Introduction
In the design of Sector 2 of the Synchrotron Radiation Instrumentation (SRI) CAT, an x-ray mirror with multiple coatings is chosen as the first optical component of the undulator beamline. Two significant advantages of using the mirror are: (1) a significant reduction in the peak radiation heat flux and total power on the downstream monochromator, and (2) availability of the wide-bandpass undulator spectrum between 0-30 keV to experimental stations with substantially reduced radiation shielding requirements. The second advantage also allows us to place the monochromator outside the first optics enclosure (FOE) at a large distance from the source to further reduce the peak heat flux on the monochromator. The combined effect is that the inclined crystal monochromator [1] may not be necessary, a multilayer monochromator can be used because the expected heat fluxes are less than the value that has been demonstrated for those monochromators [2, 3].
In this technical note, unless otherwise stated, the energy of the stored
positron beam is 7 GeV and the current is 100 mA.
Thermal Considerations
The mirror described here is vertically deflecting to minimize the mirror
size and is located 30.5 meters from the source. The grazing incidence angle
is 0.15°. The mirror length is 90 cm, and the mirror intercepts 77 mrad
of incident beam in the vertical direction. This incidence angle of 15°
is selected to obtain high reflectivities for x-ray energies up to 30 keV
(see Fig.
1) and to produce an offset of about 25 mm for the reflected beam at the
exit wall of the FOE. This is necessary to limit bremsstrahlung shielding
beyond the FOE. The peak heat flux incident on the mirror surface is 0.35
W/mm2. At this power density, thermally induced slope errors less
than 1 arcsec may be obtainable, because a slope error of about 2 arcsec
was obtained for a power density of about 2 W/mm2, but at a lower
total power than our mirror will experience [4].
The mirror has three coating materials (Al, Rh, and Pt) that are deposited
in three parallel strips on the same substrate. Figure
1 shows the calculated x-ray reflectivity as a function of x-ray energy
for a 0.15°grazing incidence angle. The three coating materials are necessary
to reduce the peak heat flux on the monochromator to less than 4 W/mm2
for the 4.2-30 keV energy range of the undulator A spectrum. For a heat flux
of 4 W/mm2, a conventional double-crystal monochromator (using
gallium cooling) that has been developed at the APS can be used [2].
The peak power density of the raw undulator A spectrum as a function of
the undulator gap size is shown in Fig.
2. Also shown in the figure are the power densities of the undulator
spectrum integrated over the three energy bands that are indicated in the
figure. It is clear from the figure that a substantial reduction in the peak
power density can be obtained by filtering out the high energy part of the
raw undulator spectrum. Because the x-ray reflectivity of a mirror is
small for x-rays of energy greater than the cutoff energy at a given incidence
angle, the power densities calculated for the three energy-integration bands
in Fig.
2 can be approximated as the power densities of the Undulator A spectrum
reflected by three mirrors with their cutoff energies being equal to 10,
20, and 30 keV, respectively. The cutoff energy is defined here as the energy
at which x-ray reflectivity drops to about 0.5. Note that a reduction in
power density of about a factor of 10 is obtained at the closed gap of 11.5
mm when a mirror with a cutoff energy of 10 keV is used.
In addition to the power density reduction, the total power of undulator
A reflected by a mirror is also reduced. Figure
3 shows the total power of the raw undulator A spectrum as a function
of the undulator gap size. Also shown in the figure are the total powers
of the spectrum integrated over the four energy-integration bands that are
indicated. The reduction of the total power reflected by a mirror reduces
the total power load on the monochromator and other downstream optical components,
and, thus, the design of these components can be more flexible.
The double crystal monochromator will be located at 56 meters from the
center of undulator A. The normal incidence heat fluxes at the monochromator
for the raw undulator A spectrum and for the three energy-integration bands
are also plotted in Fig.
2. In practice, the beam is incident on the monochromator at an angle
less than 90 degrees because the monochromator is tuned to diffract either
the first or the third harmonic of the undulator radiation. Figures 4
and 5
show the heat flux on a Si(111) monochromator surface when it is tuned to
diffract the first and the third harmonic radiation of the undulator A spectrum,
respectively. For the 4.2 - 14 keV energy tuning range of the undulator A
first harmonic radiation, the heat flux on the monochromator is less than
4 W/mm2 if an Al mirror is used for the 4.2 - 10 keV energy range
and either a Rh or Pt mirror is used for the 10 - 14 keV energy range (Fig.
