Collapsing Radiative Shock Experiments on the Omega Laser

Home , John Lindl, Omega (The Walking Dead)

by Amy B. Reighard

A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy (Physics) in The University of Michigan 2007

Doctoral Committee: Professor R. Paul Drake, Co-Chair Professor Fred C. Adams, Co-Chair Professor Carl W. Akerlof Professor James Paul Holloway Professor Gregory Tarl´e

c Amy B. Reighard 2007 All Rights Reserved To Robert L. Cooper, who helped at every step along the way with love, support, and a ﬁrm grasp of reality; I hope I am just as helpful when it is your turn. To Mom and Dad, who never doubted that I should or could do this.

ii ACKNOWLEDGEMENTS

I would first like to thank my graduate research advisor, Paul Drake, for guid- ing me on this exciting project. Thank you for allowing me to present at a dozen conferences, for encouraging me to pursue somewhat-related tangents, for flying me across the country to “see who will wander by”, for letting me do the fun stuff while you handled the unpleasant things, and for always knowing when not to tell me the answer.

Thank you also to the graduate students, past and present, in the Drake research group; Carolyn Kuranz, Eric Harding, Tony Visco, Korbie Killebrew Dannenberg, and Kelly Korreck for many useful discussions, brainstorming sessions, homework arguments, and your enduring friendship, fellowship, and support. I feel lucky to have such wonderful peers.

I would like to acknowledge the extensive contributions of the Target Fabrication

Team in the Drake group at the University of Michigan, especially Michael Grosskopf,

Douglas Kremer, Christine Krauland, and Trisha Donajkowski, who built, trans- ported, organized, and ﬁlled my targets. Eduardo Mucino also helped extensively with 1D simulation work on beryllium, and Dave Leibrandt simulated the experiment using Zeus 2D.

Thank you also to the technical staﬀ at the Omega Laser facility, without whom none of these experiments could have been executed. Thank you especially to Keith

Thorp, Steve Stagnitto, Jack Armstrong, and Chuck Source.

iii I have also had many helpful discussions with an international group of collaborators, which includes Tom Boehly, Laurent Boireau, Serge Bouquet, Michel Busquet,

Dustin Froula, Gail Glendinning, Siegfried Glenzer, Freddy Hansen, Jim Knauer,

Michel Koenig, Ted Perry, Bruce Remington, Steven Ross, and Russell Wallace.

Lastly, thank you to my committee, whose extensive input helped shape this thesis in a very positive way.

iv TABLE OF CONTENTS

DEDICATION ...... ii

ACKNOWLEDGEMENTS ...... iii

LIST OF FIGURES ...... vii

LIST OF TABLES ...... xv

LIST OF APPENDICES ...... xvii

CHAPTER

I. Introduction ...... 1

1.1 High-Energy-Density Physics ...... 2 1.2 A Brief History of HED physics ...... 2 1.3 Laboratory Astrophysics ...... 3 1.4 Tools of the Trade: High-Energy-Density Facilities ...... 6 1.4.1 High-powered laser facilities ...... 7 1.4.2 Z-pinches ...... 10 1.4.3 Petawatt Lasers ...... 11

II. Radiation Hydrodynamics ...... 12

2.1 Single-Fluid Euler Equations ...... 13 2.2 The Equation of Radiative Transfer and Radiative Hydrodynamics . . . . . 13 2.2.1 Threshold for Radiative Shocks ...... 15 2.2.2 Classiﬁcation for Meaningful Comparison ...... 16 2.2.3 Formation of a Cooling Layer and a Collapsed Shock ...... 17 2.2.4 Energy Balance in a Thick/Thin Shock ...... 21 2.3 A Brief History of Radiation Hydrodynamics Experiments ...... 22

III. Experiment Description ...... 28

3.1 Targets ...... 29 3.2 Lasers ...... 33 3.3 Backlighters ...... 37 3.4 Diagnostics ...... 40 3.4.1 Microchannel Plates and Framing Cameras ...... 40 3.4.2 Velocity Interferometry ...... 43 3.4.3 Thomson scattering ...... 48

IV. Experimental Results ...... 49

v 4.1 Radiographic Image Processing ...... 52 4.2 X-ray Radiographic Data ...... 56 4.2.1 Single-strip framing camera data from 40 µm beryllium drive disks 57 4.2.2 Single-strip framing camera data from 20 µm, beryllium drive disks 57 4.2.3 Single-strip framing camera data from 10 µm beryllium drive disk . 61 4.2.4 Single-strip framing camera data from 80 µm polyimide drive disk 62 4.2.5 Four-strip framing camera data ...... 64 4.3 Dual Radiographic Data ...... 66 4.4 Odd Radiographic Data ...... 72 4.5 Fringe Shifts from a Velocity Interferometry System for Any Reﬂector . . . . 77

V. Radiographic Image Analysis ...... 81

5.1 Shot-to-Shot Variability ...... 83 5.2 Shock Position as a Function of Time ...... 85 5.3 Shock Thickness as a Function of Time ...... 86 5.4 Structure in the Cooling Layer ...... 88

VI. Thomson Scattering Experiment in Argon Gas ...... 94

VII. Radiation Hydrodynamic Simulations ...... 110

7.1 One-Dimensional Hyades Simulations ...... 110 7.1.1 Production of a radiatively collapsed shock ...... 111 7.1.2 Drive disk thickness variation ...... 117 7.1.3 Late-time eﬀects ...... 119 7.2 Two-Dimensional Simulations ...... 121 7.2.1 FCI ...... 122 7.2.2 Zeus ...... 123 7.3 Issues Between Simulation and Experiment ...... 126 7.4 One-Dimensional Simulations in Argon Gas ...... 132 7.5 Summary of Simulation Results ...... 135

VIII. Conclusions and Future Directions ...... 136

8.1 Radiative Shocks in Astrophysics ...... 137 8.1.1 Shocks Emerging from Supernovae ...... 138 8.1.2 Cooling of Stellar Atmospheres ...... 141 8.2 Applications ...... 146 8.3 Future Directions ...... 147 8.3.1 Flux Measurements ...... 147 8.3.2 Short-Pulse Backlighters and Ungated Imaging Diagnostics . . . . 148

APPENDICES ...... 150

BIBLIOGRAPHY ...... 174

vi LIST OF FIGURES

Figure

1.1 Hubble Space Telescope picture of the Cyngus Loop. False coloring shows diﬀerent metal line emissions. Credit: NASA, HST, Jeﬀ Hester...... 4

1.2 Hubble Space Telescope image of SN 1987a, taken in 2003 with WFPC2. Here, a ring of circumstellar material lights up as the shockwave driven by the explosion heats it. Image credit: NASA and R. Kirshner...... 5

1.3 Diagram of the planned laser facility at the Naval Research Laboratory in Wash- ington, D.C ...... 8

1.4 Outside of the NIF target chamber. Square protrusions are where bundles of four beams, called quads, will enter the target chamber...... 9

1.5 Beampath of one of the NIF beams...... 10

1.6 Cutaway schematic of the Z-machine’s latest upgrade, now referred to as Z-R. Implosions happen near the axis of this large cylinder...... 11

2.1 Diagram of general structure of a collapsing radiative shock. After an initial temperature and density jump at the shock front, radiative cooling causes a decrease in electron temperature (which cools the ions collisionally), and a corresponding increase in density. The extent of this layer is dictated by energy balance of the sources of energy into and out of this transitional region, or “cooling layer”. . . . 19

2.2 Radiation ﬂow in a thick-thin shock. Radiation at the boundary between the optically thick upstream region and the transition region must be equal, and at must equal twice the ﬂux from the transition region at the shock front on the other side of the transition region...... 21

3.1 Photos of the University of Michigan Target Fabrication Center. a) System is mounted on an optics table in clean room to minimize dust and debris on optics and in stage mechanics. b) Two sets of coordinate systems aid holding and independently positioning two pieces during fabrication...... 29

3.2 2D schematic of gas-ﬁlled target and 3D CAD drawing of target with attached backlighter foil...... 31

3.3 (a) Metrology photo of target with area backlighter foil attached. Area backlighting is discussed further in section 3.3. (b) Metrology photo of gold grid attached to target. Note notches on the grid near the target body, that served as spatial indicators. Increasingly large notches were cut farther from the drive surface. (c) Metrology photo of target with no area backlighter attached...... 32

vii 3.4 (a) Diagram of spherical target chamber at the Omega Laser facility. Numbered circles indicate beams, while larger circles numbered with H, P, and TIM labels are ports for both ﬁxed and removable diagnostics. (b) Schematic of beam paths leading through charging banks and into the target chamber. Both images from the National Laser Users Facility User’s Guide...... 34

3.5 Equivalent target plane images of beams spots integrated over a 1-ns pulse width. (a) An unsmoothed spot of a frequency-tripled Omega beam. (b) Beam spot smoothed with a continuous phase plate. (c) Beam spot smoothed with SSD. From the National Laser Users Facility User’s Guide...... 35

3.6 Xenon transmission spectrum in the range of 3-8 keV and argon spectum in the range of 1-6 keV, as calculated for cold material...... 38

3.7 Diagram of backlit pinhole backlighting setup, not to scale. In the Omega chamber, with the target at target chamber center, the backlighter target was 12 mm from the target axis, while the detector was 229 mm from the target axis on the opposite side, for an image magniﬁcation of 20...... 40

3.8 Target schematic for pinhole backlighter target . Measured details for each target are ﬁlled in during fabrication and metrology...... 41

3.9 Metrology photos of pinholebacklighter targets. a) Face-on view of backlighter target. The large rectangle is the 5 mm square tantalum substrate. The dark square seen is a feature on the tantalum, while close inspection shows the 2 mm polyimide square. The dotted-line crosshairs shown are features of the viewing system, and the center of the crosshair is positioned on the 20 µm pinhole. b) XTVS view of backlit pinhole target, imaged in metrology at same angle as one of the cameras on Omega when the target is correctly positioned...... 42

3.10 Cartoon of framing camera components. An x-ray source on the right side of the cartoon shines through a target. The photons then hit a microchannel plate, which turns x-ray photons into a cascade of electrons. These electrons are then directed onto a phosphor plate via an applied potential, which emits visible photons upon electron impact. These visible photons are then imaged on ﬁlm or a CCD camera. The microchannel plate can be coated with a material to increase its gain. Image courtesy Eric Harding...... 43

3.11 Simulation of VISAR fringes from a steady-state target on a streak camera, where time is the vertical axis and position is the horizontal axis. Image from Forsman, 2001 [20]...... 45

3.12 Target setup for use with the VISAR diagnostic. The shock moves from left to right down the main cylinder, while the interferometer beams pass through the arm perpendicular to the main body tube...... 48

viii 4.1 a) Data captured by framing camera. Data from a framing camera are recorded on film, then digitized. A wedge file is created to help calibrate scanned exposure levels to x-ray illumination. b) Calibrated image. Pre-shot metrology measures the position of features on the target, to give axes in target coordinates. The gold grid shown in images provides not only a vehicle for introducing these features onto a data image, but also provides a reliable way to measure the actual image magnification. c) Data smoothed over a resolution element. Source-limited resolution limits the level at which useful data can be gathered. By smoothing over a resolution element, we remove small variations due to noise from the data image. d) Image with background variations subtracted out. Image is smoothed over a large fraction of the image, so only large scale variations remain, and then subtracted from the original image...... 54

4.2 Diagram of source limited resolution. Smear from photons passing through the same part of the target but hitting diﬀerent parts of the detector is calculated using the size of the pinhole source and similar triangles. The extent of the smear on the detector is then divided by the magniﬁcation of the image (image distance/object distance) to get the size of a source-resolution-limited element in target coordinates. 56

4.3 Single-strip framing camera from a shock driven with a 40 µm beryllium disk. a) t = 10 ns. b) t = 10ns. c) 20 ns. d) 12 ns...... 58

4.4 Single-strip framing camera from a shock driven with a 40 µm beryllium disk at 20 ns after drive beams turn on. a) Image smoothed over a resolution element. b) Image background smoothed and subtracted. This piece of data is also displayed in Figure 4.3c...... 59

4.5 Single-strip framing camera from a shock driven with a 20 µm beryllium disk at a) 8 ns, b) 10 ns, c) 14 ns, d) 14ns, and e) 15 ns. All of these images show evidence of some clumpy structure, though in images a and e it is not nearly so pronounced as the other three images. Image e also shows a relatively curved front compared to the rest, which have more planar structure...... 60

4.6 Plot of shock from 20 µm beryllium driver. a) Calibrated data smoothed over a resolution element. While the collapsed layer is visible, the contrast in the image is poor, and features in the shock are not clearly deﬁned. b) Image smoothed over 250 µm, subtracted from original image, then once again smoothed over a resolution element. Not only is the collapsed layer more clearly deﬁned, but some structure emerges on the back side of the dense layer, as well as possibly repeating structure near the top of the front side of the shock, across from features on the backside. For comparison, the large white pixels are dead pixels smoothed to a source-limited resolution element, which is smaller than the structure observed...... 61

4.7 Single-strip framing camera from a shock driven with a 10 µm beryllium disk. a) Data smoothed over a resolution element. b) Smoothed data was large scale variations subtracted out, showing more structure on both sides of the collapsed layer...... 62

4.8 Single-strip framing camera from a shock driven in xenon gas with a 80 µm polyimide drive disk. This image shows only part of the shock, as the diagnostic was timed too early. The shock is just entering the ﬁeld of view of this diagnostic. The shock is also obscured by a bright stripe across the image, which is from interference from another diagnostic. This is described further in the Dual Radiography section. 63

ix 4.9 Raw four-strip framing camera data for a shock in argon at 12 ns, launched with a 50 µm beryllium drive disk. This particular image was backlit using x-rays from L- shell transitions of tin. While grid features are visible, target walls are not, making it diﬃcult to conﬁrm radial position of the shock. On this image, only four frames have any image of the gold grid, and only one has a grid edge, the position of which was measured in metrology. Each strip is delayed 200 ps, with time beginning at the upper-left corner. Within each strip, each cell is delayed by 60 ps...... 65

4.10 Blow-up of one cell of four-strip framing camera data from August, 2002, shown in Figure 4.9. This cell is in the second column, ﬁrst row as measured from the lower left corner of the image, at time t = 12.4 ns...... 66

4.11 Raw four-strip framing camera data for a shock in xenon at 18 ns, launched with a 50 µm beryllium drive disk. This particular image was backlit with a material more suited to a shock in argon gas, but shock features are still visible, if not optimal. While grid features are visible, target walls are not, making it diﬃcult to conﬁrm radial position of the shock. All frames image the shock and the grid...... 67

4.12 Blow-up of one cell of the four-strip framing camera data from December, 2002, shown in Figure 4.11. This cell, in the second column, second row as measured from the lower left corner of the image, at time t = 18.4 ns ...... 68

4.13 Raw four-strip framing camera data for a shock in xenon at 13 ns, launched with a 80 µm plastic driver. Unlike previous four-strip framing camera data, one wall of the tube is visible in this image, as is trailing xenon gas along the wall. The other wall is obscured by a grid...... 69

4.14 Blow-up of one cell of the four-strip framing camera data from April, 2004, shown in Figure 4.13. This image uses a plastic driver in xenon gas, backlit with a vanadium source. This cell, in the fourth column, second row as measured from the lower left corner of the image, at time t = 13.4 ns ...... 70

4.15 Raw four-strip framing camera data for a shock in xenon at 15 ns, launched with a 40 µm beryllium driver. One wall of the tube is visible in this image, but the placement of the shock on the image cuts out any possible traces of xenon trailing along the wall of the tube. The other wall is obscured by a grid...... 71

4.16 Blow-up of one cell of the four-strip framing camera data from April, 2004, shown in Figure 4.13. This image uses a plastic driver in xenon gas, backlit with a vanadium source. This cell, in the fourth column, second row as measured from the lower left corner of the image, at time t = 15.4 ns ...... 72

4.17 CAD drawing of dual radiography setup. Pinhole and area backlighters were 80 or 100 degrees apart, imaging areas of the tube separated by approximately 1 mm at diﬀerent times relative to the drive beam pulse...... 73

4.18 Raw single-strip framing camera data, washed out by high-energy noise. Notice signal outside of the active area of the microchannel plate. The bright strip present in the center of this image was present on other pieces of single-strip framing camera data taken in the dual radiography setup. On some pieces of data that were washed out, a faint image of the grid on the target is still visible...... 74

4.19 Unusual data. This data was recorded 9 ns after the drive beams turned on, and does not show the normal thin, dense layer of xenon showed in most data images. . 75

x 4.20 Unusual data. This piece of data showed an exaggerated tilt of the collapsed layer from the target axis. Dotted lines show the deviation to be about 10 degrees. . . . 76

4.21 Target for experiments using the VISAR diagnostic. Arms through the radius of the target were capped on one end with a quartz window, and on the other with a coated mirror...... 77

4.22 Representative piece of VISAR data. Note the fringes from the interferometer cease before the drive beams turn oﬀ. Also note late time signal with no fringes, corresponding to the passage of the shock through the VISAR path...... 78

4.23 Only VISAR data which showed any fringe shift. The total signal length was approximately 2 ns...... 79

5.1 Darkest radiographic image and horizontal lineouts showing intensity. a) Shot 40706, taken at t = 20 ns with a 40 µm thick drive disk. This piece of data had the lowest relative intensity measurement taken. b) Horizontal lineout of the the shock. The lineout is taken over the center 400 µm of the shock, with the x-coordinate given in the ﬁgure. c) Horizontal lineout of the grid. The lineout is taken over 60 µm. The valleys of the grid wires in the image are not well resolved, as shown by the lack of a ﬂat feature at the lowest transmission point...... 82

5.2 Two images showing shot to shot variability in the data, taken at 10 ns ± 0.25 ns. Sources of the variability are discussed in the text. a) Shot number 37033, using a 38 µm drive disk. b) Shot number 37034, using a 44 µm drive disk...... 84

5.3 Plot of position data from experiments using 20 and 40 µm thick drive disks, and from simulations of those experiments using a 1D radiation hydrodynamics code HYADES. The simulations overestimate the shock position for both drive disk thicknesses, seemingly from an error in the ﬁrst few nanoseconds of the experiment. The experimental data also hints that at a late times the shock may slow, possibly from the loss of a signiﬁcant driving force from the beryllium piston...... 85

5.4 Plot of imaged thickness of dense collapsed xenon as a function of the distance the shock has traveled. Data are shown as points, with the position error bar from uncertainty estimates from metrology, and the thickness error bar from uncertainty from the density at which the collapsed layer “begins”. Though the data shows a general trend towards thicker shocks as more ground is covered by the shock, this measurement is highly susceptible to overestimating the thickness of the shock due to slight departures from perfect side-on imaging. Note that only one data point lies on the simulation curve, and the rest for both drive disk thicknesses lie well above. This eﬀect is some combination of imaging a tilted shock and radiation treatment in Hyades, discussed in the next chapter...... 87

