REVIEW OF SCIENTIFIC INSTRUMENTS 85, 11D612 (2014)
Characterization of spatially resolved high resolution x-ray spectrometers for high energy density physics and light source experimentsa) K. W. Hill,1,b) M. Bitter,1 L. Delgado-Aparacio,1 P. Efthimion,1 N. A. Pablant,1 J. Lu,2 P. Beiersdorfer,3 H. Chen,3 and E. Magee3 1
Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA Key Laboratory of Optoelectronic Technology and System of Ministry of Education, Chongqing University, Chongqing 400030, China 3 Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA 2
(Presented 2 June 2014; received 31 May 2014; accepted 2 July 2014; published online 30 July 2014) A high resolution 1D imaging x-ray spectrometer concept comprising a spherically bent crystal and a 2D pixelated detector is being optimized for diagnostics of small sources such as high energy density physics (HEDP) and synchrotron radiation or x-ray free electron laser experiments. This instrument is used on tokamak experiments for Doppler measurements of ion temperature and plasma flow velocity profiles. Laboratory measurements demonstrate a resolving power, E/E of order 10 000 and spatial resolution better than 10 μm. Initial tests of the high resolution instrument on HEDP plasmas are being performed. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4890260] I. INTRODUCTION
An instrument concept that has been a very successful diagnostic on tokamaks, spherical tori, and stellarators world wide1–7 is being adapted and optimized for small sources such as high energy density physics (HEDP), synchrotron radiation (SR), and x-ray free electron laser (XFEL) experiments.8, 9 It is a spatially resolved, high resolution x-ray imaging crystal spectrometer (XICS) which is used routinely for iontemperature (Ti ) and plasma flow velocity (v) measurements via Doppler broadening and shift, respectively, of impurity x-ray lines. It consists of a spherically bent crystal and a twodimensional (2D) photon counting pixel array x-ray detector. Although the instrument is very similar to the focusing spectrograph with spatial resolution (FSSR) spectrometer,10 which has been previously used on small source experiments, this instrument was developed independently at PPPL, using large radius (R = 1.5–5 m), precision bent spherical crystals designed for the high resolving power (E/E ∼ 10000)11 necessary for tokamak Doppler spectroscopy. Since much of the previous studies of x-ray spectroscopy on HEDP plasmas has involved, until recently, lower resolution instruments,12, 13 the present developments are hoped to ultimately lead to an XICS capable of Doppler measurement of ion temperature for HEDP experiments. The XICS concept is illustrated in Fig. 1. The spherically bent crystal at C diffracts and focuses x rays from the plasma to different points on the two-dimensional, pixelated detector. A focal point P on the detector maps not to a single point on the source side, but to a vertical focal line at Bm (meridional focus) and a horizontal line at Bs (sagittal focal line). This effect occurs because a spherical reflector has astigmaa) Contributed paper, published as part of the Proceedings of the 20th
Topical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014. b) Author to whom correspondence should be addressed. Electronic mail: [email protected] 0034-6748/2014/85(11)/11D612/3/$30.00
tism, i.e., the focal length for imaging in the horizontal plane is different than that for vertical imaging.14 It is this correspondence between the sagittal focal line near the plasma and a point on the detector that provides the excellent 1D spatial resolution. A narrow wavelength band of plasma x rays centered at λ = 2d sinθ diffracts to point P on the detector, and by rotational symmetry of the ray pattern from the spherical crystal about the line CO, as the sagittal focal line moves up and down to sample different spatial locations in the plasma, the point P moves down and up, respectively, on a cone to form the curved spectral lines shown in the image in the lower right of Fig. 1. Here, d is the lattice spacing of the crystal planes, and θ is the Bragg angle, illustrated at the crystal in Fig. 1. For good spatial resolution of a small HEDP plasma source, the source should be on the sagittal focal line. II. LABORATORY DEMONSTRATIONS
A high spectral resolution spectrum of the W Lα 1,2 lines at energies 8.3976 and 8.3352 keV, respectively, emitted by the tungsten target micro-focus x-ray tube15 is illustrated in Fig. 2. This spectrum was measured in a Johann geometry by a Si 533 crystal bent to a spherical radius of 82.3 cm with the detector approximately on the Rowland circle. The x-ray source was placed approximately on the sagittal focal line. A comparison of the widths of the two lines with measurements by Vaiclu et al.16 and Salem and Lee17 are shown in Table I. Also shown are the widths of the Mn Kα 1,2 lines at 5.887 and 5.898 keV from an 55 Fe source measured in second order using a quartz 110 crystal with a spherical radius of 75.6 cm. In both cases, the detector was a Pilatus 100 k hybrid pixel array detector18 with 196 × 487 photon counting pixels of size 172 × 172 μm2 . The line widths in Fig. 2 are determined from Lorentzian fits, which are plotted as the red and blue curves. All except one of the measured line widths in Table I differ from the reference measurements16, 17 by ≤ 0.04 eV,
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Rev. Sci. Instrum. 85, 11D612 (2014) TABLE I. Comparison of line widths of the Mn Kα and W Lα spectra with natural line widths measured by others. X-ray line This work width (eV) Reference width (eV) Reference W Lα 1 W Lα 2 Mn Kα 1 Mn Kα 2 a
FIG. 1. Schematic illustration of the principle of the XICS, described in the text.
indicating instrumental resolutions of order 0.5 eV or resolving powers greater than 10 000. In the case of the outlier, the W Lα 1 width, the stated error in the reference measurement is large. The uncertainty values for the present measurements are solely statistical uncertainties in the Lorentzian fitting. It is desirable to find independent methods of confirming the instrumental resolution of the spectrometer that do not rely on measuring the width of lines that are much broader than the instrumental resolution.11 One technique being considered is to measure the width of a very narrow line, such as a forbidden line from an electron beam ion trap, or a highly monochromatic x-ray beam from a synchrotron, Thomson scattered from a solid target. The spectral bandwidth of an XICS can be increased by working at smaller Bragg angles, θ , than the typical values of 53◦ –60◦ used for tokamaks,1 because the dispersion, dE/dθ varies as cotθ . Thus, in order to demonstrate good spectral resolution at smaller Bragg angles, laboratory demonstrations measuring various W L lines with the two spherical quartz 101 and 110 crystals in orders 2-4 were performed at Bragg angles of 26◦ , 31◦ , 37◦ , and 42◦ . For the 26◦ measurements, a spectral image on a Pilatus 100 k detector is illustrated in Fig. 3. This figure illustrates that the spectral image of the W Lα 1,2 lines and continuum from the micro-focus x-ray tube are sagittally focused to a single pixel row on the detector. x 10 4 4
counts
3 2
7.16 ± 0.07 7.28 ± 0.11 2.28 ± 0.02 2.97 ± 0.03
7.0 ± 0.5 7.3 ± 0.1 2.26a 2.92a
Vlaicu et al.16 Vlaicu et al.16 Salem and Lee17 Salem and Lee17
The values of Salem and Lee have been interpolated between Cr and Fe.
