(5): 871-879.

MAYO, R., C. CHOI, et al. (1990). “EFFECT OF NEUTRAL PARTICLES ON THE ENERGY CONFINEMENT OF SPHEROMAKS.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 2(1): 115-122.

SAHLIN, P., W. PIERCE, et al. (1990). “NUMERICAL DRIFT ORBIT CALCULATIONS FOR FORCE-FREE SPHEROMAK CONFIGURATIONS.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 2(3): 554-560.

THROUMOULOPOULOS, G. and G. PANTIS (1990). “AXISYMMETRICAL FORCE-FREE STATES AND RELAXATION OF A SPHEROIDAL SPHEROMAK.” PLASMA PHYSICS AND CONTROLLED FUSION 32(7): 541-551.

WRIGHT, B. (1990). “FIELD REVERSED CONFIGURATIONS AND SPHEROMAKS.” NUCLEAR FUSION 30(9): 1739-1759.

WYSOCKI, F., J. FERNANDEZ, et al. (1990). “IMPROVED ENERGY CONFINEMENT IN SPHEROMAKS WITH REDUCED FIELD ERRORS.” PHYSICAL REVIEW LETTERS 65(1): 40-43.

YAMADA, M., T. CHU, et al. (1990). “EXPERIMENTAL INVESTIGATION OF MAGNETIC COMPRESSION OF A SPHEROMAK PLASMA.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 2(12): 3074-3080.

AMEMIYA, N., A. HAYAKAWA, et al. (1991). “FORMATION OF FREE-BOUNDARY FLUX-CORE SPHEROMAKS.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 60(8): 2632-2644.
Free-boundary flux-core spheromaks are stably produced in the external magnetic field in the TS-3 facility. In the first experiment, a z-theta-discharge is initiated with the reversed bias magnetic field, and the axial current is supplied to amplify the magnetic flux. The flux-core spheromak can be sustained by this axial current. Its lifetime is about 120-mu-s. In the second experiment, only by the axial current, the flux-core spheromak is successfully produced in the reversed bias magnetic field. Its lifetime is larger than 100-mu-s. The force-free parameter mu-is estimated. It is almost time invariant, while the discharge current is changing sinusoidally. It is 11 m-1 in the first experiment and 12.6 m-1 in the second experiment, and is smaller than the eigenvalue of the spheromak with no external magnetic flux.

BROWN, M., A. BAILEY, et al. (1991). “CHARACTERIZATION OF A SPHEROMAK PLASMA GUN - THE EFFECT OF REFRACTORY ELECTRODE COATINGS.” JOURNAL OF APPLIED PHYSICS 69(9): 6302-6312.
In order to investigate the proposition that high-Z impurities are responsible for the anomalously short lifetime of the Caltech spheromak, the center electrode of the spheromak plasma gun has been coated with a variety of metals (bare steel, copper, nickel, chromium, rhodium, and tungsten). Visible light (230-890 nm) emitted directly from the plasma in the gun breech was monitored for each of the coated electrodes. Plasma density and temperature and spheromak lifetime were compared for each electrode. Results indicate little difference in gun performance or macroscopic plasma parameters. The chromium and tungsten electrodes performed marginally better in that a previously reported helicity injection effect [Phys. Rev. Lett. 64, 2144 (1990)] is only observed in discharges using these electrode coatings. There are subtle differences in the detailed line emission spectra from the different electrodes, but the spectra are remarkably similar. The fact that (1) contrary to expectations, attempts to reduce high-Z impurities had only marginal effect on the spheromak lifetime coupled with (2) an estimate of Z(eff) < 2 based on a O-D model suggests that it is not impurities but some other mechanism that limits the lifetime of small, cold spheromaks. We will discuss the general characteristics of the spheromak gun as well as effects due to the coatings.

BROWN, M., D. CUTRER, et al. (1991). “MOTION AND EQUILIBRIUM OF A SPHEROMAK IN A TOROIDAL FLUX CONSERVER.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 3(5): 1198-1213.
A number of experiments have been performed on spheromaks injected into the empty vacuum vessel of the Caltech ENCORE tokamak (i.e., without tokamak plasma) [Phys. Rev. Lett. 64, 2144 (1990); Phys. Fluids B 2, 1306 (1990)]. Magnetic probe arrays (in a number of configurations) have been used to make single shot, unaveraged, in situ measurements of the spheromak equilibrium. These measurements are important because (i) they reveal for the first time the equilibrium structure of spheromaks in a toroidal geometry, (ii) they provide a reliable estimate of magnetic helicity and energy of spheromak plasmas used in injection experiments [Phys. Rev. Lett. 64, 2144 (1990)], and (iii) they constitute the first measurements of spheromak motion across and interaction with static magnetic fields (which are useful in corroborating recent theories). Probe measurements in the tokamak dc toroidal field show for the first time that the spheromak exhibits a "double tilt." The spheromak first tilts while in the cylindrical entrance region, emerging into the tokamak vessel antialigned to the dc toroidal field, then expands into the tokamak vacuum vessel, and finally tilts again to form an oblate (nonaxisymmetric, m = 1) configuration. In addition, the spheromak drifts vertically in the direction given by J(center) X B(tok), where J(center) is the unbalanced poloidal current that threads the center of the spheromak torus. Probe arrays at different toroidal locations show that the spheromak shifts toroidally (horizontally left or right) in the direction opposite that of the static toroidal field. In the absence of toroidal flux, the m = 1 object develops a helical pitch, the sense of the pitch depending on the sign of the spheromak helicity. The spheromak equilibrium in the toroidal vessel is well fit by a pressureless infinite cylindrical model; however, there is evidence of deviation from m = 1 symmetry because of toroidal effects, nonuniform J/B profile, and finite beta. Experiments performed in a test facility consisting of the spheromak gun and a replica of the entrance region (with a closed end) show that the spheromak is generated with its axis coaxial with that of the gun. Coherent, m = 2 magnetic modes are observed during the formation stage rotating in the E X B direction at about 125 kHz (rotation velocity corresponding to 40% of the Alfven speed).

CHRIEN, R., J. FERNANDEZ, et al. (1991). “EVIDENCE FOR RUNAWAY ELECTRONS IN A SPHEROMAK PLASMA.” NUCLEAR FUSION 31(7): 1390-1393.
The first evidence for runaway electrons in a spheromak plasma is presented; it is based on the observation of hard X-ray emission with an energy of about 1 MeV. The hard X-rays are produced in one or more bursts occurring early in the spheromak decay phase, after the coaxial plasma gun voltage is turned off. No obvious correlation is found between the amplitude of the hard X-ray emission and other spheromak parameters. Since there is no direct acceleration mechanism for electrons to reach MeV energy levels, these observations imply that the runaway electrons are confined for an acceleration time of greater-than-or-equal-to 20-50-mu-s and a path length of greater-than-or-equal-to 5-10 km, assuming that the electrons are accelerated in the electric field of the decaying spheromak.

CLEGG, J., P. BROWNING, et al. (1991). “MAGNETIC-FIELD DIFFUSION AND FLUX LOSS WITHIN A SPHEROMAK.” IEEE TRANSACTIONS ON MAGNETICS 27(1): 688-697.
We consider the magnetic confinement of a plasma within a prototype controlled fusion experiment, the spheromak. This device has a containment vessel that is topologically spherical, offering considerable engineering advantages compared with conventional toroidal systems. Our aim has been to evaluate possible designs for the flux conserver and gun magnetic field coils, taking account of flux penetration into the walls caused by finite resistivity. The copper walls cannot remain perfect magnetic flux surfaces for the duration of the experiment, and we calculate the magnetic field penetration into the walls for a range of designs. This study is in response to recent results showing that wall conditions and flux loss are a vital element of the system's performance, with a substantial increase in global resistance arising if field becomes embedded in the walls creating a "dead space" that is not driven by the gun current. We develop a model bearing general application to magnetic field interaction with resistive walls in complex geometries, with particular reference to the UMIST spheromak experiment "SPHEX."

FARENGO, R. and T. JARBOE (1991). “CURRENT DRIVE BY TOKAMAK INJECTION.” FUSION TECHNOLOGY 20(4): 407-410.
A scheme for tokamak formation and sustainment via helicity injection is proposed. The method consists of injecting "source" tokamaks into a "steady" tokamak to sustain its current. The source tokamaks are created using an ohmic heating coil fed from one end and are accelerated toward the steady tokamak by the combined effect of line tension and a mirror field. High efficiency, conservation of toroidal symmetry, and injection of an inductively generated, fairly hot plasma are the relevant features of this method.

FINN, J. and P. GUZDAR (1991). “FORMATION OF A FLUX CORE SPHEROMAK.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 3(4): 1041-1051.
An alternate design for compact tori, specifically of the spheromak type, is studied. In this design, the "flux core spheromak" [Nucl. Fusion 29, 219 (1989)], the externally imposed bias field links the confinement region of closed flux surfaces. The advantages of this configuration are: (i) it enjoys greater stability to magnetohydrodynamic (MHD) modes, particularly the tilt and shift; (ii) it has a poloidal divertor, and an amount of poloidal flux separating the closed flux surface region from the walls; and (iii) it might be sustained by helicity injection. Results are presented showing the dependence of the geometry on the distribution of bias flux on the conducting walls and showing the optimization of the 2-D formation scheme to minimize the contact of the plasma with coils, electrodes, and walls. This last topic involves taking advantage of current sheet formation and subsequent tearing, as in formation of the MS spheromak [Phys. Fluids 28, 3154 (1985)]. The parameters which can be varied to produce this favorable formation scheme via tearing, rather than a formation that proceeds off the reversal coils, are explored. In addition, it is found that there is strong viscous heating of the ions in this early reconnection phase.

HAMMER, J., J. EDDLEMAN, et al. (1991). “EXPERIMENTAL DEMONSTRATION OF COMPACT TORUS COMPRESSION AND ACCELERATION.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 3(8): 2236-2240.
Tests of compact torus (CT) compression on the RACE device [Phys. Rev. Lett. 61, 2843 (1988)] have successfully demonstrated stable compression by a factor of 2 in radius, field amplification by factors of 2-3 to 20 kG, and compressed densities exceeding 10(16) cm-3. The results are in good agreement with two-dimensional magnetohydrodynamic simulations of the CT dynamics. The CT is formed between a pair of coaxial conical conductors that serve as both a flux conserver for stable, symmetric formation and as electrodes for the compression and acceleration phases. The CT is compressed by J x B forces (poloidal current, toroidal field) when a 120 kV, 260 kJ capacitor bank is discharged across the electrodes. The CT reaches two-fold compression to a radius of 8 cm and a length of 20-30 cm near the time of peak current, 10-mu-sec (many Alfven times) after the accelerator fire time, and is subsequently accelerated in a 150 cm straight coaxial section to velocities in the range 1.5-6.5 x 10(7) cm/sec. A new set of acceleration/focusing electrodes 740 cm in length are projected to give an additional factor of 3 in radial compression with final velocities of 1-3 x 10(8) cm/sec (similar to previously achieved on RACE) and incident power densities of a few x 10(11) W/cm2. Compact torus accelerators scaled to multimegajoules have the potential to achieve unprecedented plasma velocities and power densities with many applications in high-energy-density physics.

KAMITANI, A., S. KANEKO, et al. (1991). “STABILITY ANALYSIS OF SPHEROMAK BY ERATO-J CODE AGAINST INTERNAL-MODES.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 60(2): 512-517.
The stability of the spheromak against low n (n = 1, 2, 3, 4, 5) and localized modes is investigated by use of ERATO-J code and by means of the Mercier criterion. Here n is the toroidal mode number. The shape of the plasma is assumed to simulate the experimental plasma in the flux conserver of CTCC-II at Osaka University. The beta limits for these modes are evaluated as a function of q(axis) to elucidate which mode gives a lower limit. Here q(axis) is the value of the safety factor on the magnetic axis. As a result, the beta limit of the spheromak is shown to be determined by the n = 1, the n = 2 and the localized modes. However, the Mercier criterion is shown to give an excellent measure for the stability against internal modes, if q(axis less-than-or-equal-to 0.9.

MAYO, R., J. FERNANDEZ, et al. (1991). “TIME OF FLIGHT MEASUREMENT OF ION TEMPERATURES IN SPHEROMAKS.” NUCLEAR FUSION 31(11): 2087-2095.
The energy distribution of neutral particles is detected from spheromak plasmas by a time of flight neutral atom spectrometer. These particles originate in charge exchange interactions within the bulk plasma and carry the temperature of the majority ion component. This is the first direct measurement of temperatures of the main ion species in spheromaks. The data are found to be in the range of 500 eV during the sustainment and late decay phases and are in agreement with impurity Doppler temperatures for species expected to be localized to the plasma centre.

MAYO, R., F. WYSOCKI, et al. (1991). “A MODEL FOR DETERMINING RELAXATION ELECTRIC-FIELDS IN SPHEROMAKS.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 3(11): 3160-3166.
Past spheromak experiments have experienced poor confinement [Nucl. Fusion 28, 1555 (1988); Phys. Fluids B 2, 115 (1990)] as a result of edge-dominated helicity dissipation due to substantial field error and edge neutral inventory. Recent works have identified the importance of edge helicity loss and its effects on confinement [Phys. Fluids B 2, 115 (1990)]. Herein, the results of the edge helicity dissipation model [Phys. Fluids 30, 1177 (1987)] are applied to determine the relative magnitudes of electric fields during relaxation in spheromaks. This is achieved by quantifying the average electric field in the plasma edge region generated by (a) flux decay and (b) relaxation mechanism(s). It is shown that relaxation electric fields can be as much as three times the flux decay field in the edge. The model also correctly predicts no relaxation electric field when the spheromak is a cold, purely resistively decaying object. In addition, the model provides an estimate for the quantity of magnetic decay power from relaxation, which can be as much as 75% of the total decay power.

MAYO, R. and L. KIRSCHENBAUM (1991). “NEUTRAL PARTICLE ENERGY ANALYSIS AND CHARGE-EXCHANGE POWER LOSS IN EDGE-DOMINATED SPHEROMAKS.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 3(8): 2096-2100.
Neutral particle density profiles have previously been calculated for spheromak plasmas [Phys. Fluids B2 (1990) 115]. Here, the formalism is extended to calculate the one-dimensional (1-D) profile of the egressing neutral energy flux to correctly treat profile and attenuation effects. If is found that the energy flux profile is strongly dependent on T(i),T(e),n(e) profiles and magnitudes, and regions of the plasma have been identified as localized "hot spots" for charge-exchange power loss in some cases. In addition, the total charge exchange power loss is found to be in order-of-magnitude agreement with predictions from a zero-dimensional (0-D) model and can account for the bulk of the edge-dominated spheromak power loss.

MOLVIK, A., J. EDDLEMAN, et al. (1991). “QUASI-STATIC COMPRESSION OF A COMPACT TORUS.” PHYSICAL REVIEW LETTERS 66(2): 165-168.
We have demonstrated the formation of stable, symmetric, compact-torus (CT) plasma rings and the subsequent stable, twofold radial compression in coaxial conical electrodes with the ring accelerator experiment. The CT is compressed by J x B forces from a capacitor bank discharging across the conical electrodes. During compression, the force of the B-theta acceleration field balances the force of the CT poloidal field against the cones, in good agreement with a 2D MHD code. Power amplification factors of approximately 100 may be possible with an opening switch based on this technique.

NAGATA, M., T. MASUDA, et al. (1991). “FORMATION AND SUSTAINMENT OF A SPHEROMAK WITH BIAS FLUX BY DC HELICITY INJECTION.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 60(10): 3203-3206.
The formation and sustainment of a spheromak plasma with bias flux has been demonstrated successfully by "DC" or "electrostatic" helicity injection. The experimental results show that, as the helicity injection rate is increased, the self-generated toroidal plasma current and the toroidal flux increase significantly. By examination of the contours of poloidal flux of the sustained spheromak, we have verified the formation of the magnetic configuration with the external bias flux linking the region of the closed flux surfaces. In addition, it has been found that the lambda-spk = j parellel-to / B value of the sustained spheromak configurations with a small amount of the closed flux in the flux conserver has been affected by the ratio of the electrode current to the bias flux.

ONO, Y. and M. KATSURAI (1991). “3-DIMENSIONAL NUMERICAL-SIMULATION OF THE MULTI-HELICITY MAGNETOHYDRODYNAMIC RELAXATION PROCESS IN LOW-Q SPHEROMAKS.” NUCLEAR FUSION 31(2): 233-244.
Three-dimensional magnetohydrodynamic computer simulations have been made on the dynamic behaviour of the high temperature spheromak plasma whose conductivity profile is peaked at the magnetic axis. On the assumption of stationary spatial profiles of the plasma conductivity, these simulations examine the transient process from the current peaking to the subsequent relaxation. They reveal low-q relaxations caused by multi-helicity (current driven) kink modes. The low-q relaxations are classified into two types: the fast-type relaxation without n = 2 mode saturation and the slow-type relaxation with n = 2 mode saturation. In these simulations, resistive current loss in the outer region of the plasma causes a peaking of the current density profile, resulting in a departure from the initial Taylor state to a low-q state. As the q value at the magnetic axis, q0, decreases to < 0.5, the internal kink mode with a toroidal mode number n = 2 is first destabilized. The feature of the subsequent relaxation process depends on the degree of peaking of the conductivity profile at the magnetic axis, including its change during the relaxation phase. When the peaking of the conductivity profile is strong enough to decrease q0 to much less than 0.5, the higher mode (the n = 3 mode) is destabilized, which is found to trigger the subsequent relaxation. During the relaxation phase, the non-linear coupling of these n = 2 and 3 (and sometimes 4) modes leads to flux conversion from poloidal to toroidal and the configuration with the excessive poloidal flux can relax back to a state close to the Taylor state with a balanced ratio of the poloidal flux to the toroidal flux. This is the scenario of the fast-type relaxation. On the other hand, when the conductivity profile is weakly peaked, the slow decrease in q0 causes a slow growth of the n = 3 mode, resulting in the saturation of the n = 2 mode. Even if the coupling of the n = 2 and 3 modes triggers a relaxation, the relaxation event is weak, unclear and incomplete. This is the scenario of the slow-type relaxation. It is also found that if the peaked conductivity profile is maintained during the relaxation phase, relaxation back to the Taylor state is less complete.

ONO, Y., M. YAMADA, et al. (1991). “EXPERIMENTAL-STUDY OF THE RELAXATION CYCLE OF A DECAYING SPHEROMAK IN AN EXTERNAL MAGNETIC-FIELD.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 3(6): 1452-1460.
For high electron temperature plasma discharges in the S-1 spheromak device [Plasma Physics and Controlled Nuclear Fusion Research, 1984 (IAEA, Vienna, 1985), Vol. 2, p. 535], "sawtooth"- like oscillations appear on signals of magnetic field, flux, q value, and electron temperature. Based on the internal magnetic field profiles measured by magnetic probe scans, the mechanisms and causes of these oscillations are revealed. The cycle of one oscillation consists of a toroidal current peaking phase and a subsequent relaxation phase. In the peaking phase, resistive current decay at the edge causes the spheromak to deviate from the initial minimum-energy Taylor state. The deviation was revealed experimentally by the preferential decay of toroidal flux over poloidal flux. A simple calculation shows that a peaking of the electron temperature profile is the most probable cause for the preferential decay of toroidal flux over poloidal flux. During the peaking phase, q decreases so low as to make the configuration unstable to low-n magnetohydrodynamic (MHD) modes (mainly n = 2 mode). In the relaxation phase, these modes invoke current redistribution (relaxation), restoring the Taylor state. A significant finding in the relaxation phase is that a reversed toroidal field similar to that of the reversed-field pinch (RFP) configuration is sometimes measured at the edge of the plasma for a brief period. The disappearance or resistive decay of the reversed toroidal flux is attributed to a flux conversion through the magnetic reconnections caused by the low-n modes.

PFISTER, H. and W. GEKELMAN (1991). “DEMONSTRATION OF HELICITY CONSERVATION DURING MAGNETIC RECONNECTION USING CHRISTMAS RIBBONS.” AMERICAN JOURNAL OF PHYSICS 59(6): 497-502.
This article shows how a simple Christmas ribbon can be used to demonstrate a relatively complex physical phenomenon: the conservation of helicity during magnetic reconnection. The physical term, helicity, and the process of magnetic reconnection will be introduced and explained in detail. The "helicity meter," a very simple device that will help in the determination of the helicity of certain topological configurations, will also be introduced.

RUSBRIDGE, M. (1991). “THE RELATIONSHIP BETWEEN THE TANGLED DISCHARGE AND DYNAMO MODELS OF THE MAGNETIC-RELAXATION PROCESS.” PLASMA PHYSICS AND CONTROLLED FUSION 33(12): 1381-1389.
It is shown that these two models are closely related. The "Tangled Discharge Model" (TDM) necessarily involves a non-vanishing <v x b>, the so-called "dynamo" effect, while the effective functioning of this term in the "Dynamo" models is shown to require a stochastic magnetic field structure. There is no inconsistency between this conclusion and the fact that the fully-relaxed state may be described by analytical forms such as the "Bessel Function Model" which apparently contain good flux surfaces. The TDM is not a satisfactory description of the behaviour of present relaxed-state systems, but might be appropriate in the limit of large Lundquist number S.

SHIMAMURA, S. (1991). “FORMATION AND SUSTAINMENT OF SPHEROMAK BY USING OSCILLATING GUN CURRENT WITH DC-COMPONENT.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 60(12): 4384-4385.

TAMANO, T. (1991). “A PLASMOID MODEL FOR THE SOLAR-WIND.” SOLAR PHYSICS 134(1): 187-201.
A model describing magnetized plasmoids as a possible origin of solar wind is discussed. The magnetized plasmoids are assumed to be created and accelerated to a very high speed through reconnection processes from small-scale magnetic loops. Afterwards, the plasmoids are considered to be nearly in a relaxed state under magnetic helicity conservation and to expand freely and linearly. Characteristics of such plasmoids with finite beta are examined. The results show remarkable agreement between the model predictions and spacecraft observations including temperature characteristics such as the dependence on the heliocentric distance and ion mass. The validity of the assumptions and the applicability of the model are also discussed.

YI, P. (1991). “EQUILIBRIUM AND STABILITY OF FLUX-CORE SPHEROMAK WITH FINITE PRESSURE.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 60(10): 3359-3366.
The equilibrium and the stability of flux-core spheromak plasma with finite pressure are analyzed and the effects of the flux core are investigated. CTCC-II spheromak is used as the FC (Flux Conserver) model of the flux-core spheromak and the MHD equilibrium configurations are determined numerically. By use of these configurations, it is shown that the magnetic field profile of ordinary spheromak transits into the field profile where the toroidal magnetic field decreases monotonously with the distance from symmetric axis, when lambda decreases from lambda-0. Here, lambda is the ratio of the flux-core current to the flux of the flux core, and lambda-0 is the lowest eigenvalue of the Grad-Shafranov equation when plasma is bounded all by a conducting wall. In midway of this transition, the plasma confinement is shown to be worsened. The profiles of the safety factor q and dV/d-psi also show characteristic variation for the transition. This transition characterizes the flux-core spheromak from other reactors.

YOUNG, P., F. WYSOCKI, et al. (1991). “EXPERIMENTAL-STUDY OF A TRANSFORMER-DRIVEN SPHEROMAK PLASMA.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 3(9): 2591-2600.
An axial transformer was installed in the Proto S-1/C spheromak device [Yamada et al, Phys. Rev. Lett. 46, 188 (1981)] in order to study physics issues pertaining to sustained spheromak operation. An increase in both the toroidal plasma current and the toroidal flux was observed when the transformer current was pulsed. The ratio of these two quantities remained constant (within experimental error) indicating that the equilibrium spheromak magnetic field was maintained through a relaxation mechanism. At transformer currents of 10 kA, the toroidal current increased from 37 to 51 kA and the toroidal flux increased from 3.7 X 10(5) to 4.4 x 10(5) G cm2.

BARROW, B. and G. GOLDENBAUM (1992). “VACUUM-PLASMA BOUNDARY HELICITY INJECTION.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 4(8): 2577-2588.
The magnetic helicity inside a volume enclosed by a conducting boundary with electrodes inserted through insulator gaps has been measured. By comparing the measured time dependence of the helicity with predictions of a numerical simulation and analytic theory, the importance of the insulator gap, and injection across a vacuum-plasma boundary inside the volume has been shown.

BROWN, M. and P. BELLAN (1992). “EFFICIENCY AND SCALING OF CURRENT DRIVE AND REFUELING BY SPHEROMAK INJECTION INTO A TOKAMAK.” NUCLEAR FUSION 32(7): 1125-1137.
The first measurements of current drive (refluxing) and refuelling by spheromak injection into a tokamak are discussed in detail. The current drive mechanism is attributed to the process of helicity injection, and refuelling is attributed to the rapid incorporation of the dense spheromak plasma into the tokamak. After an abrupt increase (up to 80%), the tokamak current decays by a factor of three because of plasma cooling caused by the merging of the relatively cold spheromak with thc tokamak. The tokamak density profile peaks sharply because of the injected spheromak plasma (n(e) increases by a factor of six) and then becomes hollow, suggestive of an interchange instability. Also discussed is the energy efficiency of spheromak injection current drive and the scaling of this process to larger machines. Refuelling by spheromak injection appears to be a viable scheme for larger machines. However, refluxing by spheromak injection is limited by geometrical and electrical efficiencies (both about 10%) as well as a high repetition rate requirement.

BROWNING, P., G. CUNNINGHAM, et al. (1992). “POWER FLOW IN A GUN-INJECTED SPHEROMAK PLASMA.” PHYSICAL REVIEW LETTERS 68(11): 1718-1721.
We describe results from the gun-injected spheromak device SPHEX, which show that the power required to sustain the plasma is initially deposited in a column, about 8 cm in radius, along the geometric axis of the device, and is transmitted from the column to the remainder of the plasma by a radially propagating oscillation at about 20 kHz. These results are relevant to the process of relaxation in spheromak systems.

BROWNING, P., G. CUNNINGHAM, et al. (1992). “INJECTION AND SUSTAINMENT OF PLASMA IN A PREEXISTING TOROIDAL FIELD USING A COAXIAL HELICITY SOURCE.” PHYSICAL REVIEW LETTERS 68(11): 1722-1725.
The spheromak device SPHEX has been modified by adding a current-carrying rod along the geometric axis, providing a preexisting toroidal field. We show that plasma can be successfully injected into such a field from a helicity source; the field assists plasma ejection from the gun and improves the coupling between gun and plasma, so that T(e), T(i), and the toroidal current all increase with rod current. The mechanism or plasma sustainment appears to be the same as that of the spheromak. These results represent a step towards the achievement of steady-state tokamak operation.

