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fusion energy

Electromagnetic Gyrokinetic Simulations

S. E. Parker, Y. Chen, W. Wan, B. I. Cohen, and W. M. Nevins, “Electromagnetic gyrokinetic simulations,” Phys. Plasmas 11, 2594 (2004). FES, SciDAC

A new electromagnetic kinetic electron δf particle simulation model has been demonstrated to work well at large values of plasma ß times the ion-to-electron mass ratio. The model shows accurate shear Alfvén wave damping and microtearing physics. Zonal flows with kinetic electrons were found to be turbulent, with the spectrum peaking at zero and having a width in the frequency range of the driving turbulence. In contrast, with adiabatic electron cases the zonal flows were near stationary, even though the linear behavior of the zonal flow was not significantly affected by kinetic electrons. Zonal fields were found to be very weak, consistent with theoretical predictions for ß below the kinetic ballooning limit.

Figure 8. TORIC simulation of a D(³He) mode conversion case in the Alcator C-Mod. Note the well resolved presence of the midplane ion Bernstein wave propagating to the left, the ion cyclotron wave above and below the midplane going to the right, and the large fast wave propagating from the right to the layer, with a small amount transmitting through.

Fast Wave Mode Conversion

J. C. Wright, P. T. Bonoli, M. Brambilla, F. Meo, E. D’Azevedo, D. B. Batchelor, E. F. Jaeger, L. A. Berry, C. K. Phillips, and A. Pletzer, “Full wave simulations of fast wave mode conversion and lower hybrid wave propagation in tokamaks,” Phys. Plasmas 11, 2473 (2004). FES, ASCR-MICS, SciDAC

Two full wave codes — a parallel version of the TORIC-2D finite Larmor radius code and an all-orders spectral code, AORSA2D — have been developed which for the first time are capable of achieving the resolution and speed necessary to address mode conversion phenomena in full 2D toroidal geometry. These codes have been used in conjunction with theory and experimental data from the Alcator C-Mod to gain new understanding into the nature of fast wave mode conversion in tokamaks (Figure 8). Advanced scenarios in burning plasma devices such as the International Thermonuclear Experimental Reactor (ITER) can now be modeled with the new resolution capabilities.

Whistler Wave Turbulence

S. Galtier and A. Bhattacharjee, “Anisotropic weak whistler wave turbulence in electron magnetohydrodynamics,” Phys. Plasmas 10, 3065 (2003). FES, SciDAC, NSF, INSU, ECRTN

Whistler waves have been observed in many spacecraft traversals of the Earth’s magnetotail and the solar wind. Galtier and Bhattacharjee have developed a weak turbulence theory for electron magnetohydrodynamics in which the turbulence is mediated by the nonlinear interaction of whistler waves and is dominated by three-wave interactions. They demonstrated that the nonlinear interactions of whistler waves transfer energy and magnetic helicity mainly in the direction perpendicular to the external magnetic field. The anisotropic turbulence thus generated has exact stationary power-law solutions for energy and magnetic helicity.

Figure 9. Simulation of a wavepacket scattering from a helium atom.

Electron-Impact Ionization of Helium

M. S. Pindzola, F. Robicheaux, J. P. Colgan, M. C. Witthoeft, and J. A. Ludlow, “Electron-impact single and double ionization of helium,” Phys. Rev. A 70, 032705 (2004). FES, SciDAC

Pindzola et al. have developed a nonperturbative lattice solution of the time-dependent Schrödinger equation that appears capable of yielding accurate cross sections for Coulomb four-body breakup. They applied this method to obtain single and double ionization cross sections for helium that are in excellent agreement with experimental measurements. The total wave function for the three-electron system was expanded in nine dimensions: three dimensions were represented on a radial lattice, and a coupled channels expansion was used to represent the other six dimensions, resulting in a simulation that captured all of the scattering processes (Figure 9).

Turbulence Spreading and Transport Scaling

Z. Lin and T. S. Hahm, “Turbulence spreading and transport scaling in global gyrokinetic particle simulations,” Phys. Plasmas 11, 1099 (2004). FES, SciDAC

An intriguing observation in tokamak experiments and in simulations of ion temperature gradient turbulence is that the fluctuations are microscopic, while the resulting turbulent transport is not gyro-Bohm. Lin and Hahm have identified a possible solution to this puzzle: turbulence spreading from the linearly active (unstable) region to the linearly inactive (stable) region. Large-scale gyrokinetic simulations found that transport driven by microscopic fluctuations is diffusive and local, whereas the fluctuation intensity is determined by nonlocal effects. Turbulence spreading reduces the fluctuation intensity in the unstable region, especially for a smaller device size, and thus introduces a nonlocal dependence in the fluctuation intensity. The device size dependence of the fluctuation intensity, in turn, is responsible for the observed gradual transition from Bohm to gyro-Bohm transport scaling.