This spectrum extends from 8.232 to 8.400 keV, for a spectral window of 208 eV. The object (source to crystal) and image (crystal to detector) distances were approximately 166 and 140 cm, respectively. The spatial resolution achievable by a spectrometer is limited by the detector pixel pitch. The smallest available pitch in an x-ray CCD is 13 μm, but the effective pixel size is closer to 18-20 μm due to lateral charge spreading or “charge sharing” between neighboring pixels. Thus, to obtain a spatial resolution below 10 μm, the spectrometer needs a spatial magnification factor (M = simage /ssource ) of 2, where s is the distance from crystal to source or image. The relationship is rs = rd /M, where rs is the resolution at the source, and rd is the resolution of the detector. Thus, a spectrometer was set up with M = 2 measuring the W Lγ 1 line at 11.2859 keV from the micro-focus x-ray tube. The measurement was made using a spherical quartz 101 crystal with a radius of 75.6 cm in fourth order at a Bragg angle near 42◦ . An image of the spectrum on the CCD detector is shown in Fig. 4, and a graph of the spatial distribution of the line intensity is shown in Fig. 5. The inferred spatial width of the Lγ 1 spectral line plotted in Fig. 5 is 11.2 ± 0.4 μm, and an independent “knife-edge” measurement of the x-ray source size yields 8.5 ± 0.3 μm. Thus, subtracting these two values in quadrature, the instrumental contribution to the spatial width is estimated to be 7.3 ± 0.5 μm, where the composite error is obtained by adding the two contributing error estimates in quadrature. III. DEMONSTRATIONS ON HEDP EXPERIMENTS
The XICS concept has been demonstrated in two instruments on the TITAN laser facility at LLNL19 and an instrument on the MEC (Matter under Extreme Conditions) at the LCLS (Linac Coherent Light Source) at SLAC (Stanford National Accelerator Center). The TITAN spectrometers measured high resolution He-α spectra of Ti and Ly-β spectra of Si. Analysis of the data is underway. The MEC spectrometer was built to measure electron temperature and density profiles of a laser shock compressed WDM/HEDP plasma via
1 0 8320
8360 8400 x-ray energy (eV)
8440
FIG. 2. High resolution spectrum of the W Lα 2 (left peak) and Lα 1 (right peak) lines as dispersed by the Si 533 spherical crystal. Data are the black curve, and the red and blue curves are Lorentzian fits to determine the line width.
FIG. 3. Spectral-spatial image of the W Lα 1,2 and continuum spectrum from the W target micro-focus x-ray tube sagittally focused onto a single pixel row of a Pilatus detector.
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IV. DISCUSSION
High spectral resolution, sufficient for Doppler iontemperature measurements, and spatial resolution better than 10 μm have been demonstrated with the 1D imaging spherical crystal x-ray spectrometers. For still higher spatial resolution, geometries with magnification larger than 2 or detectors with pixel pitch smaller than 13 μm would be needed. Larger magnification can be achieved, but at the expense of reduced spectral range for a given detector size. ACKNOWLEDGMENTS FIG. 4. Spectral-spatial image of the W Lγ 1 x-ray line from the micro-focus x-ray tube. The CCD has 1024 × 1024 pixels with pitch of 13 μm.
x-ray Thomson scattering using the LCLS x-ray beam as a probe. For this experiment PPPL fielded a custom XICS with two Ge 220 crystals of radii near 22 cm. One crystal covered the 5.07-keV elastically scattered peak and part of the Compton peak, and the second crystal measured the remainder of the Compton peak. These data are currently being analyzed. An XICS type instrument is being designed for the OMEGA EP laser facility as part of a collaboration between PPPL and LLE (Laboratory for Laser Energetics of the U. of Rochester). This instrument will couple the XICS to a 2 ps x-ray streak camera in order to measure the time evolution of the temperature of solid density plasmas generated by intense laser beams. The temperature, in the 10s of eV to ∼300 eV will be inferred by the shift of Cu Kα lines due to thermal outer shell ionization.20 A successful demonstration of the XICS instrument on OMEGA EP could lead to an instrument on OMEGA and ultimately on the NIF.
counts
x 10 8 6
6
4 2 0 30 35 40 45 spatial profile (pixels)
50
FIG. 5. Spatial distribution of the W Lγ 1 x-ray line of Fig. 3 in the vertical direction. The pixel pitch is 13 μm, and the full width (standard deviation) of the distribution above the dashed line (8% of peak intensity) is 22.4 μm at the detector, indicating a source width of 11.2 μm.
This work was performed under the auspices of the (U.S.) Department of Energy (DOE) by Princeton Plasma Physics Laboratory (PPPL) under Contract No. DE-AC0209CH-11466 and Lawrence Livermore National Laboratory (LLNL) under Contract No. DE-AC52-07NA-27344. 1 M.
Bitter, K. W. Hill, A. L. Roquemore, P. Beiersdorfer, S. M. Kahn, S. R. Elliott, and B. Fraenkel, Rev. Sci. Instrum. 70, 292 (1999). 2 M. Bitter, K. W. Hill, B. Stratton, A. L. Roquemore, D. Mastrovito, S. G. Lee, J. Bak et al., Rev. Sci. Instrum. 75, 3660 (2004). 3 A. Ince-Cushman, J. E. Rice, M. Bitter, M. L. Reinke, K. W. Hill, M. F. Gu, E. Eikenberry, Ch. Broennimann, S. G. Lee, and Y. Podpaly, Rev. Sci. Instrum. 79, 10E302 (2008). 4 K. W. Hill, M. L. Bitter, S. D. Scott, A. Ince-Cushman, M. Reinke, J. E. Rice, P. Beiersdorfer et al., Rev. Sci. Instrum. 79, 10E320 (2008). 5 Y. Shi, F. Wang, B. Wan, M. Bitter, S. G. Lee, J. Bak et al., Plasma Phys. Controlled Fusion 52, 085014 (2010). 6 S. G. Lee, J. G. Bak, U. W. Nam, M. K. Moon, Y. Shi, M. Bitter, and K. W. Hill, Rev. Sci. Instrum. 81, 10E506 (2010). 7 N. A. Pablant, M. Bitter, L. Delgado-Aparicio, M. Goto, K. W. Hill, S. Lazerson, S. Morita et al., Rev. Sci. Instrum. 83, 083506 (2012). 8 K. W. Hill, M. Bitter, L. Delgado-Aparacio, N. A. Pablant, P. Beiersdorfer, M. Schneider et al., Rev. Sci. Instrum. 83, 10E125 (2012). 9 K. W. Hill, M. Bitter, L. Delgado-Aparacio, N. A. Pablant, P. Beiersdorfer, M. Sanchez del Rio, and L. Zhang, Proc. SPIE 8504, 850405 (2012). 10 S. A. Pikuz, J. D. Douglass, T. A. Shelkovenko, D. B. Sinars, and D. A. Hammer, Rev. Sci. Instrum. 79, 013106 (2008). 11 S. G. Lee, J. G. Bak, U. W. Nam, M. K. Moon, J. K. Cheon, M. Bitter, and K. Hill, Rev. Sci. Instrum. 79, 10E317 (2008). 12 R. Florido, R. C. Mancini, T. Nagayama, R. Tommasini, J. A. Delettrez, S. P. Regan et al., High Energy Density Phys. 6, 70 (2010). 13 S. P. Regan, R. Epstein, B. A. Hammel, L. J. Suter, J. Ralph, H. Scott et al., Phys. Plasmas 19, 056307 (2012). 14 M. R. Howells, New Directions in Research with Third Generation Soft XRay Synchrotron Radiation Sources, edited by A. S. Schlachter and F. J. Wuilleumier (Springer, 1994), p. 361. 15 Model L9421, Hamamatsu Corporation, Bridgewater, NJ. 16 A.-M. Vlaicu, T. Tochio, T. Ishizuka, D. Ohsawa, Y. Ito et al., Phys. Rev. A 58, 3544 (1998). 17 S. I. Salem and P. L. Lee, At. Data Nucl. Data Tables 18, 233 (1976). 18 DECTRIS Ltd., Neuenhoferstrasse, Baden, Switzerland. 19 H. Chen et al., “A high resolution imaging x-ray crystal spectrometer for high energy density (HED) plasmas,” Rev. Sci. Instrum. (these proceedings). 20 P. M. Nilson, W. Theobald, C. Mileham, C. Stoeckl, J. F. Myatt et al., Phys. Plasmas 18, 042702 (2011).