ELIEZER, S., Y. PAISS, et al. (1992). “GENERATION OF A POLOIDAL MAGNETIC-FIELD BY CIRCULARLY POLARIZED LASER-LIGHT.” PHYSICS LETTERS A 164(5-6): 416-418.
Circularly polarized laser light can be used to produce a poloidal magnetic field in laser produced inertially confined plasmas. The poloidal field combined with the naturally occurring toroidal field, gives a spheromak like magnetic field, which could be beneficial as a thermal insulator.

HORIUCHI, R., T. SATO, et al. (1992). “SIMULATION STUDY OF STEPWISE RELAXATION IN A SPHEROMAK PLASMA.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 4(3): 672-682.
The energy relaxation process of a spheromak plasma in a flux conserver is investigated by means of a three-dimensional magnetohydrodynamic simulation. The resistive decay of an initial force-free profile brings the spheromak plasma to an m = 1/n = 2 ideal kink unstable region. It is found that the energy relaxation takes place in two steps; namely, the relaxation consists of two physically distinguished phases, and there exists an intermediate phase in between, during which the relaxation becomes inactive temporarily. The first relaxation corresponds to the transition from an axially symmetric force-free state to a helically symmetric one with an n = 2 crescent magnetic island structure via the helical kink instability. The n = 2 helical structure is nonlinearly sustained in the intermediate phase. The helical twisting of the flux tube creates a reconnection current in the vicinity of the geometrical axis. The second relaxation is triggered by the rapid growth of the n = 1 mode when the reconnection current exceeds a critical value. The helical twisting relaxes through magnetic reconnection toward an axially symmetric force-free state. It is also found that the poloidal flux reduces during the helical twisting in the first relaxation and the generation of the toroidal flux occurs through the magnetic reconnection process in the second relaxation.

MAYO, R. (1992). “INITIAL RESULTS FROM ION TEMPERATURE PROFILE DECONVOLUTION IN COMPACT TORI.” FUSION TECHNOLOGY 21(3): 1635-1638.
Data from single chord Doppler ion temperature measurements in spheromaks have been analyzed with the aid of a one dimensional equilibrium charge state transport code. With electron temperature profiles known from Thomson scattering and estimates for transport rates, we can determine the radial location for the impurity line emission. The results of these analyses are the reconstruction of one dimensional ion temperature profiles. From this T(i) profile data we can now correctly calculate volume averaged confinement quantities. Our initial findings are that previously quoted values of <beta> and <tau(E)> were underestimated by a factor of approximately 4 and now the highest quoted energy confinement times are approximately 50-mu-s.

ALKARKHY, A., P. BROWNING, et al. (1993). “OBSERVATIONS OF THE MAGNETOHYDRODYNAMIC DYNAMO EFFECT IN A SPHEROMAK PLASMA.” PHYSICAL REVIEW LETTERS 70(12): 1814-1817.
We present measurements of the magnetohydrodynamic ''dynamo'' due to correlated fluctuations of velocity and magnetic field in the SPHEX spheromak. We show that there are both single-mode and turbulent dynamo processes present, although the single-mode process is in this case an ''antidynamo'' opposing the externally applied electric field. The size of the turbulent dynamo at the magnetic axis is close to that required to drive the toroidal current there.

ALY, J. (1993). “A MODEL FOR MAGNETIC ENERGY-STORAGE AND TAYLOR RELAXATION IN THE SOLAR CORONA .1. HELICITY-CONSTRAINED MINIMUM ENERGY-STATE IN A HALF-CYLINDER.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 5(1): 151-163.
The problem of the existence of a minimum energy state is studied in the set H of all the magnetic fields B: (i) occupying the half-cylinder D={r < R,z > 0}; (ii) having a normal component vanishing on the vertical part {r=R} of the boundary of D and taking given values Q(r) on its horizontal part {z=0}; (iii) having a relative helicity equal to a prescribed value H. It is first shown that the only field that may possibly be an energy minimizer in H is the unique (and therefore axisymmetric) constant-alpha force-free field B(alpha) contained in that set. Thus it is proved that Ba minimizes the energy indeed if and only if 0 less-than-or-equal-to Absolute value of H less-than-or-equal-to H(c) < infinity, where H(c) is an estimated critical value. For H(c) < Absolute value of H < infinity, on the contrary, it is possible to construct in H nonaxisymmetric fields with an energy smaller than that of B(alpha) and no minimum energy state does exist. However, B(alpha) still minimizes the energy for H(c) < Absolute value of H less than or equal to H(c)ax (with possibly H(c)ax = infinity) if attention is restricted to the axisymmetric fields of H. These results are used to put a limit on the validity of a popular model of the heating of the solar corona, in which the field of a coronal structure is supposed to release sporadically, by Taylor's relaxation, a part of the energy it continuously extracts from the kinetic energy of the photospheric motions. It is argued that, as a consequence of the results above, one of the basic assumptions of the model breaks down when the field becomes highly sheared. It is speculated that, in such a situation, a completely new regime should set up, in which helicity and energy are continuously ejected at large distances by the system.

AMEMIYA, N., A. MORITA, et al. (1993). “EXPERIMENTS OF AXIAL-COMPRESSION OF FLUX-CORE SPHEROMAK.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 62(5): 1552-1561.
The axial compression of flux-core spheromaks is successfullY made in the TS-3 facility. Magnetic measurements show that oblate and singlet magnetic configurations are obtained by the axial compression. The closed poloidal magnetic flux surrounding the magnetic axis increases up to 6 m Wb, that is three or four times larger than the closed poloidal magnetic flux obtained without the axial compression. During the early and middle phases of the compression, no global instabilities are observed, but, in the late phase, sudden collapses of the flux-core spheromak are observed. This may limit the maximum compression ratio. Fitting to an equilibrium model suggests that, by the axial compression, the ratio mu of the current density to the magnetic field, increases toward the value of the conventional spheromak without core flux.

BROWNING, P., J. CLEGG, et al. (1993). “RELAXED AND PARTIALLY RELAXED MAGNETIC EQUILIBRIA IN TIGHT-ASPECT-RATIO TORI.” PLASMA PHYSICS AND CONTROLLED FUSION 35(11): 1563-1583.
Force-free equilibrium magnetic fields in tight-aspect-ratio toroidal configurations are investigated. The study is mainly directed to modelling field configurations in the 'rodomak', a modification to the SPHEX gun-injected spheromak in which a current-carrying rod is inserted along the geometric axis. A family of analytical relaxed states (del x B = muB, mu constant) is presented for a torus of rectangular cross section, with boundary conditions allowing for flux embedded in the walls, representing the gun. Numerically calculated fields in SPHEX geometry, with mu profiles relevant to the driven phase of operation, are also given. The dependence of the field configurations and global quantities such as energy, helicity and toroidal current on the controlling parameters (gun flux, gun current and rod current) and geometry is discussed.

CHINFATT, C., A. DESILVA, et al. (1993). “FORMATION AND DECAY OF A SPHEROMAK PLASMA.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 5(6): 1816-1827.
The magnetic properties of the spheromak configuration produced by a combination of slow theta and Z discharges in the University of Maryland Spheromak experiment (MS) are reported. The magnetic structure of the plasma in MS has been mapped out by arrays of passive magnetic pickup coils. The Taylor relaxation process is observed during the formation phase. The magnetic profile evolves in such a way that the ratio of poloidal current I(p) to poloidal flux psi in the plasma approaches a constant value, where mu0I(p) = k(el)psi. When the spheromak is formed, the magnetic field configuration is close to Taylor's minimum energy state, mu0j = kB. This constant k is related to the size of the spheromak produced. A spheromak with 1.0 T maximum field, corresponding to 650 kA poloidal current, has been produced in MS. However, due to the high plasma density (6-8 X 10(20) m-3 ) and the presence of low-Z impurities (mainly carbon and oxygen), the plasma is radiation dominated with electron temperature less-than-or-equal-to 15 eV. The magnetic field decays exponentially during the decay phase. Axisymmetric equilibrium states that could exist in the configuration are calculated with a Grad-Shafranov equilibrium code. Comparison of the numerical calculation with the experimental measurements indicates that the magnetic-field structure stays close to the equilibrium state as the plasma decays.

DEGNAN, J., R. PETERKIN, et al. (1993). “COMPACT TOROID FORMATION, COMPRESSION, AND ACCELERATION.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 5(8): 2938-2958.
Research on forming, compressing, and accelerating milligram-range compact toroids using a meter diameter, two-stage, puffed gas, magnetic field embedded coaxial plasma gun is described. The compact toroids that are studied are similar to spheromaks, but they are threaded by an inner conductor. This research effort, named MARAUDER (Magnetically Accelerated Ring to Achieve Ultra-high Directed Energy and Radiation), is not a magnetic confinement fusion program like most spheromak efforts. Rather, the ultimate goal of the present program is to compress toroids to high mass density and magnetic field intensity, and to accelerate the toroids to high speed. There are a variety of applications for compressed, accelerated toroids including fast opening switches, x-radiation production, radio frequency (rf) compression, as well as charge-neutral ion beam and inertial confinement fusion studies. Experiments performed to date to form and accelerate toroids have been diagnosed with magnetic probe arrays, laser interferometry, time and space resolved optical spectroscopy, and fast photography. Parts of the experiment have been designed by, and experimental results are interpreted with, the help of two-dimensional (2-D), time-dependent magnetohydrodynamic (MHD) numerical simulations. When not driven by a second discharge, the toroids relax to a Woltjer-Taylor equilibrium state that compares favorably to the results of 2-D equilibrium calculations and to 2-D time-dependent MHD simulations. Current, voltage, and magnetic probe data from toroids that are driven by an acceleration discharge are compared to 2-D MHD and to circuit solver/slug model predictions. Results suggest that compact toroids are formed in 7-15 musec, and can be accelerated intact with material species the same as injected gas species and entrained mass greater-than-or-equal-to 1/2 the injected mass.

FINN, J. and P. GUZDAR (1993). “LOSS OF EQUILIBRIUM AND RECONNECTION IN TEARING OF 2-DIMENSIONAL EQUILIBRIA.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 5(8): 2870-2876.
Two-dimensional tearinglike behavior is studied in reduced resistive magnetohydrodynamics (MHD) with flux conserving boundary conditions on a rectangular box. The tearinglike perturbations do not destroy the symmetries of the initial state, either discrete or continuous. In such cases, in which the perturbation does not break a symmetry of the equilibrium, linear instability is typically not directly observed. However, there can be a loss of equilibrium associated with the existence of a tearing unstable state. These ideas are illustrated with three examples: a very elongated tokamak, a tokamak with pinching coils to elongate its flux surfaces, and a model for the magnetotail or for solar arcades. The loss of equilibrium is demonstrated by means of a nonlinear energy functional. The importance of the fact that the dynamics shows a loss of equilibrium is that a large amount of free energy can be released, in the form of reconnection, and that there is a possibility of hysteresis.

KATO, Y., N. SATOMI, et al. (1993). “ELECTRON-TEMPERATURE MEASUREMENT USING THE LINE-INTENSITY RATIO ON THE CTCC SPHEROMAK.” PLASMA PHYSICS AND CONTROLLED FUSION 35(11): 1513-1528.
Line-intensity ratio measurements of the electron temperature have been successfully made on the CTCC-II spheromak. The electron temperatures obtained in the core plasma are 20-80 eV, which are consistent with the values obtained by Thomson scattering. This measurement has the advantage of giving the time evolution of the electron temperature within a single plasma discharge. In the CTCC spheromak, intermittent instability (stepwise instability) and its relaxation are frequently observed. During the stepwise instability and its relaxation cycles, increase and decrease in the temperature are observed in the current-profile-peaking phase and the nonlinear saturation phase of the n = 2 mode. It is demonstrated that the temperature profile in the peripheral plasma can be controlled by an additional magnetic field (choking field), which can reduce the error field in the entrance hole of the flux conserver.

MARTIN, R., S. GEE, et al. (1993). “THE DIRECT DETERMINATION OF THE CURRENT-DENSITY AND MU-PROFILES OF A SPHEROMAK.” PLASMA PHYSICS AND CONTROLLED FUSION 35(2): 269-279.
We have used a probe containing both a Rogowski coil and a magnetic pick-up coil to measure both the current density and the mu value in the plasma of the SPHEX spheromak. The results are broadly in agreement with previous measurements but give much better spatial resolution; they reveal a discontinuity at the interface between the 'central column' and 'annulus' regions of the plasma. In the annulus, the range of values of mu spans the spheromak eigenvalue as expected from theory. When the spheromak current drive is terminated by shorting the Marshall gun, the current density at the magnetic axis initially rises to a maximum before decaying, and mu continues to rise towards the eigenvalue. These results are interpreted as showing that the relaxation process continues to operate in the decaying plasma.

MAYO, R., D. HURLBURT, et al. (1993). “ION TEMPERATURE PROFILE DECONVOLUTION AND CORRECTIONS TO CONFINEMENT PARAMETERS IN SPHEROMAKS.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 5(11): 4002-4010.
The purpose of this work is to determine ion temperature profiles in spheromaks [Nucl. Fusion 19, 489 (1979)] for the first time. Knowledge of the ion temperature profile is necessary in the correct calculation of plasma confinement parameters. The work herein details the calculation of ion temperature profiles for the Compact Torus Experiment (CTX) [Nucl. Fusion 28, 1555 (1988)] and S-1 [Phys. Rev. Lett. 46, 188 (1981)] spheromaks. Data from single chord Doppler ion temperature measurements in these devices have been analyzed with the aid of a one-dimensional equilibrium charge state transport code. Using electron temperature and density profiles from Thomson scattering, and estimates for transport rates, a most probable position for the emission of line radiation can be determined and correlated with the measured Doppler ion temperature, thus generating an ion temperature profile. From this ion temperature profile determination, plasma confinement parameters for the small solid flux conserver CTX [Phys. Fluids B 2, 1342 (1990)] spheromak can be determined, and confinement parameters for S-1 can be reevaluated, eliminating the previous confinement calculations assumption T(i)(r) = T(e)(r). The CTX device has a calculated volume averaged beta [beta] ranging from 3% to 8% and a volume averaged energy confinement time [tau(E)] between 14 and 35 musec; while the S-1 spheromak has [beta] between 15% and 40% and [tau(E)] ranging from 30 to 70 musec.

NAGATA, M., T. KANKI, et al. (1993). “RELAXATION OSCILLATIONS AND TOROIDAL-CURRENT REGENERATION IN A HELICITY-DRIVEN SPHEROMAK.” PHYSICAL REVIEW LETTERS 71(26): 4342-4345.
During the sustained phase of spheromak operation in the flux amplification compact toroid device, detailed observations were made on the discrete relaxation and toroidal current regeneration events that occurred throughout a typical quasiregular cycle. Measurements indicate that over such a cycle there appears to be a global self-organizing phenomenon which involves both the collapse and subsequent recovery of the closed flux surfaces. At the point of recovery, the partially relaxed state is characterized by a value of lambda on the central region which is greater than that on the edge region.

ONO, Y., A. MORITA, et al. (1993). “EXPERIMENTAL INVESTIGATION OF 3-DIMENSIONAL MAGNETIC RECONNECTION BY USE OF 2 COLLIDING SPHEROMAKS.” PHYSICS OF FLUIDS B-PLASMA PHYSICS 5(10): 3691-3701.
Experimental investigation of three-dimensional (3-D) effects of magnetic reconnection dynamics has been extended by use of axially colliding spheromaks [M. Yamada et al, Phys. Fluids B 3, 2379 (199 1)]. The two toroidal shape spheromak plasmas with major radii of 15-20 cm and with parallel toroidal currents of up to 30 kA collide to merge in an external equilibrium field. It is important to note that the present experimental setup allows one to investigate magnetic reconnection comprehensively from both local and global points of view. Reconnection angle theta between the merging field lines is varied by changing the polarity of the internal toroidal field and the magnitude of an external toroidal field. It is observed that the speed of counterhelicity merging with theta approximately 180-degrees is about three times faster than that of cohelicity merging with theta approximately 90-degrees. This suggests the significance of a 3-D effect on the reconnection process. This difference is attributed to the property of the neutral current sheets with and without the magnetic field component parallel to the reconnection (X) line. In the counterhelicity merging, the neutral current sheet is compressed in much shorter time than in the cohelicity merging, resulting in much higher current density and subsequent faster decay of the current sheet. This induces a faster magnetic reconnection. The reconnection speed increases proportionally with the initial approaching speed of the spheromaks, suggesting that a compressible driven reconnection model is consistent with the present reconnection experimental results.

PIERCE, W., R. MAQUEDA, et al. (1993). “INITIAL RESULTS FROM PARALLEL COIL OPERATION OF THE COAXIAL SLOW SOURCE FIELD REVERSED CONFIGURATION DEVICE.” NUCLEAR FUSION 33(1): 117-132.
The Coaxial Slow Source (CSS) is a device in which 'annular' field reversed configurations (FRCs) (small aspect ratio, elongated, toroidal plasmas with poloidal field only) are formed in the space between coaxial coils carrying toroidal currents. The device is constructed so that the plasma can be translated into a simple cylindrical chamber and re-formed as a conventional FRC. Formation of FRCs on slow time-scales (50-250 mus) at low loop voltage (87.5-700 V) has been demonstrated. The paper presents initial results from the new parallel configuration device CSSP in which the inner and outer coils are connected in parallel to the capacitor banks. The parallel coil arrangement has significantly reduced the contact of the plasma with the walls and thus the impurity content. Configurations with confinement times of 10-30 mus, densities of 3 x 10(21) m-3 and temperatures of 3-20 eV are typical. Results are presented on formation, energy balance, a non-destructive tilt instability and dynamics associated with magnetic tearing.

RAMAN, R., J. THOMAS, et al. (1993). “DESIGN OF THE COMPACT TOROID FUELER FOR CENTER-FUELING-TOKAMAK-DE-VARENNES.” FUSION TECHNOLOGY 24(3): 239-250.
Reactor particle fueling is one of the issues that remain to be resolved in the development of a tokamak fusion reactor. One of the most promising concepts of reactor fueling is the injection of high-speed compact toroids (CTs). Compact toroid formation and acceleration at the Ring Accelerator Experiment (RA CE) device at Lawrence Livermore National Laboratory has shown that CT plasmoid velocities sufficient for center fueling fusion reactors can be achieved by using coaxial accelerators. The Compact Toroid Fueler (CTF) will inject high-speed, dense spheromak plasmoids into the Tokamak de Varennes (TdeV) to examine the feasibility of this approach as a fueler for future reactors. Here, a conceptual design study of the particle fueler for TdeV is presented. The issues of CTF design that are considered are formation and relaxation of an axisymmetric CT, optimization of accelerator performance to improve injector electrical efficiency, separation of formation and acceleration phases to improve injector reproducibility, minimization of entrained impurities in the CT, and minimization of neutral gas load to the tokamak following CT fueling. The CTF injector will test theories on CT/tokamak interaction related to reactor fueling. Among the eventual physics questions addressed are the multiple-pulse requirements for future injectors, the bootstrap current enhancement factor, CT fuel confinement times, impurity effects, plasma heating, injector electrical efficiency, and the effect of gas load on the tokamak following CT injection.

SALINGAROS, N. and R. CARRERA (1993). “OSCILLATION AND RECONNECTION OF PLASMA FIBERS IN A DESCRIPTION OF TOKAMAK PHENOMENA.” FUSION TECHNOLOGY 23(3): 257-266.
A theory for the evolution of a plasma current in toroidal magnetic configurations follows from considering the plasma to be made of current fibers. The current fiber elements replace the central role of the magnetic field lines of the traditional theory. A set of simple rules determines the behavior of the plasma from energy constraints. The concept of electromechanical oscillations leads to an improved understanding of dynamic plasma behavior. Fiber theory predicts experimental observations of dense Z pinches, spheromaks, and reversed-field pinches. Some characteristic tokamak phenomena are analyzed in terms of the fiber theory.

BLACK, D., R. MAYO, et al. (1994). “2-DIMENSIONAL MAGNETIC-FIELD EVOLUTION MEASUREMENTS AND PLASMA-FLOW SPEED ESTIMATES FROM THE COAXIAL THRUSTER EXPERIMENT.” PHYSICS OF PLASMAS 1(9): 3115-3131.
Local, time-dependent magnetic field measurements have been made in the Los Alamos coaxial thruster experiment (CTX) [C. W. Barnes et al., Phys. Fluids B 2, 1871 (1990); J. C. Fernandez et al, Nucl. Fusion 28, 1555 (1988)] using a 24 coil magnetic probe array (eight spatial positions, three axis probes). The CTX is a magnetized, coaxial plasma gun presently being used to investigate the viability of high pulsed power plasma thrusters for advanced electric propulsion. Previous efforts on this device have indicated that high pulsed power plasma guns are attractive candidates for advanced propulsion that employ ideal magnetohydrodynamic (MHD) plasma stream flow through self-formed magnetic nozzles. Indirect evidence of magnetic nozzle formation was obtained from plasma gun performance and measurements of directed axial velocities up to upsilon(z) approximately 10(7) cm/s. The purpose of this work is to make direct measurement of the time evolving magnetic field topology. The intent is to both identify that applied magnetic field distortion by the highly conductive plasma is occurring, and to provide insight into the details of discharge evolution. Data from a magnetic fluctuation probe array have been used to investigate the details of applied magnetic field deformation through the reconstruction of time-dependent flux profiles. Experimentally observed magnetic field line distortion has been compared to that predicted by a simple one-dimensional (1-D) model of the discharge channel. Such a comparison is utilized to estimate the axial plasma velocity in the thruster. Velocities determined in this manner are in approximate agreement with the predicted self-field magnetosonic speed and those measured by a time-of-flight spectrometer.

FARENGO, R. and J. SOBEHART (1994). “MINIMUM DISSIPATION STATES IN TOKAMAK PLASMAS.” PLASMA PHYSICS AND CONTROLLED FUSION 36(3): 465-471.
The magnetic field and current density profiles of a steady-state tokamak are determined by assuming that the plasma relaxes to a state having the minimum rate of Ohmic dissipation. Since tokamaks do not operate with flux conservers, the constraints employed in the minimization are different from those used for RFPs or spheromaks. Energy and helicity conservation are imposed for given values of the applied electric and toroidal fields at the edge of the plasma.

JARBOE, T. (1994). “REVIEW OF SPHEROMAK RESEARCH.” PLASMA PHYSICS AND CONTROLLED FUSION 36(6): 945-990.
Spheromak research from 1979 to the present is reviewed including over 160 references. Emphasis is on understanding and interpretation of results. In addition to summarizing results some new interpretations are presented. An introduction and brief history is followed by a discussion of generalized helicity and its time derivative. Formation and sustainment are discussed including five different methods, flux core, theta-pinch z-pinch, coaxial source, conical theta-pinch, and kinked z-pinch. All methods use helicity injections. Steady-state methods and rules for designing spheromak experiments are covered, followed by equilibrium and stability. Methods of stabilizing the tilt and shift modes are discussed as well as their impact on the reactor designs. Current-driven and pressure-driven instabilities as well as relaxation in general are covered. Energy confinement is discussed in terms of helicity decay time and and betas limits. The confinement in high and low open-flux geometries are compared and the reactor implications discussed.

LORTZ, D. and G. SPIES (1994). “SPHEROMAK INSTABILITY.” PHYSICS OF PLASMAS 1(3): 682-683.
The ''classical spheromak'' (current density proportional to the magnetic field, spherical plasma-vacuum interface, homogeneous magnetic field at infinity) is unstable to global magnetohydrodynamic tilting modes, even if an arbitrary, perfectly conducting, rigid wall bounds the vacuum.

MACKAY, R. (1994). “TRANSPORT IN 3D VOLUME-PRESERVING FLOWS.” JOURNAL OF NONLINEAR SCIENCE 4(4): 329-354.
The idea of surfaces of locally minimal flux is introduced as a key concept for understanding transport in steady three-dimensional, volume-preserving flows. Particular attention is paid to the role of the skeleton formed by the equilibrium points, selected hyperbolic periodic orbits and cantori and connecting orbits, to which many surfaces of locally minimal flux can be attached. Applications are given to spheromaks (spherical vortices) and eccentric Taylor-Couette Flow.

NELSON, B., T. JARBOE, et al. (1994). “TOKAMAK FORMATION AND SUSTAINMENT BY COAXIAL HELICITY INJECTION CURRENT DRIVE.” NUCLEAR FUSION 34(8): 1111-1119.
Experiments characterizing the coaxial helicity source and helicity injection current drive on the Prototype Helicity Injected Tokamak (Proto-HIT) have been performed. Toroidal currents over 30 kA can be sustained for times much greater than the plasma resistive time. The coaxial source operates with a large toroidal field that greatly enhances the source impedance, allowing a high rate of helicity injection (high source voltage) at a low source current (high efficiency), with results showing good agreement with a simple analytical model.

RAMAN, R., F. MARTIN, et al. (1994). “EXPERIMENTAL DEMONSTRATION OF NONDISRUPTIVE, CENTRAL FUELING OF A TOKAMAK BY COMPACT TOROID INJECTION.” PHYSICAL REVIEW LETTERS 73(23): 3101-3104.

SHEFFIELD, J. (1994). “MAGNETIC FUSION COMMERCIAL POWER-PLANTS.” JOURNAL OF FUSION ENERGY 13(2-3): 167-170.
Toroidal magnetic systems offer the best opportunity to make a commercial fusion power plant. They have, between them, all the features needed; however, no one system yet meets the ideal requirements. The tokamak is the most advanced system, and the proposed International Thermonuclear Experimental Reactor (ITER) and Tokamak Physics Experiment (TPX) will build upon the existing program to prepare for an advanced tokamak demonstration plant. Complementary toroidal systems such as the spherical torus, stellarator, reversed-field pinch, field-reversed configuration, and spheromak offer, between them, potential advantages in each area and should be studied in a balanced fusion development program.