5.5 Images of shock from shot 39927, t = 14.6 ns launched with a 20 µm beryllium driver. a) Calibrated data smoothed over a resolution element. b) Image smoothed over 200 µm, subtracted from original image, then once again smoothed over a resolution element. c) Image smoothed over 100 µm, subtracted from original image, then once again smoothed over a resolution element. Notice how smoothing over a shorter distance emphasizes the darkest parts of the shock, showing that the shock image is actually somewhat knotted...... 89

xi 5.6 Images of shock from shot 38983, t = 15 ns using a 20 µm beryllium driver. a) Calibrated data smoothed over a resolution element. b) Image smoothed over 200 µm, subtracted from the original image, and smoothed over a source-limited resolution element. Smoothing in this image seems to enhance the contrast between the shock and the surrounded gas. Structure emerges in the smoothed image, as well, on both the front and back sides of the image. These structures are larger than a source-limited resolution element. The white pixel near the top edge of the shock is a dead pixel smoothed over a resolution element, showing the size comparison. . 90

5.7 Images of shock from shot 39925, t = 4 ns using a 10 µm beryllium driver. a) Calibrated data smoothed over a resolution element. b) Image smoothed over 200 µm, subtracted from the original image, and smoothed over a source-limited resolution element. In these images, the light and dark diagonal stripes are scratches on the ﬁlm. While some structure emerges in the smoothed image, the front side of the shock is obscured by a scratch...... 91

5.8 Images of shock from shot 40706, t = 20 using a 40 µm beryllium driver. a) Calibrated data smoothed over a resolution element. b) Image smoothed over 200 µm, subtracted from the original image, and smoothed over a source-limited resolution element. This image shows quite a bit of structure, and shows the largest features on the front side of the shock...... 92

6.1 2D diagram of the target used in the Thomson scattering measurement of the driven radiative shock. It is very similar to the target discussed for earlier experiments, with an extra arm and inlet and outlet holes for the probe beam and scattered light diagnostic...... 98

6.2 Metrology photos of targets used in Thomson scattering experiments...... 99

6.3 Streak camera image of collected scattered light data from TS experiment. Early in time, the detector captures light from the destroyer beam blowing oﬀ the cover on the target that points towards the collection diagnostic, which then fades. A short time later, the characteristic two-peaked spectrum of collective Thomson-scattering behavior appears...... 101

6.4 Results from atomic models, giving Z and ZTe as a function of Te...... 105

6.5 Best fit and error bars to Thomson scattered data. a) Lineout from data (purple) and best fit to data (black), with Ti = 300 eV, Te = 250 eV, and Z = 13.7, based on average atom model. b) Lineout (purple, solid) and Te error bars from fluid limit. Dashed line is Ti = 300 eV, Te = 285 eV, Z = 14.2. Dotted line is Ti = 300 eV, Te = 215 eV, Z = 13.2. These lines obviously lie well outside the lineout of the data. c) Lineout (purple, solid) and Ti error bars from fitting the data. Dashed line is Ti = 500 eV, Te = 250 eV, and Z = 13.7, while the minimum of the ion temperature is the same as the minimum of the electron temperature. That curve does not lie significantly outside the data points...... 106

7.1 Two 1D hyades simulations of density. The solid line shows the density proﬁle of a beryllium-driven shock in xenon using a multigroup treatment of radiation. The vertical line shows the boundary between these two materials, with the xenon feature being the rightmost dense feature. The dashed line shows the same experimental setup in a Hyades run with radiation transport turned oﬀ. Again, the vertical line shows the boundary between the driving beryllium plasma and the xenon plasma...... 112

xii 7.2 Proﬁle of radiatively collapsed layer in xenon gas. This simulation was done with a 20 µm beryllium drive disk in 1.1 ATM of xenon. The solid line is mass density, the dashed line is ion temperature, and the dotted line is electron temperature. The spike in ion temperature marks the position of the shock front...... 114

7.3 Formation of a collapsed shock in the ﬁrst few nanoseconds after the drive beams turn on. Note the diﬀerent peak density of collapsed plasma, which is the rightmost dense feature for each plotted curve...... 115

7.4 Density proﬁles from multigroup simulation at three times for a shock launched with a 40 µm drive disk. Note that as the shock moves farther, the thickness of the shock increases, and the maximum density decreases slightly...... 116

7.5 Density proﬁles from three multigroup simulations at the same time, 10 ns after the drive beams turn on. Each simulation used a diﬀerent thickness of drive disk, pictured from left to right on the plot, 40 µm, 20 µm, and 10 µm...... 119

7.6 a) Density and b) velocity proﬁles at 6, 12, 18, and 24 ns after the drive lasers turn on for an experiment using a 20 µm thick beryllium drive disk...... 120

7.7 Density simulation in two dimensions using the FCI-2 code at 8 ns after the drive beams turn on. The shock moves from left to right. The leftmost dense feature is the beryllium pusher, separated by a low-density region from the rightmost dense xenon feature. The coloring of the graph reﬂects the density expressed in units of the initial xenon gas density. Peak compression of the xenon gas is 45 times over initial density...... 123

7.8 a) FCI-2 density proﬁle at 8ns, shown also in Figure 7.7. b) Simulated radiograph from data in that 2D density proﬁle. This simulated radiograph shows an image of the collapsed xenon layer slightly thicker than that shown in the simulation, approximately 50 µm thick...... 124

7.9 Data points are experimentally measured positions of the beryllium/xenon interface for experiments using a 20 µm thick drive disk. The lines represent interface positions in simulations with full laser intensity and scaled laser intensities. The laser intensity must be reduced by approximately 25% to match the data...... 127

7.10 Simulations of laser driven beryllium into 0.006 g/cm3 helium gas. These simulations are identical to simulations done of the experimental setup described, except using a weakly radiating fluid. Solid lines are simulations with diffusive multigroup radiative transport, while the dotted lines are simulations with radiation artificially suppressed. Note the marked difference in the density profile of the beryllium at 10 ns between the two simulations...... 129

7.11 Multigroup simulations of a beryllium disk driven into xenon (solid lines) and helium (dashed lines). At 2.5 ns, the difference in the beryllium structure and interface position between the two simulations is minimal. By 10 ns, the difference in the structure of the beryllium is quite different. At this time, the beryllium/xenon interface has moved 250 µm further than the beryllium/helium interface. The beryllium in the xenon simulation at this time also has significantly more material to the right of the density peak, suggesting flow of beryllium ablated by the xenon radiation source...... 131

xiii 7.12 Multigroup simulations of a 20 µm beryllium disk driven into argon gas at 1.1 ATM (1 mg/cm3)...... 133

7.13 Multigroup simulations of a 20 µm beryllium disk driven into argon gas at 1.1 ATM (1 mg/cm3), showing mass density, ion temperature, and electron temperature. . . 134

8.1 Optical depth and mass proﬁles from 1D simulation of the supernova explosion of 1987a Most of the mass is within the inner 350 zones. Optical depth is calculated from the surface (zone 500) inward, and 22 zones are at an optical depth less than 1. The rise in optical depth in zone 40 marks the location of the shock front. From Ensman and Burrows, 1992...... 140

8.2 Temperature and mass density profiles from (a) Ensman and Burrows, 1992 and (b) 1D radhydro simulations of driven radiative shock experiment in xenon. While the scales are different, both the density and temperature profiles are qualitatively similar. Note the spike in temperature, followed by rapid cooling and a significant increase in the density in a thin layer. This similarity will last until the supernova shock moves into a regime where the material behind the shock becomes optically thin, farther away from the exploding star...... 141

8.3 Shock structure from computational analysis of a radiative shock in a stellar atmosphere. The solid line structure was adopted for analysis of the temperature and density structure in the radiative wake. From Fokin et. al, 2004...... 142

8.4 Temperature, mean molecular weight, and mass density proﬁle of a stationary shock in a stellar atmosphere. The x-axis is the distance from the shock front. The vertical line marks a change in scale, as quantities change more slowly farther from the shock front. From Fokin et. al, 2004...... 143

8.5 Eﬀect on cooling rates from diﬀerent contributions. This log plot gives both heating and cooling of the system, with zero on the y-scale corresponding to no heating or cooling. From Fokin et. al, 2004...... 144

8.6 Calculated cooling rate from experiment in xenon. Radiation was assumed to be thermal radiation from the cooling layer in the shocked plasma. This plot is in similar units to the cooling rate of Fokin, with cooling rates reported as negative. a) Cooling proﬁle of most of the experiment, including beryllium driver. b) Cooling proﬁle of just xenon, near the shock front...... 145

8.7 Targets for new generation of radiative shock experiments. Targets are gas tight with view up the back end of the target into cylinder. A large acrylic shield with gold wedges facing the diagnostics surrounds the drive surface. a) Three-D CAD image of target. b) Shadowed image of target prototype roughly positioned in the Omega chamber...... 149

xiv LIST OF TABLES

Table

2.1 Comparison of experimental quantities in Reighard et al. and other recent radiation hydrodynamics research. Reighard et al. produces the fastest, hottest shock in the highest density xenon gas...... 27

3.1 Target feature tolerances as a function of shot day. Items listed as unknown were either not measured (if built at U. MI) or had no measured details on the document accompanying ﬁnished targets (if built at LLNL)...... 34 C.1 Table of facility setup at the Omega laser facility for each shot day...... 163

C.2 Summary of all shots taken on the August, 2005 shot day. See table of acronyms for more details...... 164

C.3 Summary of all shots taken on the May, 2005 shot day. See table of acronyms for more details...... 165

C.4 Summary of all shots taken on the February, 2005 shot day. See table of acronyms for more details...... 166

C.5 Summary of all shots taken on the August, 2004 shot day. Much of the data on this shot day were victim to dual radiography washout (see Chapter Four). See table of acronyms for more details...... 167

C.6 Summary of all shots taken on the April, 2004 shot day. Much of the data on this shot day were victim to dual radiography washout (see Chapter Four). See table of acronyms for more details...... 168

C.7 Summary of all shots taken on the November, 2003 shot day. This shot day produced no usable data. See table of acronyms for more details...... 169

C.8 Summary of all shots taken on the July, 2003 shot day. This shot day produced no usable data, and was the ﬁrst day that used University of Michigan. See table of acronyms for more details...... 170

C.9 Summary of all shots taken on the December, 2002 shot day. Though the ﬁll gas was xenon on this day, a tin backlighter was used. See table of acronyms for more details...... 171

C.10 Summary of all shots taken on the August, 2002 shot day. This was the ﬁrst shot day for the radiative gas experiments. Laser energy information both in an online archive and personal notes is unavailable. See table of acronyms for more details. . 172

xv C.11 Target feature tolerances as a function of shot day. Items listed as unknown were either not measured (if built at U. MI) or had no measured details on the document accompanying ﬁnished targets (if built at LLNL)...... 173

C.12 Acronyms used to describe radiative shock experiments, both in the above tables and in the text...... 173

xvi LIST OF APPENDICES

Appendix

A. “Observation of collapsing radiative shocks in laboratory experiments,” [43]. . . . . 151

B. “Thomson scatttering from a shock front,” [44]...... 157

C. Shot data, diagnostics, and metrology tolerances ...... 161

xvii CHAPTER I

Introduction

With the development of lasers to advance fusion technology, a tool became accessible with which to take a step beyond observation of stars, and move to creating controlled experiments with ramiﬁcations for astrophysical systems. The types of experiments capable of extending our understanding of the most dynamic and energetic processes in the universe are getting broader at a rapid pace.

This thesis involves physics in the specific subfield of high energy density physics, with an eye towards future applications to laboratory astrophysics. High-energy- density laboratory astrophysics is a relatively new field, using the tools of plasma physics and fusion energy studies to understand astrophysics problems in the high- energy-density regime. This first chapter will provide a general introduction to high- energy-density physics, present some examples of high-energy-density astrophysical phenomena, and list some of the tools used to address the specific field of high- energy-density physics. The second chapter will treat the physics of radiation hydrodynamics, including a causal explanation of the formation of a radiative cooling layer and collapsed shock. We will describe the experiment setup, the laser facility, target fabrication, and diagnostics used in Chapter Three. The fourth chapter covers results from experiments, while Chapter Five focuses on analysis of radiographic

1 2 data. An additional experiment using Thomson scattering techniques is described in Chapter Six. Chapter Seven is devoted to discussion of simulation work in one- and two-dimensional radiation hydrodynamic codes done for this experiment. In

Chapter Eight, we discuss the conclusions we can make from this experiment, draw attention to astrophysical systems with similar optical depth proﬁles, and discuss the experiment’s future in upcoming campaigns.

1.1 High-Energy-Density Physics

High-energy-density (HED) physics is defined as the physics that happens at pressures greater than 1 million atmospheres, usually involving shock waves moving through a medium over a wide range of densities. In different units, this is a pressure of 1 Mbar, 1011 Pascals (N/m3), or 1012 ergs/cm3. The preferred unit in this field and this thesis is a Mbar, where 1 bar = 1 ATM.

In these high-pressure systems, which are often also marked by high temperature and/or high density, the material in question is ionized, and therefore does not behave like an ensemble of neutral particles. By high density, I am referring to densities that can be much higher than those covered by traditional plasma theory. These densities can reach a few times solid density, on the order of 1 g/cm3. By high temperature,

I’m referring to temperatures as high as several kilo-electron volts (keV). At these temperatures, even low-density material can support pressures of 1 Mbar.

1.2 A Brief History of HED physics

One of the ﬁrst paths of high-energy-density physics research pursued simulation and understanding of the nuclear bombs tested in the United States in the 1940s.

While the physics that happened in those explosions was most certainly in the high- energy-density regime, the focus in these tests was not a controlled scientiﬁc exper- 3 iment. Adding control and diagnosis to the creation of high-energy-density systems happened decades later. While work began towards fusion and high-energy-density experiments in the 1970s, it was not until the 1980s that many of the modern diagnostics were capable of recording relevant information (such as images, time histories, or spectra) on a sub-nanosecond timescale. This decade also saw the advent of facilities with independently controlled and timed lasers, a crucial component in many modern HED experiments [13]. A more complete review of radiation hydrodynamics experiments is given in Chapter Two.

1.3 Laboratory Astrophysics

In the mid-1990s, high-energy-density physicists begin to turn their attention to astrophysical problems. At the ﬁrst “Workshop on Laboratory Astrophysics Exper- iments with Large Lasers” in 1996 hosted by Lawrence Livermore National Lab- oratory, astrophysicists weighed in on the areas that could beneﬁt from controlled, scaled experiments. At about this time, a wealth of x-ray data was imminent from the

Chandra satellite, probing phenomena where hydrodynamic quantities were affected by radiation transport. From this, among other things, astrophysicists asked for more controlled experiments involving radiation hydrodynamics. Study of radiation hydrodynamics in a controlled environment would aid in both basic understanding of radiation hydrodynamics (rarely seen and not much studied in Earth-based systems), and give a benchmark as more and better radiation treatment was added to astrophysics codes. Challenges associated with meeting these scientific needs are discussed in Chapter Two and briefly in Chapter Eight.

This request is not unusual, when one considers how many astrophysical systems involve radiation hydrodynamic phenomena. High powered explosions, fast shock 4 waves, and low astrophysical densities make it easy for radiation to play a signiﬁcant factor in the heating, cooling, and dynamics of an astrophysical system.

For example, old supernova remnants like the Cygnus Loop, shown in Figure

1.1, can radiatively collapse into a thin shell, making them susceptible to thin-shell instabilities, which is one possible origin of clumpy, irregular structure in supernova remnants.

Figure 1.1: Hubble Space Telescope picture of the Cyngus Loop. False coloring shows diﬀerent metal line emissions. Credit: NASA, HST, Jeﬀ Hester.

Astrophysical jets at high speeds can cool signiﬁcantly through radiation. This cooling lowers their internal pressure and causes increased compression along the axis of the jet, resulting in increased density and collimation of the jet. This phenomenon is generally seen in high mach-number jets, which have ﬂow speeds much larger than their internal sound speed.

Supernova explosions also go through a radiation hydrodynamic phase at least until the shock breaks out of the denser layers of the star. Of speciﬁc relevance here, a simulation of shock breakout in SN 1987a shows the formation of a radiatively 5 collapsed shock [17] This and other relevant examples are discussed in Chapter Eight.

Figure 1.2: Hubble Space Telescope image of SN 1987a, taken in 2003 with WFPC2. Here, a ring of circumstellar material lights up as the shockwave driven by the explosion heats it. Image credit: NASA and R. Kirshner.

An obvious problem exists to the unschooled observer: the evolution of astrophysical phenomena often involve vast distances, large total masses, and long time scales. Making exact replicas of these systems is impossible, even if the power were available in advanced facilities.

Fortunately, it is not necessary to replicate a system in its full size and scope to study one a specific part of the phenomenon. As shown in Ryutov (1999) [45], equations describing the hydrodynamic evolution of a system can be scaled in space and time if radiation flux, viscosity, and heat flow can be neglected. Therefore, studying a specific phase or part of an astrophysical object or event can be possible on smaller length scales and shorter time scales if other factors are scaled as well.

When radiation flux becomes important, this scaling becomes complicated. While exact comparison to an astrophysical system is no longer possible, meaningful com- parisons are still possible. In these systems, comparison of the optical depth structure reveals systems that can be described by similar physics. If the optical depth profile 6 of two systems is similar, radiation should have similar effects in each. The other important parameter is the appropriately normalized rate of radiative emission. In the present context this is related to the strength of the shock wave. This is discussed in further detail in Chapter Two.

1.4 Tools of the Trade: High-Energy-Density Facilities

Though the scope and scale of these experiments can be many orders of magnitude smaller than their astrophysical counterparts, it still takes impressive facilities to generate the power and intensity needed to create megabars of pressure in a controlled environment. So before we discuss the physics involved in these experiments, let us brieﬂy review some of the facilities available for high-energy-density physics experiments.

Most of the laser facilities listed below focus on the study of laser-driven fusion.

This problem is approached in two ways: direct drive and indirect drive. Direct drive laser fusion involves irradiating a spherical capsule directly. This direct irradiation causes the capsule to implode, creating the compression needed to cause the internal fuel to ignite and burn. This method is hampered by the growth of non-spherical structure through hydrodynamic instabilities, which reduces the energy gain. Indi- rect drive laser fusion focuses the laser energy on a high-Z cylinder (usually gold).