REVIEW OF SCIENTIFIC INSTRUMENTS 85, 11D613 (2014)
The NIF x-ray spectrometer calibration campaign at Omegaa) F. Pérez,1 G. E. Kemp,1 S. P. Regan,2 M. A. Barrios,1 J. Pino,1 H. Scott,1 S. Ayers,1 H. Chen,1 J. Emig,1 J. D. Colvin,1 M. Bedzyk,2 M. J. Shoup III,2 A. Agliata,2 B. Yaakobi,2 F. J. Marshall,2 R. A. Hamilton,2 J. Jaquez,3 M. Farrell,3 A. Nikroo,3 and K. B. Fournier1,b) 1
Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, California 94551, USA Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA 3 General Atomics, P.O. Box 85608, San Diego, California 92186, USA 2
(Presented 2 June 2014; received 23 May 2014; accepted 12 July 2014; published online 31 July 2014) The calibration campaign of the National Ignition Facility X-ray Spectrometer (NXS) was carried out at the O MEGA laser facility. Spherically symmetric, laser-driven, millimeter-scale x-ray sources of K-shell and L-shell emission from various mid-Z elements were designed for the 2–18 keV energy range of the NXS. The absolute spectral brightness was measured by two calibrated spectrometers. We compare the measured performance of the target design to radiation hydrodynamics simulations. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4891054] The National Ignition Facility (NIF)1 X-ray Spectrometer “NXS” will record calibrated, time-resolved x-ray spectra in the 2–18 keV photon energy range. It consists of singly curved, elliptical Bragg-reflection crystals. The energy range is divided in ten partially overlapping windows, each corresponding to one crystal configuration. For each spectral window, three identical NXS assemblies are built, thus a total of 30 assemblies. On NIF, a streak camera2 will provide temporal resolution between 8 and 160 ps for a time window from 1 to 20 ns. The absolute calibration of the NXS was carried out at the O MEGA laser facility,3 replacing NIF’s streak camera with an image plate (time-integrated measurement). Within two shot days, 26 shots were taken, fielding three NXS assemblies on each shot: all 30 assemblies of NXS have acquired spectra on two shots at least. Simultaneously, two absolutely calibrated x-ray spectrometers “XRS” were fielded in order to cross-calibrate each NXS crystal, as shown in Fig. 1 (left panel). All spectra were recorded on FUJI SR-type image plates.4 Note that the shot-to-shot variation was of the order of a percent: two shots per assembly give sufficient calibration data. The performance of the targets used for the NXS calibration is the main focus of this paper. To generate the x-ray spectra in this calibration campaign, a target design has been carefully developed. As the instruments are fielded around the target in different directions, isotropic x-ray emission was required. This was accomplished with spherical targets, uniformly irradiated by the O MEGA lasers. The calculated irradiation is ∼1015 W/cm2 and its non-uniformity of ±0.5% is shown in Fig. 1 (right panel). It corresponds to the 60 laser beams (1 ns, 0.5 TW square pulses), with phase plates adapted to the 1 mm diameter spheres. To ensure a steady target size a) Contributed paper, published as part of the Proceedings of the 20th Top-
ical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014. b) [email protected]
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(i.e., a non-imploding target), solid glass beads were selected instead of spherical shells. The x-ray spectra required line emission instead of continuum in order to calibrate the spectral range and to provide contrast that can be discriminated against potential background. To this goal, various metals were coated on the bead’s surface. As these metals must all be ablated during the laser irradiation to emit x rays, they were coated as an alloy instead of layers. The ∼1.5 μm thickness of this metallic alloy was determined using the simulations described below, to ensure maximum emission. The ten NXS configurations span ten different x-rayenergy ranges from 2 to 18 keV. A number of metal coatings were selected (Si, Ti, Cr, Ni, Zn, Zr, Mo, and Ag) to produce line emission in this whole range using their K-shell or Lshell lines. To the target fabrication, only two or three metals were coated on a single bead, and four types of targets were fabricated. Working with these constraints, we designed four different alloys, denoted by A, B, C, and D, summarized in Table I. Each alloy is adapted to the x-ray range of two or three different NXS configurations, so that all ten configurations can detect line emission from one of these alloys. To have comparable brightness from the various x-ray lines as predicted by the simulations, the metallic layers have equal parts of each element. The targets were fabricated by General Atomics. The bead radius was measured to 0.6% precision with a microscope. The thickness of the coating and its composition were determined with 7% and 1.5% respective uncertainties using x-ray opacity measurements at the K-edge of each element (or electron-impact K-shell x-ray fluorescence in the case of Si coating). Two sets of simulations, with two different codes, were performed to design and address the performance of each target configuration. Simulations were performed in 1D with spherical geometry using H YDRA ,5 a multiphysics arbitrary Lagrangian-Eulerian (ALE) multi-dimensional radiationhydrodynamics code. In an earlier stage of the design process,
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Rev. Sci. Instrum. 85, 11D613 (2014) TABLE II. QEOS input parameters in the H YDRA simulations for the various target compositions.