4). For the tuning range of the third harmonic radiation, 12.6 - 42 keV,
the peak heat fluxes on the monochromator for all three energy-integration
bands are less than 4 W/mm2 (Fig.
5). Because the cutoff energy of the Al mirror is about 12 keV at the
0.15 degree grazing incidence angle, only the Rh or Pt mirror will be used
for harmonic radiation of energy larger than 12 keV. Note from Fig.
2, however, that since the normal incidence heat flux at the monochromator
can be as high as 18 W/mm2 from a Rh or Pt mirror, it may be necessary
to interlock both the mirror being selected and the monochromator angular
position in order to protect the monochromator from possible damage by excessively
high heat flux.
The thermal heat flux on a multilayer monochromator can also be estimated
based on the results obtained above. Currently the smallest d-spacing obtainable
in a multilayer is about 20 Å, which is about 7 times that for Si(111).
Therefore, the heat flux on the surface of a multilayer is at least 7 times
smaller than that on a Si(111) crystal. Since the maximum heat flux on the
surface of a Si(111) crystal can be kept to less than 4 W/mm2when
the mirror is properly selected, the maximum heat flux on a multilayer monochromator
should be kept to less than about 0.6 W/mm2. The reduction of
the power density results primarily from the smaller incidence angle for a
multilayer monochromator compared to that for a Si crystal monochromator.
This level of heat flux should not pose any real problem to most multilayers
that are planned for use on our beamline because several types of multilayers
have been shown to be able to resist heat fluxes as high as 7.5 W/mm2
[3]. In addition, smaller
heat fluxes are obtained for a multilayer monochromator with d-spacing larger
than 20Å because a smaller grazing incidence angle has to be used.
In Table 1, we list some key parameters relevant to the thermal loading
of the mirror and the monochromator. An undulator A source is assumed. The
maximum total power on the Si monochromator was obtained at the closed undulator
gap and when a mirror with a 20 keV cutoff energy is used. The 20 keV cutoff
energy was selected in order to use the 12.6 keV third-order harmonic radiation
at the closed gap.
Table 1. Key parameters relevant to the thermal loading of the mirror and the monochromator.
Radiation Shielding Considerations
The reduction of radiation shielding makes use of the low reflectivities
of x-rays of energies greater than the cutoff energy of a mirror (see Fig.
1). Figure
6 shows both the raw undulator A spectrum at the closed gap of 11.5 mm
and the spectrum being reflected from a Pt mirror at 0.15° of grazing
incidence angle. Also shown in the figure is the spectrum of the reflected
beam after passing through a shielding slab consisting of 0.25 inch of lead
and 0.125 inch of steel. The shielding structure specified here is similar
to that of a vacuum tube that has been fabricated and tested at the APS for
shielding monochromatic beam.
To assess the radiation shielding requirements, two simple cases were
considered for calculation of the radiation dose absorbed by human tissue.
In the first case, the human tissue is assumed to be positioned behind the
shielding slab that is in the direct path of undulator A radiation after
being reflected by the Pt mirror. In the second case, the shielding slab
and the human tissue behind it were assumed to be exposed to isotropically
scattered radiation of the undulator A spectrum after being reflected by the
Pt mirror. A point scatterer with 100% scattering efficiency located at the
center of a 4 inch vacuum pipe was assumed. The distance between the human
tissue and the scatter is assumed to be 2 inches. The calculated dose rates
for those two cases are about 2.8 mrem/s and 0.6 mrem/hr, respectively. While
the calculated result in the first case indicates the back wall of a hutch
needs to have a lead layer thicker than 0.25 inch, the calculated result in
the second case seems to indicate that a 0.25 inch lead shield in the side
wall of a vacuum transport component may be enough to reduce the radiation
dose to a safe level in our design. A detailed analysis regarding the radiation
shielding requirements is, however, necessary because many other senarios
for potential radiation harzards need to be considered. Nevertheless, a reduction
in radiation shielding requirements is obtained by the use of a mirror, and
this allows us to place the monochromator outside the FOE using standard
APS vacuum transport components.