A spherical, fuel-containing capsule is placed at the center of this cylinder. The lasers heat the cylinder (called a hohlraum), which then emits radiation that compresses the target. This method creates fewer instabilities than direct drive, but is less eﬃcient. 7

1.4.1 High-powered laser facilities Laboratory for Laser Energetics and the Omega laser facility

The Omega laser facility at the University of Rochester is a 60 beam neodynium:glass laser, operating at λ = 351 nm. It is capable of delivering a total of 30 kJ at 30 terawatts of power using all 60 beams, which are oriented symmetrically around the target chamber. Omega was designed to implode inertial fusion targets via direct drive, where lasers directly implode a caspsule [5].

Recently, work has begun to add a high-energy pettawatt laser system next to the main Omega laser system. The Omega EP (extended performance) laser will add two short pulse beams (pulse lengths of 10-100 ps), with energy of 2.6 kJ/beam.

These beams can provide focused intensities of up to 6 ×1020 W/cm2 for fast ignition experiments and ultrafast backlighting.

Naval Research Laboratory and the Nike, Electra and FTF laser facilities

The Nike facility at the Naval Research Laboratory is a KrF eximer laser facility

(λ = 248 nm), delivering several (3-4) kJ of energy to a target in 56 beams. The

Nike laser was designed for testing of hydrodynamic behavior relevant to direct-drive fusion targets, and boasts a very uniform beam spot; this is ideal for fusion targets, in which a hot spot on the beam can severely limit the eﬃciency of the compression.

The 700 J Electra facility at the Naval Research Laboratory is a testbed for high- repetition rate laser technology. It has been successfully tested for operation at 5 Hz for several thousand shots, and for longer duration at lower repetition rates. High repetition rates are vital to the application of fusion power to power plants.

The Naval Research Laboratory has also proposed the building of a high-repetition- rate KrF facility for direct drive fusion (where fusion fuel capsules are irradiated directly with the lasers), with the hopes of using it as the ﬁrst fusion power plant, 8

Figure 1.3: Diagram of the planned laser facility at the Naval Research Laboratory in Washington, D.C 9 called the Fusion Test Facility, or FTF [42]. This facility would have a 5 Hz repetition rate, and would be dedicated to creating the maximum amount of fusion power with minimum laser power requirements. This is the ﬁrst facility to focus on creating a commercial-grade fusion power plant.

Lawrence Livermore National Laboratory and the National Ignition Facility

The National Ignition Facility (NIF) at Lawrence Livermore National Laboratory is the newest addition to this set of facilities. Though it is not yet fully operational, with 192 lasers, the facility hopes to achieve 1 MJ of UV light on target by FY

2008 [25]. Delivering 500 terawatts of power to millimeter scale fusion targets, NIF will be capable of both direct and indirect drive fusion experiments, and help forge new paths into research of processes applicable to astrophysics. The technological advances required to complete this facility at a reasonable cost were numerous, and tested on prototype of four lasers called “Beamlet” in the early parts of this decade.

Figure 1.4: Outside of the NIF target chamber. Square protrusions are where bundles of four beams, called quads, will enter the target chamber. 10

Figure 1.5: Beampath of one of the NIF beams.

Laser MegaJoule and LULI

CEA in France is also building a very large laser facility in Bordeaux, call Laser

MegaJoule, or “LMJ”, which will be just about as large and powerful as the NIF facility at LLNL. It is currently under construction, and expected to be ﬁnished in 2010. It will have 240 lasers, and is designed to deliver 1.8 MJ of UV light on target [9]. The eight-beam cluster “Ligne D’Integration Laser”, or “LIL” became operational in 2003 to test the technology developed for this facility.

Currently in operation in France is the Laboratoire pour l’Utilisation des Lasers

Intenses, or “LULI” facility. This facility has two laser beams delivering a total of

2 kJ of UV light to a target. There is also an ultrafast laser facility housed here, delivering 30 J in 0.3 ps in its main laser, with other, short-pulse lasers that are less energetic. These lower-energy beams are used for diagnostics.

1.4.2 Z-pinches

The Z-machine at Sandia National Laboratory in Albuquerque is unique on this list in that it is not a laser, but a Z-pinch machine. Running currents through parallel wires forces them to implode, leading to stagnation on the cylindrical axis or delivering an impact to a target situated inside of the wire cluster. The Z-machine can produce 1.8 MJ of x-rays and draws tens of MA of current. In 2003 it became the

ﬁrst Z-pinch facility to create and diagnose the production of thermonuclear fusion 11 neutrons from the implosion of fuel within a hohlraum. At the time of this writing, it is currently undergoing an upgrade aimed at delivering even higher currents and voltages ([38]). Other Z-pinches are located at Cornell University in Ithaca, NY,

Imperial College in the UK, and University of Nevada, Reno.

Figure 1.6: Cutaway schematic of the Z-machine’s latest upgrade, now referred to as Z-R. Implo- sions happen near the axis of this large cylinder.

1.4.3 Petawatt Lasers

As ultrafast lasers are built with higher energy output, the power output in short

pulses also increases. It is possible to generate petawatts or terawatts of power for

a few picoseconds or femtoseconds. This leads to very high intensities, up to 1022

W/cm2, with these short pulse lasers. With this capability, one can study even

relativistic phenomena in the high-energy-density regime. Ultrafast lasers capable

of creating these conditions include those located in facilities at the University of

Michigan Center for Ultrafast Optical Science (CUOS), at Los Alamos National

Laboratory, Lawrence Livermore National Laboratory, the University of Texas at

Austin [12], and other sites around the world. CHAPTER II

Radiation Hydrodynamics

It is notoriously diﬃcult to achieve controlled radiation hydrodynamic conditions.

Facilities are required to deliver a high laser irradiance or x-ray ﬂux to a small target; enough energy must be present to heat moderate density material to tens of eV.

This must also happen in a system with sufficient optical depth for radiation and matter to interact. If radiation does not significantly affect the system, usually by heating or cooling in laboratory systems, then the system can be treated with purely hydrodynamic equations.

Some of the facilities capable of creating these conditions were listed in the Intro- duction, and the facility used for the experiment that was the focus of this dissertation research, the Omega Laser facility, is described in more detail in the Experimental

Methods chapter.

The radiative hydrodynamic experiments presented in the next chapters focus on creating a radiatively collapsed shock by launching a piston into a gas-ﬁlled target.

This launches a shock fast enough and hot enough to begin to radiate away its energy.

To understand this system and how it diﬀers from purely hydrodynamic systems, let us look at the equations that govern hydrodynamic shocks, and then explore how the inclusion of radiative eﬀects alters them. This leads to a discussion of how to

12 13 scale laboratory radiative shocks to astrophysical ones.

2.1 Single-Fluid Euler Equations

If the mean free path of a particle in a gas is much smaller than the size of the system of particles, it makes sense to treat the system as a ﬂuid, with ﬂuid elements that are much larger than a mean free path of a particle, but much smaller than the system size.

The single ﬂuid Euler equations follow by taking moments of the Boltzmann

Equation, and describe the conservation of mass, momentum, and energy of a ﬂuid: ∂ρ (2.1a) + ∇ · (ρu) = 0, ∂t ∂u (2.1b) ρ( + u · ∇u) = −∇p, ∂t ∂ ρu2 u2 (2.1c) ρ + = −∇ · ρu + + pu , ∂t 2 2 where ρ is density, u is velocity, p is scalar pressure, and is speciﬁc internal energy.

The energy equation here is expressed in conservative form.

These equations are valid in the regime where the viscosity is low, as is the heat conduction, along with the contribution of the radiative ﬂux to the dynamics. These equations admit disturbances in pressure, density,and velocity (and implicitly, temperature) as solutions. When such disturbances move faster than the sound speed

2 (cs = γp/ρ for a polytropic gas), these quantities can become discontinuous, forming a shock wave. Let’s describe how to modify these equations to account for signiﬁcant eﬀects from radiation.

2.2 The Equation of Radiative Transfer and Radiative Hydrodynamics

Though megabar material pressures are impressive, there can be one other source of significant dynamic influence in high-energy density systems. As temperatures 14 increase in these systems, the radiative flux σT 4 becomes comparable to the material

energy ﬂux, and we must consider how the ﬁrst moment of the equation of radiative

transfer begins to factor into our equations. One form of the radiative transfer

equation is:

1 ∂ ∂ (2.2) + I (x, t, n, ν) = η (x, t, n, ν) − χ (x, t, n, ν)I (x, t, n, ν), c ∂t ∂s ν ν ν ν

where ds is the length of a path element, Iν is the mean spectral intensity, which is the energy radiated per unit time-frequency-area-solid angle, in a direction n, ην is the total spectral emissivity (which includes the eﬀects of both absorption and scattering) , and χν is the total opacity.

In these equations, we consider only non-relativistic systems, as in this limit the contribution of the radiation to the Euler equations is relatively simple. In this limit, the contribution of momentum of the system by radiation is negligible. With the exception of some petawatt lasers, this is true of the regimes accessed by all the currently available laser user facilities mentioned in the previous chapter. We need not count photons in the mass continuity equation, so Equ. 2.1a remains unchanged.

The momentum equation (Equ. 2.1b) becomes

∂u (2.3) ρ( + u · ∇u) = −∇(p + p ), ∂t rad where prad is the radiation pressure in the system,

4σ (2.4) p = T 4, rad 3c

and is included for completeness.

If the radiation were not isotropic, one might need to include a pressure tensor

term instead of a scalar. In this regime, the most important quantity is the magnitude

of the radiative flux, Frad, as a term in the energy conservation equation. This 15 quantity is not affected by whether the radiation field is isotropic, though the ratio of radiative flux to radiative pressure may be affected by the isotropicness of the

ﬁeld. Additional forces, such as gravity, would contribute terms on the right-hand side of this equation. To modify the energy equation, we use the conservative form of the energy equation (equation 2.1c), and continue to neglect viscosity. Adding in contributions from the radiative pressure, ﬂux, and energy density, but excluding outside sources of heat,

(2.5) ∂ ρu2 u2 + ρε + E + ∇ · ρu ε + + (E + p + p )u = −∇ · (F ) , ∂t 2 rad 2 rad rad rad where Erad is the radiation energy density, prad is the radiation pressure, and Frad is the radiation ﬂux.

2.2.1 Threshold for Radiative Shocks

Without putting any restriction on the dependence of radiation on density and pressure, we would still like to understand when radiative effects will become important. It is not yet possible to create systems in the laboratory with significant radiative pressure, so we will limit our discussion to shocks where radiative flux levels are important. Systems with megabar radiation pressures may be accessible in the relatively near future by the National Ignition Facility and Laser MegaJoule.

Let us consider a system with a high Mach number shock wave (where the speed of the shock is more than a few times of the sound speed of the unshocked material).

As will be discussed further later in this chapter, shock waves heat and compress material, and a faster shock wave means more heating. When the temperature in a system increases, the blackbody radiation a system would have if it were optically thick increases faster than the energy ﬂux carried into the shock by the material. 16

Let us consider the ratio of the energy ﬂux lost to radiation in an optically thick system at the immediate postshock temperature T to the energy ﬂux carried in by

the material at the shock front:

4 5 σT us (2.6) Rrad = ∝ , ρouscvT ρo

where us is the shock velocity, cv is the speciﬁc heat of the gas, and ρo is the density

of the of the unshocked, upstream material. The proportionality is only true for

strong shocks, where

Am (2γ − 1) (2.7) k T = p u2. B i 1 + Z (γ + 1)2 s

The ratio in Equ. 2.6 depends on the details of the radiative transport to and in the

cooling region. As Rrad approaches and exceeds 1, the system must adjust to allow

the radiation to escape and cool the post-shock region. As temperature goes up, the

opacity of the material typically goes down. The heated region becomes optically

thin, allowing the radiation to escape. The system can then cool, allowing this ratio

to pass below 1, and then again to become optically thick.

This ratio is only strictly valid for material that is optically thick and radiating in

a continuum. If instead the heated material emits from spectral lines, this ratio would

be somewhat less. In an optically thick system, the intensity of these lines would

become maximum at the blackbody level for that temperature, so many lines would

ﬁll in the blackbody curve. In that case, Rrad would still be valid if the numerator of

the ratio included a quantity that accounted for the fraction of the blackbody curve

ﬁlled by emitting lines.

2.2.2 Classiﬁcation for Meaningful Comparison

While the transition region discussed in section 2.2.1 in all radiative shocks spews

photons in all directions (both upstream and downstream of the shock) from an op- 17 tically thin layer, what happens to those photons depends greatly on the material on either side of the shock. Therefore, there can be four diﬀerent types of radiative shocks, where either region can either be optically thick or optically thin. Exam- ples of at least three of these types of radiative shocks can be found in astrophysics.

For example, a thick downstream-thick upstream shock could be found inside the dense layers of a star as a consequence of core collapse. As shocks from core-collapse supernova emerge into lower-density outer layers of the star and low density circumstellar material, the upstream region can become optically thin, and the shock can be classiﬁed as a thick downstream-thin upstream radiative shock. Shocks that emerge from supernova continue through the circumstellar material, and can evolve back to radiative shock after behaving as a Taylor-Sedov type blast wave. Surrounded by diﬀuse material, these radiative shocks are thin downstream-thin upstream. At present, this author has no example of a thin downstream-thick upstream shock, either in astrophysics or in laboratory experiments.

The regime that applies to the experiment discussed in following chapters as well as to the speciﬁc astrophysical systems discussed in Chapter Eight is that of an optically thick downstream region and optically thin upstream material. In this regime, a cooling layer can form that loses energy through the optically thin upstream region, which produces a very thin, dense region we will call a “radiatively collapsed shock”. This situation applies to the experiment discussed in later chapters, as well as thick-thin systems that heat electrons via collisions with shock-heated ions.

2.2.3 Formation of a Cooling Layer and a Collapsed Shock

The following explanation describes the experiment that will be discussed further in the next few chapters. It also describes any collisional system with an optically thin upstream region and an optically thick downstream region. We assume that the 18 optically thin upstream gas is a uniform plasma with constant initial temperature, and that most of the radiation entering this region escapes. This type of system supports a cooling layer, an optically thin transition layer between the upstream and downstream region. Because the unshocked gas is optically thin, radiation from the hot, shocked gas can escape, carrying energy ﬂux with it. As the shocked material cools via radiation, other quantities respond. This can result in a large increase in the compression of the gas over the cooling layer, as explained further below, which we call “radiative collapse.” As the material cools and becomes more dense, the material will become optically thick, and radiation will no longer cool the material eﬃciently.

Compression of the shocked material will stop and ion and electron temperatures will level oﬀ at some post-shock value, marking the end of the cooling layer. It is in this way that the structure of the shock is dictated by the cooling layer; as the layer radiates and heats the upstream gas, the system is being pushed towards a steady state, where the upstream and downstream layers equilibrate to some ﬁnal temperature dictated by the energy output of the cooling layer [13]. Below, we describe the steps causing radiative collapse in a shocked system which is optically thin upstream. A cartoon of the general structure of the mass density, electron temperature, and ion temperature is shown in Figure 2.1.

As a shock moves through a material, it creates a quick jump in pressure, density, and ion temperature, as it accelerates all material. This happens over the course of a few ion-ion mean free paths. Though the electrons are also accelerated, they are heated only slightly, as most of the energy goes into heating the much heavier ions.

Electrons gain energy from collisions with the warm ions, according to

∂T (2.8) ion = −ν (T − T ), ∂t ie ion e 19 e r u t a r e p m e t

, y t i s n e d Position

Figure 2.1: Diagram of general structure of a collapsing radiative shock. After an initial temperature and density jump at the shock front, radiative cooling causes a decrease in electron temperature (which cools the ions collisionally), and a corresponding increase in density. The extent of this layer is dictated by energy balance of the sources of energy into and out of this transitional region, or “cooling layer”.

where νie is the ion-electron collision rate, given by

3 −9 niZ ln Λ (2.9) νie = 3.2 × 10 1.5 ATe

−3 for Te in eV and ni in cm , where ni is the ion density, Z is the average ionization

state, ln Λ is the Coulomb logarithm, A is the atomic weight of the material, and

Te is the electron temperature. The energy lost from each ion goes into heating (on average) Z electrons, so the decrease in ion temperature is proportional to in the increase in electron temperature. Electron and ion temperatures can equilibrate this way. As electrons get warmer, they are capable of radiating away a more signiﬁcant fraction of the energy in the system. The fractional energy radiation rate is given by

νrad;

4 2Frad 2κdρσTe (2.10) νrad = = ρdcvT ρdcvT

In the approximation that T = ZTe + Ti = (Z + 1)Te if Te ∼ Ti, which is true 20 after the collisional temperature equilibriation process, the fractional radiation rate simpliﬁes to

A (2.11) ν∗ = 2.2 κT 3 rad (Z + 1) e

−1 2 in sec for Te in eV and the speciﬁc opacity κ in cm /g, where A is the atomic

weight of the material in amu.

If collisional electron heating happens quickly, this can be treated as a two-step

process. If electron heating happens more slowly, cooling via radiation can begin

before the ion and electron temperature equilibrate. As the electron temperature

changes via radiation, collisions sap the ion temperature, and both the ions and

electrons cool.

As the system cools, conservation equations must still hold, and other quantities

must adjust in response to the lost energy. The pressure conservation equation is

2 2 (2.12) p1(ρ, T ) + ρ1u1 = p2(ρ, T ) + ρ2u2,

where p = ρRTi from the ideal gas equation. The quantity R is the gas constant,

which is

(Z + 1)k (2.13) R = B . Amp

In this equation, Z is the average ionization state, kB is Boltzmann’s constant, A is

the atomic weight of the material, and mp is the mass of a proton. We can use these

conservation equations to predict the eﬀect of radiative loss on compression. Since

the system in question is driven, the pressure is set, and the compression must be

the quantity to respond.

Because the average ionization state Z depends on T , we must estimate it’s be-

havior as a function of Te to estimate the eﬀect of cooling on compression. As a 21 convenient approximation, we can use the Saha equation to get Z as a function of

Te. The Saha equation is only strictly valid in equilibrium systems, as it relies on detailed balance to estimate level populations, which may not be strictly true in the experimental system in question. Z from this equation will be designated Zbal, and is: v u 3/2 !! u Te 1 (2.14) Zbal = 19.7tTe 1 + 0.19 ln − n24 2

24 −3 with Te in eV and n24 is the electron density in units of 10 cm . In this system, equilibration times are shorter than the dominant ionization mechanism, which is by collisions with electrons.