SHUMLAK, U., T. FOWLER, et al. (1994). “ROTATIONAL EFFECTS ON THE M=1 MAGNETOHYDRODYNAMIC INSTABILITY IN SPHEROMAKS.” PHYSICS OF PLASMAS 1(3): 643-647.
The effect of rotation on the magnetohydrodynamic stability of m = 1 modes in spheromaks is calculated to reveal a threshold for rotational instability at OMEGAtau(A) almost-equal-to 0.2, where OMEGA is the angular rotation frequency and tau(A) is the Alfven transit time. This result may explain the appearance of m = 1 modes in spheromak experiments in which the flux conserver aspect ratio L/R lies well below the threshold for the tilt instability (m=n=1). For flux conservers with aspect ratios above the tilt instability threshold, rotational instability dominates when OMEGAtau(A) exceeds the rotational threshold.

ASHIDA, H., H. SUGIMOTO, et al. (1995). “MAGNETOHYDRODYNAMIC INSTABILITY IN AXISYMMETRICAL SPHERICAL PLASMA WITH PARALLEL-FLOW TO MAGNETIC-FIELD.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 64(9): 3291-3299.
The instability of the axisymmetric spherical force free plasma with the parallel plasma flow to the magnetic filed is studied by using the MHD equations under the condition of incompressibility. The linear growth rate of the unstable mode with the fixed toroidal mode number n = 1 is obtained and it decreases with the increase of Alfven fven Mach number C-A in the rage of C-A < 1 in the case of the free boundary. The non-liner numerical analysis in the free boundary case shows that the tilting mode plays a main role, and the damping rate of the original helicity and the toroidal flux decreases with the increase of C-A.

DASGUPTA, B., T. SATO, et al. (1995). “FORMATION OF A FIELD-REVERSED CONFIGURATION BY COALESCENCE OF SPHEROMAKS.” FUSION TECHNOLOGY 27: 374-377.

FARRUGIA, C., V. OSHEROVICH, et al. (1995). “MAGNETIC-FLUX ROPE VERSUS THE SPHEROMAK AS MODELS FOR INTERPLANETARY MAGNETIC CLOUDS.” JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 100(A7): 12293-12306.
Magnetic clouds form a subset of interplanetary ejecta with well-defined magnetic and thermodynamic properties. Observationally, it is well established that magnetic clouds expand as they propagate antisunward. The aim of this paper is to compare and contrast two models which have been proposed for the global magnetic field line topology of magnetic clouds: a magnetic flux tube geometry, on the one hand, and a spheromak geometry (including possible higher multiples), on the other. Traditionally, the magnetic structure of magnetic clouds has been modeled by force-free configurations. In a first step, we therefore analyze the ability of static force-free models to account for the asymmetries observed in the magnetic field profiles of magnetic clouds. For a cylindrical flux tube the magnetic field remains symmetric about closest approach to the magnetic axis on all spacecraft orbits intersecting it, whereas in a spheromak geometry one can have asymmetries in the magnetic field signatures along some spacecraft trajectories. The duration of typical magnetic cloud encounters at 1 AU (1 to 2 days) is comparable to their travel time from the Sun to 1 AU and thus magnetic clouds should be treated as strongly nonstationary objects. In a second step, therefore, we abandon the static approach and model magnetic clouds as self-similarly evolving MHD configurations. In our theory, the interaction of the expanding magnetic cloud with the ambient plasma is taken into account by a drag force proportional to the density and the velocity of expansion. Solving rigorously the full set of MHD equations, we demonstrate that the asymmetry in the magnetic signature may arise solely as a result of expansion. Using asymptotic solutions of the MHD equations, we least squares fit both theoretical models to interplanetary data. We find that while the central part of the magnetic cloud is adequately described by both models, the ''edges'' of the cloud data are modeled better by the magnetic flux tube. Further comparisons of the two models necessarily involve thermodynamic properties, since real magnetic configurations are never exactly force-free and gas pressure plays an essential role. We consider a polytropic gas. Our theoretical analysis shows that the self-similar expansion of a magnetic flux tube requires the polytropic index gamma to be less than unity. For the spheromak, however, self-similar, radially expanding solutions are known only for gamma equal to 4/3. This difference, therefore, yields a good way of distinguishing between the two geometries. It has been shown recently (Osherovich et al., 1993a) that the polytropic relationship is applicable to magnetic clouds and that the corresponding polytropic index is similar to 0.5. This observational result is consistent with the self-similar model of the magnetic flux rope but is in conflict with the self-similar spheromak model.

Fowler, T. and D. Hua (1995). “Prospects for spheromak fusion reactors.” JOURNAL OF FUSION ENERGY 14(2): 181-185.
The reactor study of Hagenson and Krakowski demonstrated the attractiveness of the spheromak as a compact fusion reactor, based on physics principles confirmed in CTX experiments in many respects. Most uncertain was the energy confinement time and the role of magnetic turbulence inherent in the concept. In this paper, a one-dimensional model of heat confinement, calibrated by CTX, predicts negligible heat loss by magnetic turbulence at reactor scale.

GIBSON, K., S. GEE, et al. (1995). “ION ENERGY MEASUREMENTS IN THE SPHEX SPHEROMAK.” PLASMA PHYSICS AND CONTROLLED FUSION 37(1): 31-41.
A neutral particle analyser (NPA) and high-resolution spectrometer have been used to make ion energy and rotation measurements during the driven and decaying phases of SPHEX, the UMIST spheromak. During the driven phase NPA spectra reveal the presence of a small (less than or equal to 0.5%) population of ions, indistinguishable from a Maxwellian population, at a temperature of 300 eV. Measurements made in decaying plasmas indicate that the hot ions are closely associated with the current drive process and, in particular, with a region of high potential in the plasma known as the 'central column'. At the onset of the decay phase we find the central column density, gun current and hot-ion population all decay at a similar rate (<< 50 mu s). The surrounding toroidal plasma, however, has a separate and much slower decay rate (similar to 250 mu s) which is better correlated with the properties (rotation and temperature) of the bulk of the ion distribution.

KATSURAI, M. (1995). “REVIEW OF EXPERIMENTAL INVESTIGATIONS ON COMPACT TOROIDS AND COMPACT TOKAMAKS USING TS-3 DEVICE.” FUSION TECHNOLOGY 27: 97-103.
The TS-3 device at the University of Tokyo has been used to produce free boundary spheromaks or spheromak-like compact toroids. Plasma production is accomplished either by Z-theta discharges or by means of magnetized coaxial plasma guns installed at both ends of the device. The plasmas produced have a minor approximate to major radius of about 15 to 20 cm with a natural decay time of about 30 to 50 mu s and a toroidal plasma current of about 30 to 60 kA. A unique feature of TS-3 device is the possession of production regions at both ends of the device, and concequently the ability of producing two adjacent compact toroids which can be merged through magnetic reconnection. Another feature of TS-3 device is the possibility of external application of a toroidal field with the aid of an optional center conductor assembly that can carry an axial current ranging from 0 to +/-80 kA. This construction enables us to produce compact toroidal plasmas of various types from reversed field pinch(RFP) to tokamak in terms of the difference in q profile. The variation of both poloidal plasma current and external toroidal field current permits the change in magnetic configuration of merging plasmas, enabling the reconnection angle to continuously vary from about 20 degrees (tokamak merging) through 90 degrees (cohelicity spheromak merging) to 180 degrees (counter-helicity spheromak merging to produce field reversed configurations(FRC)). When the coaxial guns are installed at both ends of the device in place of the center conductor, a center plasma current can be injected to form flux-core spheromaks (or bumpy z-pinches). Novel research subjects that have emerged from TS-3 experiments are; (1) the investigation of three dimensional effects of magnetic reconnection in laboratory plasmas, (2) the formation of FRC plasmas by a counter-helicity spheromak merging, (3) non-OH production and merging of tight aspect ratio tokamaks, (4) the stabilization of tilt motions of tight aspect ratio tokamaks, and (5) the formation and compression (flux amplification) of free-boundary tilt stabilized flux-core spheromaks.

KENNY, R., M. NAGATA, et al. (1995). “FEASIBILITY STUDIES FOR OPTIMIZING SPHEROMAK EQUILIBRIA .1. SPHEX.” FUSION TECHNOLOGY 27: 365-368.
With reference to both the spheromak experiments SPHEX and FACT, we initiate an investigation into the extent to which a realistic equilibrium parameter-set can be determined by a measured magnetic data-set that is ultimately expected to be non-intrusive. Compared to tile tokamak, it is pointed out that the spheromak suffers from both theoretical and practical difficulties in attaining this goal, with the result that a feasibility study utilizing interior SPHEX data is first attempted. As consequence, we hope to indicate the type of global, and otherwise, data that must be measured (within the engineering constraints represented by the spheromak configuration) in the more difficult, but diagnostically more relevant, non-intrusive case.

KUKUSHKIN, A., V. RANTSEVKARTINOV, et al. (1995). “ENERGY CONCENTRATION IN A HIGH-CURRENT GAS-DISCHARGE - EXPERIMENTS ON PLASMA-FOCUS-PRODUCED DENSE-PLASMA SPHEROMAK.” FUSION TECHNOLOGY 27: 325-328.
Experimental results are presented which verify the possibility, formerly predicted,(1) of the formation of a closed, spheromak-like magnetic configuration (SLMC) in a plasma focus discharge. The model is based on the self-generated transformation of a toroidal (i.e. azimuthal) field into a poloidal one. At its final stage, the SLMC takes the form of a squeezed spheromak, which includes a combined Z-curly theta-pinch at its major axis, exhibiting a power density several orders of magnitude larger than that measured experimentally on a force-free flux-conserver-confined spheromak formed by helicity injection. The results suggest a possibility of further concentrating the plasma power density by means of compressing the SLMC-trapped plasma by the residual magnetic field.

LOEWENHARDT, P., M. BROWN, et al. (1995). “PERFORMANCE CHARACTERIZATION OF THE CALTECH COMPACT TORUS INJECTOR.” REVIEW OF SCIENTIFIC INSTRUMENTS 66(2): 1050-1055.

NAGATA, M., Y. KINUGASA, et al. (1995). “HELICITY INJECTION IN THE FACT SPHEROMAK EXPERIMENT.” FUSION TECHNOLOGY 27: 387-390.
A spheromak configuration consisting of bias flux surrounding a core region of closed flux surfaces has been successfully sustained in the Flux Amplification Compact Torus (FACT) device by DC/Coaxial helicity injection. In this experiment, the energy transfer efficiency is estimated to be about 30%. The relaxed configuration posseses a low q profile (1/3<q<1/2) whose shape implies that the current density is concentrated in the core and which is maintained by the process of MHD relaxation. The current conversion and rapid inward diffusion of the injected current is found to be significantly related to the n=1 helical deformation of the open field lines along the geometric axis. In this paper, we present some design parameters for the planned Helicity Injected Spherical Torus (HIST) which will permit a corresponding investigation to the above to be made for a tokamak.

ONO, Y. (1995). “SLOW FORMATION OF FIELD-REVERSED CONFIGURATION BY USE OF 2 MERGING SPHEROMAKS.” FUSION TECHNOLOGY 27: 369-373.
A novel slow formation method of field-reversed configuration (FRC) has been developed by magnetic reconnection of two force-free spheromaks with opposite toroidal magnetic field. The merging process cancels their opposite magnetic helicities, realizing a non-Taylor relaxation from the force-free state to the high-beta FRC state with zero helicity. A significant increase in the ion temperature has been documented up to 180eV during this fully anti-parallel reconnection. The dissipated toroidal ,magnetic energy of the merging toroids is transformed mostly to the ion thermal energy, revealing a unique relaxation mechanism to the high-beta equilibrium, The merging toroids are found to relax either to an FRC or to a new spheromak, depending on whether their total helicity is larger or smaller than a critical value.

ROBINSON, D. (1995). “COMPACT STEADY-STATE TOKAMAKS.” FUSION TECHNOLOGY 27: 144-149.
The small aspect ratio tokamak combines the attractive features of the tokamak, reverse field pinch and spheromak to produce a compact, stable, high-beta configuration with low external fields. Experiments on the Small Tight Aspect Ratio Tokamak (START) at Culham have demonstrated the production of stable, high temperature (T-e less than or equal to 1keV), naturally elongated plasmas with good confinement, at aspect ratios down to 1.25. These plasmas are, so far, free from current-terminating disruptions and exhibit a natural divertor action. Theoretical studies have demonstrated robust stability at high beta (> 30%) and self-consistent steady-state equilibria using pressure and beam driven currents. Such steady-state solutions exist for devices at the Mega Amp level, compact component test facilities and fusion power plants of modest size (R(o) similar to 2-3m).

SCHAER, S. (1995). “COAXIAL PLASMA GUN IN THE HIGH-DENSITY REGIME AND INJECTION INTO A HELICAL FIELD.” ACTA PHYSICA POLONICA A 88: S 77-S 100.
A modified coaxial plasma gun in the high density regime of 20-70 mT of He was investigated experimentally and theoretically. Tile injection of the plasma torus into a drift space was studied by diamagnetical diagnostics both with and without helical bias, where tile inner electrode was continued into the drift space by an insulated central conductor. Quasi-tokamak geometry is obtained (q approximate to 3;I-i approximate to 1.2; beta(p) approximate to 0.7) Mean speed of torus in drift space: 2.2 cm/mu s, which is in excellent agreement with tile MIID model derived. The theoretical considerations include: (1) acceleration phase, (2) ejection, (3) injection, (4) motion in tile drift space, (5) tokamak stability. Discussion of: (1) general characteristics and phenomena, (2) second half-period breakdown with autopreionization (3) prevention of transversal expansion by rarefaction waves of Mach 50 supersonic flow, (4) stability and homogeneity enhancement (factor 5), (5) agreement with model, (G) X-points and breakdown dependence, (7) velocity limitation, (8) thermal diffusion. The findings are, among other application domains, important for future designs of injectors for magnetic confinement, especially for spheromaks.

YAMADA, M., N. POMPHREY, et al. (1995). “STUDY OF THE ULTRA-LOW ASPECT RATIO TOKAMAK, ULART.” FUSION TECHNOLOGY 27: 161-166.
We investigate experimentally and theoretically the global MHD characteristics of an ultra-low aspect ratio tokamak (ULART). Since the ULART requires a substantially smaller toroidal field current, I-tf, than conventional tokamaks, it has important reactor advantages. By fully utilizing the TS-3 merging spheromak facility with a slender center conductor, we have carried out an experimental study of the ultra-low aspect ratio tokamak with aspect ratio reaching as low as 1.05. The ULART is found to be similar to the spheromak in its strong paramagnetism and magnetic helical pitch. In this extreme limit, we investigate the transition of the spheromak (q(a) = 0, I-tf = 0) to a ULART plasma (q(a) = 5-20, I-tf < I-p). It is observed that a small current at the center conductor can significantly improve the overall stability of the formed plasmas by effectively stabilizing the tilt mode. We identify a threshold of I-tf << I-p with q(cyl)(a) << 1 for global tilt/shift modes. This initial observation is in agreement with a global MHD theory.

Brown, M. and A. Martin (1996). “Spheromak experiment using separate guns for formation and sustainment.” FUSION TECHNOLOGY 30(3): 300-309.
An experiment is described that incorporates the use of separate magnetized plasma guns for formation and sustainment of a spheromak. It is shown that energy coupling efficiency approaches unity if the gun and spheromak are of comparable size. A large gun should be able to operate at lower current and therefore lower voltage. In addition, it is expected that a gun matched to the size of the spheromak will cause less perturbation to the equilibrium. It is proposed to use a smaller gun for spheromak formation and a large, efficient gun for sustainment. The theoretical basis for the experiment is developed, and the details of the experiment are described. A prediction of the equilibrium magnetic flux surfaces using the EFIT code is presented.

Drake, R., J. Hammer, et al. (1996). “Submegajoule liner implosion of a closed field line configuration.” FUSION TECHNOLOGY 30(3): 310-325.
Adiabatic compression of a preformed closed field line configuration by an imploding liner is considered. Three configurations are discussed: the field-reversed configuration, the spheromak, and the Z-pinch. It is shown that by employing a two-dimensional compression, one can reach a breakeven condition with an energy input into the plasma as low, as 100 kJ. Typical initial dimensions of the liner are length, 5 to 6 cm; radius, similar to 1 cm; and wall thickness, similar to 0.01 cm. Liner mass is in the range of a few grams. It is assumed that the initial plasma beta is of the order of unity; in this case, the final beta is much greater than 1, and the plasma is in a wall confinement regime. Typical plasma parameters for the final state (for the linear compression ratio equal to 10) are density, 10(21) cm(-3); temperature, 10 keV; and magnetic field, 10(7) G. A brief discussion of various phenomena affecting the wall confinement is presented (magnetic field diffusion, radiative losses, and impurity penetration); the conclusion is drawn that the heat losses to the walls are modest and are nor a factor that limits plasma enchancement Q. It is shown that at least for relatively thin liners, whose compressibility can be neglected, what limits Q is a relatively short liner dwell time near the maximum compression point. The scaling law for the Q versus the input parameters of the system is derived, which shows a relatively weak dependence of Q on the input energy Possible ways for increasing the dwell time are discussed. Reactor potentialities of the system are briefly, described. It is emphasized that the possibility of performing crucial experiments on small- to medium-scale experimental devices may considerably shorten the development path for the system under consideration. Some nonfusion applications of the system described are mentioned. Among them are burning and transmutation of long-lived fusion products, medical isotope production, a pulsed source of hard X rays, and fusion neutrons.

Fowler, T. (1996). “Theoretical aspects of energy confinement in spheromaks.” FUSION TECHNOLOGY 29(2): 206-209.
Despite the poor global energy confinement observed in spheromak experiments to dare, the long-term prospects may be favorable as spheromaks are scaled to larger size and higher temperatures. The present performance is traced to excessive magnetic energy loss at the edge compared to tokamaks and hear transport due to magnetic fluctuations, both of which should scale away as the temperature increases.

Hooper, E., J. Hammer, et al. (1996). “A re-examination of spheromak experiments and opportunities.” FUSION TECHNOLOGY 29(2): 191-205.
The results of spheromak experiments are re-examined in light of the hypothesis that the core energy confinement is considerably better than the global confinement and that it extrapolates favorably with magnetic Reynolds number S. The data in decaying spheromaks are found to be consistent with the hypothesis and with magnetic fluctuations scaling as S--1/2 and determining the electron thermal conductivity. No conclusion is drawn from the data for sustained spheromaks, indicating the importance of a new experiment to determine core energy confinement while helicity is injected. The characteristics of such an experiment are discussed, including the importance of using modern vacuum and wall-conditioning techniques and of minimizing magnetic field errors.

Hooper, E. and T. Fowler (1996). “Spheromak reactor: Physics opportunities and issues.” FUSION TECHNOLOGY 30(3): 1390-1394.
The spheromak is a magnetic confinement device with a more attractive fusion reactor potential than the leading geometry, the tokamak. This results in large part from the absence of a toroidal field coil and other structures linking the plasma along the geometric axis. However, because of the lack of a strong external magnetic field, the physics is more complex so that considerable research is required to learn how to achieve the reactor potential. Several critical physics issues are considered here, including stability to low mode number magnetohydrodynamic (MHD) modes, energy confinement, helicity injection and current drive, the magnetic turbulence associated with this dynamo, and the beta (ratio of plasma and magnetic pressures) which can be supported in the geometry.

Martin, A. and T. Jarboe (1996). “An equilibrium model for helicity injector operation in the helicity injected tokamak (HIT) experiment.” PLASMA PHYSICS AND CONTROLLED FUSION 38(11): 1967-1974.
The helicity injected tokamak (HIT) experiment uses coaxial helicity injection to drive current in a low aspect-ratio tokamak. In order to accurately calculate the equilibria of such objects, a model which includes the essential physics of the injector and edge region must be included. Such a model is also crucial in determining the performance of future helicity injector designs. We present a model for the helicity injector that treats the open field lines as being in a force-free equilibrium determined by the field line length, the applied injector voltage, and an effective resistivity (eta), which can have both resistive and dynamic components. This model agrees well with data for plasmas with little or no closed flux, using a uniform eta as the fitting parameter.

Mattor, N. (1996). “Scaling of magnetic turbulence with Lundquist number in relaxed state devices.” PHYSICS OF PLASMAS 3(5): 1578-1584.
The scaling of magnetic turbulence with Lundquist number, (B) over tilde(S), as generated by the dynamo in reversed-field pinches and spheromaks, is addressed. A theoretical framework is described, showing how the fluctuations arise from the dynamo and what dynamics determine the (B) over tilde(S) scaling. There are two limits of the dynamo. For a discrete (sawtoothing) dynamo, the time average of the magnetic fluctuations is given by (B) over tilde proportional to S-0, but it is argued that the averaged flux surface destroying magnetic field fluctuations scale as (B) over tilde proportional to S--1/2. For a continuous dynamo, with a steady-state saturated turbulent spectrum, the magnetic field perturbations scale as (B) over tilde proportional to S--1/4. Previous theories of S scaling are reviewed. (C) 1996 American Institute of Physics.

Mayo, R. (1996). “Approach to ignition conditions in a two fluid spheromak with direct ion heating.” NUCLEAR FUSION 36(12): 1599-1608.
The spheromak, as a compact toroidal magnetic fusion device, offers substantial advantages as a fusion reactor concept over larger, more complicated, and more costly devices such as the tokamak. The very definite advantages associated with the simply closed geometry, minimized external coil requirements and the possibility of ohmic ignition in the spheromak, represent a substantial improvement over conventional magnetic fusion reactor designs. Furthermore, recent successes in improving confinement parameters (T-e similar to 400 eV, T-i similar to 1 keV, n(e) similar to 5 x 10(14) cm(-3), B similar to 1T) have renewed interest in advancing this concept to a proof of principle, reactor prototype stage. Herein, the initial work by Fowler et al. (Comments Plasma Phys. Control. Fusion 16 (1994) 91), indicating the possibility of ohmic ignition in spheromaks, is extended to a two fluid model that includes direct ion heating. Non-ohmic magnetic dissipation, contributing to direct ion heating, and confinement scaling are quantified through comparison with the latest results from the gun driven Compact Torus Experiment (CTX) spheromak (Phys. Fluids B 2 (1990) 1342). Excellent agreement is demonstrated between experimentally measured plasma parameters and our model predictions. Extrapolation to ignition experiments and reactor relevant conditions is discussed, indicating the possibility of reaching these conditions by gun driven ohmic heating alone and illustrating the merits of direct ion heating. Conservative to pessimistic confinement estimates are used throughout so as to ensure that the promise offered by this concept does not presume unrealizable improvements in energy containment.

Mayo, R. (1996). “Direct ion heating effect on ignition conditions in spheromaks.” FUSION TECHNOLOGY 30(3): 1326-1331.
As a member of the compact toroidal class of magnetic fusion devices, the spheromak [Nucl. Fusion 19, 489 (1979)] offers substantial advantage as a fusion reactor concept over larger, more complicated, and more costly re-entrant devices like the tokamak. The compact and simply dosed geometry affording high energy density, the inherent diverted nature of the magnetic topology, the force free ((j) over right arrow x (B) over right arrow = 0 contains del x (B) over right arrow B = lambda (B) over right arrow) nature of the spheromak equilibrium minimizing external coil requirements and stresses, and the possibility of Ohmic ignition resulting from the majority of confining fields generated by internal plasma currents in the spheromak, are a few of the more prominent advantages that represent substantial improvement over conventional magnetic fusion reactor designs. Further, recent successes in improving confinement parameters (T-e similar to 400eV, T-i similar to 1 Ke V, n(e) similar to 3 x 10(14)cm(-3), B similar to 1T) have renewed the interest in advancing this concept to a proof-of-principle, reactor prototype stage. Here we extend the initial work by Fowler, et al. [Comments Plasma Phys. Controlled Fusion 16, 91 (1994)] indicating the possibility of Ohmic ignition in spheromaks, to a two fluid model that includes direct ion heating through turbulent Taylor relaxation mechanisms. The contribution to direct ion heating through this non-Ohmic magnetic dissipation, and confinement scaling are quantified through comparison with the latest results from the gun driven Compact Torus experiment (CTX) [Phys. Fluids B 2, 1342 (1990)] spheromak. We realize good agreement between experimentally measured plasma parameters and our model predictions. Extrapolation to an ignition class experiment is examined indicating the possibility of reaching these conditions by gun driven Ohmic heating alone, and illustrating the merits of direct ion heating on facilitating approach to ignition. Differences between classical (no direct ion heating) and direct ion heating cases are emphasized. Conservative confinement estimates are! used throughout.

Ono, Y., M. Yamada, et al. (1996). “Ion acceleration and direct ion heating in three-component magnetic reconnection.” PHYSICAL REVIEW LETTERS 76(18): 3328-3331.
Ion acceleration and direct ion heating in magnetic reconnection were experimentally observed during counterhelicity merging of two plasma toroids. Plasma ions are accelerated up to the order of the Alfven speed through contraction of reconnected field lines with three components. The significant ion heating ( from 10 up to 200 eV) is attributed to direct conversion of magnetic energy into ion thermal energy, in agreement magnetohydrodynamic and macroparticle simulations.

Yamada, M., N. Pomphrey, et al. (1996). “Global stability study of the ultralow aspect ratio tokamak, ULART.” NUCLEAR FUSION 36(9): 1210-1216.
By introducing a slender current carrying conductor through the geometric centre axis of the TS-3 device at Tokyo Univesity, ultralow aspect ratio tokamak (ULART) configurations have been generated with aspect ratios as low as 1.1. In this extreme limit the transition of the spheromak (q(edge) = 0, I-1f = 0) to an ULART plasma (q(edge) = 2-20) is studied. The global MHD characteristics of ULART are investigated by comparing the theoretical results viith the experimental data obtained. A small current (compared with the plasma current) in the centre conductor is found to improve significantly the global MHD stability characteristics of the plasmas formed by effectively stabilizing the global tilt/shift mode. Theoretical calculations of the threshold toroidal field current required for stability and the growth rates of the tilt/shift modes agree well with the TS-3 data.

