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9.2.3.2 Warm dense matter and plasma
9.2.3.2.1 Requirements
The Warm Dense Matter (WDM) experimental program studies dense matter rapidly
heated to temperatures exceeding 10 eV/atom. Initial studies will use the LCLS X-FEL
to heat thin samples, whose properties will then be measured by an array of diagnostics
placed around the sample. These diagnostics include an x-ray spectrometer, and a
Fourier Domain Interferometer (FDI) driven by a short-pulse optical laser. Interpretation
of these measurements requires knowledge of the x-ray photon flux incident on the
sample and the x-ray photon flux transmitted through the sample.
The experiment requires the use of the highest energy LCLS X-FEL photons, at 8.275
keV, in order to have enough penetrating power to uniformly heat the sample from front
to back. The required flux density at the sample is TBD photons/centimeter2. The heated
volume needs to have a radius of > 5 microns in order to create a large enough sample for
study.
Since the minimum required flux density is TBD x the peak flux density of the 8.275
keV beam in the near hall, the experiment requires x-ray focusing optics to achieve the
required flux densities. The use of focusing optics adds additional requirements for
alignment, which include the ability to image the spot at the position of the sample and
the capability of running at high repetition rates at reduced intensity during the alignment
process.
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250 mm
aperture
Incident Beam
Monitors
Back-scatter
x-ray
spectrometer100 mm
thick
sample
Imaging
detector
FDI
Laser
FEL
Beam
Focusing
Optic
Variable
beam
attenuator
FDI
Spectrometer
50-100 mm
aperture
Imaging
detector
(on sample
holder)
Outgoing
Beam
Monitor
Figure 9.2.3.2.1, A schematic of the warm dense matter experiment
Figure 9.2.3.2.1 shows a schematic of the WDM experiment including its auxiliary
hardware. The X FEL enters from the left and first passes through an aperture of slightly
larger diameter which blocks most of the non FEL light, then through an adjustable
attenuator, an incident beam intensity monitor and on to the focusing optic. The focusing
optic is a variant of a blazed Fresnel zone-plate operating like a thin lens in visible optics.
After passing though the lens, the light passes through another incident beam monitor,
which serves to measure the intensity of the light directed to the sample. A smaller
aperture, closer to the sample, removes stray light scattered by the optic. The samples are
arranged in a grid on a movable stage at the position of the focal spot. The sample stage
also holds an imaging detector that can be moved into position for alignment and
characterization of the focal spot. The diagram shows the back-scatter x-ray
spectrometer that measures the x-ray spectra emitted by the sample and the path of the
optical FDI laser beam used to characterize the expansion of the sample. X rays passing
through the sample are measured by the downstream beam monitor and imaging detector.
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9.2.3.2.2 Optical Design and Components
9.2.3.2.2.1 Focusing System
9.2.3.2.2.1.1 Optical design
The WDM experiment will be situated in the 4th shielded room in the near hall.
Table 1 shows the distances that are relevant for the optical design. The shielded rooms
are 13 meters long, but the PPS beam-stop limits the length available to experimenters to
10.6 meters. The sample is located approximately in the center of the room, 6.2 meters
from the upstream wall. It turns out that the flux requirements can be met with lenses
whose focal lengths are longer than the distance from the sample to the upstream wall,
but in the interests of minimizing interference between experiments, we have chosen a
position for the lens that is as far as possible from the sample, but still within the confines
of the WDM shielded room.
Table 9.2.3.2.1. Distances and specifications associated with the warm dense matter
optical components
Distances
From
To
units
Upstream wall
Upstream wall
Downstream wall
PPS Beam Stop
13.00
10.61
m
m
Upstream wall
Upstream wall
Lens
Sample
1.20
6.20
m
m
End of undulator
Source at 8.275 Kev
Upstream wall
End of undulator
72.11
19.50
m
m
Source at 8.275 Kev
Lens
Lens
Sample
92.80
5.00
m
m
4.74
131.12
5.72
m
microns FWHM
microns FWHM
2.74
6.34
microns FWHM
microns FWHM
Optic Specification
Lens Focal length
Beam size at lens position
Diffraction limited spot
Thin lens image size
Approximate focused spot size
The lens, placed 1.2 meters from the upstream wall, forms an image of the X-FEL
source at the sample. The source-to-lens and lens-to-image distances determine its focal
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length. The X-FEL source point is at the position of the waist in the Gaussian model
which is located one Rayleigh length upstream of the exit of the undulator. As the table
shows, the resulting source-to-lens distance is 92.8 meters, and the lens-to-image distance
is 5 meters, requiring a lens focal length of 4.74 meters and giving a magnification of
0.05.