Target A
B C
D
Coating (%)
δr [μm]
Si/Mo/Ag 41/28/31
1.4
Ti/Cr/Ag 30/35/35 Cr/Ni/Zn 33/33/34 Zn/Zr 48/52
1.7 1.3
1.6
NXS configurations #1 from 1.9 to 2.4 keV #2 from 2.2 to 2.9 keV #3 from 2.6 to 3.7 keV #4 from 3.0 to 4.6 keV #5 from 3.6 to 6.1 keV #6 from 5.9 to 7.4 keV #7 from 6.7 to 8.9 keV #8 from 7.9 to 11.1 keV #9 from 8.9 to 13.7 keV #10 from 10.8 to 18.2 keV
ρ¯ [g/cm3 ]
c¯s [cm/μs]
A B C D
32.17 31.45 27.36 35.20
72.05 70.32 50.76 78.82
4.32 6.73 7.66 6.80
0.46 0.40 0.39 0.34
The H YDRA results match the data better than the early A RES simulations; thus, we will mostly discuss the former. Shown in Fig. 2 is the spatially resolved evolution of the electron temperature Te , radiation energy density R in the 5.9 − 11.2 keV band and the electron density ne (green) normalized to the critical density nc ≈ 1022 cm−3 , for the target C. Throughout the simulation, we observe a peak Te in the underdense blowoff plasma (∼150 μm from the initial interface) of approximately 3 keV and R peaked at ∼0.5nc (∼25 μm from the initial interface). Power emitted into this band dies rapidly after the laser turns off. At this time, nearly 90% (by mass) of the coating has become sub-critical indicating that the laser did not completely ablate away the mid-Z layer. Target types B and D performed similarly with ∼70% ablated away by the end of the pulse whereas the coating of target type A had completely been burnt through ∼0.25 ns before the pulse turned off. The H YDRA x-ray spectra are reconstructed from a spherical harmonic decomposition of the IMC photons, recorded as they pass through a diagnostic sphere located at r ≈ 0.5 cm. The simulated laser-to-x-ray conversion efficiency, integrating the spectra from 0 to 20 keV, varies between 45% and 60%. By restricting the integration of the spectra to each
4 (a) 0.0 ns 3 2 1 0
2
T
e
ε
R
n /n e
c
101 100 10−1 10−2 10 2
4 (b) 0.5 ns 3 2 1 0
101 100 10−1 10−2 10
4 (c) 1.0 ns 3 2 1 0
101 100 10−1 10−2 10
4 (d) 1.5 ns 3 2 1 0
101 100 10−1 10−2 10
0
2
2
0.05
0.1
Normalized electron density, ne/nc
TABLE I. Target composition, thicknesses (δr), and corresponding NXS crystal configurations.
A¯
Electron temperature, Te [keV]
simulations using the A RES code had also been performed in the same geometry. Targets A−D were modeled according to the experimental design with a 0.1 cm-diameter solid SiO2 bead with the mid-Z coating. In H YDRA, the glass and coatings were treated using the Livermore equation of state (LEOS) tables and the Thomas-Fermi based quotidian equation of state (QEOS6 ) model, respectively. We used atomic-fraction¯ = weighted atomic numbers Z i fi Zi and atomic weights 7 A¯ = i fi Ai with pressure equilibrated (harmonically av eraged) mass densities 1/ρ¯ = i fi /ρi and sound speeds 1/c¯s = i fi /cs,i ; a summary of the QEOS parameters for each target is shown in Table II. In A RES, LEOS were used for all elements, simply averaging by atomic fraction. The simulations were performed in the purely Lagrangian formulation and strict mass-matching was observed across the glass/mid-Z interface. The 3ω laser was treated using the 3D ray-tracing algorithm8 in H YDRA, and with a similar approach in A RES. Guided by the model developed by Colvin et al.,9 H YDRA employs the Lee-More electron thermal conductivity formulation10 with a large flux limiter (f = 0.2) to account for non-local electron transport, non-LTE rates with detailed super-configuration atomic models (DCA) from C RETIN,11 and implicit Monte Carlo (IMC) photonics for radiation transport12 with ∼106 photons and ∼480 radiation bins. A RES simply uses the Lee-More model without flux limiter, radiation diffusion with 60 bins, LTE rates, and a multi-group opacity model. It uses C RETIN only to post-process the x-ray spectra.
Z¯
Radiation energy density (hν = 5.9−11.2 keV), εR [x200 J/cm3]
FIG. 1. Calibration campaign setup. Blue and red lines identify the lines of sight of different diagnostics.
Target
0.15
r [cm] FIG. 2. (a)–(d) H YDRA-simulated profiles of electron temperature Te , radiation energy density R in the 5.9 − 11.2 keV band, and electron density ne (normalized to the critical density nc ), for target type C.
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FIG. 3. Simulated spectra for targets A–D in J/keV/sr are given for both codes, as well as experimental spectra from the XRS spectrometer. The relative intensities between cases A and D can be different for a given code as they correspond to different targets, densities, ablation rates, etc.
x-ray range of interest (see Table I) for targets A–D, we obtain conversion efficiencies of 19%, 14%, 1.2%, and 0.3%, respectively. Figure 3 provides the four simulated spectra in absolute units corresponding to the four target types, together with a few experimental spectra from the calibrated XRS spectrometer. Line locations and ratios are overall in good agreement with the H YDRA simulations. Note that this comparison is preliminary, since the published photoresponse calibration of the image plates13 may not be sufficient for the photon energies of interest. Results from A RES show poorer agreement, due to the reduced hydrodynamics and atomic physics models employed. Future publications will report the NXS spectra acquired during this campaign, and the corresponding calibration analysis. To this goal, the XRS spectra will be analyzed, especially focusing on the response of the image-plate detectors, which will be precisely characterized in the x-ray range of interest with gamma sources. Overall, we described the target design that led to a successful calibration campaign of the NXS. The simulated spectra were good enough to configure the spectrometers and record a signal within the dynamic range of the detectors. All crystals have acquired spectra and will be cross-calibrated to the absolutely calibrated XRS instrument. The reflectivity and
surface quality of each crystal will then be reported for use on NIF experiments. The authors thank M. Patel and M. Marinak for their contribution to the simulations. This work was performed under the auspices of the (U.S.) Department of Energy (DOE) by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and supported by the Defense Threat Reduction Agency under IAA 10027-5009 BASIC, “DTRA time-resolved x-ray spectrometer for the National Ignition Facility.” 1 G.
H. Miller, E. I. Moses, and C. R. Wuest, Opt. Eng. 43, 2841 (2004). P. Opachich et al., Rev. Sci. Instrum. 83, 125105 (2012). 3 T. Boehly, Opt. Commun. 133, 495 (1997). 4 B. R. Maddox et al., Rev. Sci. Instrum. 82, 023111 (2011). 5 M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, Phys. Plasmas 8, 2275 (2001). 6 R. M. More, K. H. Warren, D. A. Young, and G. B. Zimmerman, Phys. Fluids 31, 3059 (1988). 7 P. Sterne, private communication (2013). 8 T. B. Kaiser, Phys. Rev. E 61, 895 (2000). 9 J. D. Colvin, K. B. Fournier, J. Kane, S. Langer, M. J. May, and H. A. Scott, High Energy Density Phys. 7, 263 (2011). 10 Y. T. Lee and R. M. More, Phys. Fluids 27, 1273 (1984). 11 H. Scott and S. Hansen, High Energy Density Phys. 6, 39 (2010). 12 J. A. Fleck, Jr. and J. D. Cummings, Jr., J. Comput. Phys. 8, 313 (1971). 13 A. L. Meadowcroft, C. D. Bentley, and E. N. Stott, Rev. Sci. Instrum. 79, 113102 (2008). 2 Y.