Alladio, F. and P. Micozzi (1997). “Reconstruction of spherical torus equilibria in absence of magnetic measurements in the central cavity.” NUCLEAR FUSION 37(12): 1759-1774.
Magnetic measurements alone on spherical tori should allow a very good separation of the poloidal beta beta(P) from the internal self-inductance l(i)/2 and should even permit an accurate estimate of the current density j(phi) profile. However, the reduced space allowed for magnetic sensors near the central conductor in a spherical tokamak, and the possibility of producing flux core spheromak configurations without a central conductor, could imply that magnetic probes are not present in the cavity of the spherical torus. The fluxes and fields of a variety of calculated spherical torus configurations, all endowed with a single or double null separatrix, are analysed in terms of spherical multipolar moments obtained from simulated magnetic measurements located only upon a sphere surrounding the spherical plasma. The solution to the problem of the absence of magnetic measurements in the cavity of the spherical torus is to fix from non-magnetic measurements (e.g., spectroscopy) the plasma inboard boundary tau(in) on the equatorial plane. This constraint is added to the constraints of matching the spherical multipolar expansion in an iterative solution of the Grad-Shafranov equation, on the basis of a spherical geometry. The convergence of the spherical reconstructive equilibrium code is extremely fast and gives an error on the total plasma current I-p of less than 1% at an aspect ratio A = 1.2, an error on the position of the plasma boundary of less than 2% of the radius of the plasma sphere, an error on beta(P) Of at most 15% and, finally, the j(phi) profile is extremely well reconstructed in peaked, flat and even hollow cases. The effect of an uncertainty +/-delta tau(in), upon the spectroscopic identification of the plasma inboard boundary on the equatorial plane tau(in) is assessed.

Brown, M. (1997). “Experimental evidence of rapid relaxation to large-scale structures in turbulent fluids: Selective decay and maximal entropy.” JOURNAL OF PLASMA PHYSICS 57: 203-229.
There is abundant experimental, theoretical and computational evidence that certain constrained turbulent fluid systems self-organize into large-scale structures. Examples include two-dimensional (geostrophic) fluids, guiding-centre plasmas and pure-electron plasmas, as well as two- and three-dimensional magnetofluids such as reversed-field pinches and spheromaks. The theoretical understanding of relaxation phenomena is divided into two quite different constructs: selective decay and maximal entropy. Theoretical foundations of both of these principles are largely due to Montgomery and his collaborators. In this paper, selective decay and maximal entropy theories of turbulent relaxation of fluids are reviewed and experimental evidence is presented. Experimental evidence from both 2D fluids and from 3D magnetofluids is consistent with the selective decay hypothesis. However, high-resolution computational evidence strongly suggests that formation of large scale structures is dictated bur maximal-entropy principles rather than selective decay.

Cunningham, G. (1997). “Impurities and impurity transport in the spheromak SPHEX.” PLASMA PHYSICS AND CONTROLLED FUSION 39(9): 1339-1354.
Absolute spectroscopic measurements are made of all significant ionization states of the dominant impurities in SPHEX during sustained operation, and these are compared with a diffusive transport model to derive average plasma parameters. Statistical tests are used to establish the reliability of these results. A line ratio measure is also made and compares well with the ionization balance. The electron power balance in these discharges is estimated assuming that only Spitzer dissipation (a small fraction of the total source power) heats the electrons. Titanium gettering is used to reduce recycling, and thus to measure the fraction of impurity due to recycling relative to that directly injected from the Marshall gun. It is established that during sustainment the electrons are radiation dominated everywhere, so that the rise in T-e when Ti is used is quite moderate, from 30 to 50 eV. However, the impurity transport rate is substantially reduced by gettering, implying that high transport rates are not intrinsic to the spheromak configuration. Some more qualitative data pertaining to the decaying spheromak is also presented.

Duck, R., P. Browning, et al. (1997). “Structure of the n=1 mode responsible for relaxation and current drive during sustainment of the SPHEX spheromak.” PLASMA PHYSICS AND CONTROLLED FUSION 39(5): 715-736.
The structure of the n = 1 mode in the SPHEX spheromak, which plays a central role in relaxation during sustainment, is investigated by analysing the measured voltage fluctuations in the central plasma column. By combining these results with a suitably defined helical magnetic Bur function, the mode is found to be due to a rotating helical distortion of the open linked flux. We propose that the distortion is due to a saturated current-driven kink mode of the open flux tube. The prolongation of this 'helical column' an its return around the outside of the closed flux is found to be strongly asymmetric. Previously published measurements of the Poynting Bur and mu-profile are re-analysed in the light of these results, and implications for the mechanism of relaxation and non-inductive current drive are discussed.

Fowler, T. and D. Hua (1997). “Model predictions for auxiliary heating in spheromaks.” PLASMA PHYSICS REPORTS 23(9): 719-722.
Calculations are presented showing the temperatures to be expected from auxiliary heating in spheromaks, based on a model that appears to agree with earlier experiments with ohmic heating. The model incorporates heat loss due to the magnetic fluctuations generated during self-organization into a Taylor state. The model shows that keV temperatures could be achieved in a small device with a flux conserver radius of only 0.3 m.

Himura, H., H. Wada, et al. (1997). “Drift motion of field-reversed-configuration plasma across a curved magnetic field.” PHYSICAL REVIEW LETTERS 78(10): 1916-1919.
We report the first observation of the behavior of a field-reversed-configuration (FRC) plasma translated into a curved magnetic field B-cur. The FRC shows a unique behavior in B-cur. The plasma splits into two parts: one is a bulk plasma confined in a field-reversed magnetic geometry, deflecting strongly across B-cur despite beta(E) (the ratio of directed to transverse magnetic-field energy density) much greater than 1; the other is probably a peripheral plasma outside the separatrix, propagating rigidly along B-cur. This motion of the FRC may be due to E x B drifting, rather than displacement of the vacuum field by diamagnetic currents.

Kukushkin, A., V. RantsevKartinov, et al. (1997). “Formation of a spheromak-like magnetic configuration by a plasma focus self-transformed magnetic field.” FUSION TECHNOLOGY 32(1): 83-93.
Experimental results are presented that verify the formerly predicted possibility of the formation of a closed spheromak-like magnetic configuration (SLMC) by the natural magnetic field of a plasma focus discharge. The model is based on the self-generated transformation of a toroidal (i.e., azimuthal) magnetic field into a poloidal one. At the final stage of the discharge, the SLMC takes the form of a squeezed spheromak, which includes a combined Z-theta-pinch at its major axis, exhibiting a power density several orders of magnitude larger than that measured experimentally on a force-free flux-conserver-confined spheromak formed by helicity injection. The results suggest the possibility of further concentrating the plasma power density by means of compressing the SLMC-trapped plasma by the residual magnetic field of the plasma focus discharge. A qualitative model is given for the scenario of the SLMC-producing plasma focus discharge. Special emphasis is placed on the difference of this approach front conventional approaches to the role of magnetic field reconnection processes in plasma focus dynamics. The operational conditions necessary to stimulate SLMC formation in high-current gaseous discharge systems and the uses of SLMC-trapped plasmas are discussed briefly.

Moir, R. (1997). “Liquid first walls for magnetic fusion energy configurations.” NUCLEAR FUSION 37(4): 557-566.
Liquids (similar to 7 neutron mean free paths thick), with certain restrictions, can probably be used in magnetic fusion designs between the burning plasma and the structural materials of the fusion power core. If this works there would be a number of profound advantages: a cost of electricity lower by as much as a factor of 2; removal of the need to develop new first wall materials, saving over 4 billion US dollars in development costs; a reduction of the amount and kinds of wastes generated in the plant; and the wider choice of materials permitted. The amount of material that evaporates from the liquid which can be allowed to enter the burning plasma is estimated to be less than 0.7% for lithium, 1.9% for Flibe (Li2BeF4 or LiBeF3) and 0.01% for Li17Pb83. The ability of the edge plasma to attenuate the vapour by ionization appears to exceed this requirement. This ionized vapour would be swept along open field lines into a remote burial chamber. The most practical systems would be those with topological open field lines on the outer surface, as is the case with a field reversed configuration (FRC), a spheromak, a Z pinch or a mirror machine. In a tokamak, including a spherical tokamak, the field lines outside the separatrix are restricted to a small volume inside the toroidal coil making for difficulties in introducing the liquid and removing the ionized vapour, i.e., the configuration is not open ended.

Morita, A., Y. Ono, et al. (1997). “Experimental investigation on tilt stabilizing effect of external toroidal field in low aspect ratio tokamak.” PHYSICS OF PLASMAS 4(2): 315-322.
This paper describes experimental investigations on the equilibrium and global stability of low aspect ratio tokamaks with different aspect ratios ranging from 1.1 to 1.9. The Z-theta pinch spheromak formation technique is used to produce low aspect ratio tokamaks in an external toroidal field generated by the center conductor. Using this operation, the plasma stability has been investigated in the transition regime from tokamaks to spheromaks. It has been found that there exists a lower critical value of the center conductor current to surpress the global plasma instability of the n = 1 tilt and/or shift modes. The ratio of this critical current to plasma current is experimentally measured for the first time as a function of the aspect ratio. Glass-tube cylindrical limiters with different radii are installed along the symmetric center axis of the Spherical Torus-3 device [Y. Ono et al., Phys. Fluids B 5, 3691 (1993)]. As the aspect ratio is decreased from 1.9 to 1.1, it is observed that the critical ratio of the center conductor current to plasma current decreases from 1.2 to 0.2. The safety factor q at the plasma edge corresponding to this critical current is roughly 1.5 to 3.0. Similar experiments are also carried out with a thin metal cover surrounding the surface of the glass tube limiter. The thin metal cover permits the decrease in the critical current and the corresponding edge q value of q similar to 1. These experimental results of the critical current ratio are found to be comparable to that predicted from theoretical models where the restoring force against the tilt motion is considered to be generated by the interaction of the external toroidal field with the n = 1 induced surface currents in the tilt motion. (C) 1997 American Institute of Physics.

Moroz, P. (1997). “Stellarator-spheromak.” PHYSICS LETTERS A 236(1-2): 79-83.
A novel concept for magnetic plasma confinement, the stellarator-spheromak (SSP), is considered. Actually, this is a nonaxisymmetric spheromak where the outboard stellarator windings are used to produce the stellarator effects and the strong outboard magnetic field. The MHD equilibrium in an SSP with very high beta (plasma pressure/magnetic field pressure) of the confined plasma is demonstrated. This configuration retains the main advantages of spheromaks, such as compact design and absence of material structures in the center of the torus. At the same time, an SSP has a potential for improving the spheromak concept regarding its main problems: the difficulty of plasma start-up and steady-state operation, and the tilt/shift instability. (C) 1997 Elsevier Science B.V.

Omelchenko, Y. and R. Sudan (1997). “A 3-D Darwin-EM hybrid PIC code for ion ring studies.” JOURNAL OF COMPUTATIONAL PHYSICS 133(1): 146-159.
A new, 3-D electromagnetic (EM), hybrid, particle-in-cell (PIC) code, FLAME has been constructed to study low-frequency, large orbit plasmas in realistic cylindrical configurations. The stability and equilibrium of strong ion rings in magnetized plasmas are the first issues suitable for its application. In FLAME the EM-field is governed by Maxwell's equations in the quasi-neutral Darwin approximation (with displacement current neglected), the ion components are represented by discrete macro-particles, and the plasma electrons are modeled as a massless cold fluid. All physical quantities are expanded into finite Fourier series in the azimuthal (theta) direction. The discretization in the poloidal (r, z) plane is done by a finite-difference staggered grid method. The electron fluid equations include a finite scalar resistivity and macro-particles experience slowing-down collisions. A substantial reduction of computation time is achieved by enabling separate time advances of background and beam particle species in the time-averaged fields. FLAME has been optimized to run on parallel, MIMD systems, and has an object-oriented (C++) structure. The results of normal mode tests intended to verify the code ability to correctly model plasma phenomena are presented. We also investigate in 3-D the injection of a powerful annular ion beam into a plasma immersed in a magnetic cusp followed by an axially ramped applied magnetic field. A nonaxisymmetric perturbation is applied to the magnetic field and its effect on ion ring formation is analysed. (C) 1997 Academic Press.

Ono, Y., M. Inomoto, et al. (1997). “Experimental investigation of three-component magnetic reconnection by use of merging spheromaks and tokamaks.” PHYSICS OF PLASMAS 4(5): 1953-1963.
A laboratory experiment of magnetic reconnection has been developed in the Tokyo University Spherical Torus (TS-3) [Y. Ono er al., Phys. Fluids B 5, 3691 (1993)] merging device, using two colliding plasma toroids with cohelicity and counterhelicity. The conventional two-component reconnection was extended experimentally to three-component reconnections by introducing a new field component B-x parallel to the X-line, an external force and a reconnection-driven global equilibrium transition. Selective ion heating accompanied by a field-aligned jet was documented during the counterhelicity reconnection without B-x, indicating its direct energy-conversion into the ion thermal energy. Ion heating, current-sheet resistivity and reconnection rate all increase significantly with decreasing B-x and with increasing the external force, indicating three-component and driven effects of reconnection. The anomalous sheet-current dissipation and the ion heating are both found to depend on whether the current-sheet is compressed shorter than the ion gyroradius or not. (C) 1997 American Institute of Physics.

Ordonez, C. and R. Peterkin (1997). “Compression of a toroidal plasma to thermonuclear ignition.” FUSION TECHNOLOGY 32(4): 655-659.
In the worldwide controlled thermonuclear fusion research effort, ignition of a magnetically confined plasma is yet to be achieved. Consequently, it is not known whether a plasma's approach to ignition is associated with a change (degradation or enhancement) of the confinement of plasma energy. Knowledge of this, however can have a significant impact on the design criteria (and thus cost) of the planned International Thermonuclear Experimental Reactor (ITER). Fast adiabatic compression for producing short-timescale ignited toroidal plasmas is proposed as a means to gain this knowledge using existing resources.

Raman, R., F. Martin, et al. (1997). “Experimental demonstration of tokamak fuelling by compact toroid injection.” NUCLEAR FUSION 37(7): 967-972.
The most promising concept for deep fuelling a reactor is by the injection of compact toroid (CT) plasmoids. The first results showing CT fuelling of a tokamak plasma, without any adverse perturbation to the tokamak discharge, are reported. The Compact Toroid Fueller (CTF) device was used to inject a CT-spheromak plasmoid into the TdeV tokamak. Following the CT penetration, the tokamak particle inventory increased by 16%, the loop voltage and the plasma current did not change, and there was no increase in magnetohydrodynamic (MHD) activity The number of injected impurities was low and dominated by non-metallic elements. The plasma diamagnetic energy and the energy confinement time increased by more than 35%.

Rusbridge, M., S. Gee, et al. (1997). “The design and operation of the SPHEX spheromak.” PLASMA PHYSICS AND CONTROLLED FUSION 39(5): 683-714.
We describe the design and operation of the SPHEX spheromak device and present an overview of its behaviour. The plasma is formed by ejection from a magnetized Marshall gun, and can be sustained as long as the gun is energized; The plasma is divided into the annulus comprising the closed toroidal Bur, linked with the open Bur forming the central column. The column current is driven directly by the central gun electrode, and the toroidal current in the annulus is driven indirectly by a mechanism associated with a coherent n = 1 oscillation of the column. The configuration exemplifies the operation of the process of relaxation to a state of minimum magnetic energy, which leads to magnetic configurations similar to those observed; to sustain these configurations requires some mechanism of toroidal current drive. Associated with this is the amplification of the poloidal flux, which is typically a factor of about five larger than the flux generated by the gun solenoid; the constancy (to a first approximation) of this factor plays a controlling role in spheromak behaviour. In standard operating conditions there is a 'hard' limit, set by the solenoid flux, on the current carried by the column; any current driven by the external circuit above this apparently does not emerge from the gun. Evidence is presented that the column current is carried largely (>50%) by accelerated ions with energy up to the gun voltage (approximate to 500 V for a typical gun current of 60 kA). These ions are poorly magnetized and can escape across the magnetic field to the wall, a likely mechanism for the observed 'loss' of current. Hydrogen is the normal operating gas: other gases (D-2 and He) have been used, but the current drive is found to be less effective than in H-2, With lower toroidal current maintained in the annulus.

Vandas, M., S. Fischer, et al. (1997). “Propagation of a spheromak .1. Some comparisons of cylindrical and spherical magnetic clouds.” JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 102(A11): 24183-24193.
A series of our papers in the Journal of Geophysical Research, 1995-1996, was devoted to simulations of propagation of cylindrical magnetic clouds (flux ropes) having different orientation of their axes to the ecliptic plane and initial parameters. In this paper we supplement our study with the case of detached spherical plasmoids. By varying the velocity, density, temperature, and the magnetic field strength inside clouds, we simulate a number of plasmoid scenarios that can be compared with observations and with existing models and simulations of flux ropes. Initially, the spherical clouds have a poloidal magnetic field configuration within a sphere. During the propagation they evolve into toroids (i.e., closed flux ropes). Radial profiles of magnetic field and plasma quantities in these toroids are similar to cylindrical magnetic clouds. However, they are different in the central (now external) part of the cloud, where the poloidal axis was originally situated, that is, in the toroid's hole. Here the magnetic field is greatly enhanced but does not rotate, and the temperature decrease is absent. The deceleration and transit time to 1 AU is comparable between spherical and cylindrical clouds. The shock wave ahead of a spherical cloud is about 2 times closer than for a corresponding cylindrical cloud.

Watanabe, T., T. Sato, et al. (1997). “Magnetohydrodynamic simulation on co- and counter-helicity merging of spheromaks and driven magnetic reconnection.” PHYSICS OF PLASMAS 4(5): 1297-1307.
A magnetohydrodynamic relaxation process of spheromak merging is studied by means of an axisymmetric numerical simulation. As a result of counter-helicity merging, a field-reversed configuration is obtained in the final state, while a larger spheromak is formed after co-helicity merging. In the counter-helicity case, a clear pressure profile of which iso-surfaces coincide with flux surfaces is generated by thermal transport of a poloidal flow induced by driven reconnection. It is also found that a sharp pressure gradient formed in the vicinity of a reconnection point causes a bouncing motion of spheromaks. According to the bounce motion, the reconnection rate changes repeatedly. As shown by the Tokyo University Spherical Torus No. 3 (TS-3) experiments [M. Yamada, et al., Phys. Rev. Lett. 65, 721 (1990)], furthermore, strong acceleration of a toroidal flow and reversal of a toroidal field in the counter-heIicity merging were observed. (C) 1997 American Institute of Physics.

Yamada, M., H. Ji, et al. (1997). “Identification of Y-shaped and O-shaped diffusion regions during magnetic reconnection in a laboratory plasma.” PHYSICAL REVIEW LETTERS 78(16): 3117-3120.
Two strikingly different shapes of diffusion regions are identified during magnetic reconnection in a magnetohydrodynamic laboratory plasma. The shapes depend on the third vector component of the reconnecting magnetic fields. Without the third component (antiparallel or null-helicity reconnection), a thin double-Y-shaped diffusion region is identified. In this case, the neutral sheet current profile is accurately measured to be as narrow as the order of the ion gyro-radius. In the presence of an appreciable third component (cohelicity reconnection), an O-shaped diffusion region appears and grows into a spheromak configuration.

Yamada, M., H. Ji, et al. (1997). “Study of driven magnetic reconnection in a laboratory plasma.” PHYSICS OF PLASMAS 4(5): 1936-1944.
The magnetic reconnection experiment has been constructed to investigate the fundamental physics of magnetic reconnection in a well-controlled laboratory setting, This device creates an environment satisfying the criteria for a magnetohydrodynamic plasma (S much greater than 1, (rho i) much less than L) The boundary conditions can be controlled externally, and experiments with fully three-dimensional reconnection are now possible. In the initial experiments, the effects of the third vector component of reconnecting fields have been studied, Two distinctively different shapes of neutral sheet current layers, depending on the third component, are identified during driven magnetic reconnection. Without the third component (antiparallel or null-helicity reconnection), a thin double-Y-shaped diffusion region is identified, A neutral sheet current profile is measured accurately to be as narrow as the order of the ion gyroradius. In the presence of an appreciable third component (co-helicity reconnection), an O-shaped diffusion region appears and grows into a spheromak configuration. (C) 1997 American Institute of Physics.

Bellan, P. and J. Hansen (1998). “Laboratory simulations of solar prominence eruptions.” PHYSICS OF PLASMAS 5(5): 1991-2000.
Spheromak technology is exploited to create laboratory simulations of solar prominence eruptions. It is found that the initial simulated prominences are arched, but then bifurcate into twisted secondary structures which appear to follow fringing field lines. A simple model explains many of these topological features in terms of the trajectories of field lines associated with relaxed states, i.e., states satisfying del X B = lambda B. This model indicates that the field line concept is more fundamental than the flux tube concept because a field line can always be defined by specifying a starting point whereas attempting to define a flux tube by specifying a starting cross section typically works only if lambda is small. The model also shows that, at least for plasma evolving through a sequence of force-free states, the oft-used line-tying concept is in error. Contrary to the predictions of line-tying, direct integration of field line trajectories shows explicitly that when lambda is varied, both ends of field lines intersecting a flux-conserving plane do not remain anchored to fixed points in that plane. Finally, a simple explanation is provided for the S-shaped magnetic structures often seen on the sun; the S shape is shown to be an automatic consequence of field Line arching and;the parallelism between magnetic held and current density for force-free states. (C) 1998 American Institute of Physics.

Cohen, B., L. LoDestro, et al. (1998). “Simulations of broadband short-pulse reflectometry for diagnosing plasma density and magnetic-field profiles.” PLASMA PHYSICS AND CONTROLLED FUSION 40(1): 75-89.
Numerical simulations of the use of ultra-short-pulse reflectometry to diagnose plasma density and magnetic-field profiles are presented. Numerical solutions of Maxwell's equations are used to model the propagation of ordinary modes into a plasma from whose reflected signals' time-of-flight (group delay) as a function of frequency is deduced the electron density profile. Similar methods are used to simulate the propagation and reflection of extraordinary waves, from which is deduced the magnetic-field profile if the electron density is already known (the cutoff relation for the extraordinary mode depends jointly on the electron density and the magnetic field). The simulation results presented here demonstrate that the determination of plasma density and magnetic-field profiles from ultra-short-pulse reflectometry is relatively robust. In order to use more realistic plasma and magnetic-field configurations in the reflectometry simulations as well as to be able to simulate, assess, and tune the performance of the diagnostic in the experimental configurations of interest, O-mode and X-mode reflectometry simulation packages have been merged into the CORSICA comprehensive plasma modelling framework. Examples of CORSICA reflectometry simulations of the DIII-D tokamak and the SSPX spheromak being built at the Lawrence Livermore National Laboratory are presented.

Dasgupta, B., P. Dasgupta, et al. (1998). “Relaxed states of a magnetized plasma with minimum dissipation.” PHYSICAL REVIEW LETTERS 81(15): 3144-3147.
The relaxed state of a slightly resistive and turbulent magnetized plasma is obtained by invoking the principle of minimum dissipation, which leads to del x del x del x B = Lambda B. A solution of this equation is accomplished using the analytic continuation of the Chandrasekhar-Kendall eigenfunctions in the complex domain. The new features of this theory show (i) that a single fluid can relax to an MHD equilibrium which can support a pressure gradient even without a long-term coupling between mechanical flow and magnetic field, and (ii) field reversal in states that an not force free. [S0031-9007(98)07284-6].

Geddes, C., T. Kornack, et al. (1998). “Scaling studies of spheromak formation and equilibrium.” PHYSICS OF PLASMAS 5(4): 1027-1034.
Formation and equilibrium studies have been performed on the Swarthmore Spheromak Experiment (SSX). Spheromaks are formed with a magnetized coaxial plasma gun and equilibrium is established in both small (d(small)=0.16 m) and large (d(large)=3d(small)=0.50 m) copper flux conservers. Using magnetic probe arrays it has been verified that spheromak formation is governed solely by gun physics (in particular the ratio of gun current to flux, mu(0)I(gun)/Phi(gun)) and is independent of the flux conserver dimensions. It has also been verified that equilibrium is well described by the force free condition del xB=lambda B (lambda=constant), particularly early in decay. Departures from the force-free state are due to current profile effects described by a quadratic function lambda=lambda(psi). Force-free SSX spheromaks will be merged to study magnetic reconnection in simple magnetofluid structures. (C) 1998 American Institute of Physics.

Kanki, T., M. Nagata, et al. (1998). “Partially relaxed magnetohydrodynamic equilibria with bias-flux leakage obtained in a helicity-driven spheromak.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 67(1): 140-146.
In the flux amplification compact torus experiment, the bias flux penetrates the wall of the flux conserver because it has been switched on a suitably long time prior to the production of a seed spheromak. The magnetohydrodynamic equilibrium configurations with a non-constant lambda(= mu(0)j.B/\B\(2)) profile of a helicity-driven spheromak incorporating the situation of the bias-flux leakage out of the flux conserver are numerically determined by using the novel combination of the finite difference and the boundary element method. Here mu(0), j and B are the permeability of vacuum. the current density and the magnetic field, respectively. The results of computations show that the effects of the bias-flux leakage cause a slight rise of the entire safety factor q in the case of I-C/I-P = 0.4 (I-C and I-P denote the total current of coil and plasma, respectively) because of the decrease in poloidal field over all space. Then, they also give rise to a 22.0% decrease in the magnetic flux inside the separatrix.

Kornack, T., P. Sollins, et al. (1998). “Experimental observation of correlated magnetic reconnection and Alfvenic ion jets.” PHYSICAL REVIEW E 58(1): R36-R39.
Correlations between magnetic reconnection and energetic ion flow events have been measured with merging force free spheromaks at the Swarthmore Spheromak Experiment. The reconnection layer is measured with a linear probe array and ion flow is directly measured with a retarding grid energy analyzer. Flow has been measured both in the plane of the reconnection layer and out of the plane. The most energetic events occur in the reconnection plane immediately after formation as the spheromaks dynamically merge. The outflow velocity is nearly Alfvenic. As the spheromaks form equilibria and decay, the flow is substantially reduced.

Kukushkin, A. and V. RantsevKartinov (1998). “Dense Z-pinch plasma as a dynamical percolating network: From laboratory plasmas to a magnetoplasma universe.” LASER AND PARTICLE BEAMS 16(3): 445-471.
The results of a high-resolution processing, based on techniques of fractal dimension analysis, of experimental data from earlier experiments on the linear Z-pinches are presented, which prove the electric current-carrying plasmas to be a random fractal medium. The basic building block of this medium is identified to be an almost-closed helical filamentary magnetoplasma configuration (we call it heteromac). The heteromacs are coupled together through long-range self-sustained filamentation and, thus, form a dynamical percolating network with dissipation. The results (i) extend recently identified phenomenon of the 3D large-scale (up to several centimeter size) helical filamentary plasma structures (Kukushkin et al. 1994, 1995, 1997a) in plasma focus gaseous discharges to the case of Z-pinch gaseous discharges and (ii) provide a novel view into the dynamics of Z-pinch's necks, plasma spikes, and magnetic bubbles as well as into generic features of electric current-carrying plasmas varying from low-electric current laboratory plasmas to cosmic plasmas. This covers about 30 orders of magnitude of length scale and suggests unprecedented opportunities for interpolating between and extrapolating from well-understood phenomena. A magnetoplasma universe model is suggested.