2.2.4 Energy Balance in a Thick/Thin Shock

Figure 2.2: Radiation ﬂow in a thick-thin shock. Radiation at the boundary between the optically thick upstream region and the transition region must be equal, and at must equal twice the ﬂux from the transition region at the shock front on the other side of the transition region.

Consideration of the sources of radiation ﬂux at each boundary yields information

about the structure of the shock transition and the extent of the cooling layer. At the

boundary of the downstream region and the cooling layer, the ﬂux from the cooling

layer ﬂowing into the downstream region must balance the blackbody radiation from

the shock-heated gas ﬂowing into the cooling layer. The cooling layer is optically

thin to this radiation, and so at the boundary of the cooling layer at the shock 22 transition, flux is flowing from the cooling layer, as is the blackbody radiation from the downstream region (see figure 2.2). By noting that at the shock transition there is no contribution to flux from the upstream region, one can find the inverse compression just after the shock transition in terms of the final inverse compression: ρ γ − 1 2γ ρ (2.15) o = + o , ρi γ + 1 γ + 1 ρf

where ρo is the density of matter in the upstream region, ρi is the density of matter

immediately after the shock transition (at the edge of the cooling layer), and ρf is

the density of matter in the downstream region.

The energy supplying the radiated ﬂux comes from the shocked material, and so

the radiation lost from the system must equal the energy ﬂux lost from the cooling

layer. Balancing ﬂuxes results in the ﬁnal inverse compression of the gas: s√ ρ 1 + 8Q − 1 (2.16) o = , ρf 4Q

5 4 where Q = 2usσ/(R ρo), the radiative strength parameter, and R is the gas constant.

This shows that the faster the shock is launched, the greater the compression (ρf /ρo)

of the shocked gas [13].

2.3 A Brief History of Radiation Hydrodynamics Experiments

Extensive work on laser-driven fusion to produce ignition and high gain begin-

ning in the 1970s. Much of the work done in the United States was classiﬁed until

the 1990s, at which point certain elements of the laser-driven fusion program were

declassified. A summary of the declassified work is given by John Lindl, first in a

review paper in Physics of Plasmas [35], and then in greater detail in his 1998 book

[36].

“Directly driven” means that lasers are incident on a target capsule with fusion

fuel at its center, and that the laser energy is used to compress the fuel. In contrast, 23

“indirectly-driven” targets have lasers incident on a high-z material surrounding a target capsule, which creates a radiation source to implode the fusion fuel. Early calculations predicted that laser energies as low as 1 kJ could achieve energy gains of larger than unity [41] on a directly driven bare drop of deuterium-tritium fuel, but that laser energies on the order of 1 MJ would be required for high gain. Later, simulations showed that instabilities grew at a much higher rate in directly driven targets than was predicted, and that hot-electron production and reduced laser absorption also severely hampered successful ignition for lasers in the energy range of

1-100 kJ, and so higher laser energies were required for ignition. Beam quality and uniformity were also issues for early lasers. The challenge of controlling hot electron production prompted a move to shorter wavelength lasers.

Hohlraums produce an environment which must be examined using radiation hydrodynamics. Successes and failures of early hohlraum experiments shaped fusion research in the 1980s. Hohlraums designed to scale to larger ignition experiments were used to assess coupling efficiency, hot electron losses, and parametric instabilities on the largest lasers available, including Nova, Gekko, and Omega. Experiments assessed the value of using a double-shelled target to increase implosion velocity, and found that hydrodynamic instabilities were amplified. The need for more complete diagnosis resulted in extensive research. Advances in laser technology gave higher quality beams which could sacrifice beam coherence for beam uniformity, and when coupled with with overlapping beam spots could produce very uniform illumination.

In 1985, experiments on Nova achieved a hohlraum temperature of 200 eV while maintaining low levels of hot-electron preheat, which refers to heating of the fuel by hot electrons before the target is shocked and compressed. The experiments that followed, along with extensive modeling, investigated beam symmetry control, 24 quantitative Rayleigh-Taylor instability studies, pulse shaping beneﬁts, and drive temperature scaling. Successes in these experiments gave conﬁdence that a larger laser (1-2 MJ) would have a chance for ignition and modest gain.

Scientists from Germany and Japan also began to study indirectly driven inertial fusion, using the Gekko XII laser in at the Institute for Laser Engineering in Osaka,

Japan. In the 1990s, these scientists began to publish work on laser-irradiated gold cavities, which would become hohlraums for indirect-drive fusion experiments. In a series of papers in 1991 and 1992, R. Sigel and coworkers reported on laser-driven radiation hydrodynamics experiments in gold cavities on the Gekko XII laser facility in Osaka, Japan ([48], [49], [40]), and reported initial success creating high levels of radiation in a gold hohlraum. Work built on that, with scientists measuring the x-ray re-emission of materials initially heated with hohlraum x-rays ([19], [16]), and launching high-pressure shocks using hohlraum x-ray sources [37]. These radiation- cavity-driven targets were ﬁelded on the Nova laser [26], and will be used on the

National Ignition Facility [30].

Experiments using complex targets called “dynamic hohlraums” are currently being tested on Z-pinch machines. These targets seek to use the smooth radiation source of a hohlraum in a converging geometry. A cylindrical array of high-Z wires

is imploded onto a low-density foam, with a fuel cell at the center, ﬁlled with a low-

density argon gas tracer for diagnostic purposes. This setup uses the radiation from

the high-Z walls as an imploding radiation source. To ensure uniform heating, the

foam must not be optically thick, but must have enough material present to convert

the radiation to thermal energy. This technique has successfully produced hot dense

capsule implosions [4], and measurable neutron yields [32]. Laser-driven dynamic

hohlraum investigations are also underway, where a xenon-ﬁlled capsule is directly 25 imploded, launching a radiative shock wave in gas surrounding a central fuel cell in a spherically converging geometry.

While radiation hydrodynamics played a signiﬁcant role in the dynamics of these indirectly driven targets, they did not involve radiative shocks. Laser heating in an optically thick shell created very warm plasma, but not a fast-moving shock wave.

One can launch a radiative heating wave without launching a radiative shock, as has been observed in several experiments. Experiments in laser-driven plastic foam showed the presence of a supersonic heat wave through a radiogram of an ionization front [1]. A laser-driven shock experiment in foam which inferred a temperature profile from K-shell absorption spectra produced significant amounts of radiative preheating [24]. A radiation wave, or Marshak wave [54], was detected diffusing through a radiatively heated foam that was a few optical depths in extent in experiments by

Back et al. ([3], [2]). Bozier [7] saw evidence of a radiation wave in xenon gas.

Work on radiative shocks in the literature generally focus on one of two types of radiative phenomena. The ﬁrst is that of a radiative blast wave in a low-density gas, where a strong shock is launched in gas, but not driven after the initial laser pulse.

The second launches a strong shock, driven or not, and studies the behavior of a radiative precursor in the unshocked gas. The threshold shock velocity for creating a radiative precursor is lower than the threshold for creating a radiatively collapsed shock.

Blast wave studies were generally done in xenon gas. Shigemori [47] launched cylindrically divergent shock waves in xenon gas, which showed signs of increased density and a radiative precursor. In 1999, Budil et. al [8] suggested that the

Petawatt laser facility at the University of Texas could be used as a radiation hydrodynamics testbed, and speciﬁcally suggested supernova blast wave experiments. 26

Experiments to reproduce and reanalyze the Shigemori results, discussed by Edwards et al. [15] produced us ∼ 8 km/s in a cylindrical blast wave produced with an ul-

trafast laser, and observed radiative cooling eﬀects that resulted from heating of the

shocked gas by electron heat conduction. Experiments by Hansen et al. showed the

formation of a second shock wave ahead of a quasi-spherical radiative blast wave in

xenon gas ([22], [23]).

At higher us, experiments can exceed the threshold for the formation of a thermal

radiative precursor, in which thermal radiation from matter heated by the shock

itself heats the matter ahead of (“upstream of) the shock. Radiative precursors have

been observed in experiments by Bozier et al. [7], Grun et al. [21], Keiter et al. [27],

and Koenig, Bouquet, and coworkers ([28], [6], [39], [50]). The experiment of Grun

et. al. produced a quasi-spherical radiative blast wave, in which radiation during

the shock transition is calculated to play a key role [29]. Experiments by Edens et

al. [14] in nitrogen gas studied the polytropic index of shocked gases, which could

play an important role in linking the Grun experiments to the Vishniac instability

([51], [52]).

This dissertation research revolves around an experiment that is performed in

xenon gas, like many of these experiments, but at a higher density. These experiments

are of a shock driven by an ablatively-launched piston, and so will not evolve like

a blast wave, which is the focus of many of these studies. While some diagnostics

performed on the experiment conﬁrm the existence of a precursor, the propagation

and evolution of that radiative precursor is not the main radiation hydrodynamic

eﬀect studied. The experiment discussed in the next few chapters is that of a driven,

radiatively collapsed shock wave in xenon gas. In this experimental setup, a very

fast (i.e., strong) shock in launched in 6 mg/cm3 xenon gas, in a planar geometry. 27

This shock heats the gas to very high temperatures (∼ 250 eV), and the gas radiates away a signiﬁcant amount of energy. The gas then becomes highly compressed as a response to this energy loss, as explained in earlier sections of this chapter. The shocks in these systems are much faster and hotter than the shocks reported in prior contemporary research in xenon. Very fast, hot shocks are launched in the case of a dynamic hohlraum in CH foam, but much faster, hotter shocks are needed to make CH radiative [13]. For comparison, the experimental conditions reported in this dissertation are compared with results in Hansen et al. [22], Edwards et al. [15],

Grun et al. [21], Keiter et al. [27], Koenig et al. [28], and Bailey et al. [4] in Table

2.1.

Geometry Shocked Initial Den- Shock Ve- Estimated Material sity locity peak Te Reighard et al. Driven, pla- Xenon gas 6 mg/cm3 <100 250 eV nar km/sec Hansen et al. Spherical Xenon gas .07 10 5 eV blast wave mg/cm3 km/sec Grun et al. Spherical Xenon gas .04 10 none re- blast wave mg/cm3 km/sec ported Edwards et al. Cylindrical Xenon gas .2-2 8 km/sec 1 eV in pre- blast wave mg/cm3 cursor Keiter et al. Planar SiO2 aero- ∼10 70 30 eV in pre- gel foam mg/cm3 km/sec cursor Koenig et al. Planar Xenon gas .5-1 40-80 15-20 eV in mg/cm3 km/sec precursor Bailey et al. Cylindrical Tungsten 14 mg/cm3 350 220eV into CH km/sec foam

Table 2.1: Comparison of experimental quantities in Reighard et al. and other recent radiation hydrodynamics research. Reighard et al. produces the fastest, hottest shock in the highest density xenon gas. CHAPTER III

Experiment Description

This chapter is devoted to the description of experiments designed to create and diagnose a driven, planar, radiative shock through a gas-ﬁlled target for observation of the structure of the shocked layer. These designs were modiﬁed from an original design conceived in collaboration with, and constructed at Lawrence Livermore

National Laboratory. As of July 2003, target speciﬁcation and modeling, including

2D building schematics and 3D CAD models, were done by me and built by the

University of Michigan Target Fabrication team. An example of a 3D CAD diagram of the target is shown below in Figure 3.2. Target design and modiﬁcation were done collaboratively between the target fabrication team and myself.

The U of M target fabrication and metrology facility was built and managed by

Korbie Killebrew Dannenberg, under the supervision of Paul Drake, and is currently managed by Michael Grosskopf. It consists of 11 motorized stages with µm precision.

These stages are arranged into two separate coordinate systems; one set of stages is used for holding and positioning a target, while the second set of stages is used to hold and position a target component while it is aﬃxed to the main target. The fabrication process is aided by the use of three orthogonal viewers. Pictures of the system and clean room surrounding it are shown in Figure 3.1.

28 29

Detailed pre-shot target characterization, or “metrology”, was done by me for each target for the purpose of accurate positioning of the target in the Omega Laser facility target chamber. This characterization was also vital in the interpretation of data after the experiment, as each target was destroyed as the shock passed through it. This was done on one set of precision stages also used for fabrication, using two of the three orthogonal views. Measurements were aided by crosshairs on the views, allowing measurements with approximately 25 µm precision. Generally, metrology

measurements included positions of relevant features for data analysis, examination

of targets from diagnostic views, imaging of the target from target chamber viewer

angles, and measurement of angular deviations from nominal.

Figure 3.1: Photos of the University of Michigan Target Fabrication Center. a) System is mounted on an optics table in clean room to minimize dust and debris on optics and in stage mechanics. b) Two sets of coordinate systems aid holding and independently positioning two pieces during fabrication.

3.1 Targets

The basic construction of the target consisted of a planar disk attached to a cylin-

der to form a gas-tight assembly. Other features were added to facilitate diagnostic

use or to speed the alignment process. The basic design and structure of the radiative

gas experiment targets are shown in Figure 3.2. 30

A crucial component was the planar disk, usually made of solid beryllium. In the

ﬁrst experiments, this disk was initially 40 ± 10% µm thick and 2.5 mm in diameter.

The thickness of this disk was varied in later experiments, to 20 ± 10% µm and 10

± 20% µm thick and 2 mm in diameter. This thickness was measured as part of the

fabrication process with calipers, and was known to within 2 µm. It was essential

that this surface be a solid, low-density material, to launch a faster piston for a given

laser ablation pressure. To this end, some early disks were also made with 80 µm

thick polyimide overcoated with approximately 20 µm of PVA. This thickness gave

the same areal density as 40 µm of beryllium, with fewer risks than working with

beryllium.

This disk was centered on a polyimide tube, ID 575 µm, OD 625 µm, and approximately 5 mm in length. The polyimide tube was faced with a microlathe, to ensure a right angle edge on the face upon which the beryllium disk was ﬁxed. This joint was inspected to measure concentricity of the disk and tube on the fabrication system, with measured deviations from concentricity being less than 50 µm for acceptable assemblies by the ﬁnal shot day. A step in the inspection process at this point in the construction ensured that little or no glue from the joint seeped into the target, onto the beryllium opposite the side on which the laser was incident, or the

“driven side.” This would have aﬀected the time of shock propagation through the drive disk, as well as the total amount of material launched by the laser pressure, slowing the initial acceleration of the material into the gas cell. The driven surface of the beryllium disk was also free of any glue.

A gold grid was also placed radially on the target facing an imaging diagnostic as a spatial and magniﬁcation ﬁducial. The separation of the wires on any grid square was 63.5 µm. The total length of the grid was approximately 2.5 mm on most 31

Figure 3.2: 2D schematic of gas-ﬁlled target and 3D CAD drawing of target with attached backlighter foil. targets. Regular, individual features were built into the grid on the side nearest the target tube, giving several points of reference as spatial indicators. These features were hand-cut, by removing wires from individual squares on an edge of the grid approximately every 0.5 mm down its length. Gold was chosen because it is opaque to x-ray photons in the range we discuss for backlighting later in this chapter, and therefore provides a reliably dark feature on data images. When the target was ideally positioned in the laser chamber, this opaque feature blocked little to no area inside the target tube, and by extension blocked little to no data from the shocked material. A metrology photo showing the grid and ﬁducials is shown in Figure 3.3b.

The target assembly was gas tight, with a stainless steel hypodermic tube in the back end for evacuating the target of air and filling the target with gas. The steel tube was fitted with a length of plastic tubing which ended in a voltage transducer. The target was filled through this transducer, which measured the gas pressure inside the target. In this way, the gas pressure of the target could be monitored up until about 32

(a) (b) (c)

Figure 3.3: (a) Metrology photo of target with area backlighter foil attached. Area backlighting is discussed further in section 3.3. (b) Metrology photo of gold grid attached to target. Note notches on the grid near the target body, that served as spatial indicators. In- creasingly large notches were cut farther from the drive surface. (c) Metrology photo of target with no area backlighter attached.

10 seconds before it was destroyed by the laser pulse. Most targets had a gas-leak rate of about 1 torr/minute from a volume nominally at 835 torr, so the 10 second blackout just before the laser pulse lead to a negligible error in the measurement of the gas pressure at the time of the experiment. The leak rate on each target was measured, and targets were overﬁlled to accommodate the time between gas ﬁll and the laser pulse. As a step in the fabrication, targets were pressure tested to up to 4

ATM, which is approximately 3000 torr, to test glue bond strength and leak rates.

Targets were routinely test filled again to more than 2 ATM on shot day, equivalent to 1520 torr. Steel hypodermic tubing blocked the last 0.5 mm to 1 mm of the length of the plastic tube from the diagnostics, so experiments were confined to the first 4 mm of the target as measured from the drive disk position. Two metrology photos of targets are shown in Figures 3.3a and 3.3c.

This target was filled with 99.99% xenon or argon gas. After assessing the leak rate on each target on shot day, it was evacuated and then overfilled to shoot at approximately 1.1 ATM of gas, corresponding to 6 mg/cc of xenon, or 1.5 × 1019 33 atoms cm−3. For targets filled with argon gas, this corresponds to a mass density of 1 mg/cc. This evacuation-and-refill process limited the amount of gas other than the intended gas in the final target. Other gases could have diffused out from the materials in the target, which had been stored in air and previously filled with nitrogen. On shot day, targets were regularly overfilled to accommodate more than an hour of time between fill and experiments, usually amounting to an extra 100 torr of gas over the nominal 1.1 ATM.

Targets at built at LLNL were built by experienced fabrication professionals to a high standard of accuracy. Tolerances on the construction of these targets were inferred from documents accompanying finished targets with final angle and distance measurement of features. When the fabrication was taken over by the staff and students at the University of Michigan, it was not possible to initially build targets to equally high accuracy. As the fabrication team became more adept at building targets and I became more conscious of the need for quality checking, the accuracy of the features of the targets improved. The tolerances for these targets were based on checks done during the build process and during metrology. A list of the tolerances of targets for each shot day are listed in Table 3.1, and can also be found in Appendix

3.2 Lasers

These experiments were performed at the Omega Laser facility at the University of Rochester’s Laboratory for Laser Energetics in Rochester, NY. This 60-laser beam system is capable of delivering up to 30 kJ of laser energy to a target. The laser is a Nd:glass laser operated at its frequency-tripled wavelength, λ3ω = 0.351 µm. The conﬁguration of the lasers at this facility are shown in Figure 3.4a. The full facility, 34

Table 3.1: Target feature tolerances as a function of shot day. Items listed as unknown were either not measured (if built at U. MI) or had no measured details on the document accompanying ﬁnished targets (if built at LLNL). including target bay and capacitor banks, are shown in Figure 3.4b.