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Figure 9.2.3.2.2. Details of the lens design
Figure 9.2.3.2.2 shows details of the lens design. The lens is carved into the face of a
C disk and mounted over a hole drilled through a 25.4 mm diameter Cu mount. The C
disk is 650 microns thick except in the center where it thins down to 400 microns. The
active portion of the lens is 200 microns in diameter and consists of 6 concentric grooves
machined to a maximum depth of 18.8 microns. The plot of the beam profile at the lens,
figure 2g, shows that the 200 micron lens diameter nicely captures most of the beam.
The shape of the grooves was determined by calculating, at the position of the lens,
the phase change necessary to convert the diverging Gaussian X-FEL beam from the
undulator to a converging Gaussian waveform whose waist is at the sample position. The
radial phase profile was converted to a depth profile by multiplying by the optical
constant for C which, at 8.275 KeV, is 18.8 microns / 2 radians phase change ( with
respect to vacuum.)
The stage used to position the lens will have positioning precision of < 5 microns and
angular precision of < 1 mRad.
9.2.3.2.2.1.2 lens fabrication
Diamond tool
Diamond tool
carves lens pattern
here
Reference
flat
Al rod
Al rod
viewed in
cross section
Figure 9.2.3.2.3. Lens manufacturing technique
The C lens will be machined from a C rod by single-point diamond turning as
illustrated in figure 9.2.3.2.3. The tool first machines the end of the rod flat to provide a
reference surface. Then a disk of material is removed from the center providing a
recessed area for the protection of the lens. Then the lens profile is machined into the
base of the recess.
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Glue
diamond turned
rod end
to glass
Glass slide
with surface
polished to
level of B 4 C
Mounting Block
Shim
B 4C
Polish back of lens
to level of B 4 C
Figure 9.2.3.2.4. Mounting the lens
After diamond turning, the end of the rod is carefully sliced off and its reference flat
is glued onto the polished glass surface of a specially prepared thinning fixture illustrated
in figure 4. The thinning fixture consists of a glass slide mounted on a mounting block
on top of a Cu shim whose thickness is equal to the desired final thickness between the
bottom of the lens, and the reference flat. Alongside of the blocks are a set of B4C (boron
carbide) sticks whose surfaces have been previously polished flat and parallel. Because
the B4C is much harder than the glass it is easy to polish the surface of the glass so that it
is level with the B4C. The reference surface of the lens is then glued to the glass surface
with a very thin glue. The shim is removed, lowering the mounted lens so that the
desired back surface of the lens is in the plane of the B4C sticks. The lens is then
polished to this level and removed for mounting over the hole in the Cu mount.
9.2.3.2.2.1.3 Lens Survivability.
C was chosen as the material for the lens based on its capability to withstand the
energy density of the full X FEL beam. Table 2 is a list of the lowest Z materials
amenable to single-point diamond-turning. The table gives the optical constants, the
calculated dose from the peak of the full beam at the lens position, and the dose needed to
bring the material up to its melting temperature. Cu and Al are ruled out because the
doses to these materials are enough to bring them to their melting temperature. C has
both a low dose and high melting point, and therefore will survive the full beam intensity.
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The dose to polystyrene is also very low, but it's large phase shift length results in too
large an aspect ratio for single-point diamond-turning.
Table 9.2.3.2.2. Doses to low-Z materials amenable to diamond turning
l = 0.15 nm
1 pi
phase shift atten
dose
dose
dose
length
length at lens to mp* through mp
micron
micron eV/atom eV/atom eV/atom
Cu
3.27
24.1
0.23
0.21
0.35
Al
9.34
85.7
0.09
0.09
0.2
C
9.41
997
0.004
0.86
0.86
9.2.3.2.2.2 Apertures
Survivability is also an issue in the design of the two apertures. The basic concept is
to utilize a laminate consisting of 4 mm of B4C, 150 microns of Al, and 200 microns of
Ta. As shown in table 9.2.3.2.2, this laminate has sufficient absorption to block x-rays up
to the 3rd harmonic. Furthermore the B4C attenuates the direct X-FEL beam enough to
prevent damage to the Al which further attenuates the beam enough to prevent damage to
the Ta.