MacLeod, M. (1998). “The spherical curl transform of a linear force-free magnetic field.” JOURNAL OF MATHEMATICAL PHYSICS 39(3): 1642-1658.
The description of linear force-free magnetic fields in terms of the Moses eigenfunctions of the curl operator begun previously is here completed by the derivation of a general expression for the held's spherical curl transform. This enables the transform space representation of a given field to be determined and compared with that of other fields, assisting the analysis and classification of this type of magnetic field as well as providing a basis for generalization. The result obtained gives the spherical curl transform as a weighted projection of the vector Radon transform of the field on the appropriate curl eigenvector. The process is exemplified by the determination of the transforms of three fields: the simplest force-free magnetic field, and the Lundquist and classical spheromak fields. The latter two are both of interest as models of the magnetic fields of solar magnetic clouds, while the classical spheromak field is relevant to the design of nuclear fusion reactors as well. The use of the transform in generalizing the Lundquist field is briefly discussed. As before, all results apply equally well to the description of the Trkalian subset of Beltrami fields in fluid dynamics. (C) 1998 American Institute of Physics.

McLean, H., D. Hwang, et al. (1998). “Design and operation of a passively switched repetitive compact toroid plasma accelerator.” FUSION TECHNOLOGY 33(3): 252-272.
The design and operation of a spheromak-like compact toroid (SCT) plasma accelerator is described. As an example application, some principles are presented for using the device as a plasma injector to fuel a tokamak plasma. The device forms and accelerates an SCT plasma. The SCT is a self-contained structure of plasma with embedded poloidal and toroidal magnetic fields and their associated currents that provide plasma confinement and structural integrity The SCT is formed in a magnetized coaxial plasma gun and then accelerated within coaxial electrodes. The typical mass of an SCT for tokamak fueling is from several tens to several hundreds of micrograms and is accelerated up to a velocity of similar to 2 X 10(5) m/s. Larger-mass SCTs can be produced, and higher velocities are possible. This is important for other applications such as space propulsion, X-ray generation, fast-opening plasma switches, and low-temperature high-density plasma simulators. The novel features of the device are as follows: (a) it can be operated in a repetitive mode, (b) the high-energy capacitor bank to form the SCT is switched by initiating breakdown with fast gas injection, (c) the required delay between formation and acceleration is achieved passively with saturable inductors that switch the high-energy accelerator capacitor bank, and (d) a drift section has been added within the toroidal field region to study cross-field propagation prior to tokamak penetration. With the device installed on the Davis Diverted Tokamak (DDT), measurements are taken to study tokamak fueling. Typical rep-rated parameters are as follows: the SCT poloidal magnetic field at the outer electrode 0.4 T the stored formation bank energy = 1600 J, and the stored accelerator bank energy = 3600 J. The lower bound on SCT kinetic energy leaving the accelerator = 40 J (inferred from electron line density measurements). Typical SCT velocity is 15 to 20 cm/mu s. The maximum rep-rate achieved so far with the device is 0.2 Hz and is currently limited by vacuum pumping capacity. Reliable operation has been demonstrated for 1000 consecutive shots. Higher-energy single shots have also been taken to study SCT propagation through an open guide tube and to study penetration of the SCT into the DDT tokamak vessel with both tokamak plasma discharges and vacuum toroidal magnetic field only.

Miyazawa, J., H. Yamada, et al. (1998). “Possibility of profile control using compact toroid injection on large helical device.” JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS SHORT NOTES & REVIEW PAPERS 37(12A): 6620-6627.
Compact toroid (CT) injection is an attractive method for central fueling into hot fusion plasmas, induction of plasma rotation is expected by momentum input along the three-dimensional trajectories of the injected CT. The CT trajectories in the magnetic field of a large helical device (LHD) are calculated while changing the initial injection velocity and injection point, to determine the optimum conditions for CT injection into LHD. The possibility of central fueling is confirmed with a model CT with a diameter of 20 cm, 10(22) m(-3) electron density, and 300 km/s initial velocity, in the case of CT injection into an LHD magnetic field of 1.5 T. The input profiles of the density and the momentum obtained assuming a simple CT decay model show the potential of CT injection as a profile control method.

Schultz, J. (1998). “Cost-effective superconducting magnet design for next-step fusion experiments.” JOURNAL OF FUSION ENERGY 17(3): 261-262.
It is widely believed that the use of superconducting magnets in next-step fusion experiments is driven only by the reactor relevance of low circulating power in a fusion plant. However, there is a broad range of fusion magnet applications in which the use of superconducting magnets in near-term experiments will reduce the capital cost of an experiment, along with further reductions in the operating cost. This claim extends to Proof-of-Principle and Proof-of-Performance experiments for Steady-State and Spherical Tori, Compact Stellarators, Spheromaks, and Heavy Ion Fusion Drivers.

Shkolnik, V., Y. Cherepnin, et al. (1998). “Spherical tokamak for material research.” FUSION TECHNOLOGY 34(3): 1179-1181.
At present spherical tokamaks are assumed to be prospective candidates for construction of thermonuclear reactors. These machines combine the advantages of spheromaks (compactness) and of tokamaks (improved plasma confinement). Such a combination allows achievement of higher plasma parameters in the presence of relative compactness and low cost of the main machine. Spherical tokamaks are also used for testing power stressed elements of the first wall and divertor under loads approaching those in experimental thermonuclear power reactors.

Thomassen, K., E. Hooper, et al. (1998). “The spheromak path to fusion.” JOURNAL OF FUSION ENERGY 17(3): 193-199.
Options for a spheromak fusion-energy reactor are described and provide examples of the attractive opportunities which this magnetic configuration offers. However, the ability of the spheromak to confine plasma energy has not yet been demonstrated. The physics issues, including confinement in the presence of current drive by a magnetic dynamo driven by helicity injection, are summarized. These are being studied in the Sustained Spheromak Physics Experiment at LLNL.

Vandas, M., S. Fischer, et al. (1998). “Propagation of a spheromak - 2. Three-dimensional structure of a spheromak.” JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 103(A10): 23717-23725.
Magnetic clouds are commonly modeled as flux ropes and, less frequently, as spheromaks or toroids. In a previous paper,we performed a numerical study of the propagation of a spheromak in the inner heliosphere using a three-dimensional, self-consistent, MHD description. In this second paper on propagating spheromaks we study the interaction of their initial internal field (depending on the orientation of their axes) with the ambient interplanetary magnetic field and their three-dimensional structure near 1 AU. It is shown by our simulation that a spheromak with a poloidal field expands into a toroid during its propagation. It develops into an oblate shape by virtue of its momentum interaction with the solar wind. Draping of magnetic field lines around it causes its polar axis (evolving into the toroid's hole) to be aligned with the radial direction irrespective of its initial orientation. This means that a hypothetical spacecraft can cross the resulting toroid only once, thereby observing signatures similar to a flux rope crossing. Double crossings are excluded even near the Sun (0.3 AU). Therefore the observations of magnetic clouds which resemble a double flux rope crossing must be explained in a way other than within the spheromak or toroidal model.

Viana, R. (1998). “MHD equilibrium equation with azimuthal rotation in a curvilinear coordinate system.” INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 37(10): 2657-2667.
We derive, according to a procedure introduced by Maschke and Perrin, an equation for MHD stationary equilibrium with azimuthal rotation in an orthogonal curvilinear coordinate system. We assume that there is an ignorable coordinate so that surface quantities like the magnetic flux and the rotation frequency do not depend on it. The temperature is also considered a surface quantity. As an application of the formalism, we consider prolate spheroidal coordinates, which are convenient for studying plasma rotation in compact tori configurations like Spheromaks.

Xiao, C., A. Hirose, et al. (1998). “Trajectory of a compact toroid tangentially injected into a tokamak.” NUCLEAR FUSION 38(2): 249-256.
A compact toroid (CT) penetrating into a tokamak discharge is modelled as a conducting solid sphere with an intrinsic magnetic moment. Equations of CT motion in tokamak discharges are derived and used to calculate the trajectory of a CT with parameters pertinent for penetrating the ITER tokamak. The advantage of tangential CT injection and the optimal direction of the initial magnetic moment are discussed.

Brennan, D., P. Browning, et al. (1999). “Stability studies and the origin of the n=1 mode in the SPHEX spheromak experiment.” PHYSICS OF PLASMAS 6(11): 4248-4259.
Oscillations with toroidal mode number n=1 are ubiquitous in helicity injected spheromaks and spherical tokamaks, and play a crucial role in current drive. It has been proposed that these arise from a current driven instability of the open flux tube. Stability calculations are presented to confirm this, and they are compared with experimental data from the Spheromak Experiment (SPHEX) [M. Rusbridge , Plasma Phys. Control. Fusion 39, 683 (1997)]. The equilibria are modelled as piece-wise constant mu profile force-free plasmas with different values for the mu in the open (mu(c)) and closed (mu(a)) flux regions. A stability map in mu(c),mu(a) space is then calculated. The SPHEX experimental data is also reduced to the same space both as a culmination of direct single point measurements of mu and as a time history of the reconstructed equilibrium from a particular shot. The results show a favorable comparison of the stability map with experiment, both in magnitude and shape. The effect of inserting a central current-carrying rod on the stability is also discussed. (C) 1999 American Institute of Physics. [S1070- 664X(99)00811-3].

Brown, M. (1999). “Experimental studies of magnetic reconnection.” PHYSICS OF PLASMAS 6(5): 1717-1724.
Laboratory magnetic reconnection experiments have been performed for nearly 20 years. Elegant experiments by Stenzel and Gekelman [R. L. Stenzel and W. Gekelman, Phys. Rev. Lett. 42, 1055 (1979); W. Gekelman and R. L. Stenzel, Phys. Rev. Lett. 54, 2414 (1985)] focused on the measurement of field quantities with a single movable probe in a highly reproducible plasma. Observations included a very thin current sheet (on the order of c/omega(pe)), accelerated electrons, and whistler waves. The argon ions were unmagnetized in these experiments. Recent magnetohydrodynamic (MHD) experiments by Yamada and Ono have used merging plasmoids [M. Yamada, Y. Ono, A. Hayakawa, M. Katsurai, and F. W. Perkins, Phys. Rev. Lett. 65, 721 (1990); Y. Ono, M. Yamada, T. Akao, T. Tajima, and R. Matsumoto, Phys. Rev. Lett. 76, 3328 (1996)] and have measured three dimensional effects and ion acceleration. We have observed correlations between magnetic reconnection and energetic ion flow events with merging force free spheromaks at the Swarthmore Spheromak Experiment (SSX) [T.W. Kornack, P. K. Sollins, and M. R. Brown, Phys. Rev. E 58, R36 (1998)]. The reconnection layer is measured with linear and two dimensional probe arrays and ion flow is directly measured with a retarding grid energy analyzer. Flow has been measured both in the plane of the reconnection layer and out of the plane. The outflow velocity is nearly Alfvenic in the reconnection plane and the scale of the magnetic structures is consistent with collisionless reconnection theories (on the order of c/omega(pi)). Results from the two dimensional array show the formation of magnetic islands correlated with super-Alfvenic ions accelerated normal to the layer. (C) 1999 American Institute of Physics. [S1070-664X(99)96805-2].

Cohen, B., E. Hooper, et al. (1999). “Theoretical aspects of the use of pulsed reflectometry in a spheromak plasma.” REVIEW OF SCIENTIFIC INSTRUMENTS 70(2): 1407-1415.
Pulsed reflectometry using both ordinary (O) and extraordinary (X) modes has the potential of providing time- and space-resolved measurements of the electron density, the magnitude of the magnetic field, and the magnetic shear as a function of radius. Such a diagnostic also yields the current profile from the curl of the magnetic field. This research addresses theoretical issues associated with the use of reflectometry in the Sustained Spheromak Physics Experiment spheromak experiment at the Lawrence Livermore National Laboratory. We have extended a reflectometry simulation model to accommodate O- and X-mode mixed polarization and linear mode conversion between the two polarizations. A Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) formula for linear mode conversion agrees reasonably well with direct numerical solutions of the wave equation, and we have reconstructed the magnetic pitch-angle profile by matching the results of the WKBJ formula with the mode conversion data observed in simulations using a least-squares determination of coefficients in trial functions for the profile. The reflectometry data also yield information on fluctuations. Instrumental issues, e.g., the effects of microwave mixers and filters on model reflectometry pulses, have been examined to optimize the performance of the reflectometry diagnostics. (C) 1999 American Institute of Physics. [S0034-6748(99)70801-4].

Cohen, B., E. Hooper, et al. (1999). “Modeling of ultra-short-pulse reflectometry.” PHYSICS OF PLASMAS 6(5): 1732-1741.
Pulsed reflectometry using both ordinary (O) and extraordinary (X) modes can provide time- and space-resolved measurements of the electron density, the magnitude of the magnetic field, the magnetic shear as a function of radius, and information on density and magnetic fluctuations. Such a diagnostic also yields the current profile from the curl of the magnetic field. This research addresses theoretical issues associated with the use of pulsed reflectometry with particular emphasis on applications in the Sustained Spheromak Physics Experiment (SSPX) at the Lawrence Livermore National Laboratory [E. B. Hooper et al., "Sustained Spheromak Physics Experiment,'' in Proceedings of the 17th International Atomic Energy Agency (IAEA) Fusion Energy Conference, Yokohama, Japan, October 19-24, 1998, Lawrence Livermore National Laboratory Report UCRL-JC-132034 (September 29, 1998)]. Simulation results are presented for O- and X-mode mixed-polarization reflectometry and linear mode conversion in two spatial dimensions. The profile reconstruction algorithms depend on Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) formulae for group delays and linear mode conversion, which agree reasonably well with direct numerical solutions of the wave equation. Reconstructions of the electron density and modulus of the magnetic field are relatively robust in the presence of two-dimensional electron density and magnetic perturbations of the plasma. (C) 1999 American Institute of Physics. [S1070-664X(99)90205-7].

Frank, A. (1999). “Magnetic reconnection and current sheet formation in 3D magnetic configurations.” PLASMA PHYSICS AND CONTROLLED FUSION 41: A687-A697.
The problem of magnetic reconnection in three-dimensional (3D) magnetic configurations has been studied experimentally. The research has concentrated on the possibilities of formation of current sheets, which represent crucial objects for a realization of magnetic reconnection phenomena. Different types of 3D magnetic configurations were examined, including configurations with singular lines of the X-type, non-uniform fields containing isolated magnetic null-points and without null-points. It was revealed that formation of quasi-one-dimensional current sheets is the universal process for plasma dynamics in 3D magnetic fields both with null-points and without. At the same time the peculiarities of current sheets, plasma dynamics and magnetic reconnection processes depend essentially on characteristics of 3D magnetic configurations. The result of principal significance obtained was that magnetic reconnection phenomena can take place in a wide range of 3D magnetic configurations as a consequence of their ability to form current sheets.

Geranios, A., S. Fischer, et al. (1999). “The magnetic cloud of January 10, 1997.” PHYSICS AND CHEMISTRY OF THE EARTH PART C-SOLAR-TERRESTIAL AND PLANETARY SCIENCE 24(1-3): 73-77.
The magnetic cloud of January 10-11, 1997, was observed by SOHO and WIND spacecraft ahead of the Earth's magnetosphere. Plasma parameters registered by their instrumentation show remarkable differences in the solar wind speed, proton density and temperature that is difficult to explain taking into account simply their distance, The interplanetary magnetic field (measured on board WIND only), would be fitted nearly equivalently by both cylindrical and spherical models. In order to explain observed divergences we speculate on possible model of a poloidal spheromak that develops into a toroid during its propagation (C) 1998 Elsevier Science Ltd. All rights reserved.

Hooper, E., L. Pearlstein, et al. (1999). “MHD equilibria in a spheromak sustained by coaxial helicity injection.” NUCLEAR FUSION 39(7): 863-871.
Spheromaks sustained by coaxial helicity injection differ from unsustained spheromaks in the profiles of the ratio of current to magnetic field and of the safety factor. Ideal MHD modelling with Taylor relaxed profiles in the injector predicts that the safety factor in the confined region will generally lie between 0.5 and 1, with a divergence on the separatrix since the open field lines carry current from the injector. The safety factor can be single or double valued, depending on the current profile. The modelling predicts that there are no mode rational surfaces with m = 1 except very near the separatrix; this is expected to determine the unstable resistive tearing modes associated with the dynamo which drives the discharge current. The resulting low magnetic shear has a beta (similar to 2%) at the Mercier limit, which can be improved by current profiles differing significantly from the Taylor state or by other effects such as plasma flow. Examples are presented for the Sustained Spheromak Physics Experiment recently constructed at LLNL.

Jarboe, T. (1999). “Steady inductive helicity injection and its application to a high-beta spheromak.” FUSION TECHNOLOGY 36(1): 85-91.
A steady inductive helicity injection (SIHI) method is described that has the following properties: (a) helicity is injected at a nearly constant rate; (b) neither magnetic energy nor helicity flow out of plasma at any time; (c) no open field lines penetrate the walls; (d) the equilibrium is produced in a close-fitting flux conserver; (e) a rotating magnetic structure is produced directly; and (f) in the frame of the rotating field, the current profile is nearly time independent and nearly optimum for the application discussed. SIHI can be applied to any toroidal plasma. Application of SIHI to a high-beta spheromak is described.

Jensen, T. and A. Garofalo (1999). “Effects of finite feedback loop gain and bandwidth on stabilization of magnetohydrodynamic instabilities by an "intelligent shell".” PHYSICS OF PLASMAS 6(7): 2757-2761.
The "intelligent shell" [C. M. Bishop, Plasma Phys. Contr. Fusion 31, 1179 (1989)] utilizes a feedback system intended to make a resistive wall appear perfectly conducting to a plasma. It can thus be used for stabilizing modes of the plasma which are unstable when the plasma is surrounded by a resistive wall, but stable if the wall were perfectly conducting. Several concepts of magnetic confinement, such as reversed field pinches, spheromaks, and tokamaks may benefit from an intelligent shell. The paper addresses the question of the dependency of the stabilizing effect on the gain and bandwidth of the feedback circuits (assumed linear). A simple model for the phenomena involved is made and solved numerically for certain parameter values. A characteristic time of the model is a resistive time tau of the wall; the calculations suggest that an upper cutoff frequency of similar to 50/tau and sufficient gain provides a stabilization similar to that of ideal circuits with infinite bandwidth and gain. Under laboratory circumstances with tau similar to 10(-3) s it is thus practical to obtain mass produced components which make the circuits as effective as ideal circuits. (C) 1999 American Institute of Physics. [S1070-664X(99)01207-0].

Ono, Y., M. Inomoto, et al. (1999). “New relaxation of merging spheromaks to a field reversed configuration.” NUCLEAR FUSION 39(11Y): 2001-2008.
A novel high beta relaxation to a field reversed configuration (FRC) has been investigated by axially colliding two spheromaks with opposing toroidal magnetic fields. The beta value of the merging toroids increases from 0.1 to 0.7-1.0 within 15 mu s: indicating an equilibrium transition from the low beta spheromak to the high beta FRC. An important finding is that the merging spheromaks relax either to a high beta FRC or to another low beta spheromak; depending on whether the initial normalized magnetic helicity given to these spheromaks is smaller or larger than a threshold value. This fact suggests that the FRCs are equipped with some global stability as robust as the Taylor magnetic energy minimum state.

Robinson, D. (1999). “Alternative approaches: concept improvements in magnetic fusion research.” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 357(1752): 515-530.
While the conventional tokamak, as embodied in JET, is the front-runner in the magnetic-confinement approach to fusion, other concepts are being developed that might, in the long term, prove more attractive for power generation ('concept improvement' research). Also, in the shorter term, these concepts might offer a more-rapid and cheaper way of studying ignited or near-ignited plasmas. Their advantages, and disadvantages, are described. The stellarator offers steady-state operation at the cost of coil complexity, new advanced stellarators with overall size comparable to JET are either under construction or being commissioned in Japan and Germany. 'Spherical-torus' configurations, of which the most promising is currently the spherical tokamak, offer high-pressure containment in a compact device, but the high power density may mean power-plant technology will be more challenging (e.g. suitable materials). New spherical tokamaks will soon come into operation in the UK, USA and Russia and will test properties in larger higher-current longer-pulse plasmas. Meanwhile, other concepts such as the 'reversed-field pinch', magnetic-mirror systems and the dense Z-pinch, have their own advantages, though they are less well developed. The status of the various concepts are summarized as are their potential fusion applications that include electricity generation, acting as a fusion neutron source, and providing a driver for inertial fusion.

Robinson, D. (1999). “The physics of spherical confinement systems.” PLASMA PHYSICS AND CONTROLLED FUSION 41: A143-A157.
Spherical torus magnetic confinement systems, covering spheromaks and spherical tokamaks (STs), are reviewed. As well as being potentially very important for fusion, spherical tori research is enhancing our understanding of magnetic confinement systems with wider applications than fusion research. The studies contribute to the conventional tokamak, for example, ITER via a range of scalings, as well as to our understanding of 'quiescent' plasmas and those subject to 'turbulent magnetohydrodynamic (MHD) relaxation'. The theoretical and experimental properties are described, showing how these vary with configuration and contrasting them with the conventional aspect ratio tokamak. Topics covered include equilibrium, refuelling, helicity injection, influence of trapped particle fraction, plasma heating, confinement, stability (including pressure limits and energetic particle instabilities) and disruption resilience.

Shumlak, U. and T. Jarboe (1999). “Higher mode stability in spheromak equilibria.” PHYSICS OF PLASMAS 6(11): 4382-4383.
Spheromak equilibria with current profiles varying from peaked to hollow are analyzed for higher mode stability using a linear magnetohydrodynamic (MHD) code. For a cylindrical flux conserver with a radius equal to length the n=2, m=2 mode is found to be marginally unstable for the same hollow current profile as the n=1, m=1 mode. While the growth rate for this n=2 mode is much lower than the n=1 mode, the presence of the n=2 mode may explain experimentally observed relaxation phenomena involving short wavelength turbulence in spheromak equilibria with sufficiently hollow current profiles. (C) 1999 American Institute of Physics. [S1070-664X(99)00411-5].

Stenzel, R., J. Urrutia, et al. (1999). “Laboratory studies of magnetic vortices. II. Helicity reversal during reflection of a magnetic vortex at a conducting boundary (vol 6, pg 3217, 1999).” PHYSICS OF PLASMAS 6(12): 4458-+.
The reflection of a magnetic vortex from a conducting boundary is studied experimentally in a large laboratory plasma. The parameter regime is that of electron magnetohydrodynamics and the vortex consists of a spheromak-like magnetic field perturbation propagating in the whistler mode along a uniform background magnetic field. In this work we focus on the helicity properties of the vortex magnetic field, electron velocity, and vorticity. The reflection conserves magnetic energy but reverses the sign of all helicities. The change in topology arises from a self-consistent reversal of one linked vector field without involving helicity injection, reconnection, or dissipation processes. The breakdown of helicity conservation and the frozen-in concept is explained by the presence of a vacuum-like sheath at the plasma-boundary interface. (C) 1999 American Institute of Physics. [S1070-664X(99)03108-0].

Stenzel, R., J. Urrutia, et al. (1999). “Laboratory studies of magnetic vortices. II. Helicity reversal during reflection of a magnetic vortex at a conducting boundary.” PHYSICS OF PLASMAS 6(8): 3217-3225.
The reflection of a magnetic vortex from a conducting boundary is studied experimentally in a large laboratory plasma. The parameter regime is that of electron magnetohydrodynamics and the vortex consists of a spheromak-like magnetic field perturbation propagating in the whistler mode along a uniform background magnetic field. In this work we focus on the helicity properties of the vortex magnetic field, electron velocity, and vorticity. The reflection conserves magnetic energy but reverses the sign of all helicities. The change in topology arises from a self-consistent reversal of one linked vector field without involving helicity injection, reconnection, or dissipation processes. The breakdown of helicity conservation and the frozen-in concept is explained by the presence of a vacuum-like sheath at the plasma-boundary interface. (C) 1999 American Institute of Physics. [S1070-664X(99)03108-0].

Tsypin, V., I. Nascimento, et al. (1999). “Alfven and fast wave forces, affecting ions in magnetic traps with closed magnetic surfaces.” PHYSICS OF PLASMAS 6(4): 1378-1381.
General expressions for time- and surface-averaged radio frequency forces, affecting ions in closed toroidal devices, are obtained in this paper. Toroidal effects are included in these forces. These effects can, for example, be important to calculate Alfven or fast wave forces in stellarators, spheromaks, or for toroidicity induced Alfven wave eigenmodes (TAE) in axially symmetric tokamaks. The further simplification of obtained expressions should be fulfilled for the proper kind of rf waves and toroidal devices. It is hoped that these rf force expressions can, for example, be useful for the computer simulations of the transport barrier formation by Alfven and fast waves in toroidal devices. (C) 1999 American Institute of Physics. [S1070-664X(99)04004-5].

Watanabe, T., T. Hayashi, et al. (1999). “Modeling of magnetic island formation in magnetic reconnection experiment.” PHYSICS OF PLASMAS 6(4): 1253-1257.
Formation of a magnetic island found in the Magnetic Reconnection Experiment (MRX) [M. Yamada, H. Ji, S. Hsu, et al., Phys. Plasmas 4, 1936 (1997)] is investigated by a magnetohydrodynamic (MHD) relaxation theory and a numerical simulation. In the cohelicity injection with a mean toroidal field, the growing process of the island into a spheromak-type configuration is explained by quasistatic transition of the force-free and minimum energy state to a state with larger normalized helicity. It also turns out that no magnetic island would be generated in the counterhelicity case. The MHD simulation with inhomogeneous electric resistivity agrees with experimental results, which clearly shows formation and growth of the magnetic island in a diffusion region where the reconnection takes place. (C) 1999 American Institute of Physics. [S1070-664X(99)03904-X].

Willet, D., P. Browning, et al. (1999). “The internal magnetic structure and current drive in the SPHEX spheromak.” PLASMA PHYSICS AND CONTROLLED FUSION 41(5): 595-612.
Steady-state current drive by helicity injection has been demonstrated in the SPHEX spheromak. In order to understand the processes by which plasma toroidal current is driven on the closed flux, it is necessary first to diagnose the internal magnetic held and current structure. A method is described which fits force-free equilibria to magnetic held data from a linear insertable probe. It is shown that the overall field configuration and associated global parameters can be well fitted, though the detailed shape of the internal current profile is sensitive to small errors in the data and the choice of fitting function. The current drive process is closely associated with fluctuations having toroidal mode number n = 1. We investigate in detail shots with Ti gettering, when the n = 1 mode is episodic, showing that the current drive mechanism is switched on and off for periods during a single shot, corresponding to the presence or absence of the mode. This provides definitive evidence that the n = 1 mode is responsible for the current drive.