Summary and Remarks
An x-ray mirror can be used as the first optical component in an undulator
beamline to reduce both the thermal loading on the monochromator in a way
such that a conventional double-crystal or multilayer monochromator can be
used. A significantly reduction in the radiation shielding requirements is
also obtained in a way that access to the wide-bandpass undulator radiation
up to 30 keV may be possible using the standard beamline vacuum transport
components that are designed at the APS.
In the preceding analysis, we have only considered the reduction of peak
power density and the radiation shielding requirements for the case in which
one of the three mirrors with different energy cutoffs is at a fixed incidence
angle to the incident beam. Other possibilities, such as using two parallel
mirrors at a fixed incidence angle or decreasing the incidence angle with
the undulator gap size can also be considered. Significant reduction in the
peak power density and the total power of the reflected beam and particularly
in the radiation shielding requirements should be obtainable by the use of
a two mirror system compared to the single mirror case considered here.
An example of the heat flux reduction using a pair of parallel mirrors
tuned to have a cutoff energy to be 1.2 times the first harmonic radiation
is illustrated in Fig.
7. This figure shows the peak heat fluxes at 56 meters from the source
as a function of undulator gap for the spectrum reflected by the mirror pair
as well as the gap-dependent heat fluxes for the entire undulator A spectrum
at normal incidence and at the surface of a Si(111) crystal tuned to diffract
the first harmonic radiation. A significant reduction in the peak heat fluxes
on a downstream monochromator is obtained if the mirror pair is used. In
Fig.
7, the peak heat fluxes on the surface of a Si(111) crystal are also
shown when both the mirror pair and the Si(111) crystal are tuned. Note that
heat fluxes less than about 1.7 W/mm2on the crystal surface are
obtained over the entire gap range.
In conclusion, we believe that an optimized thermal management scheme
using a proper combination of mirrors and crystal geometry can be developed
to handle most of the thermal loading problems with undulator radiation at
the APS. A combination of a mirror and an inclined monochromator [1, 2] may
be able to handle even higher thermal loading problems that may arise with
an increase of the energy and the current of the stored positron beam beyond
the values calculated in this technical note and with increased undulator
length. Expansion of the x-ray energy coverage beyoud 30 keV may be obtained
by having a strip of the mirror coated with a multilayer. At 0.15 degree
of grazing incidence angle, x-rays of energy up to 100 keV can be reflected
by a multilayer with a d-spacing of 20Å or longer.
Acknowledgments:
We would like to thank D. Shu, K. Randall, I. McNulty, and D. Legnini
for useful discussions.
1. A. Khounsary, Rev. Sci. Instrum. 63, 461 (1992).
4. S. Mourikis, W. Jark, E. E. Koch,
and V. Sail, Rev. Sci., Instrum.60, 1474 (1989).
Fig. 1. X-ray reflectivity as a function of x-ray energy for Al, Rh, and
Pt mirrors at 0.15 degree of incidence angle. Note the cutoff energy for
the Pt mirror is about 32 keV.
Fig. 2. Calculated peak power densities and peak normal incidence heat
fluxes at 56 meters from the source for the entire undulator A spectrum and
for the three energy bands indicated in the figure.
Fig. 3 Calculated total power of the entire undulator A spectrum and the
total powers integrated over the four energy bands that are indicated in
the figure.
Fig. 5. Calculated heat fluxes on the surface of a Si(111) crystal that
is located at 56 meters from the source and tuned to diffract the third harmonic
of the undulator A radiation. Calculations are for the entire undulator A
spectrum and for the three energy bands that are indicated in the figure.
Fig. 6. Calculated spectrum of (a) the raw undulator A spectrum at the
closed gap of 11.5 mm, (b) the same spectrum after being reflected by a Pt
mirror at 0.15 degree of grazing incidence angle, and (c) the transmitted
spectrum of (b) through a shielding slab consisting of 0.25 inch lead and
0.125 inch of steel.
Fig. 7. Calculated normal-incidence heat fluxes at 56 meters from the source as a function of undulator gap for the spectrum reflected by the mirror pair, as well as the gap-dependent heat fluxes for the entire undulator A spectrum at normal incidence and at the surface of a Si(111) crystal tuned to diffract the first harmonic radiation. Also shown in the figure are the peak heat fluxes on the surface of a Si(111) when both the mirror pair and the Si(111) crystal are tuned.