Figure 3.4: (a) Diagram of spherical target chamber at the Omega Laser facility. Numbered circles indicate beams, while larger circles numbered with H, P, and TIM labels are ports for both ﬁxed and removable diagnostics. (b) Schematic of beam paths leading through charging banks and into the target chamber. Both images from the National Laser Users Facility User’s Guide.

Ten beams of the 60 total beams of the Omega Laser facility struck the beryllium drive surface of the target, the midpoint of the rising edge of the beam pulse deﬁning t = 0 in the experiment. These beams each had an energy which varied between

350 - 450 J, just below 400 J/beam for most shots. These beams used Distributed

Phase Plates (DPPs) to help smooth them. This involves using a removable optic 35

Figure 3.5: Equivalent target plane images of beams spots integrated over a 1-ns pulse width. (a) An unsmoothed spot of a frequency-tripled Omega beam. (b) Beam spot smoothed with a continuous phase plate. (c) Beam spot smoothed with SSD. From the National Laser Users Facility User’s Guide. that reduces spatial non-uniformities in the far field of the frequency-tripled beams of the facility. This is done by modifying the beam’s near field coherence, changing focusing properties, and shifting energy towards higher spatial frequencies, which can then be rapidly blurred by temporal beam smoothing techniques. This temporal blurring technique is called Smoothing by Spectral Dispersion (SSD), and was also employed to create a more uniform time-averaged irradiance. The relative effect of different smoothing techniques is shown in Figure 3.5.

The beryllium disk was accelerated much like a piston into the xenon gas via laser ablation pressure. Ablation pressure is the consequence of momentum conservation as material is heated and flows away from the target surface. As a drive laser boils off material from a surface, the remaining material feels a force equal and opposite to the flow of momentum from the surface. We can estimate the pressure on the drive surface with a few assumptions. First, we use a flux-limited model for heat conduction from the laser. We also assume that as the material boils off, part of the laser energy goes into heating the lower-density material, while the rest penetrates to the critical surface. In addition, we assume that the full laser irradiance is absorbed 36 by the material, which is a good assumption for UV lasers, but is less accurate at longer wavelengths. The generated ablation pressure is equal and opposite of the √ flow of momentum from the critical surface. If this flow happens at 2 times the

sound speed, as is a common estimate in the literature for a UV-laser absorption

proﬁle [13], then

r r Zk T + 3k T n Zk T + 3k T (3.1) P = 2M B e B i × c B e B 1 . abl M Z M

For typical laser coronae values of Z = 3 and Ti = Te/3 simpliﬁes to

Z + 1 (3.2) P = 2n k T = 8.0I2/3λ−2/3, abl c B e Z 14 µ

where the second equality gives pressures in Mbars. In Equations 3.1 and 3.2, M is

the ion mass, Z is the average ionization state of the plasma (again, approximated

as Z = 3 for the second equality in Equation 3.2), kB is Boltzmann’s constant, Te is

electron temperature, Ti is ion temperature, nc is critical density of the plasma, I14

14 2 is the irradiance on target in units of 10 W/cm , and λµ is the laser wavelength in

units of µm.

In this experiment, the force from laser ablation pressure ﬁrst launches a shock

through the material, heating and compressing the beryllium disk with a strong

shock. Once the shock passes through the thickness of the material, this disturbance

from the laser is then subsonic. This force can then accelerate the bulk of the material

for the remainder of the length of the laser pulse. When the laser turns oﬀ, the

beryllium continues to move with the momentum imparted by the ablation pressure,

with material from the drive side expanding in a rarefaction wave. This accelerated

beryllium drives a strong shock in the xenon gas, as described in the Radiation 37

Hydrodynamics chapter. Radiation from the xenon layer helps drive a supersonic

ﬂow at the boundary between the beryllium and xenon, which can initially outrun the rarefaction wave. As the shock moves through the xenon and builds up more material, the system will slow, and the rarefaction wave will overcome the ﬂow layer.

Eventually, the rarefaction wave will overtake the xenon layer as well, at which point the system is no longer driven by the beryllium plasma.

3.3 Backlighters

An additional, sometimes separate target was necessary to provide x-rays for illumination of the primary target to image the shock. These x-rays were produced by illuminating a thin metal foil with additional lasers. These lasers shocked and heated the metal, producing a hot coronal plasma. Helium-α-like transitions in the

coronal plasma produce x-rays with energy of several keV. The backlighter metal was

chosen such that the emission provided a good contrast on the features of interest.

In this experiment, we wished to see absorption features from dense xenon or argon.

Xenon absorbs eﬃciently in the range of 4.75- 5.3 keV due to L-shell transitions,

while argon absorbs eﬃciently in the range of 3-4 keV. The absorption spectra for

xenon and argon are shown in Figure 3.6 for a volume of cold xenon that is 600 µm

thick and density of 0.06 g/cm3. This density is 10 times the initial gas density in

the target in question. Vanadium has He-α-like emission at 5.2 keV, making the

emission from this metal highly absorptive by xenon. In contrast, the absorption

of this wavelength by both beryllium and polyimide is very low. Therefore, there

were no absorption features on radiography images of beryllium, and the only plastic

visible on these images was the target wall at the very edge of the target, due to limb

darkening. 38

Figure 3.6: Xenon transmission spectrum in the range of 3-8 keV and argon spectum in the range of 1-6 keV, as calculated for cold material.

Two methods were used to backlight the target. On early targets, the method used was called “area backlighting.” Area backlighting used a thin metal foil with large area (usually 4 mm square) which was suspended oﬀ the side of the main target using a metal wire. This foil was hung approximately 4 mm along the radius of the cylinder of the main target. This foil was then illuminated with several laser beams to make a large laser spot on the foil, usually approximately 1 mm in diameter. This created a sea of x-ray photons into 4π steradians, some of which pass through the target. Those x-rays were then passed through a 16-pinhole mask, which created 16 images of the target on a framing camera using a microchannel plate with four active strips, as discussed below. This foil can be seen in Figure 3.1b.

The second method, called “pinhole backlighting”, was developed over the course of this experiment, and is illustrated in Figure 3.7. This method used tantalum as a high-Z substrate to block the x-rays from the illuminated foil except those which passed through a small pinhole in the substrate. This tantalum piece was

5 mm square and 80 µm thick. The pinhole in the center was nominally 20 µm in 39 diameter. A small foil (usually 1 mm square), was placed on one side of the tantalum substrate, centered over the small pinhole in the center of the substrate, offset from the tantalum by approximately 100 µm by a plastic spacer foil. A plastic piece was also placed on the side of the substrate opposite the foil to reduce solid spall launched towards expensive diagnostic equipment. This package was mounted on a separate target, and positioned independently from the main target. Two to six laser beams illuminated the metal foil, which also created a sea of x-ray photons. Those which moved in the general direction of the target were blocked, except those which passed through the pinhole. Those photons that made it through the pinhole passed through the target and were imaged on a framing camera using a single active strip across most of its area. In this way, using a backlit pinhole allowed detection of images that were of much higher magnification. The resolution of the image created by this method was limited by the size of the effective source through the pinhole. The size of the effective source was somewhat smaller than the actual size of the pinhole, as the thickness of the substrate caused vignetting.

A backlighter target schematic is shown in Figure 3.8. Metrology photos are shown in Figure 3.9. When correctly positioned in the Omega target chamber, these targets are placed 12 mm away from the main target, well away from the center of the target chamber. Viewers used to position targets in the target chamber can clearly image features on targets when they are within approximately 4 mm of the center of the target chamber, but objects positioned farther from the center will be out of focus in the viewers. Careful metrology of features that are still well distinguishable even out of focus was used to correctly position the target. In particular, the four corners of the rectangular substrate can still be seen somewhat distinctly, allow for accurate positioning of the backlighter target. For better accuracy, rotational alignment of 40

5 keV x-rays Vanadium-backed pinhole sandwich

Dense shock

Xenon-filled Target Detector

Figure 3.7: Diagram of backlit pinhole backlighting setup, not to scale. In the Omega chamber, with the target at target chamber center, the backlighter target was 12 mm from the target axis, while the detector was 229 mm from the target axis on the opposite side, for an image magniﬁcation of 20. these targets is performed at target chamber center, before positioning in space.

Fabrication tolerances for backlighter targets are listed in Table 3.1.

3.4 Diagnostics

Several diagnostics were used on each shot to gather data and ensure that beams were properly placed on targets. Below, we discuss the primary diagnostics used on shot days. A summary of shot day diagnostics set up as well as laser information is included in Table 2 in Appendix C.

3.4.1 Microchannel Plates and Framing Cameras

The main diagnostic tool used in these experiments was x-ray radiography. Using the backlighting schemes just described, an x-ray source was created and photons were allowed to pass through the main target. On successful shots, dense features in the gas absorbed photons from the source, while x-rays passing through other 41

Target Date Completed Assembler Metrologist

Tin foil: 1mm x 1mm, 5 µm thick Use Omega Mount Ta Pinhole substrate: 5 mm x 5mm, 50 µm thick, 20 µm pinhole CH squares: 2 X 100 µm thick X 2 mm dia. Exposed Ta coated with PVA H2 H2 stalk TIM 6 view 79.20°

Ta substrate

20 µm pinhole on center line foil towards TIM 4

Thickness of total package before adding foil =______µm 1mm

2mm 5mm CH

Ta substrate

Tin foil stalk H2

Figure 3.8: Target schematic for pinhole backlighter target . Measured details for each target are ﬁlled in during fabrication and metrology. 42

Figure 3.9: Metrology photos of pinholebacklighter targets. a) Face-on view of backlighter target. The large rectangle is the 5 mm square tantalum substrate. The dark square seen is a feature on the tantalum, while close inspection shows the 2 mm polyimide square. The dotted-line crosshairs shown are features of the viewing system, and the center of the crosshair is positioned on the 20 µm pinhole. b) XTVS view of backlit pinhole target, imaged in metrology at same angle as one of the cameras on Omega when the target is correctly positioned. features were not absorbed. In this way, important features in the gas were imaged as absorption features.

An x-ray framing camera detected and ampliﬁed x-ray light and converted it to visible light, which was then recorded on a piece of ﬁlm or CCD camera. An x- ray framing camera consists of a gating mechanism, a microchannel plate, and a phosphor, behind which the image recording device is placed. A cartoon showing the setup of these components is shown in Figure 3.10.

When an x-ray enters one of these channels, it may free an electron from the material. This electron is accelerated down the pore by the electric ﬁeld. When the electron hits the wall of the pore as it passes through, it frees more electrons, which are accelerated down the tube, and whose collisions with the pore walls will free even more electrons, amplifying the signal. Eventually, the freed electrons exit the tube in a spray, where they are accelerated towards a phosphor plate. This 43

Figure 3.10: Cartoon of framing camera components. An x-ray source on the right side of the cartoon shines through a target. The photons then hit a microchannel plate, which turns x-ray photons into a cascade of electrons. These electrons are then directed onto a phosphor plate via an applied potential, which emits visible photons upon electron impact. These visible photons are then imaged on film or a CCD camera. The microchannel plate can be coated with a material to increase its gain. Image courtesy Eric Harding. spray of electrons has some finite shape and distribution, and produces a smear of electrons. The voltage applied between the microchannel plate and the phosphor helps minimize the spread of the spot as it travels towards the phosphor. When the electrons impact the phosphor, they release visible photons, which are then focused onto the film or CCD camera situated behind the phosphor.

3.4.2 Velocity Interferometry

Velocity interferometry is an active diagnostic generally used to time shock breakout from a material, or to record the changes in the velocity of a reﬂective surface via the Doppler shift. This is accomplished by recording fringe shifts due to changing optical path lengths of the arms of the interferometer. In principle, any process that 44 changes the optical path length of the interferometer beams will cause fringe shifts, such as a physical change of the path length from a moving, reﬂective surface, or a changing index of refraction along the beam path.

The arms of the interferometer have almost identical beam paths; both arms of the interferometer probe the same physical path (through a plasma or oﬀ of a mirror).

But one arm, referred to below as the “long” arm, passes through an extra optical component called an “etalon”. The etalon has a different index of refraction than the other components of the system, and can vary in length. It is the time difference of the propagation of a disturbance in the system between the arms due to the etalon that causes fringe shifts. In the discussion below, the etalon ranged from 3-30 mm in thickness. Because of this, a VISAR system is sensitive to the rate of change of the optical path, instead of to instantaneous differences in the optical path like a standard interferometer.

If the mirrors in the interferometer are a small angle to the probe beam in the plane of the interferometer, the electric ﬁelds of the two plane waves are

i(ω0t−k1·r) i(ω0t−kx) (3.3a) Ee1 = E0e = E0e

i(ω0t−k2·r) i(ωt−kx cos α−ky sin α) (3.3b) Ee2 = E0e = E0e ,

where kkk = kk1k = kk2k, and α is the tilt of the mirror.

The intensity pattern of the interference of these two beams is

∗ (3.4) I = (Ee1 + Ee2)(Ee1 + Ee2)

2 (3.5) = 2E0 (1 + cos ((k − kx)x − kyy)), 45

where kx = k cos α and ky = k sin α. In the plane of the beam splitter (the y-z plane in this coordinate system), the spatial proﬁle of the intensity is

2 (3.6) Iseparation(y) = 2E0 (1 + cos (ky sin α)) .

This fringe pattern is shown in Figure 3.11.

Figure 3.11: Simulation of VISAR fringes from a steady-state target on a streak camera, where time is the vertical axis and position is the horizontal axis. Image from Forsman, 2001 [20].

If a disturbance in the system aﬀects the phase of the interferometer, the eﬀective change in the frequency of the light in the interferometer is

dΦ (3.7) ω = ω + = ω + Φ0 0 dt 0

0 In this equation, Φ changes slowly compared to 1/ω0. The electric ﬁelds will change:

0 i(ω0t+Φ t−kx) (3.8a) Ee1 = E0e

0 i([ω0+Φ ](t−τ)−kxx−kyy) (3.8b) Ee2 = E0e , 46

In this case, the intensity pattern is

2 0 (3.9) I = 2E0 (1 + cos [ω0 + Φ (t − τ)) τ + ky sin α]

In the short arm of the interferometer, the optical path length L1 at some time t is

(3.10) L1(t) = L1(0) + 2d (n(t) − n(0)) ,

and in the long arm of the interferometer the optical path length L2 is

(3.11) L2(t − τ) = L2(τ) + 2d (n(t − τ) − n(0)) where d is the width of the argon plasma, n is the refractive index, given by

s N (t) (3.12) n(t) = n(0) 1 − e , Nc

Ne is the electron density, Nc is the critical electron density, described in Chapter

Two, and τ is the time delay caused by the etalon. The diﬀerence in these optical

path lengths L(t), given by

2d (3.13) L(t) = L (t − τ) − L (t) = (n(t − τ) − n(t)) 2 1 λ gives a fringe shift, F (t), of

L(t) − L(0) 2d (3.14) F (t) = = (n(t − τ) − n(t)) . λ λ 47

For electron densities much lower than critical density, Ne Nc, the expression

for fringe shift becomes

dn(0) (3.15) F (t) = (Ne(t − τ) − Ne(t)) , λNc so the fringe shift gives an electron density change,

λN (3.16) N (t) = N (t − τ) − c F (t). e e dn(0)

The total phase change (assuming the change in the laser wavelength is small) is

Z t 0 0 2π dL(t − τ) dL(t ) 0 (3.17) ∆Φ(t) = 0 − 0 dt , λ 0 dt dt

where

s dL(t) d Ne(t) n(0)d (3.18) = n(0) ∗ 2d 1 − = Ne(t) dt dt Nc dt

If Ne/Nc is small (we expect it to be less than 1%), then we are left with an expression

for phase change as a function of changing electron density:

dn(0) (3.19) ∆Φ(t) = 2πF (t) = 2π (Ne(t − τ) − Ne(t)) . λNc

This diagnostic was implemented to probe possible density changes in the radiative shock experiments in a side-on setup. A diagram of the target used with the VISAR

(Velocity Interferometry System for Any Reﬂector) diagnostic is shown in Figure

3.12. As the material ahead of the shock was preheated and ionized, we hoped to detect a change in electron density, which would change the index of refraction of 48

Figure 3.12: Target setup for use with the VISAR diagnostic. The shock moves from left to right down the main cylinder, while the interferometer beams pass through the arm perpendicular to the main body tube. the plasma. The VISAR diagnostic at the Laboratory for Laser Energetics, used on the Omega laser system, employs a Mach-Zender style interferometer at small angles using a laser beam with λ = 532 nm. The beam probed a distance approximately 2 mm from the driven surface, radially along the main target axis.

3.4.3 Thomson scattering

Another diagnostic employed on a small number of experiments was a Thomson scattering diagnostic, with the scattering spectrum recorded onto a UV streak camera. The changes in the experimental setup are discussed extensively in the Thomson

Scattering chapter. CHAPTER IV

Experimental Results

The experiment described in the previous chapter has been successfully ﬁelded

on nine separate shot days over the last four years, which includes 4 half-days and 5

full days of shots on the Omega laser. Success of these shot days depended on target

quality and availability, target alignment speed, diagnostic understanding, and laser

performance, among other things.

The bulk of the useable data came from a single-strip framing camera diagnostic,

illuminating a shock in xenon gas by a pinhole backlighter. Some data came from a

four-strip framing camera, in experiments that used either xenon gas or argon gas.

One remarkable piece of data came from a spectrometer coupled with an UV streak

camera, which will be discussed in detail in the Thomson Scattering Experiment

chapter.

Another distinguishing characteristic between pieces of data is the composition

and thickness of the piston launched into the gas to drive the shock. A large fraction

of the data is from either 40 µm or 20 µm thick beryllium drive disks. One piece of data is from a 10 µm beryllium disk. A small amount of data is from approximately

80 µm thick polyethelyne, or thicker (50 µm) beryllium. These characteristics will be spelled out for each reported result in this chapter, and should be noted when

49 50 comparing images whether they are targets of the same type.

Most of the data presented here are from x-ray radiography imaging diagnostics.

Two other primary diagnostics were used over the course of this experimental cam- paign. The ﬁrst, fringe shift data from a VISAR diagnostic, will be discussed at the end of this chapter. The second, spectral data recorded on a UV streak camera, will be discussed in the Thomson Scattering Experiment, which describes in detail the experiment designed to measure a Thomson-scattered spectrum.

Uncertainties on positions in x-ray framing camera images include contributions from metrology measurements and shot day alignment, compounding errors in fabrication. This warrants a separate discussion from that of the discussion of fabrication tolerances in the previous chapter. The uncertainties in the relative x-ray intensities are not important here, because the present work makes no attempt to infer conclusions from the magnitude of the x-ray intensity.