Cantarella, J., D. DeTurck, et al. (2000). “The spectrum of the curl operator on spherically symmetric domains.” PHYSICS OF PLASMAS 7(7): 2766-2775.
This paper presents a mathematically complete derivation of the minimum-energy divergence-free vector fields of fixed helicity, defined on and tangent to the boundary of solid balls and spherical shells. These fields satisfy the equation del xV=lambda V, where lambda is the eigenvalue of curl having smallest nonzero absolute value among such fields. It is shown that on the ball the energy minimizers are the axially symmetric spheromak fields found by Woltjer and Chandrasekhar-Kendall, and on spherical shells they are spheromak-like fields. The geometry and topology of these minimum-energy fields, as well as of some higher-energy eigenfields, are illustrated. (C) 2000 American Institute of Physics. [S1070-664X(00)04005-2].

Clegg, J., P. Browning, et al. (2000). “On the representation of inhomogeneous linear force-free fields.” JOURNAL OF MATHEMATICAL PHYSICS 41(10): 6783-6807.
It is shown that there is a false assumption hidden in the description of a relaxed state with inhomogeneous boundary conditions as the vector sum of a potential field, satisfying the boundary conditions, and a sum of eigenfunctions of the associated eigenvalue problem expanded by certain coefficients. In particular, although the Jensen and Chu formula (1984) can provide the correct expansion coefficients, it contains an implicit paradox in its derivation according to a general vector theorem. The same paradox led Chu (1999) to be concerned about a contradiction obtained by taking the curl of their magnetic field expansion which, if permitted, becomes inconsistent with a current normal to the surface. The assumption that the curl can be commuted across an infinite sum of terms is the mechanism leading to these, apparently paradoxical, conclusions. Two mechanisms for resolving this apparent paradox are possible, one of which will be described in some detail below and the other discussed further in a forthcoming, more theoretical paper (Laurence , 2000). The decomposition of the magnetic field above is valid with convergence in the mean squared sense, but a decomposition of the current needs to be reinterpreted in terms of negative Sobolev spaces. To avoid this, and remain in a more easily managable and familiar setting, we derive the expansion coefficients in a way that involves the commuting of the inverse curl (as opposed to the curl) and the series. The resulting series converges in a mean square sense. When this is done the calculation can conform to the general vector theorem and a new gauge-invariant expression for the coefficients is obtained. However the consequence of the non-commutability is nullified in the Jensen and Chu formula, in both simply and multiply connected domains, by the important extra requirement of a boundary condition on the vector potential eigenfunctions; this excludes magnetic field eigenfunctions that carry flux, but there remains a complete set for the expansion and all flux is carried by the potential field. The two formulas are then identical. On a different issue, it is shown that if the general expansion is taken over a half-space, by combining positive and negative eigenvalue terms, then the coefficients are anisotropic, that is they are tensors except when evaluated at the first eigenvalue. A specific example is presented to illustrate the situation and to validate the new method of deriving the coefficients. (C) 2000 American Institute of Physics. [S0022-2488(00)03909-8].

Clegg, J., P. Browning, et al. (2000). “The linear force-free field in a spherical shell using a new method to determine the coefficients of the eigenfunction expansion.” ASTRONOMY & ASTROPHYSICS 361(2): 743-758.
The linear force-free field of a plasma in between spherical shells is found allowing for inhomogeneous boundary conditions. A three-dimensional solution is found by analysis and used as a benchmark to test a solution in terms of an expansion of eigenfunctions where the coefficients are determined by a new method. Alternative methods are also applied in the context of the spherical shell example and used to illustrate some mathematical constraints that can affect their validity. The solution is used to model the solar coronal field in the presence of a large low-latitude coronal hole; SOHO-MDI data provide the inner boundary conditions.

Coomer, E., C. Hartman, et al. (2000). “An experimental and computational study of compact torus formation, decay and heating in the Berkeley Compact Torus Experiment.” NUCLEAR FUSION 40(9): 1669-1681.
A spheromak type compact torus (CT) plasma is investigated by studies of the gun type plasma formation mechanism and from the characteristics of the magnetic decay following the establishment uf a CT equilibrium in the flux conserver. Radiofrequency heating in the lower hybrid range (432 MHz) is used tu study the electron heat confinement using a 20 MW, 100 mu s power pulse. While electron temperatures up to 200 eV have been measured with RF heating, the impact on magnetic decay from the RF heating is relatively weak. A simple model based upon parallel electron heat transport along stochastic magnetic field lines gives a scaling lan for magnetic decay which fits the experimental data. Results: of two dimensional MHD code calculations are given which match many details of the experimentally observed formation physics.

Finn, J., C. Sovinec, et al. (2000). “Chaotic scattering and self-organization in spheromak sustainment.” PHYSICAL REVIEW LETTERS 85(21): 4538-4541.
Flux core spheromak sustainment by electrostatic helicity injection is studied in resistive MHD. The geometry has magnetized electrodes at the ends held at a potential difference V. For V > V-c the central current column is kink unstable. The nonlinear state with V just above V-c has a large volume of flux surfaces, with rotational transform provided by the helical kinking of the column. As V increases the kink becomes stronger, the tori are destroyed, and the field lines exhibit chaotic scattering. The distribution of field line lengths L, related to confinement and parallel current density, is studied. At larger V or larger Lundquist number S, a limit cycle appears.

Gibson, S. and B. Low (2000). “Three-dimensional and twisted: An MHD interpretation of on-disk observational characteristics of coronal mass ejections.” JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 105(A8): 18187-18202.
A physical interpretation of observed coronal "on-disk" manifestations of an Earth-directed coronal mass ejection (CME) is presented. The fundamental question of how the CME;'s magnetic field and its plasma distribution are related is largely unanswered, because a crucial piece of the puzzle, that is the three-dimensional (3-D) morphology of the CME, remains difficult to ascertain so long as coronal observations are limited to projections onto a single plane of the sky. In order to understand the relationship between observations of CMEs projected at the solar limb and those projected on the solar disk, some sort of model of the 3-D CME is required. In this paper we address both the question of the 3-D morphology of the CME and the more fundamental question of the nature of the plasma-magnetic field relationship, by comparing the limb and on-disk CME representations of an analytic 3-D MHD model based on a spheromak-type flue; rope magnetic field configuration. In particular, we show that the morphology of twin dimmings (also referred to as transient coronal holes) observed in X ray and EUV can be reproduced by the CME model as the on-disk projection of the prominence cavity modeled for limb CMEs. Moreover, the bright core of a limb CME, generally corresponding to the material in an erupting prominence, may be interpreted to be the S-shaped central core of the modeled on-disk CME, splitting the cavity into twin dimmings when observed head-on without obstruction. The magnetic field structure of this central core exhibits many of a filament's magnetic field features required to match observations. Finally, we consider the nature of S-shaped filaments and X-ray "sigmoids" in the context of the model, in terms of localized heating and cooling acting on the modeled CME magnetic field structure.

Gibson, K., P. Browning, et al. (2000). “Current amplification in SPHEX operated as a spherical tokamak.” PLASMA PHYSICS AND CONTROLLED FUSION 42(12): 1331-1347.
We report on further studies of current drive in the SPHEX spheromak device when operated as a spherical tokamak. Previous work has demonstrated that the current amplification factor, defined as the ratio of the toroidal plasma current to the driving gun current, increased linearly with the applied toroidal field. Results are presented from a more detailed analysis of this scaling for a fixed gun current of 60 kA, utilizing direct internal measurements of current density and equilibrium modelling of internal magnetic fields. The data indicate that the increase in the current amplification factor is largely the result of changes in the wavelength of the helical distortion of the open flux (identified with the global n = 1 mode) connected to the helicity injector: the increase in toroidal current on closed flux surfaces is much more modest. We discuss changes in current profiles at differing applied toroidal fields and demonstrate the operating regime over which helicity-injected current drive is effective in SPHEX. The implications of this work for proposed helicity injection schemes in the next generation of spherical tokamaks are discussed.

Hooper, E., R. Cohen, et al. (2000). “Theory of edge plasma in a spheromak.” JOURNAL OF NUCLEAR MATERIALS 278(1): 104-110.
Properties of the edge plasma in the SSPX spheromak during the plasma formation and sustainment phases are discussed. For the breakdown and formation phase, the main emphasis is on the analysis of possible plasma contamination by impurities from the electrodes of the plasma gun (helicity injector). The issue of an azimuthally uniform breakdown initiation is also discussed. After the plasma settles down in the main vacuum chamber, one has to sustain the current between the electrodes, in order to continuously inject helicity. We discuss properties of the plasma on the field lines intersecting the electrodes. We conclude that the thermal balance of this plasma is maintained by Joule heating competing with parallel heat losses to the electrodes. The resulting plasma temperature is in the range 15-30 eV. Under the expected operational conditions, the 'current' velocity of the: electrons is only slightly below their thermal velocity. Implications of this observation are briefly discussed. (C) 2000 Elsevier Science B.V. All rights reserved.

Hwang, D., H. McLean, et al. (2000). “Interaction of a spheromak-like compact toroid with a high beta spherical tokamak plasma.” NUCLEAR FUSION 40(5): 897-905.
Recent experiments using accelerated spheromak-like compact toroids (SCTs) to fuel tokamak plasmas have quantified the penetration mechanism in the low beta regime; i.e. external magnetic field pressure dominates plasma thermal pressure. However, fusion reactor designs require high beta plasma and, more importantly, the proper plasma pressure profile. Here, the effect of the plasma pressure profile on SCT penetration, specifically, the effect of diamagnetism, is addressed. It is estimated that magnetic field pressure dominates penetration even up to 50% local beta. The combination of the diamagnetic effect on the toroidal magnetic field and the strong poloidal field at the outer major radius of a spherical tokamak will result in a diamagnetic well in the total magnetic field. Therefore, the spherical tokamak is a good candidate to test the potential trapping of an SCT in a high beta diamagnetic well. The diamagnetic effects of a high beta spherical tokamak discharge (low aspect ratio) are computed. To test the penetration of an SCT into such a diamagnetic well, experiments have been conducted of SCT injection into a vacuum field structure a which simulates the diamagnetic field effect of a high beta tokamak. The diamagnetic field gradient length is substantially shorter than that of the toroidal field of the tokamak, and the results show that it can still improve the penetration of the SCT. Finally, analytic results have been used to estimate the effect of plasma pressure on penetration and the effect of plasma pressure was found to be small in comparison with the magnetic field pressure. The penetration condition for a vacuum field only is reported. To study the diamagnetic effect in a high beta plasma, additional experiments need to be carried out on a high beta spherical tokamak.

Iwasawa, N., A. Ishida, et al. (2000). “Ideal magnetohydrodynamic stability of static field reversed configurations.” JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 69(2): 451-463.
The ideal magnetohydrodynamic (MHD) stability of static field-reversed configurations is investigated. For the first time, the eigenvector fields and eigenvalues for a variety of global modes are found by applying the Rayleigh-Ritz technique to the variational principle using a verifiably complete basis set. This method is applied to a wide range of equilibria and mode types, including kink and sausage-like modes, modes with intermediate azimuthal mode number, and higher-harmonic modes with respect to the minor radius structure. The findings include the following. Modes with intermediate azimuthal mode number are somewhat more unstable than the well-known tilt mode. The tilt is not stabilized by proper current profile and separatrix shape. The inverse scaling of the tilt growth rate with the elongation (found in previous studies) is not valid in general. This suggests that large elongation alone cannot be relied on for stability when non-MHD corrections are added.

Mattor, N. (2000). “Spatiotemporal signal analysis via the phase velocity transform.” PHYSICAL REVIEW LETTERS 84(26): 6022-6025.
The phase velocity transform (PVT) is an integral transform that divides a function of space and time into components that propagate at uniform phase velocities without distortion. This paper examines the PVT as a method to analyze spatiotemporal fluctuation data. The transform is extended to systems with discretely sampled data on a periodic domain, and applied to data from eight azimuthally distributed probes on the Sustained Spheromak Physics Experiment (SSPX). This reveals features not shown by Fourier analysis, particularly regarding nonsinusoidal mode structure.

Ono, Y. and M. Inomoto (2000). “Ultra-high-beta spherical tokamak formation by use of an oblate field-reversed configuration.” PHYSICS OF PLASMAS 7(5): 1863-1869.
A new slow formation of oblate field-reversed configuration (FRC) has been developed in the Tokyo University Spherical Torus No. 3 (TS-3) merging experiment using two merging spheromaks with opposing toroidal field. This unique technique was extended to a novel formation of ultra-high-beta (50%-70%) spherical tokamak (ST) by applying an external toroidal field B-t,B-ext to the FRC so produced. The high-beta ST was found to have a diamagnetic toroidal field in sharp contrast with low-beta STs with strong paramagnetic toroidal fields. High-beta properties of FRCs including their hollow current profile were maintained during the equilibrium transition, suggesting a close relationship between FRCs and high-beta STs in the second stability regime. (C) 2000 American Institute of Physics. [S1070-664X(00)92405-4].

Ray, N. and K. Bhattacharya (2000). “Analysis of spiky net toroidal current in the magnetized toroidal plasma from the point of view of helicity conservation.” PLASMA PHYSICS AND CONTROLLED FUSION 42(12): 1321-1329.
It has been observed that 'runaway oscillations' in the toroidal current of the magnetized resistive toroidal plasma may cause continuous tearing activity, resulting in 'spiky' net toroidal current and modulation of toroidal and poloidal magnetic fields of the plasma with a definite phase relationship, depending upon the magnitude of vertical magnetic field. The present experimental results on current decay and recovery are explained from the point of view of helicity conservation.

Shumlak, U. and T. Jarboe (2000). “Stable high beta spheromak equilibria using concave flux conservers.” PHYSICS OF PLASMAS 7(7): 2959-2963.
Ideal magnetohydrodynamic stability to the n=1 and n=2 modes are calculated for spheromak equilibria in flux conserver shapes, which include a midplane gap, conforming outer wall, and concave side walls. The equilibria are force-free (del xB=lambda(psi)B) but not minimum energy states and, therefore, have nonuniform lambda(psi) profiles. For each flux conserver shape, the equilibrium with the most hollow linear lambda(psi) profile is found that is stable to the n=1 and n=2 modes. The Mercier beta limit is calculated for each flux conserver shape using the most hollow current profile constrained by the stability boundary. The results show that a stable high <beta > (> 10%) spheromak equilibrium can be produced using a concave flux conserver, improving energy confinement times and plasma performance. (C) 2000 American Institute of Physics. [S1070-664X(00)04707-8].

Stenzel, R., J. Urrutia, et al. (2000). “Vortices and flux ropes in Electron MHD plasmas I.” PHYSICA SCRIPTA T84: 112-116.
Laboratory experiments are reviewed which demonstrate the existence and properties of three-dimensional vortices in Electron MHD (EMHD) plasmas. In this parameter regime the electrons form a magnetized fluid which is charge-neutralized by unmagnetized ions. The observed vortices am time-varying flows in the electron fluid which produce currents and magnetic fields, the latter superimposed on a uniform de magnetic field B-0. The topology of the time-varying flows and fields can be described by linked toroidal and poloidal vector fields with amplitude distributions ranging from spherical to cylindrical shape. Vortices can be excited with pulsed currents to electrodes, pulsed currents in magnetic loop antennas, and heat pulses, The vortices propagate in the whistler mode along the mean held B-0. In the presence of dissipation, magnetic self-helicity and energy decay at the same rate. Reversal of B-0 or propagation direction changes the sign of the helicity. Helicity injection produces directional emission of vortices. Reflection of a vortex violates helicity conservation and field-line tying. Part I of two companion papers reviews the linear vortex properties while the companion Part II describes nonlinear EMHD phenomena and instabilities.

Suzuki, Y., T. Watanabe, et al. (2000). “Three dimensional simulation study of spheromak injection into magnetized plasmas.” NUCLEAR FUSION 40(2): 277-288.
The three dimensional dynamics of a spheromak-like compact toroid (SCT) plasmoid, which is injected into a magnetized target plasma region, is investigated by using MHD numerical simulations. It is found that the process of SCT penetration into this region is much more complicated than that which has been analysed so far by using a conducting sphere (CS) model. The injected SCT suffers from a tilting instability, which grows with a similar timescale to that of the SCT penetration. The instability is accompanied by magnetic reconnection between the SCT magnetic field and the target magnetic field, which disrupts the magnetic configuration of the SCT. Magnetic reconnection plays a role in supplying the high density plasma, initially confined in the SCT magnetic field, to the target region. The penetration depth of the SCT high density plasma is also examined. It is shown to be shorter than that estimated from the CS model. The SCT high density plasma is decelerated mainly by the Lorentz force of the target magnetic field, which includes not only the magnetic pressure force but also the magnetic tension force. Furthermore, by comparing the SCT plasmoid injection with the bare plasmoid injection, magnetic reconnection is considered to relax the magnetic tension force, i.e. the deceleration of the SCT plasmoid.

Suzuki, Y., T. Hayashi, et al. (2000). “Deceleration mechanism of spheromak-like compact toroid penetrating Into magnetized plasmas.” PHYSICS OF PLASMAS 7(12): 5033-5037.
To understand the fueling process in a fusion device by a spheromak-like compact toroid (SCT) injection method, magnetohydrodynamic numerical simulations, where a SCT is injected into magnetized tal get plasmas, have been carried out so far. As a result, it has been found that the SCT penetration into magnetized target plasmas is accompanied by complex physical dynamics, which is not adequately described by the conventional simple theoretical model. In this study, based on the previous simulation results, a new theoretical model to determine the penetration depth of the SCT is represented. Here, the SCT is considered to be decelerated not only by the magnetic pressure force but also by the magnetic tension force, which is generated by the bending of the target magnetic field as a result of the SCT penetration. Furthermore, by comparing the penetration depth of the SCT estimated from the theoretical model with that in the simulation, the accuracy of the model is examined. Finally, the effect of magnetic reconnection on the SCT penetration is discussed. (C) 2000 American Institute of Physics. [S1070-664X(00)04212-9].

Taylor, J. (2000). “Relaxation revisited.” PHYSICS OF PLASMAS 7(5): 1623-1629.
Relaxation is the result of turbulence in a plasma that behaves essentially as an ideal conducting fluid, but has a small resistivity and viscosity. These small effects are locally enhanced by the turbulence and lead to reconnection of magnetic field lines. This destroys an infinity of topological constraints, leaving only the total magnetic helicity as a valid invariant. The plasma therefore rapidly reaches a specific state of minimum energy. This minimum energy "relaxed state" can be calculated from first principles and has many striking features. These depend on the topology of the system. They include spontaneous field reversal, symmetry-breaking and current limitation in toroidal pinches, and flux generation and flux amplification in Spheromaks. In addition the relaxed states can be controlled and maintained by injection of helicity from an external circuit. These features, and the profiles of the relaxed states themselves, have been verified in many laboratory experiments. [S1070-664X(00)90505-6].

Urrutia, J., R. Stenzel, et al. (2000). “Laboratory studies of magnetic vortices. III. Collisions of electron magnetohydrodynamic vortices.” PHYSICS OF PLASMAS 7(2): 519-528.
Magnetic vortices in the parameter regime of electron magnetohydrodynamics are studied in a large laboratory plasma. The vortices consist of magnetic field perturbations, which propagate in the whistler mode along a uniform dc magnetic field. The magnetic self-helicity of the spheromak-like field perturbations depends on the direction of propagation. Vortices with opposite toroidal or poloidal fields are launched from two antennas and propagated through each other. The vortices collide and propagate through one another without an exchange of momentum, energy, and helicity. The absence of nonlinear interactions is explained by the force-free fields of electron magnetohydrodynamic (EMHD) vortices. (C) 2000 American Institute of Physics. [S1070-664X(00)01202-7].

Yee, J. and P. Bellan (2000). “Taylor relaxation and lambda decay of unbounded, freely expanding spheromaks.” PHYSICS OF PLASMAS 7(9): 3625-3640.
A magnetized coaxial gun is discharged into a much larger vacuum chamber and the subsequent evolution of the plasma is observed using high speed cameras and a magnetic probe array. Photographic results indicate four distinct regimes of operation, labeled I-IV, each possessing qualitatively different dynamics, with the parameter lambda(gun)=mu(0)I(gun)/Phi(bias) determining the operative regime. Plasmas produced in Regime II are identified as detached spheromak configurations. Images depict a donut-like shape, while magnetic data demonstrate that a closed toroidal flux-surface topology is present. Poloidal flux amplification shows that Taylor relaxation mechanisms are at work. The spatial and temporal variation of plasma lambda=mu(0)J(phi)/B-phi indicate that the spheromak is decaying and expanding in a manner analogous to a self-similar expansion model proposed for interplanetary magnetic clouds. In Regime III, the plasma is unable to detach from the gun due to excess bias flux. Analysis of toroidal and poloidal flux as well as the lambda profile shows that magnetic flux and helicity are confined within the gun for this regime. (C) 2000 American Institute of Physics. [S1070-664X(00)01709-2].

Bellan, P., J. Yee, et al. (2001). “Spheromaks, solar prominences, and Alfven instability of current sheets.” EARTH PLANETS AND SPACE 53(6): 495-499.
Three related efforts underway at Caltech are discussed: experimental studies of spheromak formation, experimental simulation of solar prominences, and Alfven wave instability of current sheets, Spheromak formation has been studied by using a coaxial magnetized plasma gun to inject helicity-bearing plasma into a very large vacuum chamber. The spheromak is formed without a flux conserver and internal lambda profiles have been measured. Spheromak-based technology has been used to make laboratory plasmas having the topology and dynamics of solar prominences. The physics of these structures is closely related to spheromaks (low beta, force-free, relaxed state equilibrium) but the boundary conditions and symmetry are different. Like spheromaks. the equilibrium involves a balance between hoop forces, pinch forces, and magnetic tension. It is shown theoretically that if a current sheet becomes sufficiently thin (of the order of the ion skin depth or smaller), it becomes kinetically unstable with respect to the emission of Alfven waves and it is proposed that this wave emission is an important aspect of the dynamics of collisionless reconnection.

Belova, E., S. Jardin, et al. (2001). “Numerical study of global stability of oblate field-reversed configurations.” PHYSICS OF PLASMAS 8(4): 1267-1277.
Global stability of the oblate (small elongation, E <1) Field-Reversed Configuration (FRC) has been investigated numerically using both three-dimensional magnetohydrodynamic (MHD) and hybrid (fluid electrons and kinetic ions) simulations. For every nonzero value of the toroidal mode number n, there are three MHD modes that must be stabilized. For n=1, these are the interchange, the tilt and the radial shift; while for n >1 these are the interchange and two co-interchange modes with different polarization. It is shown that the n=1 tilt mode becomes an external mode when E <1, and it can be effectively stabilized by close-fitting conducting shells, even in the small Larmor radii (MHD) regime. The tilt mode stability improves with increasing oblateness, however at sufficiently small elongations the radial shift mode becomes more unstable than the tilt mode. The interchange mode stability is strongly profile dependent, and all n greater than or equal to1 interchange modes can be stabilized for a class of pressure profile with separatrix beta larger than 0.035. Our results show that all three n=1 modes can be stabilized in the MHD regime, but the stabilization of the n >1 co-interchange modes still remains an open question. (C) 2001 American Institute of Physics.

Bhattacharyya, R., M. Janaki, et al. (2001). “Field-reversed configuration (FRC) as a minimum-dissipative relaxed state.” PHYSICS LETTERS A 291(4-5): 291-295.
The field-reversed configuration (FRC) with a completely null toroidal field and finite plasma beta is shown to result from a relaxation mechanism based on the principle of minimum dissipation of energy. (C) 2001 Published by Elsevier Science B.V.

Buchenauer, D., B. Mills, et al. (2001). “Characterization and conditioning of SSPX plasma facing surfaces.” JOURNAL OF NUCLEAR MATERIALS 290: 1165-1170.
The Sustained Spheromak Physics Experiment (SSPX) will examine the confinement properties of spheromak plasmas sustained by DC helicity injection. Understanding the plasma-surface interactions is an important component of the experimental program since the spheromak plasma is in close contact with a stabilizing wall (flux conserver) and is maintained by a high current discharge in the coaxial injector region. Peak electron temperatures in the range of 400 eV are expected, so the copper plasma facing surfaces in SSPX have been coated with tungsten to minimize sputtering and plasma contamination, Here, we report on the characterization and conditioning of these surfaces used for the initial studies of spheromak formation in SSPX. The high pressure plasma-sprayed tungsten facing the SSPX plasma was characterized in situ using beta -backscattering and ex situ using laboratory measurements on similarly prepared samples. Measurements showed that water can be desorbed effectively through baking while the removal rates of volatile impurity gases during glow discharge and shot conditioning indicated a large source of carbon and oxygen in the porous coating. (C) 2001 Elsevier Science B.V. All rights reserved.

Caputi, K. and R. Farengo (2001). “Anisotropic resistivity effects on the minimum dissipation states of tokamak plasmas sustained by coaxial helicity injection.” PLASMA PHYSICS AND CONTROLLED FUSION 43(6): 795-804.
The minimum dissipation states of a tokamak-like plasma sustained by helicity injection are determined. The Ohmic energy dissipation rate is minimized using the helicity balance as a constraint and considering different resistivity values in the directions parallel and perpendicular to the magnetic field inside the plasma. The resulting Euler-Lagrange equations are solved, assuming axial symmetry, for different values of the ratio between the parallel and perpendicular resistivities (eta (parallel to)/eta (perpendicular to)) It is shown that previously published results are not completely correct and that the radial profile of mu (0)j(phi)/B-phi, (the ratio between the toroidal current density and the toroidal magnetic field) changes significantly when eta (parallel to)/eta (perpendicular to) decreases.