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Characterization of spatially resolved high resolution x-ray spectrometers for high energy density physics and light source experimentsa) K. W. Hill,1,b) M. Bitter,1 L. Delgado-Aparacio,1 P. Efthimion,1 N. A. Pablant,1 J. Lu,2 P. Beiersdorfer,3 H. Chen,3 and E. Magee3 1
Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA Key Laboratory of Optoelectronic Technology and System of Ministry of Education, Chongqing University, Chongqing 400030, China 3 Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA 2
(Presented 2 June 2014; received 31 May 2014; accepted 2 July 2014; published online 30 July 2014) A high resolution 1D imaging x-ray spectrometer concept comprising a spherically bent crystal and a 2D pixelated detector is being optimized for diagnostics of small sources such as high energy density physics (HEDP) and synchrotron radiation or x-ray free electron laser experiments. This instrument is used on tokamak experiments for Doppler measurements of ion temperature and plasma flow velocity profiles. Laboratory measurements demonstrate a resolving power, E/E of order 10 000 and spatial resolution better than 10 μm. Initial tests of the high resolution instrument on HEDP plasmas are being performed. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4890260] I. INTRODUCTION
An instrument concept that has been a very successful diagnostic on tokamaks, spherical tori, and stellarators world wide1–7 is being adapted and optimized for small sources such as high energy density physics (HEDP), synchrotron radiation (SR), and x-ray free electron laser (XFEL) experiments.8, 9 It is a spatially resolved, high resolution x-ray imaging crystal spectrometer (XICS) which is used routinely for iontemperature (Ti ) and plasma flow velocity (v) measurements via Doppler broadening and shift, respectively, of impurity x-ray lines. It consists of a spherically bent crystal and a twodimensional (2D) photon counting pixel array x-ray detector. Although the instrument is very similar to the focusing spectrograph with spatial resolution (FSSR) spectrometer,10 which has been previously used on small source experiments, this instrument was developed independently at PPPL, using large radius (R = 1.5–5 m), precision bent spherical crystals designed for the high resolving power (E/E ∼ 10000)11 necessary for tokamak Doppler spectroscopy. Since much of the previous studies of x-ray spectroscopy on HEDP plasmas has involved, until recently, lower resolution instruments,12, 13 the present developments are hoped to ultimately lead to an XICS capable of Doppler measurement of ion temperature for HEDP experiments. The XICS concept is illustrated in Fig. 1. The spherically bent crystal at C diffracts and focuses x rays from the plasma to different points on the two-dimensional, pixelated detector. A focal point P on the detector maps not to a single point on the source side, but to a vertical focal line at Bm (meridional focus) and a horizontal line at Bs (sagittal focal line). This effect occurs because a spherical reflector has astigmaa) Contributed paper, published as part of the Proceedings of the 20th
Topical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014. b) Author to whom correspondence should be addressed. Electronic mail: [email protected] 0034-6748/2014/85(11)/11D612/3/$30.00
tism, i.e., the focal length for imaging in the horizontal plane is different than that for vertical imaging.14 It is this correspondence between the sagittal focal line near the plasma and a point on the detector that provides the excellent 1D spatial resolution. A narrow wavelength band of plasma x rays centered at λ = 2d sinθ diffracts to point P on the detector, and by rotational symmetry of the ray pattern from the spherical crystal about the line CO, as the sagittal focal line moves up and down to sample different spatial locations in the plasma, the point P moves down and up, respectively, on a cone to form the curved spectral lines shown in the image in the lower right of Fig. 1. Here, d is the lattice spacing of the crystal planes, and θ is the Bragg angle, illustrated at the crystal in Fig. 1. For good spatial resolution of a small HEDP plasma source, the source should be on the sagittal focal line. II. LABORATORY DEMONSTRATIONS
A high spectral resolution spectrum of the W Lα 1,2 lines at energies 8.3976 and 8.3352 keV, respectively, emitted by the tungsten target micro-focus x-ray tube15 is illustrated in Fig. 2. This spectrum was measured in a Johann geometry by a Si 533 crystal bent to a spherical radius of 82.3 cm with the detector approximately on the Rowland circle. The x-ray source was placed approximately on the sagittal focal line. A comparison of the widths of the two lines with measurements by Vaiclu et al.16 and Salem and Lee17 are shown in Table I. Also shown are the widths of the Mn Kα 1,2 lines at 5.887 and 5.898 keV from an 55 Fe source measured in second order using a quartz 110 crystal with a spherical radius of 75.6 cm. In both cases, the detector was a Pilatus 100 k hybrid pixel array detector18 with 196 × 487 photon counting pixels of size 172 × 172 μm2 . The line widths in Fig. 2 are determined from Lorentzian fits, which are plotted as the red and blue curves. All except one of the measured line widths in Table I differ from the reference measurements16, 17 by ≤ 0.04 eV,
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Rev. Sci. Instrum. 85, 11D612 (2014) TABLE I. Comparison of line widths of the Mn Kα and W Lα spectra with natural line widths measured by others. X-ray line This work width (eV) Reference width (eV) Reference W Lα 1 W Lα 2 Mn Kα 1 Mn Kα 2 a
FIG. 1. Schematic illustration of the principle of the XICS, described in the text.
indicating instrumental resolutions of order 0.5 eV or resolving powers greater than 10 000. In the case of the outlier, the W Lα 1 width, the stated error in the reference measurement is large. The uncertainty values for the present measurements are solely statistical uncertainties in the Lorentzian fitting. It is desirable to find independent methods of confirming the instrumental resolution of the spectrometer that do not rely on measuring the width of lines that are much broader than the instrumental resolution.11 One technique being considered is to measure the width of a very narrow line, such as a forbidden line from an electron beam ion trap, or a highly monochromatic x-ray beam from a synchrotron, Thomson scattered from a solid target. The spectral bandwidth of an XICS can be increased by working at smaller Bragg angles, θ , than the typical values of 53◦ –60◦ used for tokamaks,1 because the dispersion, dE/dθ varies as cotθ . Thus, in order to demonstrate good spectral resolution at smaller Bragg angles, laboratory demonstrations measuring various W L lines with the two spherical quartz 101 and 110 crystals in orders 2-4 were performed at Bragg angles of 26◦ , 31◦ , 37◦ , and 42◦ . For the 26◦ measurements, a spectral image on a Pilatus 100 k detector is illustrated in Fig. 3. This figure illustrates that the spectral image of the W Lα 1,2 lines and continuum from the micro-focus x-ray tube are sagittally focused to a single pixel row on the detector. x 10 4 4
counts
3 2
7.16 ± 0.07 7.28 ± 0.11 2.28 ± 0.02 2.97 ± 0.03
7.0 ± 0.5 7.3 ± 0.1 2.26a 2.92a
Vlaicu et al.16 Vlaicu et al.16 Salem and Lee17 Salem and Lee17
The values of Salem and Lee have been interpolated between Cr and Fe.