Errors from metrology arise from two sources. The first occurs if the calibration of the azimuthal position of the metrology system is not correct. In this setup, the azimuthal position is the position of the target as it rotates around it’s stalk when mounted in the metrology system. Metrology relies on the definition of angle measurements that correspond to angular locations in the target chamber. To do this, the target must first be situated in a known position, from which we can then define the rest of the locations. The polar coordinate θ was absolutely calibrated

between the two systems, but the azimuthal location φ varied, as the placement of

the target in the target holder varied around the axis of the stalk. For these targets,

we deﬁned φ = 0 to be when the projection of the target axis pointed towards the

front viewer. This was deﬁned by a combination of the ellipse made by the drive

disk, the long axis of which would lie parallel to a horizontal crosshair on the front 51 viewer, and the target body tube, which would lie parallel to a vertical crosshair on the same viewer. Using this method for repeated positioning of the same target in metrology, as was done for several targets, the variation in the azimuthal angle deﬁnition was ∆φ = 0.25 degrees.

The second source of error from metrology was from using a set of crosshairs of

ﬁnite width to make position measurements. Positions of features which were later visible on data images were measured relative to the center of the drive disk. This was done from a view on the metrology system that would be equivalent to the angular position of the collection diagnostic. These features were measured using a set of crosshairs that at the highest magniﬁcation of the system appeared approximately

25 µm thick. While care was taken to measure the features in the same way, such as always approaching the measured feature from the same direction until it was just barely obscured by the crosshairs, this ﬁnite width introduces a compounding ± 25

µm error on all position measurements.

Other sources of error arose in the positioning of targets on shot days. After careful

metrology, each target was positioned in shadow in the Omega target chamber. Main

targets were located with some feature at target chamber center, and so were usually

in focus in the two viewers, named XTVS and YTVS. For early experiments, correct

rotational positioning was achieved using a set of circular reticles imposed on the

YTVS screen. The target was rotated until the main tube lined up on the circles.

Imitating this procedure using a 3D CAD program, the estimated accuracy of this

technique was ± 1 degree. For later experiments, an extra wire was attached to the target for rotational alignment. After correctly aligning the target on the metrology system, the target was rotated until this alignment wire barely touched the edge of the gold grid in the YTVS view, and the rotated angle was noted. On shot day, 52 the target was positioned such that the wire touched the grid in the same view, and then rotated by the measured angle in the opposite sense, so the target was at the correct angle. Again using a 3D CAD program to imitate this procedure, the estimated accuracy of this method was ± 0.5 degrees. This method also proved faster, a signiﬁcant plus on shot days. After achieving rotational alignment, the target was positioned in space using reticles on the drive disk and along the target axis. The estimated accuracy using this method was ± 25 µm.

On all shot days, drive beams were positioned at the beginning of the day and were

left untouched for the day. These beams were precisely positioned by the Omega staﬀ,

and alignment checked using low-powered pulses. The uncertainty on the position

of these beams was very small; much smaller than the uncertainty of the drive disk

position. Backlighter beams were also precisely positioned at the beginning of the

day, but were often moved after a few shots to diagnose a diﬀerent section of the

experiment. The beam termination point was routinely moved a millimeter down the

target axis using a method referred to at the Omega facility as “blind repointing”.

This repointing process introduced an uncertainty that was approximately 20% of

the distance moved, giving a possible error of the position of the beams of 200 µm

at their new position.

Errors from fabrication, metrology, and target positioning compounded into the

errors reported for measurements in collected data.

4.1 Radiographic Image Processing

Framing cameras were used to image absorption features from the driven shock.

As explained in the Radiation Hydrodynamics chapter, a shock that loses a signiﬁcant

fraction of it’s energy can be compressed to much higher levels than normal for a 53 non-radiative strong shock. Backlighter energies were chosen for each ﬁll gas to be highly absorbed by dense features in the gas, and to be transparent to beryllium and plastic, the other main components of the target. Gold is opaque to very high energy, and so was used to calibrate the magniﬁcation and positions of the image.

In these images, a dark feature across the diameter of the shock tube is radiatively collapsed shocked gas layer.

Data images are calibrated using information from pre-shot metrology. Raw, uncalibrated data are shown in Figure 4.1a. In these experiment, the laser pulse that launches the piston into the gas to drive a shock is intense enough to completely destroy the target. When target mounts are retrieved after an experiment, all that usually remains is part of the hypodermic ﬁll tube and plastic hose attached opposite the drive end of the target. Therefore, careful measurements must be made before the actual experiment to help interpret the data. Metrology measurements give the target coordinates of the location of edges of the gold grid mounted on the target (as discussed in the Experimental Description chapter), as well as the features cut into the grid at regular intervals. The origin of the target is measured as the center of the drive disk, which generally aligns very well with the center of the target cylinder.

In the data photos, the beryllium from the drive disk does not appear, as beryllium is transparent at these backlighter energies. However, the edges of the polyimide cylinder are visible on all data images. Polyimide is somewhat more absorptive at these levels, but does not obscure data when looking eﬀectively radially through the

25 µm thick target walls. Only when we approach the target edges in the picture, where we look almost tangentially through the polyimide, can you see noticeable absorption. In all calibrated images, the shock moves from left to right.

Data captured with a single-strip framing camera are smoothed to help minimize 54

Figure 4.1: a) Data captured by framing camera. Data from a framing camera are recorded on film, then digitized. A wedge file is created to help calibrate scanned exposure levels to x-ray illumination. b) Calibrated image. Pre-shot metrology measures the position of features on the target, to give axes in target coordinates. The gold grid shown in images provides not only a vehicle for introducing these features onto a data image, but also provides a reliable way to measure the actual image magnification. c) Data smoothed over a resolution element. Source-limited resolution limits the level at which useful data can be gathered. By smoothing over a resolution element, we remove small variations due to noise from the data image. d) Image with background variations subtracted out. Image is smoothed over a large fraction of the image, so only large scale variations remain, and then subtracted from the original image. 55 the effect of the noise. Sources of noise on the image include photon statistics and framing camera induced noise. To make sure no useful data is lost this way, smoothing is done on smaller scales than the level of source-limited resolution, or smearing from the pinhole source of light. In these experiments using a single strip framing camera, the pinholes used to backlight the target were 20 µm in diameter on an 80

µm thick substrate. The thickness of the backlighter substrate causes vignetting of the light through the pinhole, shrinking the effective source size to 14 µm. Source- limited resolution arises when light from different parts of the source pass through the same point on the target, then continue on a straight line path onto different parts of the imaging component of the framing camera, smearing the data from the image slightly as shown in the diagram in Figure 4.2. In this target geometry, the 14

µm source creates a 210 µm smear on the microchannel plate of the framing camera.

Since the target image is magniﬁed to 20x at the imaging surface, this translates to resolution elements of 10.5 µm in target coordinates. For the images in question,

10.5 µm is equivalent to 9 pixels. Thus, smoothing over 9 pixels in these images min- imizes small scale variations from noise without smoothing out resolved data details.

The eﬀect of smoothing over a resolution element in the data is shown next to an unsmoothed image in Figure 4.1 b and c.

Variations in the level of overall image intensity complicates the data analysis.

Non-uniform illumination could occur due to mispointing of the backlighter target by more than 2.0 degrees, which would rotate the cone of photons from the pinhole away from the center of the target and detector. On some images, dark strips occur near the center of the ﬁlm, while illumination levels near the edges of the image are equal, which may result from gain variations in the microchannel plate of the framing camera. We used a smoothing technique to help remove large scale variations in the 56

Figure 4.2: Diagram of source limited resolution. Smear from photons passing through the same part of the target but hitting different parts of the detector is calculated using the size of the pinhole source and similar triangles. The extent of the smear on the detector is then divided by the magnification of the image (image distance/object distance) to get the size of a source-resolution-limited element in target coordinates. data from both these sources. To remove these variations, the calibrated image was smoothed over large fractions of the image, 200-300 pixels in all images, which leaves only features larger than 220-330 µm. In all these images, the only features that were that large were large-scale intensity variations. That ultra-smoothed image was then subtracted from the data image, removing some of the effect of the variations.

The result of this process is shown in Figure 4.1d.

4.2 X-ray Radiographic Data

Most of the data collected is in the form of radiographic data of shocked xenon gas, diﬀering in drive disk thickness, timing, pointing, and type of framing camera. Data were collected over seven shot days over the course of 3 years. Below, the radiographic images are organized by collection device and drive disk thickness. A table of the information for each shot taken, including both successful and unsuccessful shots, is given in Appendix C. This table includes laser irradiances, speciﬁc target details, 57 and failure modes for shots, if known.

4.2.1 Single-strip framing camera data from 40 µm beryllium drive disks

Firstly, let us look at data produced from targets with a 40 µm drive disk, using a single strip framing camera diagnostic. Shown in Figure 4.3a is an image taken 10 ns after the drive beams turn on. Unfortunately, the dark feature from the collapsed shock is somewhat compromised by a bright stripe through the data that was too thin to be eﬀectively removed from the image without possibly smoothing over data. The source of this bright stripe is high-energy noise from an area backlighter, discussed in the Dual Radigraphy section. Figure 4.3b was also taken at 10 ns after the drive beams turn on. Here, the image has better contrast. This shock is tilted slightly from the target axis, and is about 65 µm thick.

Figure 4.3c is by far the thickest collapsed layer imaged, measuring 150 µm thick.

It is also the latest time recorded in the experiment, taken at 20 ns after the drive beams turn on. It also shows quite a bit of structure on the front and back sides.

Lineouts in all directions show slight variations in the transmission levels through the shock, having pockets of slightly higher transmission in the thickest part of the layer.

For reference, Figure 4.4 shows data smoothed over a resolution element versus the data background smoothed and subtracted. Figure 4.3d was taken at 12 ns after the drive beams turn on. This image was captured with part of the shock cut oﬀ, as the image was taken too early, and the shock was just entering the ﬁeld of view of the camera.

4.2.2 Single-strip framing camera data from 20 µm, beryllium drive disks

Figure 4.5 shows the ﬁve data points collected on a single-strip framing camera, using a 20 µm beryllium drive disk. Over the course of time imaged, 8 ns to 15 ns, 58

(a) (b)

Figure 4.3: Single-strip framing camera from a shock driven with a 40 µm beryllium disk. a) t = 10 ns. b) t = 10ns. c) 20 ns. d) 12 ns. 59

Figure 4.4: Single-strip framing camera from a shock driven with a 40 µm beryllium disk at 20 ns after drive beams turn on. a) Image smoothed over a resolution element. b) Image background smoothed and subtracted. This piece of data is also displayed in Figure 4.3c. the evolution of the shock does not seem to diﬀer signiﬁcantly. All shocks imaged here have an average velocity between 135 and 150 km/sec at the time they are imaged, as measured from the right side of the collapsed layer. All the images show a shock that is roughly the same thickness, ranging from 50 µm thick to 95 µm thick,

not necessarily in order of increasing time. Four of the shocks are relatively planar,

while the latest shock, imaged at 15 ns, has a curved structure. All the shocks have

some degree of structure on both the front and rear surfaces of the shock. 60 µ m beryllium disk at a) 8 ns, b) 10 ns, c) 14 ns, d) 14ns, and e) 15 ns. All of these images show evidenceImage of some e clumpy also structure, shows though a in relatively images curved a front and compared e to it the is rest, not which nearly have so more pronounced planar as structure. the other three images. gure 4.5: Single-strip framing camera from a shock driven with a 20 Fi 61

The most unique shock imaged here, shown in Figure 4.5e, is shown below in

Figure 4.6, to show how the structure emerges when the background is smoothed and subtracted away. Semi-regular features near the top of the front side of the shock were especially surprising to see; only one other shock imaged has more regular features than this.

Figure 4.6: Plot of shock from 20 µm beryllium driver. a) Calibrated data smoothed over a resolution element. While the collapsed layer is visible, the contrast in the image is poor, and features in the shock are not clearly deﬁned. b) Image smoothed over 250 µm, subtracted from original image, then once again smoothed over a resolution element. Not only is the collapsed layer more clearly deﬁned, but some structure emerges on the back side of the dense layer, as well as possibly repeating structure near the top of the front side of the shock, across from features on the backside. For comparison, the large white pixels are dead pixels smoothed to a source-limited resolution element, which is smaller than the structure observed.

4.2.3 Single-strip framing camera data from 10 µm beryllium drive disk

Experiments with 10 µm thick beryllium drive disks were ﬁelded on one shot day, and produced one piece of radiographic data. These data are shown in Figure 4.7, and were taken 4 ns after the drive beams turned on. This image shows the front of the shocked layer, and the front of the collapsed layer is shown at 1200 µm from the initial beryllium disk position. The dark line features cutting diagonally across the 62

Figure 4.7: Single-strip framing camera from a shock driven with a 10 µm beryllium disk. a) Data smoothed over a resolution element. b) Smoothed data was large scale variations subtracted out, showing more structure on both sides of the collapsed layer. image are flaws on the film. The average velocity over the first 4 ns is 300 km/sec, the fastest average shock velocity recorded for these experiments. The collapsed layer is

85 µm thick, measured through the center of the dark feature. It shows a slight tilt with respect to the target axis. Subtracting out large scale variations on the image shows some structure on both sides of the collapsed layer, though a ﬂaw in the ﬁlm blocks a clear view of the front side of the layer.

4.2.4 Single-strip framing camera data from 80 µm polyimide drive disk

One shot using a polyimide drive disk was successful. On this shot, both single- strip and four-strip data was collected, so it was also one of the few shots with successful dual radiography, discussed further below. This piece of single strip data is shown in Figure 4.8. 63

Figure 4.8: Single-strip framing camera from a shock driven in xenon gas with a 80 µm polyimide drive disk. This image shows only part of the shock, as the diagnostic was timed too early. The shock is just entering the ﬁeld of view of this diagnostic. The shock is also obscured by a bright stripe across the image, which is from interference from another diagnostic. This is described further in the Dual Radiography section. 64

4.2.5 Four-strip framing camera data

The ﬁrst successful diagnostic ﬁelded in the radiative shock experiments were four-strip framing cameras. These side-on radiographic images were taken in argon gas using a tin area backlighter, as described in the previous chapter, using a 50 µm

thick drive disk. These data are shown in Figure 4.9. In this image, and all four-strip

framing camera images, time increases from left to right, and from top to bottom of

the ﬁgure. Each strip is delayed from the nominal backlighter timing by an extra

200 ps from the strip before it, and within each strip, each cell is delayed by 60 ps

from the last.

The shock is visible in each cell of this image, but only the cells in the ﬁrst two

columns have images of the grid, which gives the position of the shock. In addition,

the position of the shock can only be determined if the edge of the grid is in the

image, which was a feature measured in metrology. Only one cell gives a clear image

of a grid edge, and this cell was calibrated to metrology measurements, and shown

in Figure 4.10. A signiﬁcant diﬀerence between this data and the single-strip data

shown above is that the target walls are not visible in this image, nor any signs of

absorption by plasma trailing along the target wall. However, these targets were

built with beryllium shock tubes, as opposed to plastic tubes for later experiments,

which should have lower absorption.

Later, in eﬀorts to do radiography from two directions at two diﬀerent times,

we obtained our only four-strip data of shocks driven with polyethylene, as well as

an additional piece of data with a beryllium driver. These experiments were done

using 1.1 ATM xenon gas, using a vanadium backlighter source. The plastic driven

four-strip data is shown in Figure 4.13.

Zooming in on one cell, we see this is the thinnest shock image seen to date. 65

Figure 4.9: Raw four-strip framing camera data for a shock in argon at 12 ns, launched with a 50 µm beryllium drive disk. This particular image was backlit using x-rays from L-shell transitions of tin. While grid features are visible, target walls are not, making it diﬃcult to conﬁrm radial position of the shock. On this image, only four frames have any image of the gold grid, and only one has a grid edge, the position of which was measured in metrology. Each strip is delayed 200 ps, with time beginning at the upper-left corner. Within each strip, each cell is delayed by 60 ps. 66

Figure 4.10: Blow-up of one cell of four-strip framing camera data from August, 2002, shown in Figure 4.9. This cell is in the second column, ﬁrst row as measured from the lower left corner of the image, at time t = 12.4 ns.

Shown in Figure 4.14 is the cell in row two, column four as measured from the lower left of the four-strip image. This shock is approximately 45 µm thick, and is slightly curved.

Four-strip data collected with a 40 µm beryllium driver at 15 ns is shown in Figure

4.15. Timing of this shot was not optimal, as the shock is imaged near the edge of the frames.

The cell with the most complete image of the shock, in the second row, fourth cell as measured from the lower left of the image, is shown in Figure 4.16.

4.3 Dual Radiographic Data

On experiments in July, 2003, April, 2004, and February, 2005, targets were fielded with the intent of doing radiography from two different directions with different 67

Figure 4.11: Raw four-strip framing camera data for a shock in xenon at 18 ns, launched with a 50 µm beryllium drive disk. This particular image was backlit with a material more suited to a shock in argon gas, but shock features are still visible, if not optimal. While grid features are visible, target walls are not, making it diﬃcult to conﬁrm radial position of the shock. All frames image the shock and the grid. 68

Figure 4.12: Blow-up of one cell of the four-strip framing camera data from December, 2002, shown in Figure 4.11. This cell, in the second column, second row as measured from the lower left corner of the image, at time t = 18.4 ns timings. On these shots, targets were constructed and positioned to use a pinhole backlighter to image the shock on a single-strip framing camera, then a short time later use area backlighting to image the shock on a four-strip framing camera. The delay between these two diagnostics was 3-6 ns, using plas-delayed beams on the same driver. Radiography directions were almost orthogonal (100 degrees apart), and both directions were perpendicular to the target axis. A diagram of this target setup is shown in Figure 4.17.

In this diagnostic scheme, two shots collected single-strip framing camera data, and four shots collected four-strip framing camera data. Only 2 shots collected information from both diagnostics on the same shot, and single-strip cameras on both of these shots were timed earlier than optimal, placing the image of the shock on the far edge of the image. In these cases, only part of the shock structure is seen. 69

Figure 4.13: Raw four-strip framing camera data for a shock in xenon at 13 ns, launched with a 80 µm plastic driver. Unlike previous four-strip framing camera data, one wall of the tube is visible in this image, as is trailing xenon gas along the wall. The other wall is obscured by a grid. 70

Figure 4.14: Blow-up of one cell of the four-strip framing camera data from April, 2004, shown in Figure 4.13. This image uses a plastic driver in xenon gas, backlit with a vanadium source. This cell, in the fourth column, second row as measured from the lower left corner of the image, at time t = 13.4 ns

These data are shown above in the four-strip section, in Figure 4.13 and Figure 4.15, and in the single-strip section in Figure 4.3d and Figure 4.8.