Figure 10. Poloidal flux at times t = 0 (a) and t = 5 (b) and plasma current at times t = 0 (c) and t = 5 (d) for the tilt mode problem with N = 40. Singular currents can be seen developing in (d).

A Triangular Finite Element for MHD

S. C. Jardin, “A triangular finite element with first-derivative continuity applied to fusion MHD applications,” J. Comp. Phys. 200, 133 (2004). FES, SciDAC

A 2D triangular finite element known as the reduced quintic has been used in structural engineering studies since the late 1960s, but has apparently been overlooked by the extended magnetohydrodynamics (MHD) community. Jardin has shown that the reduced quintic is well suited for many problems arising in fusion MHD applications, including a 2D elliptic problem, the solution of the anisotropic heat conduction problem, a time-dependent reduced-MHD problem (Figure 10), and the 2D axisymmetric toroidal equilibrium problem. The element requires only three unknowns per triangle, which is considerably less than other high-order elements of comparable accuracy.

Trapped Electron Mode Turbulence

D. R. Ernst, P. T. Bonoli, P. J. Catto, W. Dorland, C. L. Fiore, R. S. Granetz, M. Greenwald, A. E. Hubbard, M. Porkolab, M. H. Redi, J. E. Rice, K. Zhurovich, and the Alcator C-Mod Group, “Role of trapped electron mode turbulence in internal transport barrier control in the Alcator C-Mod Tokamak,” Phys. Plasmas 11, 2637 (2004). FES

To understand basic particle transport processes underlying spontaneous formation and subsequent control of the internal particle and energy transport barriers in the Alcator C-Mod Tokamak, Ernst et al. simulated trapped electron mode (TEM) turbulence using the nonlinear gyrokinetic turbulence code GS2. They found that toroidal ion temperature gradient driven modes are suppressed inside the barrier foot, but continue to dominate in the outer half-radius. As the density gradient steepens further, TEMs are driven unstable. The onset of TEM turbulence produces an outflow that strongly increases with the density gradient, upon exceeding a new nonlinear critical density gradient, which significantly exceeds the linear critical density gradient. The TEM turbulent outflow ultimately balances the inward Ware pinch, leading to steady state.

Using Finite Elements in NIMROD

C. R. Sovinec, A. H. Glasser, T. A. Gianakon, D. C. Barnes, R. A. Nebel, S. E. Kruger, D. D. Schnack, S. J. Plimpton, A. Tarditi, and M. S. Chu (the NIMROD Team), “Nonlinear magnetohydrodynamics simulation using high-order finite elements,” J. Comp. Phys. 195, 355 (2004). FES, SciDAC

The NIMROD Team has applied a conforming representation composed of 2D finite elements and finite Fourier series to 3D nonlinear non-ideal MHD using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Benchmark cases and a nonlinear simulation demonstrated the effectiveness of the algorithm, which is suitable for many applications in magnetic confinement fusion.

Smoothness of Turbulent Transport

J. Candy, R. E. Waltz, and M. N. Rosenbluth, “Smoothness of turbulent transport across a minimum-q surface,” Phys. Plasmas 11, 1879 (2004). FES, SciDAC

Some controversy exists over the role of weak or reversed shear in the formation of internal transport barriers. One theory attributes the formation of internal transport barriers to a gap in global wave structures in the minimum-q region. In simulations made with the GYRO gyrokinetic code, Candy et al. showed that in general no such gap exists. All of their findings — linear and nonlinear, local and global — supported the conclusion that transport generally decreases steadily as shear is decreased from positive to negative values.

Understanding Plasma Pedestals

C. S. Chang, S. Ku, and H. Weitzner, “Numerical study of neoclassical plasma pedestal in a tokamak geometry,” Phys. Plasmas 11, 2649 (2004). FES, KBSI

The increase in plasma energy content associated with the formation of a pedestal in the plasma edge is becoming a crucial performance measure for future tokamak reactors such as ITER. Consequently, the pedestal’s formation mechanism and behavior are high research priorities. Chang et al. used the parallel numerical guiding center code XGC to investigate the fundamental neoclassical properties of a steep plasma pedestal and found that its properties are closely tied to neoclassical orbital dynamics. The orbit effect across a steep pedestal generates a self-consistent radial electric field and dramatically reduces the pedestal width to a level comparable with experimental observations.