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Optional
hi-pass
Be
filter
4 mm
B4C
150 mm
Al
200 mm
Ta
1 mm
500 mm
250 mm
100 mm
Fixed
1 mm
apetrure
Selectable
Aper tures
onm oving
stage
Figure 9.2.3.2.5. Apertures for the warm dense matter experiment
A series of holes having diameters from 1 mm down to 100 microns will be drilled
through the laminate which will then be mounted on a movable stage that provides both
rotation and translation of the laminate. A second, fixed, laminate having a single 1 mm
diameter hole keeps light from passing through all but a single hole in the movable
laminate as shown in figure 9.2.3.2.5. The ability to rotate the laminate is necessary
because of the large aspect ratio of the holes. Using a downstream intensity monitor, and
starting with the largest diameter hole, the movable laminate will be rotated into a
position that maximizes the signal. The laminate will be shifted to the next smaller
diameter hole and rotated again to achieve highest intensity downstream. This process
will be repeated with successively smaller holes until the hole of the desired diameter is
positioned and aligned.
The stages used to position the apertures will have positioning precision < 10 microns
and angular precision of < 1 mRad.
We note that, because the first harmonic of the spontaneous emitted undulator
spectrum has the same divergence as the coherent line, and both lines overlap in space,
only even harmonics and the off axis intensity of odd harmonics will be stopped in
apertures. Edges interfering with the coherent beam will cause diffraction patterns, so
that apertures may be restricted to >2 times the local coherent beam size..
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9.2.3.2.2.3 Attenuator
The WDM experiment requires a local attenuator for calibration and to prevent
damage to sensitive components during alignment. Preventing damage at the focused
spot requires the highest attenuation. Table 9.2.3.2.3 shows an estimate of the dose to a
selection of materials at the focal spot in comparison to their tolerable doses (10% of
melting temperature.) To reduce the dose to Cu to a tolerable level requires an
attenuation of at least 10-4.
Table 9.2.3.2.3. Estimated dose to given materials at the focal spot
Material
Cu
Si
Al
C
B4C
polystyrine
Be
dose at
focused
spot
eV/atom
Tolerable
dose
eV/atom
Needed
attenuation
Needed
Thickness
B4C
mm
207.68
115.91
82.11
2.90
1.93
1.93
0.97
0.021
0.026
0.009
0.086
0.068
0.010
0.023
1.0E-04
2.2E-04
1.1E-04
3.0E-02
3.5E-02
5.2E-03
2.4E-02
16.3
14.9
16.1
6.2
5.9
9.3
6.6
The table also shows the thickness of B4C required to provide the needed attenuation.
Macroscopic thicknesses of B4C make good attenuators for 8.275 KeV radiation and, as
discussed in the section on apertures, can withstand the full (unfocused) beam intensity.
Table 9.2.3.2.4. Thickness of Boron carbide required for attenuation
desired
attenuation
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
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B4C
thickness
mm
4.1
2.8
2.1
1.6
1.2
0.9
0.6
0.4
0.2
0.0
desired
attenuation
1.E-01
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
B4C
thickness
mm
4.1
8.1
12.2
16.3
20.4
24.4
28.5
32.6
36.7
40.7
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Relative calibration of the downstream intensity monitors is best done with a
combination of variable attenuators that provide both linear and logarithmic variations in
intensity. Table 4 shows the sets of B4C thicknesses needed to vary the attenuation
linearly from 0.1 to 1 and logarithmically from 10-1 to 10-10.
Log attenuator
4 mm
Beam
B4C
1 cm
32.6 mm
4 mm
Linear attenuator
Figure 9.2.3.2.6. A linear attenuator
The attenuators will be fashioned from single plates of B4C milled in a staircase
pattern to the thicknesses specified in the table as shown in figure 9.2.3.2.6. The linear
and logarithmic attenuators will be mounted on separate translation stages allowing all
combinations of linear and logarithmic attenuation to be applied.
The attenuator translation stages will provide motion in the X and Y directions with a
precision of < 1 mm.
9.2.3.2.2.4 Beam intensity monitors
The beam intensity monitors are required to measure the absolute flux incident on the
samples and the amount of flux transmitted through the samples. These monitors will be
of the simple ion chamber type as described in the common diagnostics section (9.2...).
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9.2.3.2.3 Beam Diagnostics
9.2.3.2.3.1 Beam intensity monitors
The beam intensity monitors are required to measure the absolute flux incident on the
samples and the amount of flux transmitted through the samples. These monitors will be
of the simple ion chamber type as described in the common diagnostics section.
9.2.3.2.3.2 Imaging detectors
The WDM experiment requires imaging detectors to assist in the alignment and to
determine the size of the heated volume. Beam transport simulations indicate that a
spatial resolution of <5 microns is necessary for these purposes. Furthermore it is
desirable to obtain the entire image in a single shot. It would also be desirable if the
detector could take the full beam intensity but since the alignment could be done in an
attenuated beam this is not necessary.
9.2.3.2.4 Layout and other equipment
The equipment necessary to initiate the experiments is found in the requirements
document, , specifically as a layout and hardware list.
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