This spectrum extends from 8.232 to 8.400 keV, for a spectral window of 208 eV. The object (source to crystal) and image (crystal to detector) distances were approximately 166 and 140 cm, respectively. The spatial resolution achievable by a spectrometer is limited by the detector pixel pitch. The smallest available pitch in an x-ray CCD is 13 μm, but the effective pixel size is closer to 18-20 μm due to lateral charge spreading or “charge sharing” between neighboring pixels. Thus, to obtain a spatial resolution below 10 μm, the spectrometer needs a spatial magnification factor (M = simage /ssource ) of 2, where s is the distance from crystal to source or image. The relationship is rs = rd /M, where rs is the resolution at the source, and rd is the resolution of the detector. Thus, a spectrometer was set up with M = 2 measuring the W Lγ 1 line at 11.2859 keV from the micro-focus x-ray tube. The measurement was made using a spherical quartz 101 crystal with a radius of 75.6 cm in fourth order at a Bragg angle near 42◦ . An image of the spectrum on the CCD detector is shown in Fig. 4, and a graph of the spatial distribution of the line intensity is shown in Fig. 5. The inferred spatial width of the Lγ 1 spectral line plotted in Fig. 5 is 11.2 ± 0.4 μm, and an independent “knife-edge” measurement of the x-ray source size yields 8.5 ± 0.3 μm. Thus, subtracting these two values in quadrature, the instrumental contribution to the spatial width is estimated to be 7.3 ± 0.5 μm, where the composite error is obtained by adding the two contributing error estimates in quadrature. III. DEMONSTRATIONS ON HEDP EXPERIMENTS
The XICS concept has been demonstrated in two instruments on the TITAN laser facility at LLNL19 and an instrument on the MEC (Matter under Extreme Conditions) at the LCLS (Linac Coherent Light Source) at SLAC (Stanford National Accelerator Center). The TITAN spectrometers measured high resolution He-α spectra of Ti and Ly-β spectra of Si. Analysis of the data is underway. The MEC spectrometer was built to measure electron temperature and density profiles of a laser shock compressed WDM/HEDP plasma via
1 0 8320
8360 8400 x-ray energy (eV)
8440
FIG. 2. High resolution spectrum of the W Lα 2 (left peak) and Lα 1 (right peak) lines as dispersed by the Si 533 spherical crystal. Data are the black curve, and the red and blue curves are Lorentzian fits to determine the line width.
FIG. 3. Spectral-spatial image of the W Lα 1,2 and continuum spectrum from the W target micro-focus x-ray tube sagittally focused onto a single pixel row of a Pilatus detector.
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IV. DISCUSSION
High spectral resolution, sufficient for Doppler iontemperature measurements, and spatial resolution better than 10 μm have been demonstrated with the 1D imaging spherical crystal x-ray spectrometers. For still higher spatial resolution, geometries with magnification larger than 2 or detectors with pixel pitch smaller than 13 μm would be needed. Larger magnification can be achieved, but at the expense of reduced spectral range for a given detector size. ACKNOWLEDGMENTS FIG. 4. Spectral-spatial image of the W Lγ 1 x-ray line from the micro-focus x-ray tube. The CCD has 1024 × 1024 pixels with pitch of 13 μm.
x-ray Thomson scattering using the LCLS x-ray beam as a probe. For this experiment PPPL fielded a custom XICS with two Ge 220 crystals of radii near 22 cm. One crystal covered the 5.07-keV elastically scattered peak and part of the Compton peak, and the second crystal measured the remainder of the Compton peak. These data are currently being analyzed. An XICS type instrument is being designed for the OMEGA EP laser facility as part of a collaboration between PPPL and LLE (Laboratory for Laser Energetics of the U. of Rochester). This instrument will couple the XICS to a 2 ps x-ray streak camera in order to measure the time evolution of the temperature of solid density plasmas generated by intense laser beams. The temperature, in the 10s of eV to ∼300 eV will be inferred by the shift of Cu Kα lines due to thermal outer shell ionization.20 A successful demonstration of the XICS instrument on OMEGA EP could lead to an instrument on OMEGA and ultimately on the NIF.
counts
x 10 8 6
6
4 2 0 30 35 40 45 spatial profile (pixels)
50
FIG. 5. Spatial distribution of the W Lγ 1 x-ray line of Fig. 3 in the vertical direction. The pixel pitch is 13 μm, and the full width (standard deviation) of the distribution above the dashed line (8% of peak intensity) is 22.4 μm at the detector, indicating a source width of 11.2 μm.
This work was performed under the auspices of the (U.S.) Department of Energy (DOE) by Princeton Plasma Physics Laboratory (PPPL) under Contract No. DE-AC0209CH-11466 and Lawrence Livermore National Laboratory (LLNL) under Contract No. DE-AC52-07NA-27344. 1 M.
Bitter, K. W. Hill, A. L. Roquemore, P. Beiersdorfer, S. M. Kahn, S. R. Elliott, and B. Fraenkel, Rev. Sci. Instrum. 70, 292 (1999). 2 M. Bitter, K. W. Hill, B. Stratton, A. L. Roquemore, D. Mastrovito, S. G. Lee, J. Bak et al., Rev. Sci. Instrum. 75, 3660 (2004). 3 A. Ince-Cushman, J. E. Rice, M. Bitter, M. L. Reinke, K. W. Hill, M. F. Gu, E. Eikenberry, Ch. Broennimann, S. G. Lee, and Y. Podpaly, Rev. Sci. Instrum. 79, 10E302 (2008). 4 K. W. Hill, M. L. Bitter, S. D. Scott, A. Ince-Cushman, M. Reinke, J. E. Rice, P. Beiersdorfer et al., Rev. Sci. Instrum. 79, 10E320 (2008). 5 Y. Shi, F. Wang, B. Wan, M. Bitter, S. G. Lee, J. Bak et al., Plasma Phys. Controlled Fusion 52, 085014 (2010). 6 S. G. Lee, J. G. Bak, U. W. Nam, M. K. Moon, Y. Shi, M. Bitter, and K. W. Hill, Rev. Sci. Instrum. 81, 10E506 (2010). 7 N. A. Pablant, M. Bitter, L. Delgado-Aparicio, M. Goto, K. W. Hill, S. Lazerson, S. Morita et al., Rev. Sci. Instrum. 83, 083506 (2012). 8 K. W. Hill, M. Bitter, L. Delgado-Aparacio, N. A. Pablant, P. Beiersdorfer, M. Schneider et al., Rev. Sci. Instrum. 83, 10E125 (2012). 9 K. W. Hill, M. Bitter, L. Delgado-Aparacio, N. A. Pablant, P. Beiersdorfer, M. Sanchez del Rio, and L. Zhang, Proc. SPIE 8504, 850405 (2012). 10 S. A. Pikuz, J. D. Douglass, T. A. Shelkovenko, D. B. Sinars, and D. A. Hammer, Rev. Sci. Instrum. 79, 013106 (2008). 11 S. G. Lee, J. G. Bak, U. W. Nam, M. K. Moon, J. K. Cheon, M. Bitter, and K. Hill, Rev. Sci. Instrum. 79, 10E317 (2008). 12 R. Florido, R. C. Mancini, T. Nagayama, R. Tommasini, J. A. Delettrez, S. P. Regan et al., High Energy Density Phys. 6, 70 (2010). 13 S. P. Regan, R. Epstein, B. A. Hammel, L. J. Suter, J. Ralph, H. Scott et al., Phys. Plasmas 19, 056307 (2012). 14 M. R. Howells, New Directions in Research with Third Generation Soft XRay Synchrotron Radiation Sources, edited by A. S. Schlachter and F. J. Wuilleumier (Springer, 1994), p. 361. 15 Model L9421, Hamamatsu Corporation, Bridgewater, NJ. 16 A.-M. Vlaicu, T. Tochio, T. Ishizuka, D. Ohsawa, Y. Ito et al., Phys. Rev. A 58, 3544 (1998). 17 S. I. Salem and P. L. Lee, At. Data Nucl. Data Tables 18, 233 (1976). 18 DECTRIS Ltd., Neuenhoferstrasse, Baden, Switzerland. 19 H. Chen et al., “A high resolution imaging x-ray crystal spectrometer for high energy density (HED) plasmas,” Rev. Sci. Instrum. (these proceedings). 20 P. M. Nilson, W. Theobald, C. Mileham, C. Stoeckl, J. F. Myatt et al., Phys. Plasmas 18, 042702 (2011).