Griskey, M. and R. Stenzel (2001). “Magnetic helicity reversal of a whistler vortex transmitted through a three-dimensional magnetic null point.” PHYSICS OF PLASMAS 8(11): 4810-4815.
The transmission of a magnetic vortex through a magnetic null point on a separatrix surface is studied experimentally in a large laboratory plasma. The plasma is in the electron magnetohydrodynamic parameter regime and the vortex is an antenna-produced magnetic field perturbation propagating in the whistler mode. Topologically, the background field is separated into two regions; a closed field line region and an open field line region. The two regions are separated by a surface of magnetic field lines with two cusp null points referred to as the separatrix. The vortex propagates into one of the null points. Its energy is partially transmitted through the separatrix and partially spreads away from the null along curving field lines. The self and mutual-helicity of the transmitted vortex reverses, thus the total magnetic helicity is not conserved. Helicity conservation breaks down because the field lines are not frozen to electron flows in the unmagnetized plasma region around the magnetic null point. (C) 2001 American Institute of Physics.

Holcomb, C., T. Jarboe, et al. (2001). “Nonperturbing field profile measurements of a sustained spheromak.” REVIEW OF SCIENTIFIC INSTRUMENTS 72(1): 1054-1058.
In this article we discuss the measurement of the field profile in the sustained spheromak physics experiment (SSPX). We have built a transient internal probe (TIP) diagnostic to measure the internal field profile in a SSPX plasma sustained by dc coaxial helicity injection. TIP is a diagnostic that makes a spatially resolved (i.e., not chord averaged) measurement of the local magnetic field using Faraday rotation. A 1-cm by 4-mm-diameter verdet probe is fired through the plasma at about 2 km/s by a two-stage light gas gun. The probe is illuminated by an argon ion laser throughout the traverse of the plasma-the retro-reflected light is then analyzed with an ellipsometer to determine the field at each location. The speed, small size of the probe, and the probe cladding make this measurement possible even in hot plasmas (100 s of eV). The measurement is accurate enough (1 MHz, +/-7 G, 1-cm spatial resolution) to map out magneto hydrodynamic (MHD) mode amplitudes from the edge to the magnetic axis. (C) 2001 American Institute of Physics.

Hua, D., T. Fowler, et al. (2001). “Magnetic relaxation in spheromaks using spectral expansions in cylindrical geometry.” JOURNAL OF PLASMA PHYSICS 66: 275-294.
A code has been developed to study self-organization in spheromaks using the Galerkin method in which the magnetic and velocity fields appearing in the incompressible dissipative MID equations are expanded in a spectrum of Chandrasekhar-Kendall eigenstates of the curl. The ultimate goal is to apply the Galerkin method in actual spheromak geometry to calculate turbulence levels and associated transport. The present work employs the straight-cylinder approximation, known to give a good representation of internal ideal MHD modes in spheromaks and applied here to resistive tearing modes. Our main result to date is a demonstration that the Galerkin method can exhibit tearing island formation with only a few states in the spectrum. Example quasilinear calculations are presented for a decaying spheromak and for a spheromak created by gun injection.

Jones, S., S. Parker, et al. (2001). “Low-cost high-performance scientific visualization.” COMPUTING IN SCIENCE & ENGINEERING 3(4): 12-17.
The authors discuss the development of a low-cost stereoscopic visualization system using commonly available components. The system is used to improve understanding about the field-line structure and associated dynamics, confinement, and geometry of spheromak plasma. Such a system might interest research groups doing remote large-scale computing.

Lukin, V., G. Qin, et al. (2001). “Numerical modeling of magnetohydrodynamic activity in the Swarthmore Spheromak Experiment.” PHYSICS OF PLASMAS 8(5): 1600-1606.
Results from a three-dimensional axisymmetric resistive magnetohydrodynamic (MHD) simulation are compared to experimental data from the Swarthmore Spheromak Experiment (SSX) [M. R. Brown, Phys. Plasmas 6, 1717 (1999)]. The MHD simulation is run under conditions and with dimensionless parameters similar to the experiment (Lundquist number S=1000, plasma beta beta =0.1). The simulation is shown to reproduce global equilibrium magnetic field profiles of the spheromaks as well as much of the detailed reconnection dynamics measured when two spheromaks are merged. It is concluded that SSX merger dynamics may be characterized as MHD reconnection, with the likelihood that extensions are needed to account for kinetic effects in the associated current sheet. High spatial and temporal resolution MHD simulation data will be used as input for a particle orbit and energization code. (C) 2001 American Institute of Physics.

McLean, H., A. Ahmed, et al. (2001). “Plasma diagnostics for the sustained spheromak physics experiment.” REVIEW OF SCIENTIFIC INSTRUMENTS 72(1): 556-561.
In this article we present an overview of the plasma diagnostics operating or planned for the sustained spheromak physics experiment device now operating at Lawrence Livermore National Laboratory. A set of 46 wall-mounted magnetic probes provide the essential data necessary for magnetic reconstruction of the Taylor relaxed state. Rogowski coils measure currents induced in the flux conserver. A CO2 laser interferometer is used to measure electron line density. Spectroscopic measurements include an absolutely-calibrated spectrometer recording extended domain spectrometer for obtaining time-integrated visible ultraviolet spectra and two time-resolved vacuum monochrometers for studying the time evolution of two separate emission lines. Another time-integrated spectrometer records spectra in the visible range. Filtered silicon photodiode bolometers provide total power measurements, and a 16 channel photodiode spatial array gives radial emission profiles. Two-dimensional imaging of the plasma and helicity injector is provided by gated television cameras and associated image-processing software. An array of fiber-coupled photodetectors with H alpha filters view across the midplane and in the injector region to measure neutral hydrogen concentrations. Several novel diagnostics are being fielded including a transient internal probe (TIP) and an ultrashort-pulse reflectometer (USPR) microwave reflectometer. The TIP probe fires a very high velocity optical bullet through the plasma and will provide fairly nonpertabative internal magnetic field and current measurements to compare with an equilibrium code model fitted to wall-mounted probes. The USPR is being designed to study edge density and turbulent fluctuations. A multipoint Thomson scattering system is currently being installed to give radial temperature and density profiles. (C) 2001 American Institute of Physics.

Miyazawa, J., H. Yamada, et al. (2001). “Design of spheromak injector using conical accelerator for Large Helical Device.” FUSION ENGINEERING AND DESIGN 54(1): 1-12.
Optimization of CT injector for LHD has been carried out and conical electrode for adiabatic CT compression is adopted in the design. Point-model of CT acceleration in a co-axial electrode is solved to optimize the electrode geometry and the power supplies. The condition to attain the large acceleration efficiency is researched and it is shown to be a function of the ratio of the electrode inductance to the external inductance. Acceleration efficiency of 34% is to be obtained with 3.2 m long conical accelerator and 40 kV-42 kJ power supply. The machine overview of a CT injector named SPICA Mk.I (SPheromak Injector using Conical Accelerator) consisting of 0.8 m conical accelerator is also given. (C) 2001 Elsevier Science B.V. All rights reserved.

Mogahed, E., H. Khater, et al. (2001). “A helium cooled Li2O straight tube blanket design for cylindrical geometry.” FUSION TECHNOLOGY 39(2): 639-643.
A tritium-breeding blanket design is investigated for a D-T Field-Reversed Configuration (FRC) scoping study. The thrust of our initial effort on the blanket has been to seek solutions as close to present-day technology as possible, and we have therefore focused on steel structure with helium coolant. The simple FRC cylindrical geometry has allowed us reasonable success due to the low FRC magnetic field and relatively easy maintenance. In this design the breeder is Li2O tubes. The design is modular with 10 modules each 2.5 m long. The inner radius of the first wall is 2.0 m and the FW/blanket/shield thickness is about 2 m. The surface heat flux will be radiation dominated, fairly uniform, and relatively low, because most of the charged particles follow the magnetic flux tubes to the end walls. The neutron wall loading is 5 MW/m(2) In this design the surface heat flux equals 0.19 MW/m(2). The maximum Li2O tube temperature is 1003 degreesC. The helium exit temperature from the heat exchanger is about 800 degreesC which allows a thermal efficiency of about 52%. The local tritium breeding ratio (TBR) equals 1.1 and is sufficient because in the FRC geometry the plasma has nearly full coverage. The helium pumping power is I MW. The coolant routing is optimized to limit the steel maximum temperature to 635 degreesC. The same concept would be applicable to a spherical torus and spheromak.

Nagata, M., N. Fukumoto, et al. (2001). “Behaviour of compact toroid injected into an external magnetic field.” NUCLEAR FUSION 41(11): 1687-1694.
The interactions of a compact toroid (CT) plasma with an external magnetic field and a tokamak plasma have been studied experimentally on the FACT and JFT-2M devices. Fast framing camera and soft X ray emission profile measurements indicate shift and/or reflection motions of the CT plasma. New electrostatic probe measurements indicate that the CT plasma reaches at least up to the separatrix for discharges with toroidal field strengths of 1.0-1.4 T and that there exists a trailing plasma behind the CT. A large amplitude fluctuation on the ion saturation current and magnetic coil signals is observed. Power spectrum analysis suggests that this fluctuation is related to magnetic reconnection between the CT plasmoid and the toroidal field. The CT, including much of the trailing plasma, may be able to move across the external magnetic field more easily in the drift region of the injector owing to the Hall effect.

Omelchenko, Y., M. Schaffer, et al. (2001). “Nonlinear stability of field-reversed configurations with self-generated toroidal field.” PHYSICS OF PLASMAS 8(10): 4463-4469.
The field-reversed configuration (FRC) is a high-beta compact toroidal plasma confinement scheme in which the external poloidal field is reversed on the geometric axis by azimuthal (toroidal) plasma current. A quasineutral, hybrid, particle-in-cell (PIC) approach [Y. A. Omelchenko and R. N. Sudan, Phys. Plasmas 2, 2773 (1995)] is applied to study long-term nonlinear stability of computational FRC equilibria to a number of toroidal modes, including the most disruptive tilt mode. In particular, a self-generated toroidal magnetic field is found to be an important factor in mitigating the instability and preventing the confinement disruption. This is shown to be a unique FRC property resulting from the Hall effect in the regions of vanishing poloidal magnetic field. The instability-driven toroidal field stabilizes kink formation by increasing the magnetic field energy without destabilizing curvature-driven plasma motion. Finally, the tilt instability saturates due to nonlinear, finite Larmor radius (FLR) effects and plasma relaxation to a quasisteady kinetic state. During this transition the FRC is shown to dissipate a substantial amount of initially trapped flux and plasma energy. These effects are demonstrated for kinetic and fluid-like, spherical and prolate FRCs. (C) 2001 American Institute of Physics.

Qin, G., V. Lukin, et al. (2001). “Energetic particles and magnetohydrodynamic activity in the Swarthmore Spheromak Experiment.” PHYSICS OF PLASMAS 8(11): 4816-4825.
Results from the Swarthmore Spheromak Experiment (SSX) [M. R. Brown, Phys. Plasmas 6, 1717 (1999)] indicate that formation and partial merging of two spheromak plasmas can be described well by a magnetohydrodynamic (MHD) picture in which there is substantial evolution towards force free states within each vessel, while reconnection activity, also described reasonably well by MHD, occurs in the region of interaction. MHD simulations [V. S. Lukin , Phys. Plasmas 8, 1600 (2001)] support and provide further detail to this interpretation. In the present study, test particle equations are integrated using MHD data from SSX simulations to further understand the energetic particle fluxes that are observed experimentally. The test particle simulation is run with dimensionless parameters similar to the experiment, and particles are permitted to escape when they encounter the simulated SSX boundaries. MHD activity related to reconnection is responsible for accelerating charged particles. The process includes two phases-a strong but short duration direct acceleration in the quasi-steady reconnection electric field, and a weaker longer lived stochastic component associated with turbulence. (C) 2001 American Institute of Physics.

Raman, R., T. Jarboe, et al. (2001). “Non-inductive current generation in NSTX using coaxial helicity injection.” NUCLEAR FUSION 41(8): 1081-1086.
Coaxial helicity injection (CHI) oil the National Spherical Torus Experiment (NSTX) has produced 240 kA of toroidal current without the use of the central solenoid. Values of the current multiplication ratio (CHI produced toroidal current/injector current) up to 10 were obtained, in agreement with predictions. The discharges, which lasted for up to 200 ms, limited only by the programmed waveform, arc, more than an order of magnitude longer in duration than any CHI discharges previously produced in a spheromak or a spherical torus.

Roh, Y., C. Domier, et al. (2001). “Ultrashort pulse reflectometry for electron density profile measurements on SSPX.” REVIEW OF SCIENTIFIC INSTRUMENTS 72(1): 332-335.
A broadband ultrashort pulse reflectometry (USPR) diagnostic has been developed for measuring electron density profiles of the sustained spheromak physics experiment (SSPX) device. In USPR, an extremely short pulse or chirped wave form is propagated which contains a broad range of frequency components spanning the desired plasma density profile (or a significant fraction thereof). Upon reflection, each frequency component in the incident waveform reflects from a different spatial location (density layer) in the plasma, thus spreading out the reflected wave packet in time. By simultaneously collecting double-pass time delay data at many distinct frequencies, the time delay data may then be inverted to generate plasma density profiles using a single source and a single set of measurements. On SSPX, wideband mixers are utilized to up- and downconvert 6-18 GHz chirp signals to millimeter-wave frequencies (33-158 GHz) to form a 48 channel O-mode reflectometer system. In this article we describe details of the new USPR system installed on the SSPX device and provide preliminary time-of-flight results. (C) 2001 American Institute of Physics.

Romashets, E. and M. Vandas (2001). “Dynamics of a toroidal magnetic cloud in the solar wind.” JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 106(A6): 10615-10624.
Knowledge about the behavior of compact toroidal magnetic force-free objects in ambient magnetic field may help to better understand dynamical processes in association with coronal mass ejections and their interplanetary counterparts. The problem to find the diamagnetic force acting on a toroidal object in an inhomogeneous magnetic field is solved analytically. At first the drapery of the inhomogeneous magnetic field caused by an insertion of a toroid was found, and then the force acting on the toroid by this disturbed magnetic field was obtained. The problem is considered in purely toroidal coordinates. The obtained solution can be used for calculations of the repulsing diamagnetic force acting on isolated objects in the solar corona such as magnetic clouds of a toroidal shape and for the determination of their velocity profiles, Deformations of toroidal transients due to this melon seed force are not investigated here. Only the force acting on the toroid as a whole is taken in consideration.

Ryutov, D. and R. Siemon (2001). “Magnetized plasma configurations for fast liner implosions: A variety of possibilities.” COMMENTS ON MODERN PHYSICS 2(5): C185-C201.
A variety of plasma configurations suitable for adiabatic compression by fast liners has been identified. Among them there are field-reversed configurations, spheromaks, diffuse Z pinches, spherical tokamaks, and others. The initial plasma is assumed to have density in the range of 10(17)-10(18) cm(-3) and the temperature of the order of 100 eV. Relative advantages and disadvantages of various plasma configurations are discussed. The very fact of the existing broad spectrum of plasma configurations compatible with the liner compression increases the probability of a success in this branch of fusion research.

Sovinec, C., J. Finn, et al. (2001). “Formation and sustainment of electrostatically driven spheromaks in the resistive magnetohydrodynamic model.” PHYSICS OF PLASMAS 8(2): 475-490.
The nonlinear time-dependent equations of resistive magnetohydrodynamics are solved in simply connected domains to investigate spheromak formation and sustainment with electrostatic current drive. Spheromak magnetic fields are generated in three-dimensional computations as the nonlinear state resulting from an unstable pinch. Perturbations convert continuously supplied toroidal magnetic flux into poloidal magnetic flux, leading to "flux amplification" of field embedded in the electrodes. Relaxation of the axisymmetric component of the parallel current profile can be substantial, and the final nonlinear state is steady over a wide range of parameters. However, for sufficiently large values of Lundquist number or sufficiently large applied potential, nonsteady final states are observed with periodic relaxation events in some cases. Under most conditions, the saturated configuration exhibits chaotic scattering of the magnetic field lines. Conditions just above the marginal point of pinch instability sustain large closed flux surfaces in steady state; a weakly kinked pinch current threads the toroidal region of closed flux surfaces and imposes stellarator-like helical transform. Closed flux surfaces also form during decay, due to reduced fluctuation levels and average toroidal current driven directly by inductive electric field.

Srinivasan, R., K. Avinash, et al. (2001). “High beta compact toroidal equilibria.” PHYSICS OF PLASMAS 8(10): 4483-4488.
The relationship of the recently proposed tokamak with spheromak shell (STSS) with other compact equilibria in the low aspect ratio A regime, e.g., spherical tokamaks, field reversed configurations, is studied. It is shown that these equilibria are complementary to equilibria with a magnetic hole studied earlier by Cowley [S. C. Cowley, P. K. Kaw, R. S. Kelly, and R. M. Kulsrud, Phys. Fluids B 3, 2066 (1991)] in the large A regime. The former is perfectly paramagnetic while the latter is perfectly diamagnetic. Relevance of these results to the study of compact equilibria conducted recently on Tokyo University Spherical Torus(TS)-3 and TS-4 [M. Inomoto, Y. Ueda, Y. Ono, T. Murakami, M. Tsurda, M. Yamada, and M. Katsurai, Proceedings of the 17th Conference on Fusion Energy, Yokohama, 1998 (International Atomic Energy Agency, Vienna, 1998), Vol. 3, p. 927] is briefly discussed. (C) 2001 American Institute of Physics.

Steinhauer, L., H. Yamada, et al. (2001). “Two-fluid flowing equilibria of compact plasmas.” PHYSICS OF PLASMAS 8(9): 4053-4061.
The properties of two-fluid flowing equilibria are explored. This is facilitated by limiting attention to compact toroids in a "stationary-energy" state with uniform density. Flowing equilibria are found to fall into two classes, force-free and non-force-free, referring to the absence or presence of a jxB force. The force-free class may have significant flows. Spheromaks are in this class. The non-force-free class is diamagnetic and has Alfvenic poloidal flows. Field reversed configurations (FRCs) are in this class. Both classes admit arbitrarily large equilibria. Both classes occupy certain "allowed" regions in "helicity space," a two-dimensional parameter map with the electron and ion helicities as coordinates. Allowed regions for the two classes overlap; in the overlap region the non-force-free class is energetically favorable. This sheds light on the FRC-spheromak bifurcation observed in experiments. Two-dimensional analytic equilibria are also found that span both classes. These may play a role similar to the familiar Hill's vortex and Bessel function models in static, magnetohydrodynamic equilibria. (C) 2001 American Institute of Physics.

Stenzel, R., J. Urrutia, et al. (2001). “3D EMHD reconnection in a laboratory plasma.” EARTH PLANETS AND SPACE 53(6): 553-560.
In a large laboratory plasma, reconnection of three-dimensional (3D) magnetic fields is studied in the parameter regime of electron magnetohydrodynamics (EMHD). The field topologies are spheromak-like with two-dimensional null lines and three-dimensional spiral null points. The relaxation of an initial vortex field by spontaneous reconnection is studied in the absence of boundary effects, Reconnection rates and energy conversion from fields to particles are measured. The frozen-in condition appears to be destroyed by viscous effects rather than inertia or collision. Finally, the non-driven merging of two EMHD spheromaks into a long-lived FRC is observed. These basic physics experiments demonstrate that reconnection is an important process in the parameter regime of unmagnetized ions, which is always encountered near absolute magnetic null points.

Suzuki, Y., T. Hayashi, et al. (2001). “Dynamics of spheromak-like compact toroids in a drift tube.” NUCLEAR FUSION 41(6): 769-777.
In order to supply plasma fuel confined in spheromak-like compact toroids (SCTs) to a fusion device, the SCTs must be successfully guided through a drift tube region, in which they might be influenced by the magnetic field leaking from the fusion device. To reveal the SCT dynamics in a drift tube, MHD numerical simulations, where the SCTs are accelerated in a co-axial perfectly conducting cylinder with an external magnetic field, are carried out. In addition, the effect of an extended central electrode is examined by changing the length of the inner conducting cylinder. It is revealed that the SCT penetration depth is shorter than that estimated from the conventional conducting sphere model and that the SCTs are further accelerated by extending the inner conducting cylinder. These results are consistent with the results of the compact toroid injection experiment performed on the TEXT Upgrade tokamak. Finally, the deceleration mechanism of the SCTs is discussed by comparing the simulation result with the proposed theoretical model.

Suzuki, Y., T. Hayashi, et al. (2001). “Theory and MHD simulation of fuelling by compact toroid injection.” NUCLEAR FUSION 41(7): 873-881.
The process of fuelling by injection of a spheromak-like compact toroid (SCT) is investigated Ly using MHD numerical simulations, where the SCT is injected into a magnetized target plasma region corresponding to a fusion device. In a previous study, the authors proposed a theoretical model ii, determine the penetration depth of the SCT into the target region on the basis of simulation results; in that study the SCT is decelerated not only by the magnetic pressure force but also by the magnetic tension force. However, since both ends of the target magnetic field are fixed on the boundary wall in the simulation, the deceleration caused by the magnetic tension force would be overestimated. In the present study, the dependence of the boundary condition of the target magnetic field on the SCT penetration process is examined. On the basis of these results, the theoretical model previously proposed is improved to include the effect that the fluctuations of the target magnetic field propagate with thf Alfven velocity. In addition, by carrying out the simulation with the torus domain, it is confirmed that the theoretical model can be applied to estimate the penetration depth of the SCT under such conditions. The dependence of the injection position (side injection and top/bottom injection) on the penetration process is also examined.

Suzuki, Y., T. Hayashi, et al. (2001). “Effect of magnetic reconnection on CT penetration into magnetized plasmas.” EARTH PLANETS AND SPACE 53(6): 547-551.
To understand the fuelling process in a fusion device by a compact toroid (CT) injection method, three dimensional MHD numerical simulations, where a spheromak-like CT (SCT) is injected into magnetized target plasmas, has been carried out. It has been found that the SCT penetration into magnetized target plasmas is accompanied by complex physical dynamics, which is not simply described by the conventional simple theoretical model. One of the most remarkable phenomena is magnetic reconnection. Magnetic reconnection plays a role in supplying the high density plasma, initially confined in the SCT magnetic field, to the target region. Furthermore, it is suggested that magnetic reconnection relaxes the deceleration of the SCT.

Ueda, Y. and Y. Ono (2001). “Experimental comparison of compact RFPs, spheromaks and STs under controlled current drive.” NUCLEAR FUSION 41(8): 981-984.
A comparative experiment on low aspect ratio (A approximate to 1.5) torus plasmas, including compact reversed field pinches (RFPs), spheromaks and spherical tokamaks (STs), has been performed in the TS-3 and TS-4 compact toroid (CT) devices. In particular, a compact RFP with q(o) as large as 0.3 was found to have a low n dynamo mode, n = 3, while a spheromak with q(o) approximate to 0.5 had an n = 2 mode. Under OH current sustainment, the magnetic fluctuation and loop voltage of the CT were observed to increase inversely with its q value. A now method of edge current drive was developed using axial CT merging, which together with the OH current drive created a balanced current drive. This current drive was found to reduce the dynamo fluctuations of compact RFPs and spheromaks by a factor of 3. Multiple CT merging is a promising method of edge current drive because of its intermittent current drive and its detailed control of current profiles using varied size of colliding CTs.

Vandas, M. and A. Geranios (2001). “November 17-18, 1975, event: A clue to an internal structure of magnetic clouds?” JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 106(A2): 1849-1858.
During November 17-18, 1975, a magnetic cloud was observed by the IMP 8 satellite. The cloud was analyzed in several papers. It draws attention because it is the most clear example where the magnetic field components behave differently from the current single flux rope model. Various models and fits have been presented to explain the magnetic field measurements for this particular event: single-polarity cylindrical flux rope, spheromak, toroidal flux rope, and two subsequent flux ropes (flux rope twins). We critically examine these models and fits and stress that not only magnetic field data but also plasma data must be taken into account. There is a remarkably sharp drop in the density inside the magnetic cloud. The most consistent explanation of the behavior of magnetic field and plasma data for this event is that the magnetic cloud consists of a dual-polarity flux rope with a low density and strong magnetic field core surrounded by an annular region of the same chirality but opposite polarity. An implication of this possibility to explain other magnetic cloud observations is discussed.

Wang, Z., G. Wurden, et al. (2001). “Density and H-alpha diagnostics and results for the sustained spheromak physics experiment.” REVIEW OF SCIENTIFIC INSTRUMENTS 72(1): 1059-1062.
A newly installed density diagnostic using CO2 laser interferometry and an H-alpha diagnostic using interference filters and photomultiplier tubes for the recently constructed sustained spheromak physics experiment (SSPX) are described. First diagnostic results of the H-alpha diagnostic were useful to understand the breakdown physics in the new SSPX experiments. Low-noise density data validates techniques to reduce vibration and electronic pickup. The data-processing electronics of the new interferometer can yield unambiguous density data that is equivalent to 16 fringe shifts. Density data is also critical to understand the particle source, and the J/n(e) parameter for SSPX. (C) 2001 American Institute of Physics.

Wang, Z. and C. Barnes (2001). “Exact solutions to magnetized plasma flow.” PHYSICS OF PLASMAS 8(3): 957-963.
Exact analytic solutions for steady-state magnetized plasma flow (MPF) using ideal magnetohydrodynamics formalism are presented. Several cases are considered. When plasma flow is included, a finite plasma pressure gradient delp can be maintained in a force-free state JxB = 0 by the velocity gradient. Both incompressible and compressible MPF examples are discussed for a Taylor-state spheromak B field. A new magnetized nozzle solution is given for compressible plasma when U parallel toB. Transition from a magnetized nozzle to a magnetic nozzle is possible when the B field is strong enough. No physical nozzle would be needed in the magnetic nozzle case. Diverging-, drum- and nozzle-shaped MPF solutions when U perpendicular toB are also given. The electric field is needed to balance the UxB term in Ohm's law. The electric field can be generated in the laboratory with the proposed conducting electrodes. If such electric fields also exist in stars and galaxies, such as through a dynamo process, then these solutions can be candidates to explain single and double jets.

Wood, R., D. Hill, et al. (2001). “Particle control in the sustained spheromak physics experiment.” JOURNAL OF NUCLEAR MATERIALS 290: 513-517.
In this paper we report on density and impurity measurements in the sustained spheromak physics experiment (SSPX) which has recently started operation. The SSPX plasma is sustained by coaxial helicity injection for a duration of 2 ms with peak toroidal currents of up to 0.5 MA. plasma-facing components consist of tungsten-coated copper to minimize sputtering, The surfaces are conditioned by a combination of baking at 150 degreesC, glow discharge cleaning, titanium gettering, and pulse-discharge cleaning with helium plasmas. In this way we achieve density control with n(e) similar to1-4 x 10(20) m(-3). However, gas input has only a weak effect on plasma density; injector current is the dominant factor. Conditioning reduces the impurity radiation to the point where it is no longer important to the energy balance, so that the lifetime of the spheromak discharge is ultimately governed by MHD which grows rapidly about 1.5-2.0 ms after helicity injection ends. (C) 2001 Elsevier Science B.V, All rights reserved.