On many shots in this scheme, high-energy noise generated by the area backlighter washed out data collected on the single strip framing camera. This signal was collected while the gating mechanism on the single-strip framing camera was closed, bypassing the microchannel plate and exciting the phosphor directly. This is evident because area outside the active strip on the framing camera shows signal; area outside the active strip was never opened via the voltage gate, and so collected no data from x-rays entering the microchannel plate pores. An example of washed- out single-strip framing camera data is shown in Figure 4.18. Initial investigation showed no obvious link to higher laser energies on the area backlighter target and the 71

Figure 4.15: Raw four-strip framing camera data for a shock in xenon at 15 ns, launched with a 40 µm beryllium driver. One wall of the tube is visible in this image, but the placement of the shock on the image cuts out any possible traces of xenon trailing along the wall of the tube. The other wall is obscured by a grid. 72

Figure 4.16: Blow-up of one cell of the four-strip framing camera data from April, 2004, shown in Figure 4.13. This image uses a plastic driver in xenon gas, backlit with a vanadium source. This cell, in the fourth column, second row as measured from the lower left corner of the image, at time t = 15.4 ns presence of the high energy noise. Some correlation was shown between geometry and the presence of noise. Variations of the positioning and tilt of the area backlighter target may have exposed more of the laser-irradiated area of the foil to the single-strip backlighter, increasing the amount of high-energy noise it detected.

4.4 Odd Radiographic Data

While most data exhibited a thin layer with the normal of the dense layer parallel to the axis of the cylinder, some data were unusual. Two pieces of data in particular departed from the norm. The ﬁrst was a shock launched with a 40 µm beryllium disk, which was recorded with a single-strip framing camera at 9 ns after drive beams turned on. Instead of launching a planar shock, this shock launched a shock that looks like a bubble. The data from this shot are shown in Figure 4.19. 73

Figure 4.17: CAD drawing of dual radiography setup. Pinhole and area backlighters were 80 or 100 degrees apart, imaging areas of the tube separated by approximately 1 mm at diﬀerent times relative to the drive beam pulse.

The ﬁrst route to explore to try to explain this odd data piece is to make sure that the target contained xenon gas at the time the shock was launched. If the target were empty, no planar collapsed shock would form, and the image on the data might be just the edge of the driven beryllium expanding into the empty cylinder. Even though beryllium is virtually transparent at these x-ray energies, we may see the edge of the beryllium due to phase contrast imaging, which may show more features at sharp edges in density. The gas pressure inside the tube was recorded approximately 10 seconds before the laser beams ﬁred, and showed a pressure of 1.12 ATM at that time.

The camera trained on the voltage transducer measuring the target gas pressure is turned oﬀ during the shot, to prevent damage to the camera from the high voltages in the target chamber. Within a few seconds after the shot, the camera turns back on, and it was noted that the pressure recorded by the transducer dropped to zero.

This detail is important because it conﬁrms that we were measuring the pressure in 74

Figure 4.18: Raw single-strip framing camera data, washed out by high-energy noise. Notice signal outside of the active area of the microchannel plate. The bright strip present in the center of this image was present on other pieces of single-strip framing camera data taken in the dual radiography setup. On some pieces of data that were washed out, a faint image of the grid on the target is still visible. the target, and not in a clogged ﬁll hose.

A second explanation is that either the drive beams or the target was mispointed, and so the beryllium piston was not launched evenly. If the target were misaligned significantly, this would be evident from the radiography image. The target would not be centered on the framing camera strip, or at the very least look different than subsequent data images taken by the same camera at the same pointing. The target position looks identical to those images. This was the first shot of the day, and the lasers were aligned to the proper position that morning. No changes were made to the laser pointing for the next shots, and those shots resulted in successfully launched shocks. No other shots resulted in similar looking data images, ruling out mispointed laser beams. It is possible the target was mispointed, however, metrology of the target shows no features out of the ordinary. 75

Figure 4.19: Unusual data. This data was recorded 9 ns after the drive beams turned on, and does not show the normal thin, dense layer of xenon showed in most data images.

Though the target drive disk backside was inspected for glue after it had been attached to the body tube, it is conceivable that some glue escaped notice, and aﬀected the structure of the shock.

The second piece of strange data produced a relatively normal dense collapsed layer. However, this piece of data was the only collapsed layer which had a significant tilt with respect to the target walls. This data was produced by launching a 20 µm thick beryllium disk, and was imaged with a single strip framing camera

8 ns after drive beams turned on, and is shown in Figure 4.20. Dotted lines are

superimposed to show the deviation of the shock normal from the target axis. This

tilt is approximately 10 degrees from the target axis, by far the most of any piece of

shocked data. Also, it seems that less xenon is imaged as trailing close to the target

walls, as it is in most pieces of single strip data. 76

Figure 4.20: Unusual data. This piece of data showed an exaggerated tilt of the collapsed layer from the target axis. Dotted lines show the deviation to be about 10 degrees.

A possible explanation for the exaggerated tilt of this shock is that the drive disk may have not been uniformly illuminated. One drive beam was lost on this shot, which may have aﬀected the overall uniformity of the beam spot the 10 drive beams usually make on the beryllium disk. This target may also have been misaligned in the target chamber. If the center of the tube was not within 100 µm of the center

of the spot created by the drive beams, the beryllium may not have been launched

evenly down the tube. This kind of error could have occurred, for example, if the

center of the tube was oﬀ by 50 µm from the center of the drive disk, combined in

the correct sense with a 2 degree mounting error, which could translate to a 35 µm

move of the center of the beam spot, due to the tilted surface, plus the small error

in positioning the drive disk in the reticles. 77

4.5 Fringe Shifts from a Velocity Interferometry System for Any Reﬂec- tor

The Velocity Interferometry System for Any Reflector (VISAR) diagnostic was deployed in early experiments, using a slightly modified target design that included two openings in the side of the target; one covered by a quartz window, the other covered with a quartz window with a reflective coating on one side, acting as a mirror, as shown in Figure 4.21. Again, it was hoped that as the electron density increased as the shock collapsed, the changing optical path for the interferometer beam would cause fringe shifts.

Figure 4.21: Target for experiments using the VISAR diagnostic. Arms through the radius of the target were capped on one end with a quartz window, and on the other with a coated mirror.

Unfortunately, radiative preheat from the shocked layer very quickly heated and ionized the gas contained in the target. This ionization was significant enough that before the drive beams even turned off, the probe beam used in the VISAR system was significantly attenuated due to collisional absorption. Shown in Figure 4.22, the fringes from the VISAR diagnostic cease even before the drive lasers turn off. In this image, time increases to the right. 78

Figure 4.22: Representative piece of VISAR data. Note the fringes from the interferometer cease before the drive beams turn oﬀ. Also note late time signal with no fringes, corresponding to the passage of the shock through the VISAR path. 79

This does not mean that this diagnostic was completely unsuccessful. While it didn’t work in the way originally intended, several lessons were learned from the data. Firstly, we know from these results that the preheat in the unshocked gas is large enough to cause some level of ionization, causing the collisional absorption of the green-light VISAR beam. We currently do not have an exact measure of this level of preheat, but to cause ionization it must be on the order of 10 eV. Secondly, examining the right side of Figure 4.22 (later in time), one sees a featureless blip in signal on the interferometer. This blip (labeled thus because of the lack of fringe data) corresponds to the time when the shock would have passed by the VISAR window. It is logical then that the data comes from the reﬂection of the VISAR probe beam oﬀ of the dense shock front.

Figure 4.23: Only VISAR data which showed any fringe shift. The total signal length was approximately 2 ns.

Only one piece of data showed any successful fringe shift. A small shift was noticed on one shot, early in time, well before the shock could have approached the scattering volume. These data are shown in Figure 4.23. After approximately 2 ns, these fringes also fall prey to collisional absorption of the probe beam. Calculations from 80 collaborators estimate that this fringe shift would have been caused by a maximum electron density of 1019 cm−3 . There is no discernible experimental reason why this shot was successful while all others failed. CHAPTER V

Radiographic Image Analysis

In the previous chapter, radiographic data from 9 shot days were reviewed. A summary of all shots, both successful and unsuccessful, is given in Appendix C, Table

3. In the radiographic data, the presence of a dark feature spanning the diameter of the shock tube was reported as detection of the collapsed shock. Other components of the target, mainly beryllium and plastic, are transparent at the backlighter energies used, 5.2 keV for xenon using a vanadium backlighter, and 3.6 keV for argon using a tin backlighter. Gold is opaque for all backlighter energies used, and provided an important means of calibrating both position and magniﬁcation in the radiographic images.

From these images, we can discern the shock position, which gives us an average velocity at the time of measurement. This measure is not an instantaneous velocity, which has not been measured. We can also measure imaged thickness, though the caveat remains that this thickness is at best an upper limit due to alignment considerations.

We cannot easily measure density as a function of transmission. Most of the light that reaches the detector from the backlighter source is centered around the He-α-like transition line from the material. Some of the light is from other transitions to the

81 82

Figure 5.1: Darkest radiographic image and horizontal lineouts showing intensity. a) Shot 40706, taken at t = 20 ns with a 40 µm thick drive disk. This piece of data had the lowest relative intensity measurement taken. b) Horizontal lineout of the the shock. The lineout is taken over the center 400 µm of the shock, with the x-coordinate given in the ﬁgure. c) Horizontal lineout of the grid. The lineout is taken over 60 µm. The valleys of the grid wires in the image are not well resolved, as shown by the lack of a ﬂat feature at the lowest transmission point.

K- and L- shells of the material. But a small fraction of emitted photons are very energetic; energetic enough to pass directly through the tantalum substrate instead of only through the pinhole on backlit pinhole images. These same high-energy photons also pass through the microchannel plate in the framing camera to hit the phosphor of the framing camera, creating a high-energy background on the image. This should be relatively uniform across the image, so one might suspect it could be subtracted out. Experimentally, the contribution to the intensity from high-energy photons could be measured using the nominal backlighter setup and placing a ﬁlter before the detector of the same material of the backlighter. At a suﬃcient thickness, this

filter would absorb photons generated from K- and L- shell transitions. However, this filter should be transparent to the high-energy component, which could then be recorded on the detector. As a comparison, beryllium filters used to shield the framing camera from shrapnel was 0.010”, equivalent to 250 µm, and the foil used

to generate the backlighter x-rays was 5 µm. This particular measurement was not 83 made for the data in the previous chapter, as it would have the unfortunate side eﬀect of blocking important data. However, a high-energy background should be detectable even where the image was completely opaque, as the photons need not have passed through the target by way of a pinhole. In the radiography images in the previous chapter, the dense shock was not completely opaque, as seen in a lineout of one of the darkest shock images, shown in Figure 5.1. The gold grid in the radiography images should be opaque, but covers a small surface area, so an average is taken over a small number of pixels. The wires on the gold grid are only 20 µm thick, covering only 2 source-limited resolution elements. As you can see from the lineout shown in

Figure 5.1c over 60 µm of the grid, it is not well resolved in this shot. If the grid were well resolved, the peaks and valleys of the lineout would be ﬂat, which they are not in this image. Therefore, examination of transmission through the grid wires does not give a measurement of the high-energy background, either. To measure this contribution on future shots, a larger piece of highly opaque material could be placed on the targets, which would provide the necessary measurement without the loss of any shots for data.

5.1 Shot-to-Shot Variability

Each data image from a single-strip framing camera was taken on a single shot, which introduces the question of shot-to-shot variability. Though we strived to use identical laser conditions on each shot, average laser energy varied by up to 20%, and the orientation of the target changed between shot days to accommodate other experiments, decreasing the amount of time spent adjusting the laser and increasing the amount of shot data obtained. Small differences in the targets could also make a difference. As the University of Michigan team learned more about target fabri- 84 cation, targets were produced with more uniform features, and were produced with tighter specifications. When we could not control the specifications on a component, such as for components produced in other facilities, measurements were made in the laboratory of the deviations from nominal values. The most important example of this was that the beryllium drive disks were produced with a 10% tolerance on thickness. These thicknesses were measured with micron accuracy using calipers at the

University of Michigan.

Figure 5.2: Two images showing shot to shot variability in the data, taken at 10 ns ± 0.25 ns. Sources of the variability are discussed in the text. a) Shot number 37033, using a 38 µm drive disk. b) Shot number 37034, using a 44 µm drive disk.

As an example of the importance of tracking these individual contributions to shot-to-shot variability, let us examine two pieces of single-strip framing camera data, taken at 10 ns ± 0.25 ns after the drive beams turned on to illuminate a 40

µm beryllium drive disk. These two pieces of data are shown in Figure 5.2. Part a of this image is shot 37033, and part b is shot 37034; these data were taken on the same day, one after the other. The target used for shot 37033 had a 38 µm ± 1 µm drive disk, while the target used for 37034 had a 44 µm ± 1 µm drive disk. Metrology of 85 these two targets was double-checked for consistency, and is accurate to within the tolerances discussed in Chapters 3 and 4, as is positioning in the target chamber.

All of these things contribute to shot-to-shot variability. The data is consistent with the diﬀerent drive thicknesses measured; the slightly thinner disk used in Figure 5.2a moved farther than the thicker disk.

5.2 Shock Position as a Function of Time

Measured and Simulated Position vs. Time

3500

40 µm position 3000 20 µm position 40 µm sim position 20 µm sim position

2500 m)

! 2000

1500 Position ( 1000

500.0

0.000 4 6 8 10 12 14 16 18 20 Time (ns)

Figure 5.3: Plot of position data from experiments using 20 and 40 µm thick drive disks, and from simulations of those experiments using a 1D radiation hydrodynamics code HYADES. The simulations overestimate the shock position for both drive disk thicknesses, seemingly from an error in the ﬁrst few nanoseconds of the experiment. The experimental data also hints that at a late times the shock may slow, possibly from the loss of a signiﬁcant driving force from the beryllium piston. 86

A plot of shock position versus time shows two important features. Firstly, when compared with shock positions given by 1-D radiation hydrodynamic simulations, it shows that experiments are signiﬁcantly slower than predicted. From the plot shown in Figure 5.3, it seems that the discrepancy in the prediction comes from early time interactions, as the simulation curves lie well above the data even at the earliest measured position . This is discussed further in the Radiation Hydrodynamics Sim- ulations chapter. Secondly, the plot shows at some late time for both the 20 and 40

µm drive disk, the shock may slow. This transition marks when the rarefaction wave acting on the driven side of the beryllium moves all the way through the slab, and begins to rarify the backside of the collapsed gas layer. At this point, the evolution of the shocked gas will change. In simulations, the shock slows, and collapsed layer becomes more extended as a rarefaction begins to aﬀect the side of the layer near the rareﬁed beryllium.

5.3 Shock Thickness as a Function of Time

As the shock moves through the gas in these experiments, the shocked gas gets denser as it loses energy to radiation. It continues this density collapse until it is optically thick, as explained in more detail in the Radiation Hydrodynamics chapter.

As the shock continues through the gas-ﬁlled tube, the thickness of the collapsed layer increases, as the shocked then cooled gas piles on the front of the already optically thick layer of xenon. This prediction is echoed by radiation hydrodynamic simulations, discussed in Chapter 7. In Figure 5.4, we plot the measured thicknesses of collapsed layers from 20 µm and 40 µm thick drivers as points, as well as a predicted layer thicknesses from simulations as lines.

This eﬀect proves diﬃcult to measure, as the measured thickness of the collapsed 87

Measured and Simulated Thickness vs. Position

160.0

140.0

120.0 m) !

100.0

80.00

60.00 Layer Thickness (

40 µm layer thickness 40.00 20 µm layer thickness 40 µm sim thickness 20 µm sim thickness

20.00 500 1000 1500 2000 2500 3000 3500 Position (!m)

Figure 5.4: Plot of imaged thickness of dense collapsed xenon as a function of the distance the shock has traveled. Data are shown as points, with the position error bar from uncertainty estimates from metrology, and the thickness error bar from uncertainty from the density at which the collapsed layer “begins”. Though the data shows a general trend towards thicker shocks as more ground is covered by the shock, this measurement is highly susceptible to overestimating the thickness of the shock due to slight departures from perfect side-on imaging. Note that only one data point lies on the simulation curve, and the rest for both drive disk thicknesses lie well above. This eﬀect is some combination of imaging a tilted shock and radiation treatment in Hyades, discussed in the next chapter. 88 layer depends greatly on the alignment of the target with respect to the imaging plane. A target that is imaged perfectly side-on will give the actual thickness of the collapsed layer, plus some amount of smearing due to the ﬁnite length of time that the shutter is open. Any variation from perfect alignment introduces a projection of the layer’s width to the measurement. Most of the imaged shocks have a width between

50 and 120 µm. However, the depth of these collapsed layers will be approximately the target diameter. Because the depth is so big compared to the width of the shock, the eﬀects of misalignment are great. Tolerances for target construction allow a ± 2 degree error in mounting angle around the target axis. An additional error from target mounting angle on the stalk makes the compound error even greater.

In addition to this eﬀect, the shock may be tilted from the target axis. This would happen if the spot made by the drive beams on the beryllium surface was oﬀset from the center of the target tube. Evidence of tilted shocks, and therefore some error in positioning the target, exists on pieces of data shown in Figure 4.20, discussed in the last chapter. At most, we suspect that the target may be imaged as 5 degrees away from side-on. A 5 degree misalignment of a 50 µm wide shocked layer can

result in the imaging of a 90 µm wide feature on the ﬁlm. This is explained further

in the Radiation Hydrodynamics Simulations chapter, in the creation of a simulated

radiograph from 2D simulation data. Structure in the collapsed layer may also cause

the layer to spread more than the 1D predictions suggest.

5.4 Structure in the Cooling Layer

Images from single-strip framing cameras underwent additional image processing

to help compensate for non-uniform illumination. Despite strong eﬀorts to make

sure the area that was imaged was illuminated uniformly by the backlighter, data 89 images often showed dark vertical strips on images, as well as scratches and other irregular features. In an eﬀort to at least remove large scale variations on the data, calibrated images were smoothed over large areas (much larger than the collapsed layer thickness), and then subtracted from data images. This large scale smoothing left the data, grid, and target wall features intact on the image, but removed any features which were larger than the smoothed elements. These elements ranged from

100 to 300 µm, depending on the results for an individual image.

(a) (b) (c)

Figure 5.5: Images of shock from shot 39927, t = 14.6 ns launched with a 20 µm beryllium driver. a) Calibrated data smoothed over a resolution element. b) Image smoothed over 200 µm, subtracted from original image, then once again smoothed over a resolution element. c) Image smoothed over 100 µm, subtracted from original image, then once again smoothed over a resolution element. Notice how smoothing over a shorter distance emphasizes the darkest parts of the shock, showing that the shock image is actually somewhat knotted.