REVIEW OF SCIENTIFIC INSTRUMENTS 85, 11D613 (2014)
The NIF x-ray spectrometer calibration campaign at Omegaa) F. Pérez,1 G. E. Kemp,1 S. P. Regan,2 M. A. Barrios,1 J. Pino,1 H. Scott,1 S. Ayers,1 H. Chen,1 J. Emig,1 J. D. Colvin,1 M. Bedzyk,2 M. J. Shoup III,2 A. Agliata,2 B. Yaakobi,2 F. J. Marshall,2 R. A. Hamilton,2 J. Jaquez,3 M. Farrell,3 A. Nikroo,3 and K. B. Fournier1,b) 1
Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, California 94551, USA Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA 3 General Atomics, P.O. Box 85608, San Diego, California 92186, USA 2
(Presented 2 June 2014; received 23 May 2014; accepted 12 July 2014; published online 31 July 2014) The calibration campaign of the National Ignition Facility X-ray Spectrometer (NXS) was carried out at the O MEGA laser facility. Spherically symmetric, laser-driven, millimeter-scale x-ray sources of K-shell and L-shell emission from various mid-Z elements were designed for the 2–18 keV energy range of the NXS. The absolute spectral brightness was measured by two calibrated spectrometers. We compare the measured performance of the target design to radiation hydrodynamics simulations. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4891054] The National Ignition Facility (NIF)1 X-ray Spectrometer “NXS” will record calibrated, time-resolved x-ray spectra in the 2–18 keV photon energy range. It consists of singly curved, elliptical Bragg-reflection crystals. The energy range is divided in ten partially overlapping windows, each corresponding to one crystal configuration. For each spectral window, three identical NXS assemblies are built, thus a total of 30 assemblies. On NIF, a streak camera2 will provide temporal resolution between 8 and 160 ps for a time window from 1 to 20 ns. The absolute calibration of the NXS was carried out at the O MEGA laser facility,3 replacing NIF’s streak camera with an image plate (time-integrated measurement). Within two shot days, 26 shots were taken, fielding three NXS assemblies on each shot: all 30 assemblies of NXS have acquired spectra on two shots at least. Simultaneously, two absolutely calibrated x-ray spectrometers “XRS” were fielded in order to cross-calibrate each NXS crystal, as shown in Fig. 1 (left panel). All spectra were recorded on FUJI SR-type image plates.4 Note that the shot-to-shot variation was of the order of a percent: two shots per assembly give sufficient calibration data. The performance of the targets used for the NXS calibration is the main focus of this paper. To generate the x-ray spectra in this calibration campaign, a target design has been carefully developed. As the instruments are fielded around the target in different directions, isotropic x-ray emission was required. This was accomplished with spherical targets, uniformly irradiated by the O MEGA lasers. The calculated irradiation is ∼1015 W/cm2 and its non-uniformity of ±0.5% is shown in Fig. 1 (right panel). It corresponds to the 60 laser beams (1 ns, 0.5 TW square pulses), with phase plates adapted to the 1 mm diameter spheres. To ensure a steady target size a) Contributed paper, published as part of the Proceedings of the 20th Top-
ical Conference on High-Temperature Plasma Diagnostics, Atlanta, Georgia, USA, June 2014. b) [email protected]
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(i.e., a non-imploding target), solid glass beads were selected instead of spherical shells. The x-ray spectra required line emission instead of continuum in order to calibrate the spectral range and to provide contrast that can be discriminated against potential background. To this goal, various metals were coated on the bead’s surface. As these metals must all be ablated during the laser irradiation to emit x rays, they were coated as an alloy instead of layers. The ∼1.5 μm thickness of this metallic alloy was determined using the simulations described below, to ensure maximum emission. The ten NXS configurations span ten different x-rayenergy ranges from 2 to 18 keV. A number of metal coatings were selected (Si, Ti, Cr, Ni, Zn, Zr, Mo, and Ag) to produce line emission in this whole range using their K-shell or Lshell lines. To the target fabrication, only two or three metals were coated on a single bead, and four types of targets were fabricated. Working with these constraints, we designed four different alloys, denoted by A, B, C, and D, summarized in Table I. Each alloy is adapted to the x-ray range of two or three different NXS configurations, so that all ten configurations can detect line emission from one of these alloys. To have comparable brightness from the various x-ray lines as predicted by the simulations, the metallic layers have equal parts of each element. The targets were fabricated by General Atomics. The bead radius was measured to 0.6% precision with a microscope. The thickness of the coating and its composition were determined with 7% and 1.5% respective uncertainties using x-ray opacity measurements at the K-edge of each element (or electron-impact K-shell x-ray fluorescence in the case of Si coating). Two sets of simulations, with two different codes, were performed to design and address the performance of each target configuration. Simulations were performed in 1D with spherical geometry using H YDRA ,5 a multiphysics arbitrary Lagrangian-Eulerian (ALE) multi-dimensional radiationhydrodynamics code. In an earlier stage of the design process,
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Rev. Sci. Instrum. 85, 11D613 (2014) TABLE II. QEOS input parameters in the H YDRA simulations for the various target compositions.