Yamada, M. (2001). “Review of the recent controlled experiments for study of local reconnection physics.” EARTH PLANETS AND SPACE 53(6): 509-519.
The present paper reviews the recent laboratory experiments on magnetic reconnection focussing on the local features of the reconnection region. It is very important to recognize that magnetohydrodynamics (MHD) often breaks down locally in the thin reconnection layer, while globally, the reconnecting plasma has large Lundquist number and is well approximated by MHD equations. Precise measurements of the neutral sheet profile can provide important clues to help understand the non-MHD physics mechanisms of reconnection. Thanks to significant progress in data acquisition technology, the detailed magnetic field structure of the neutral sheet has been measured in laboratory plasmas. Extensive data have been accumulated in highly conductive MHD plasmas with large Lundquist numbers S = 10-1000. In this review we primarily focus on the physics data of the neutral sheet from the most recent laboratory experiments.

Zhang, H., I. Sokolov, et al. (2001). “Oscillations, shocks, and fine wave structures arising during the coalescence of two force-free current loops.” PLASMA PHYSICS REPORTS 27(4): 303-314.
Two-dimensional numerical simulations of the magnetic reconnection of two parallel force-free current loops are carried out using a high-resolution MHD code in which an artificial wind scheme is employed. Two typical cases (namely, co-helicity and counter-helicity reconnection) are investigated. The simulation results show that co-helicity reconnection involves only the reconnection of the poloidal component of the magnetic field, while counter-helicity reconnection involves the reconnection of both the poloidal and axial components of the magnetic field. Therefore, counter-helicity reconnection is much more complicated and violent as compared to co-helicity reconnection. In both cases, jetlike flows are generated. Counter-helicity reconnection is accompanied by oscillations of both the axial magnetic field and the axial component of the velocity. Due to these oscillations, quasi-steady models of a current sheet appear to be inapplicable, because the current sheet structure also changes. The complicated and unsteady structure of the current distribution shows that magnetic reconnection occurs not only in the central sheet between two loops in the earlier stage of the process, but also inside each loop in later stages. Rather complicated hows and waves with fine structures are also generated during reconnection. Some of the waves appear to be shock waves. (C) 2001 MAIK "Nauka/Interperiodica".

Bellan, P. (2002). “Thermal instability of electrolytic capacitor bank used for gas puff valve.” REVIEW OF SCIENTIFIC INSTRUMENTS 73(8): 2900-2905.
It is shown that self-heating of electrolytic capacitors causes the output current of a capacitor bank to increase with successive shots even though the charge voltage is held constant. Self heating of only 10 degreesC can cause a near tripling in the gas output of the gas puffing valves commonly used in spheromak research. By using metallized polypropylene film capacitors instead of electrolytic capacitors the reproducibility is substantially improved (the shot-to-shot variation in gas output is reduced to be <0.5%). (C) 2002 American Institute of Physics.

Bellan, P. (2002). “Generalization of cylindrical spheromak solution to finite beta and large reversed shear.” PHYSICS OF PLASMAS 9(7): 3050-3056.
The well-known analytic solution for a spheromak in a cylindrical flux conserver is generalized to the situation of finite beta with the shape of the flux conserver now being a dependent quantity. Analytic expressions are found for the poloidal flux surfaces, beta, the safety factors at both the magnetic axis and the wall, and the wall profile. A large reversed shear (i.e., ratio of safety factor on magnetic axis to safety factor at the wall) can be obtained at finite beta. This feature may be important because reversed shear in the core of tokamaks has been shown to permit stable operation at high beta. (C) 2002 American Institute of Physics.

Brennan, D., P. Browning, et al. (2002). “A two-dimensional magnetohydrodynamic stability model for helicity-injected devices with open flux.” PHYSICS OF PLASMAS 9(8): 3526-3535.
Models of the ideal magnetohydrodynamic (MHD) stability of spheromaks and spherical tokamaks are presented, including the effects of current on the open flux which plays a key role in helicity-injected current drive. The stability of spheromak equilibria with both open and closed flux and realistic current profiles representative of helicity-injected state is investigated, where a kink instability in the open flux is shown to dominate a tilt mode in the closed flux as the open flux current density is increased. A previous one-dimensional model is extended to more realistic two-dimensional equilibria which properly incorporate a region of closed magnetic flux as well as open flux penetrating the boundaries at electrodes. A new stability code SCOTS has been developed and benchmarked which can determine the growth rates of ideal MHD modes in this geometry. The coordinate system for this code has been developed such that it extends smoothly across the separatrix between closed and open flux, thus not imposing any unphysical discontinuities in mode structures. From the results, the operating conditions of devices can be predicted since helicity-injection current drive requires fluctuations which arise from the saturated current driven instability in the open flux, and since these systems operate near the stability boundary for this mode. (C) 2002 American Institute of Physics.

Brown, M., C. Cothran, et al. (2002). “Energetic particles from three-dimensional magnetic reconnection events in the Swarthmore Spheromak Experiment.” PHYSICS OF PLASMAS 9(5): 2077-2084.
Measurements are presented from the Swarthmore Spheromak Experiment (SSX) [M. R. Brown, Phys. Plasmas 6, 1717 (1999)] showing a population of superthermal, super-Alfvenic ions with <(E)over &CONG;90 eV and E-max&GE;200 eV accelerated by reconnection activity in three-dimensional magnetic structures. These energetic ions are temporally and spatially correlated with three-dimensional magnetic reconnection events (measured with a 3D probe array) and are accelerated along the X-line normal to the local 2D plane of reconnection. In a typical SSX discharge, the peak reconnection electromotive force E=vBL&LE;(10(5) m/s)(0.05 T)(0.1 m)=500 V consistent with our observations. In addition, test particle simulations using magnetohydrodynamic (MHD) data from SSX simulations and run with dimensionless parameters similar to the experiment (S=1000, &beta;=0.1) show acceleration of ions up to 2v(Alf) in a few Alfven times consistent with the measurement. The process includes two phases-a strong but short duration direct acceleration in the quasi-steady reconnection electric field, and a weaker longer lived sub-diffusive component associated with turbulence. (C) 2002 American Institute of Physics.

Burgess, D. (2002). “Camera captures spheromak plasmas.” PHOTONICS SPECTRA 36(11): 38-39.

Dasgupta, B., M. Janaki, et al. (2002). “Spheromak as a relaxed state with minimum dissipation - art. no. 046405.” PHYSICAL REVIEW E 65(4): 046405-6405.
The principle of minimum dissipation of energy is utilized to obtain the spheromak configuration as a relaxed state. The Euler-Lagrange equation for the minimum dissipative relaxed state is solved in terms of Chandrasekhar-Kendall eigenfunctions analytically generalized in the complex domain. This state is non-force-free and further shows the nonconstancy of the ratio of parallel current to the magnetic field.

Farengo, R., A. Lifschitz, et al. (2002). “Theoretical studies of non inductive current drive in compact toroids.” BRAZILIAN JOURNAL OF PHYSICS 32(1): 65-75.
Three non inductive current drive methods that can be applied to compact toroids axe studied. The use of neutral beams to drive current in field reversed configurations and spheromaks is studied using a Monte Carlo code that includes a complete ionization package and follows the exact particle orbits in a self-consistent equilibrium calculated including tile beam and plasma currents, Rotating magnetic fields are investigated as a current drive method for spherical tokamaks by employing a two dimensional model with fixed ions and massless electrons. The time evolution of the axial components of the magnetic field and vector potential is obtained by combining an Ohm's law that includes the Hall term with Maxwell's equations. The use of helicity injection to sustain a flux core spheromak is studied using the principle of minimum rate of energy dissipation. The Euler-Lagrange equations obtained using helicity balance as a constraint axe solved to determine the current and magnetic field profiles of the relaxed states.

Farengo, R. and K. Caputi (2002). “Relaxed, minimum dissipation states, for a flux core spheromak sustained by helicity injection.” PLASMA PHYSICS AND CONTROLLED FUSION 44(8): 1707-1722.
Minimum dissipation states of a flux core spheromak sustained by helicity injection are presented. Helicity balance is used as a constraint and the resistivity is considered to be non-uniform. Two types of relaxed states are found: one has a central core formed by the flux that links the electrodes surrounded by a toroidal region of closed flux surfaces and the other has the open flux wrapped around the closed flux surfaces. The analysis includes two important features: a self-consistent calculation of the magnetic flux through the electrodes and a resistivity which depends upon the poloidal flux. Non-uniform resistivity effects can be very important because of the qualitative and quantitative changes they produce in the safety factor profile.

Fowler, T. and D. Hua (2002). “Heat confinement in spheromaks.” PLASMA PHYSICS REPORTS 28(9): 773-775.
Calculations are presented showing the temperatures expected in a spheromak sustained by continuous injection of helicity, based on a model previously shown. to agree with temperatures achieved in spheromak experiments carried out in the 1980's. New experiments with Thomson scattering measurements of electron temperature will provide an experimental test. (C) 2002 MAIK "Nauka/Interperiodica".

Greenwald, M. (2002). “Density limits in toroidal plasmas.” PLASMA PHYSICS AND CONTROLLED FUSION 44(8): R27-R80.
In addition to the operational limits imposed by MHD stability on plasma current and pressure, an independent limit on plasma density is observed in confined toroidal plasmas. This review attempts to summarize recent work on the phenomenology and physics of the density limit. Perhaps the most surprising result is that all of the toroidal confinement devices considered operate in similar ranges of (suitably normalized) densities. The empirical scalings derived independently for tokamaks and reversed-field pinches are essentially identical, while stellarators appear to operate at somewhat higher densities with a different scaling. Dedicated density limit experiments have not been carried out for spheromaks and field-reversed configurations, however 'optimized' discharges in these devices are also well characterized by the same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary: thus, it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core apparently have no effect on density limit physics. While there is no widely accepted, first principles model for the density limit, research in this area has focussed on mechanisms which lead to strong edge cooling. Theoretical work has concentrated on the consequences of increased impurity radiation which may dominate power balance at high densities and low temperatures. These theories are not entirely satisfactory as they require assumptions about edge transport and make predictions for power and impurity scaling that may not be consistent with experimental results. A separate thread of research looks for the cause in collisionality enhanced turbulent transport. While there is experimental and theoretical support for this approach, understanding of the underlying mechanisms is only at a rudimentary stage and no predictive capability is yet available.

Hooper, E. and L. Pearlstein (2002). “Hyper-resistive modeling in the Spheromak.” PLASMA PHYSICS REPORTS 28(9): 765-772.
Current drive by coaxial helicity injection in the Sustained Spheromak Physics Experiment (SSPX) is modeled by a hyper-resistive term in Ohm's law for discharges in which magnetic fluctuations are small (1-3%). The current on the open magnetic field lines from the applied vacuum bias flux is assumed completely relaxed; interior to the spheromak, the helicity flux balances the ohmic losses. The poloidal area of the spheromak is found to depend on the strength of the hyper-resistive diffusion coefficient, allowing potentially large amplifications of the vacuum flux and discharge current. One discharge is examined in detail; the best fit to the experimental data finds that a limited fraction of the helicity injected into the flux conserver is effectively applied to current drive interior to the spheromak. (C) 2002 MAIK "Nauka/Interperiodica".

Hsu, S. and P. Bellan (2002). “Study of magnetic helicity injection via plasma imaging using a high-speed digital camera.” IEEE TRANSACTIONS ON PLASMA SCIENCE 30(1): 10-11.
The evolution of a plasma generated by a novel planar coaxial gun is photographed using a state-of-the-art digital camera, which captures eight time-resolved images per discharge. This experiment is designed to study the fundamental physics of magnetic helicity injection, which is an important issue in fusion plasma confinement, as well as solar and astrophysical phenomena such as coronal mass ejections and accretion disk dynamics. The images presented in this paper are not only beautiful but provide a powerful way to understand the global dynamics of the plasma.

Hsu, S. and P. Bellan (2002). “A laboratory plasma experiment for studying magnetic dynamics of accretion discs and jets.” MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 334(2): 257-261.
This work describes a laboratory plasma experiment and initial results which should give insight into the magnetic dynamics of accretion discs and jets. A high-speed multiple-frame CCD camera reveals images of the formation and helical instability of a collimated plasma, similar to MHD models of disc jets, and also plasma detachment associated with spheromak formation, which may have relevance to disc winds and flares. The plasmas are produced by a planar magnetized coaxial gun. The resulting magnetic topology is dependent on the details of magnetic helicity injection, namely the force-free state eigenvalue alpha(gun) imposed by the coaxial gun.

Lifschitz, A., R. Farengo, et al. (2002). “Numerical calculations of neutral beam injection in spheromaks.” PLASMA PHYSICS AND CONTROLLED FUSION 44(9): 1979-1997.
A numerical study of neutral beam injection into spheromaks is presented. The beam evolution is calculated through a Monte-Carlo simulation and the plasma MHD equilibrium is determined self-consistently with the current produced by the beam. The exact equations of motion are used for the beam particles instead of the usual guiding-centre approximation. The guiding-centre trajectories are clearly different from the actual particle trajectories and this difference produces discrepancies in the total driven current and in the current profiles. A reduction of the plasma effective charge, Z(eff), does not result in an improvement in the current drive efficiency because the reduction of the stopping cross section is compensated by an increase in the electron cancelling current. The safety factor profile of the self-consistent equilibria shows a clear sensitivity to the driven current profile. The value at the magnetic axis (q(0)) diminishes when the beam is injected at the magnetic axis and increases for injection above the axis. Power deposition profiles for simple injection configurations are also shown.

McCollam, K. and T. Jarboe (2002). “Magnetic relaxation in coaxial helicity injection.” PLASMA PHYSICS AND CONTROLLED FUSION 44(5): 493-517.
The Helicity Injected Torus (HIT-II) (Jarboe T R 1998 Phys. Plasmas 5 1807) is operated with either cathode or anode central column (CC) during coaxial helicity injection (CHI). The CC polarity has a strong effect on tokamak behaviour. For cathode CC operation, the magnetic profile is inferred from surface data to be more relaxed, and then = 1 mode is stronger and more slowly rotating than for anode CC operation. Mode toroidal rotation follows the applied E x B direction. Ion toroidal spin-up in the core is consistent with electromotive action. Apparently, some type of mode asymmetry, effected by the plasma flow and mode rotation, is integral to the current drive observed. This is discussed in terms of electromotive effects, and the picture is shown to be consistent with observations. Some possible implications are outlined, including those concerning parallel fluid velocity shear and other magnetic confinement configurations.

McLean, H., S. Woodruff, et al. (2002). “Suppression of MHD fluctuations leading to improved confinement in a gun-driven spheromak - art. no. 125004.” PHYSICAL REVIEW LETTERS 88(12): 125004-5004.
Magnetic fluctuations have been reduced to similar to1% during discharges on the Sustained Spheromak Physics Experiment by shaping the spatial distribution of the bias magnetic flux in the device. In the resulting quiescent regime, the safety factor pro le is nearly at in the plasma and the dominant ideal and resistive MHD modes are greatly reduced. During this period, the temperature pro le is peaked at the magnetic axis and maps onto magnetic flux contours. Energy confinement time is improved over previous reports in a driven spheromak.

Wang, Z., C. Barnes, et al. (2002). “Large-amplitude electron density and H alpha fluctuations in the sustained spheromak physics experiment.” NUCLEAR FUSION 42(6): 643-652.
New types of toroidally rotating fluctuations (toroidal mode numbers n = 1 and n = 2) of line-integrated electron density and H-alpha emission, with frequencies ranging from 10 to 100 kHz, are observed in the sustained spheromak physics experiment (SSPX). The rotating directions of these fluctuations are the same as the direction determined by E x B, while the E and B directions are determined by the gun voltage and gun magnetic flux polarities, respectively. These results take advantage of one distinctive signature of spheromaks, i.e. it is possible to observe toroidal MHD activity during decay and sustainment at any toroidal angle. A theoretical constraint on line-integrated measurement is proposed and is found to be consistent with experimental observations. Fluctuation analysis in the time and frequency domains indicates that the observed density and H-alpha fluctuations correlate with magnetic modes. Observation of H-alpha fluctuations correlating with magnetic fluctuations indicates that, at least in some cases, MHD n = 1 modes are due to the so-called 'dough-hook' current paths that connect the coaxial gun to the flux conserver, rather than internal kink instabilities. These results also show that electron density and H-alpha emission diagnostics complement other tools for spheromak mode study.

Wang, Z., V. Pariev, et al. (2002). “Laminar plasma dynamos.” PHYSICS OF PLASMAS 9(5): 1491-1494.
A new kind of dynamo utilizing flowing laboratory plasmas has been identified. The conversion of plasma kinetic energy to magnetic energy is verified numerically by kinematic dynamo simulations for magnetic Reynolds numbers above 210. As opposed to intrinsically-turbulent liquid-sodium dynamos, the proposed plasma dynamo corresponds to laminar flow topology. Modest plasma parameters (1-20 eV temperatures, 10(19)-10(20) m(-3) densities in 0.3-1.0 m scale-lengths driven by velocities on the order of the Alfven critical ionization velocity) self-consistently satisfy the conditions needed for the magnetic field amplication. Growth rates for plasma dynamos are obtained numerically with different geometry and magnetic Reynolds numbers. Magnetic-field-free coaxial plasma guns can be used to sustain the plasma flow and the dynamo. (C) 2002 American Institute of Physics.

Woodruff, S. and M. Nagata (2002). “Instantaneous current and field structure of a gun-driven spheromak for two gun polarities.” PLASMA PHYSICS AND CONTROLLED FUSION 44(12): 2539-2553.
The instantaneous plasma structure of the SPHEX spheromak is determined here by numerically processing data from insertable Rogowski and magnetic field probes. Data is presented and compared for two modes of gun operation: with the central electrode biased positively and negatively. It is found that while the mean-, or even instantaneous-, field structure would give the impression of a roughly axisymmetric spheromak, the instantaneous current structure does not. Hundred per cent variations in J measured at the magnetic axis can be explained by the rotation of a current filament that has a width equal to half of the radius of the flux-conserving first wall. In positive gun operation, current leaves the filament in the confinement region leading to high wall current there. In negative gun operation, wall current remains low as all injected current returns to the gun through the plasma. The plasma, in either instance, is strongly asymmetric. We discuss evidence for the existence of the current filament in other gun-driven spheromaks and coaxial plasma thrusters.

Bhattacharyya, R., M. Janaki, et al. (2003). “Relaxation phenomenon in the field reversed configuration.” PLASMA PHYSICS AND CONTROLLED FUSION 45(1): 63-70.
The relaxation phenomenon for a driven plasma system is studied using minimum dissipation rate principle. For the class of equilibria supporting field-aligned flows the Euler-Lagrange equations are shown to support bifurcated solutions. One of the branches depicts the topology of the field reversed configuration sustaining flow whereas the other branch resembles the classical spheromak configuration.

Browning, P. and R. Van der Linden (2003). “Solar coronal heating by relaxation events.” ASTRONOMY & ASTROPHYSICS 400(1): 355-367.
A coronal heating model is proposed which predicts heating by a series of discrete events of various energies, analogous to the observed range of events from large scale flares through various transient brightening phenomena down to the often discussed "nanoflares". We suggest that an energy release event occurs when a field becomes linearly unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to reconnection in fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parameterised by two values of a (the ratio of current density to field strength). Different initial a profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes, but our model predicts an observationally realistic minimum size for these events.

Ebrahimi, F., S. Prager, et al. (2003). “The three-dimensional magnetohydrodynamics of ac helicity injection in the reversed field pinch.” PHYSICS OF PLASMAS 10(4): 999-1014.
ac magnetic helicity injection (also known as oscillating field current drive, OFCD) has been proposed as a technique to sustain the plasma current in a reversed field pinch. The three-dimensional, resistive magnetohydrodynamics computation is employed to examine the full nonlinear dynamics of OFCD, including the behavior of plasma fluctuations and instabilities. The three-dimensional results are also compared with one-dimensional classical and relaxed-state modeling. In OFCD, helicity is injected by oscillating the toroidal and poloidal surface loop voltages. This technique is able to sustain the plasma current, with the edge current mainly driven directly by the OFCD-generated fields, and the core current driven by plasma fluctuations. Fluctuations increase with OFCD, although the increase is concentrated mainly in one global, nearly ideal, mode. (C) 2003 American Institute of Physics.

Landreman, M., C. Cothran, et al. (2003). “Rapid multiplexed data acquisition: Application to three-dimensional magnetic field measurements in a turbulent laboratory plasma.” REVIEW OF SCIENTIFIC INSTRUMENTS 74(4): 2361-2368.
Multiplexing electronics have been constructed to reduce the cost of high-speed data acquisition at the Swarthmore Spheromak Experiment (SSX) and Redmond Plasma Physics Laboratory. An application of the system is described for a three-dimensional magnetic probe array designed to resolve magnetohydrodynamic time scale and ion inertial spatial scale structure of magnetic reconnection in a laboratory plasma at SSX. Multiplexing at 10 MHz compresses 600 pick-up coil signals in the magnetic probe array into 75 digitizer channels. An external master timing system maintains synchronization of the multiplexers and digitizers. The complete system, calibrated and tested with Helmholtz, line current, and magnetofluid fields, reads out the entire 5 x 5 x 8 probe array every 800 ns with an absolute accuracy of approximately 20 G, limited mainly by bit error. (C) 2003 American Institute of Physics.

McLean, H., D. Hill, et al. (2003). “Laser-based diagnostic for tracing magnetic-field lines in spheromaks and other self-organized magnetically confined plasmas.” REVIEW OF SCIENTIFIC INSTRUMENTS 74(3): 1547-1550.
We are in the process of testing a technique for measuring the magnetic-field line topology in magnetically confined plasmas. The basic idea is to use a high-powerful short-pulse laser to launch a burst of energetic (similar to100 keV) electrons from a target passing through the plasma of interest; these electrons then generally follow field lines until they strike a solid surface, where a burst of x rays is produced and then detected. The field line connection length can be determined from the time delay between the laser pulse and the burst of x rays. The topology of the field lines can be inferred by measuring the connection length as a function of initial target location inside the plasma. Measuring the spatial distribution of the x-ray production will provide further information on-the field topology, including the effects of magnetic-field fluctuations and stochasticity. The work will eventually include testing the appropriate x-ray detectors, measuring the background x-ray emission in a spheromak plasma, measuring the energetic electron production by a short-pulse high-power laser, and making preliminary measurements of the edge field line topology in the Sustained Spheromak Physics Experiment using a pulsed electron-beam source as a prototype for a laser-based source. This technique may have broad application to a variety of plasma configurations and provide physics data applicable to a wide range of plasma physics problems. (C) 2003 American Institute Of Physics.

Roh, Y., C. Domier, et al. (2003). “Ultrashort pulse reflectometry for density profile and fluctuation measurements on SSPX.” REVIEW OF SCIENTIFIC INSTRUMENTS 74(3): 1518-1521.
A broadband, multichannel ultrashort pulse reflectometry (USPR) diagnostic on the Sustained Spheromak Physics eXperiment device has recently undergone a number of system upgrades, which has resulted in significant improvements in the signal-to-noise ratio of the USPR signals and a dramatic reduction in the number of "lost signals" in which the amplitude of the reflected wave form drops below detection threshold. This has greatly enhanced the ability of USPR to study relatively fast density profile modifications, and allows the simultaneous monitoring of multiple density layers with as short as a 3 mus pulse repetition rate. This article provides details of the upgraded USPR system together with density profiles and fluctuation data. (C) 2003 American Institute of Physics.

Ryzhkov, S., V. Khvesyuk, et al. (2003). “Progress in an alternate confinement system called a FRC.” FUSION SCIENCE AND TECHNOLOGY 43(1T): 304-308.
The high fusion power density resulting from high beta (the ratio of the plasma to magnetic energy density) and natural divertor make the field-reversed configuration (FRC) a prime candidate for fusion reactor other than tokamak, the so-called alternate concept. Brief review of the simple compact system with natural advantages and reactor potential is given. Theoretical and experimental results over the last seven years are discussed.

Wang, Z. and G. Wurden (2003). “Hypervelocity dust beam injection for internal magnetic field mapping.” REVIEW OF SCIENTIFIC INSTRUMENTS 74(3): 1887-1891.
Injecting neutral atoms into high-temperature plasmas forms the basis for several important diagnostics, such as motional Stark effect and charge exchange recombination spectroscopy. We describe an alternative approach to seeding the plasma with neutrals, via "hypervelocity dust beam injection" (HDBI), using micron-sized dusts. Among its many potential applications, HDBI mapping of two-dimensional internal magnetic fields inside medium-sized (50-500 eV) plasmas is discussed in detail. Electrostatic acceleration at similar to100-200 kV will launch a stream of (0.2-10 Am-sized) dust grains of lithium or carbon to hypervelocities (1-10 km/s). Each dust grain, acting. as a "microcomet" in the plasma, forming a plume (tail), which if photographed, will reveal the direction of the local magnetic field, with anywhere from 10-100 microcomets in the plasma at any time, a full profile of the B-field direction could be obtained per high resolution image. Due to the small dust grain size, the perturbation to the plasma will be minimal. HDBI could be a simple low cost approach to obtain internal magnetic field information in plasmas with magnetic field structures that are significantly different than vacuum fields, such as in spherical tokamaks, FRC's, RFP's, and spheromaks. (C) 2003 American Institute of Physics.

Woodruff, S., D. Hill, et al. (2003). “New mode of operating a magnetized coaxial plasma gun for injecting magnetic helicity into a spheromak - art. no. 095001.” PHYSICAL REVIEW LETTERS 90(9): 095001-5001.
By operating a magnetized coaxial plasma gun continuously with just sufficient current to enable plasma ejection, large gun-voltage spikes (similar to1 kV) are produced, giving the highest sustained voltage similar to500 V and highest sustained helicity injection rate observed in the Sustained Spheromak Physics Experiment. The spheromak magnetic field increases monotonically with time, exhibiting the lowest fluctuation levels observed during formation of any spheromak ((B) over tilde /Bgreater than or equal to2%). The results suggest an important mechanism for field generation by helicity injection, namely, the merging of helicity-carrying filaments.