Target A
B C
D
Coating (%)
δr [μm]
Si/Mo/Ag 41/28/31
1.4
Ti/Cr/Ag 30/35/35 Cr/Ni/Zn 33/33/34 Zn/Zr 48/52
1.7 1.3
1.6
NXS configurations #1 from 1.9 to 2.4 keV #2 from 2.2 to 2.9 keV #3 from 2.6 to 3.7 keV #4 from 3.0 to 4.6 keV #5 from 3.6 to 6.1 keV #6 from 5.9 to 7.4 keV #7 from 6.7 to 8.9 keV #8 from 7.9 to 11.1 keV #9 from 8.9 to 13.7 keV #10 from 10.8 to 18.2 keV
ρ¯ [g/cm3 ]
c¯s [cm/μs]
A B C D
32.17 31.45 27.36 35.20
72.05 70.32 50.76 78.82
4.32 6.73 7.66 6.80
0.46 0.40 0.39 0.34
The H YDRA results match the data better than the early A RES simulations; thus, we will mostly discuss the former. Shown in Fig. 2 is the spatially resolved evolution of the electron temperature Te , radiation energy density R in the 5.9 − 11.2 keV band and the electron density ne (green) normalized to the critical density nc ≈ 1022 cm−3 , for the target C. Throughout the simulation, we observe a peak Te in the underdense blowoff plasma (∼150 μm from the initial interface) of approximately 3 keV and R peaked at ∼0.5nc (∼25 μm from the initial interface). Power emitted into this band dies rapidly after the laser turns off. At this time, nearly 90% (by mass) of the coating has become sub-critical indicating that the laser did not completely ablate away the mid-Z layer. Target types B and D performed similarly with ∼70% ablated away by the end of the pulse whereas the coating of target type A had completely been burnt through ∼0.25 ns before the pulse turned off. The H YDRA x-ray spectra are reconstructed from a spherical harmonic decomposition of the IMC photons, recorded as they pass through a diagnostic sphere located at r ≈ 0.5 cm. The simulated laser-to-x-ray conversion efficiency, integrating the spectra from 0 to 20 keV, varies between 45% and 60%. By restricting the integration of the spectra to each
4 (a) 0.0 ns 3 2 1 0
2
T
e
ε
R
n /n e
c
101 100 10−1 10−2 10 2
4 (b) 0.5 ns 3 2 1 0
101 100 10−1 10−2 10
4 (c) 1.0 ns 3 2 1 0
101 100 10−1 10−2 10
4 (d) 1.5 ns 3 2 1 0
101 100 10−1 10−2 10
0
2
2
0.05
0.1
Normalized electron density, ne/nc
TABLE I. Target composition, thicknesses (δr), and corresponding NXS crystal configurations.
A¯
Electron temperature, Te [keV]
simulations using the A RES code had also been performed in the same geometry. Targets A−D were modeled according to the experimental design with a 0.1 cm-diameter solid SiO2 bead with the mid-Z coating. In H YDRA, the glass and coatings were treated using the Livermore equation of state (LEOS) tables and the Thomas-Fermi based quotidian equation of state (QEOS6 ) model, respectively. We used atomic-fraction¯ = weighted atomic numbers Z i fi Zi and atomic weights 7 A¯ = i fi Ai with pressure equilibrated (harmonically av eraged) mass densities 1/ρ¯ = i fi /ρi and sound speeds 1/c¯s = i fi /cs,i ; a summary of the QEOS parameters for each target is shown in Table II. In A RES, LEOS were used for all elements, simply averaging by atomic fraction. The simulations were performed in the purely Lagrangian formulation and strict mass-matching was observed across the glass/mid-Z interface. The 3ω laser was treated using the 3D ray-tracing algorithm8 in H YDRA, and with a similar approach in A RES. Guided by the model developed by Colvin et al.,9 H YDRA employs the Lee-More electron thermal conductivity formulation10 with a large flux limiter (f = 0.2) to account for non-local electron transport, non-LTE rates with detailed super-configuration atomic models (DCA) from C RETIN,11 and implicit Monte Carlo (IMC) photonics for radiation transport12 with ∼106 photons and ∼480 radiation bins. A RES simply uses the Lee-More model without flux limiter, radiation diffusion with 60 bins, LTE rates, and a multi-group opacity model. It uses C RETIN only to post-process the x-ray spectra.
Z¯
Radiation energy density (hν = 5.9−11.2 keV), εR [x200 J/cm3]
FIG. 1. Calibration campaign setup. Blue and red lines identify the lines of sight of different diagnostics.
Target
0.15
r [cm] FIG. 2. (a)–(d) H YDRA-simulated profiles of electron temperature Te , radiation energy density R in the 5.9 − 11.2 keV band, and electron density ne (normalized to the critical density nc ), for target type C.
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FIG. 3. Simulated spectra for targets A–D in J/keV/sr are given for both codes, as well as experimental spectra from the XRS spectrometer. The relative intensities between cases A and D can be different for a given code as they correspond to different targets, densities, ablation rates, etc.
x-ray range of interest (see Table I) for targets A–D, we obtain conversion efficiencies of 19%, 14%, 1.2%, and 0.3%, respectively. Figure 3 provides the four simulated spectra in absolute units corresponding to the four target types, together with a few experimental spectra from the calibrated XRS spectrometer. Line locations and ratios are overall in good agreement with the H YDRA simulations. Note that this comparison is preliminary, since the published photoresponse calibration of the image plates13 may not be sufficient for the photon energies of interest. Results from A RES show poorer agreement, due to the reduced hydrodynamics and atomic physics models employed. Future publications will report the NXS spectra acquired during this campaign, and the corresponding calibration analysis. To this goal, the XRS spectra will be analyzed, especially focusing on the response of the image-plate detectors, which will be precisely characterized in the x-ray range of interest with gamma sources. Overall, we described the target design that led to a successful calibration campaign of the NXS. The simulated spectra were good enough to configure the spectrometers and record a signal within the dynamic range of the detectors. All crystals have acquired spectra and will be cross-calibrated to the absolutely calibrated XRS instrument. The reflectivity and
surface quality of each crystal will then be reported for use on NIF experiments. The authors thank M. Patel and M. Marinak for their contribution to the simulations. This work was performed under the auspices of the (U.S.) Department of Energy (DOE) by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and supported by the Defense Threat Reduction Agency under IAA 10027-5009 BASIC, “DTRA time-resolved x-ray spectrometer for the National Ignition Facility.” 1 G.
H. Miller, E. I. Moses, and C. R. Wuest, Opt. Eng. 43, 2841 (2004). P. Opachich et al., Rev. Sci. Instrum. 83, 125105 (2012). 3 T. Boehly, Opt. Commun. 133, 495 (1997). 4 B. R. Maddox et al., Rev. Sci. Instrum. 82, 023111 (2011). 5 M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, Phys. Plasmas 8, 2275 (2001). 6 R. M. More, K. H. Warren, D. A. Young, and G. B. Zimmerman, Phys. Fluids 31, 3059 (1988). 7 P. Sterne, private communication (2013). 8 T. B. Kaiser, Phys. Rev. E 61, 895 (2000). 9 J. D. Colvin, K. B. Fournier, J. Kane, S. Langer, M. J. May, and H. A. Scott, High Energy Density Phys. 7, 263 (2011). 10 Y. T. Lee and R. M. More, Phys. Fluids 27, 1273 (1984). 11 H. Scott and S. Hansen, High Energy Density Phys. 6, 39 (2010). 12 J. A. Fleck, Jr. and J. D. Cummings, Jr., J. Comput. Phys. 8, 313 (1971). 13 A. L. Meadowcroft, C. D. Bentley, and E. N. Stott, Rev. Sci. Instrum. 79, 113102 (2008). 2 Y.
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