This smoothing revealed formerly obscured structure in some images, and showed

more detail of structure in others. The data from a 20 µm drive disk at 14 ns after

the drive beams turned on proves to beneﬁt greatly from this subtraction technique.

Shown in Figure 5.5, we compare the data smoothed over a resolution element in part

(a) with the same image smoothed over 200 µm, subtracted from the unsmoothed

image, and then smoothed over a resolution element. This piece of data is the most

striking example of structure on the front and back side of the collapsed layer. As

this piece of data was smoothed to diﬀerent degrees, diﬀerent features became visible, 90 as is shown by examining Figures 5.5b and c. Regular structure emerges from the image when the background is smoothed out and subtracted over 200 µm elements, but knots of denser structure appear when the image is smoothed and subtracted over smaller elements. The clumps of dark material seem in Figure 5.5c are several times larger than a source-limited resolution element, with most of the visible clumps being about 30-40 µm in diameter.

Figure 5.6: Images of shock from shot 38983, t = 15 ns using a 20 µm beryllium driver. a) Cal- ibrated data smoothed over a resolution element. b) Image smoothed over 200 µm, subtracted from the original image, and smoothed over a source-limited resolution element. Smoothing in this image seems to enhance the contrast between the shock and the surrounded gas. Structure emerges in the smoothed image, as well, on both the front and back sides of the image. These structures are larger than a source-limited resolution element. The white pixel near the top edge of the shock is a dead pixel smoothed over a resolution element, showing the size comparison.

Smoothing signiﬁcantly increased the contrast of the image from shot 38983,

shown in Figure 5.6. It also revealed small, clumpy structure on the front side of the

shock, most visible near the top-right of the shocked layer in Figure 5.6b. A white

pixel smeared over a source-limited resolution element conﬁrms that the structures

are a few times larger than a resolution element. Three knots of material are about

30 µm in diameter, and are somewhat regularly spaced. 91

Figure 5.7: Images of shock from shot 39925, t = 4 ns using a 10 µm beryllium driver. a) Calibrated data smoothed over a resolution element. b) Image smoothed over 200 µm, subtracted from the original image, and smoothed over a source-limited resolution element. In these images, the light and dark diagonal stripes are scratches on the ﬁlm. While some structure emerges in the smoothed image, the front side of the shock is obscured by a scratch.

Some structure is also visible on the only successfully imaged shock driven with a 10 µm beryllium drive disk, imaged at 4 ns after the drive lasers turned on. This shock is shown in Figure 5.7. The features are clearer in Figure 5.7b, which was smoothed over 200 µm and subtracted from the original image. Unfortunately, a scratch in the ﬁlm makes it diﬃcult to discern features on the front side of the shock, but features on the backside that are 30-40 µm long and 20-30 µm wide are visible.

The densest and thickest shock imaged also shows quite a lot of structure, and is shown again in Figure 5.8. The single-strip image from shot 40706, taken at t = 20 ns, driven with a 40 µm thick drive disk shows features on the front side, back side, and top side of the shocked layer (near the target wall). On the front side of the shock, the largest structure feature measures approximately 40 µm in diameter, the largest feature on the front side of a shock imaged to date. The features on the back side are also larger than in other images, with a large clump near the center of the 92

Figure 5.8: Images of shock from shot 40706, t = 20 using a 40 µm beryllium driver. a) Calibrated data smoothed over a resolution element. b) Image smoothed over 200 µm, subtracted from the original image, and smoothed over a source-limited resolution element. This image shows quite a bit of structure, and shows the largest features on the front side of the shock. tube on the backside (visible as a dark spot in Figure 5.8b) measuring approximately

50 µm in diameter. The longest ﬁnger of dark material not trailing along the edge of the target measures almost 100 µm in length.

It seems odd that if this structure was caused by an instability that the dramatic features be always on the backside of the shock. Some of this bias may be explained by the finite shutter length for the image. The voltage spike that effectively opens the camera is 200 ps long. For a shock moving 100 km/sec, this leads to a smear of 20 µm. Most of the structure imaged is on the order of 30-40 µm. On the back side of the shock, the moving layer would drag out the effect of structure, making it appear longer and more pronounced. On the front side of the shock, the features would be obscured by the densest part of the layer as it moved forward during the open shutter. At these high velocities, this could be a sizable effect. The actual distribution and cause of this structure is an interesting topic for future graduate 93 student work. CHAPTER VI

Thomson Scattering Experiment in Argon Gas

The previously described experiment was novel, and is poised to make a significant contribution to the study of radiation hydrodynamics. It explored a radiative shock that was faster than those of previous research in denser material, producing significant radiative effects. The possible extensions of the experiment may cover new regimes, especially with the National Ignition Facility at the Lawrence Livermore

National Laboratory. In the meantime, new experiments to measure temperatures and densities will extend the practical capabilities of existing diagnostics, priming them for use on the problem of ignition in inertial fusion.

As an eﬀort to begin using existing techniques in the novel setting produced in the collapsing radiative shock experiment, we performed an experiment using Thomson scattering techniques on a radiative shock driven in argon.

Thomson scattering is a technique that probes the characteristics of a plasma. A coherent light source at a certain wavelength is Thomson scattered oﬀ of electrons in a system. The spectrum of the scattered light is aﬀected by the state of the plasma. This technique can give information about the electron temperature, the ion temperature, and the density of the probed plasma.

Thomson scattering operates in two distinct regimes, which give information

94 95 about diﬀerent plasma phenomena. The measure of this is the scattering parameter, α, which is proportional to the ratio of the ﬂuctuation wavelength (λ) to the

Debye length (λDe) in the probed plasma;

1 λ (6.1) α = ∝ . kλDe λDe The Debye length of a plasma in cgs units is given by the expression

r kBTe (6.2) λDe = 2 , 4πnee

where ne is the electron density of the plasma, Te is the electron temperature, and kB

is the Boltzmann’s constant. When α is large, or the ratio of the probed wavelength

is large compared to a Debye length, Thomson scattering will probe collective wave

eﬀects over many plasma scale lengths. Collective scattering easily probes electrons

in the Debye sphere of ions aﬀected by wave phenomena, such as low-frequency

ion-acoustic waves and higher frequency electron-plasma waves. When α is small,

or when the ratio of the probed wavelength is small compared to a Debye length,

Thomson scattering will probe individual electron eﬀects on scale lengths shorter

than the Debye length.

One can probe the desired eﬀects by correctly choosing the Thomson scattering

probe laser beam wavelength (k = 2π ), compared to the wavelength of the observed ts λts scattered light(k = 2π ), taking into account the direction of observation with respect s λs to the incident light (θ). For wavelength shifts between the incident and observed

light that are small, the wave-vector probed (k) is

θ (6.3) k = 2k sin . ts 2 96

This equation is valid for low-frequency ﬂuctuations, for example from ion-acoustic

ﬂuctuations in the plasma, but not for scattering from higher frequency electron- plasma waves. The light scattered from these low frequency ﬂuctuations results in two spectral peaks, scattered from the ion-acoustic waves propagating parallel and anti-parallel to the probed wave-vector.

In the collective regime, the separation between the measured peaks of the scattered light is proportional to the sound speed of the probed wave in a plasma. For this experiment, the important wave phenomenon is the ion-acoustic wave, which has a sound speed of ([46])

2 ZTekB 1 3Ti (6.4) ciaw = + . mi 1 + (kλDe) ZTe

The separation of the peaks is given by

2λ (6.5) ∆λ = probe (c k ), iaw 2πc iaw iaw

where λprobe is the wavelength of the probe beam and kiaw is the wave-number of the

probed ion acoustic wave. If the ions have a ﬂow velocity relative to the laboratory

frame and parallel to the probed ion acoustic wave, the scattered light peaks will be

shifted from the central wavelength by

2λ (6.6) ∆λ = probe (v · k ), flow 2πc flow iaw

where vflow is the flow velocity of the probed plasma. The wavelength shift from the flow can also be derived from the relation between the k-vectors. The probed 97 vector k is equal to the difference between the incoming wave-vector and the vector

of the scattered light, k = ks − ko. For small shifts, ko ≈ ks, so

θ ω θ (6.7) k ≈ 2k sin = 2 o sin . o 2 c 2

Given that ω = k · v, this equation is equivalent to a frequency shift,

2vω θ (6.8) ω = o sin . c 2

2π Converting to wavelength, ω = λ , we obtain

2π 2π π 2v θ (6.9) − = sin λ λo λo c 2

∆λ Rearranging to get the fractional wavelength shift, λ ,

∆λ 2v θ (6.10) = sin λ c 2

In this experiment, the wavelength of the probe beam was 263.3 nm. The Debye length of a plasma is given by

kT 1/2 (6.11) λ = e = 7.43 × 109T 1/2n−1/2 nm De 4πne2 e e

−3 for Te in eV and ne in cm .

Usually, Thomson scattering is used to probe a uniform or slowly changing plasma.

In this way, the separation and width of the peaks and the intensity of the scattered

light gives the electron and ion temperature, and the electron density of the plasma. 98

If one of these quantities changes over the course of the experiment, it may be detected on a streak camera by the changing peak width, separation, or intensity as a function of time.

Scattered light exit hole Ar gas cell (towards TIM 2)

Omega Drive Beams

Be Drive Disk Gas fill tube

4! entry hole (towards P9)

Figure 6.1: 2D diagram of the target used in the Thomson scattering measurement of the driven radiative shock. It is very similar to the target discussed for earlier experiments, with an extra arm and inlet and outlet holes for the probe beam and scattered light diagnostic.

The experimental setup was similar to that in the radiative shock experiment

described in Chapter 3, and a diagram showing the main features of the target is

shown in Figure 6.1. Here, a 20 µm thick, 2 mm diameter beryllium disk is mounted

on a 575 µm ID, 625 µm OD polyimide tube. This tube was ﬁtted with a hypodermic

ﬁll tube, attached to a transducer to measure gas pressure just before the laser shot.

In addition to this geometry, another polyimide tube was mounted at a 45 degree

angle to the main polyimide tube axis. The axis of this tube intersects the center of

the main target axis at 3.7 mm from the beryllium drive surface. When the target

is oriented correctly in the laser target chamber, the axis of this tube points towards

the probe beam port through target chamber center. The end of this tube closest to

the probe beam was covered with a 3000 A˚ thick polyimide ﬁlm, while the opposing

end of the tube was ﬁlled with epoxy. At a scattering angle of 100 degrees and

also at an angle of 45 degrees from the main target axis, another hole was drilled

in the target that, when properly oriented, pointed at the scattered light collection 99 diagnostic. This opening was also covered with a 3000 A˚ thick polyimide ﬁlm. This assembly was gas tight, and was ﬁlled with argon gas at 1.1 ATM, equivalent to

0.001 g/cm3 or 1.5 x 1019 atoms/cm3. Metrology photos of the assembled target are shown in Figure 6.2.

Figure 6.2: Metrology photos of targets used in Thomson scattering experiments.

A driven shock was produced in the argon gas as in previous experiments, by focusing 10 laser beams of the Omega laser facility in a 1 mm spot on the beryllium disk in a 1 ns square pulse. The beam energy was a maximum of 400 J/beam, resulting in a total drive irradiance of 4.8 x 1014 W/cm2. The beams were smoothed

once again by SSD (Smoothing by Spectral Dispersion) and using Distributed Phase

Plates (DPPs) to produce as uniform a laser spot as possible. The midpoint of the

rising edge of the laser pulse deﬁnes t = 0. At t = 13 ns after the start of the drive

beams, 4 backlighter beams ﬁred in a 2 ns square pulse and at a 400 µm spot on a 5

µm thick tin foil. This resulted in a backlighter irradiance of 1.5 x 1014 W/cm2, and

used no beam smoothing. At t = 16 ns after the drive beams ﬁred, a single destroyer

beam with no beam smoothing struck the plastic covering over the scattered light

exit hole. This beam was approximately 400 J in energy in a 1 mm spot, in a 2 ns

square pulse, resulting in an irradiance of 6 x 1012 W/cm2, used to explode the thin 100 covering to allow the scattered light to escape. At t = 19 ns after the drive beams

ﬁred, a frequency-quadrupled (4ω, λ = 263 nm) probe beam was directed to target chamber center (tcc) at 200 J in a 2 ns square pulse and in a 100 µm spot. This beam destroyed the thin plastic cover to the entrance hole on the target as it propagated through the arm tube to scatter from the plasma on the axis of the target.

Let us ﬁrst check that this experiment does in fact fall into the collective regime.

Both the temperature and the density change throughout the system, so we will examine certain points of interest. In the unshocked argon gas, the material density

(at 1.1 ATM) is 1.5 × 1019 cm−3. We do not have a good measurement of the temperature of the unshocked gas, but let us estimate that it is approximately 10 eV, the same as the estimate given in the xenon gas temperatures discussed in the earlier chapters. This is a good estimate based on VISAR experimental results in xenon given in Chapter Four, which show that the gas must be at least a few eV and partially ionized. In this case, the Debye length of the gas would be about 6 nm. The wavelength of the probe beam scattered from the plasma is 263.3 nm, which gives a scattering parameter α = 43. As the shock moves through the gas, compressing and ionizing the material, the Debye length gets slightly shorter. For example, in the regime near full radiative compression, where the ions reach a compression of more than 20 times the original density, the gas reaches an average ionization state

Z ∼ 10 − 15, and the maximum electron temperature is 200 eV. Here, the Debye length is shorter, at 1.9 nm. This gives a scattering parameter α = 138, well into the collective regime. Farther behind the shock, temperatures drop while compression remains high, which would result in an even shorter Debye length. Therefore, the probed plasma is in the collective regime through the entire experiment.

Collected scattered light was observed for approximately 300 ps during the middle 101 elength Wav Time

Figure 6.3: Streak camera image of collected scattered light data from TS experiment. Early in time, the detector captures light from the destroyer beam blowing oﬀ the cover on the target that points towards the collection diagnostic, which then fades. A short time later, the characteristic two-peaked spectrum of collective Thomson-scattering behavior appears. of the 2 ns window during which the probe beam was on. Scattered light was collected with a spectrometer using a 3600 lines/mm grating, giving a dispersion of 0.036

A/pixel.˚ This spectrum was recorded on a UV streak camera, with a sweep window duration of 5 ns, centered at t = 20 ns after the drive beams turn on, with a time resolution of 6.0 ps/pixel. The collected spectrum is shown in Figure 6.3. Data collected showed that emission caused by the destroyer beam to be fading away, shortly after which classic two-peaked scattered light signal was detected. The onset of the collection of scattered light from warm plasma happens as the shock front crosses the scattering volume, both heating and compressing the material. Here, the ion temperature would have peaked, while the electron temperature would have been raised only slightly by the shock. The cessation of signal happened more than a nanosecond before the probe beam itself turned oﬀ. This would have happened 102

either as the cooling, collapsing gas became more dense than the reﬂection density

at that wavelength and angle, or as the signal got refracted away from the detector

as the density increased. The reﬂection wavelength is

21 2 1.1 × 10 2 (6.12) nreflection = nc cos θ = 2 cos θ, λµm

where nc is the critical density of the gas, θ is the angle of probe laser incidence, and

λµm is the probe laser wavelength in microns, For a probe wavelength of 0.2633 µm

21 and an incident laser angle θ = 45 deg, this reﬂection density is nreflection = 7.9×10

cm3.

Between the near-instantaneous increase of temperature and density at the shock

front and the high-density cutoﬀ of the signal, the Thomson scattering diagnostic will

probe large gradients in ion temperature, electron temperature, and electron density,

or mass density and average ionization state. This means that the signal detected

will actually be a weighted average of the plasma parameters, where high electron

temperatures will be responsible for most of the signal. If measured quantities are

changing at a rate near or faster than the electron plasma frequency, these changes

may not be resolved on the detector. The electron plasma frequency is

s 2 ωpe 1 4πnee (6.13) fpe = = . 2π 2π me

An estimate of the frequency in this region of changing parameters is possible,

using the initial shock compressed value of the ion density, ni, and an educated guess

of the average charge state of the plasma. The unshocked ion density of the argon

gas is 1.5 × 1019 ions/cm3. Shock relations say that the initial density increase as a strong shock compresses the system is a factor of 4 to 10, depending on the value 103 of the polytropic index of the gas. Average charge state is a function of electron temperature, which doesn’t increase until after collisions with shock-heated ions.

We will need to use an average charge state somewhat lower than the average charge state at the estimated peak of the electron temperature. This happens farther away from the shock front, and Z = 10 is a good estimate of this value. This results

20 in an estimate of the electron density just after the shock front of ne = 6 × 10 electrons/cm3, and gives an electron plasma frequency of 2.2 × 1014 sec−1. At such a high frequency, smearing of the signal as the electrons cool is not expected.

The ﬂow velocity was measured to high accuracy by examining the shift of both of the peaks of the scattered light away from λo by Doppler shift. On the Thomson- scattered spectra, we see a wavelength shift of 1.41 ± 0.1 A,˚ where λo was obtained from measurements of stray (unscattered) probe beam light recorded on the streak camera. From this, the measured ﬂow velocity of the shocked plasma is 110 ± 7 km/sec.

The onset of detected signal marks the arrival of the shock at the scattering volume, and therefore gives a measurement of average shock velocity. Because the shock reached the scattering volume at 20.1 ± 0.2 ns after the drive beams turned on, the average velocity over that period of time was 193 ± 5 km/sec. The probe beam was on before the shock reached the scattering volume, and could scatter oﬀ of the preheated gas ahead of the shock. However, no signal was seen from this lower temperature, lower electron-density region. It is possible that with a more sensitive spectrometer, Thomson scattering could be used to measure temperatures in the upstream, unshocked region, but the spectrometer used did not detect signal on this experiment.

The separation of the two scattered peaks is proportional to ZTe +3Ti in the limit 104

of a ﬂuid treatment of the plasma. The separation is equal to

λ2 (6.14) ∆λ = probe (kc ), πc s where λprobe is the wavelength of the probe beam, k is the wavenumber of the probed

ion-acoustic wave, given in Equation 6.3, and cs is the ion-acoustic sound speed,

given in Equation 6.4. Substituting and rearranging into a useful quantity,

1/2 mi ∆λ c (6.15) ZTe + 3Ti = kB λprobe 4 sin θ/2

Recall for this experiment that the probe wavelength (λprobe) is 263.3 nm, the scattering angle (θ) is 101 degrees, and the atomic weight of argon is 40 amu.

We measure the separation of the peaks by ﬁtting the lineout of each peak with a

Gaussian curve, and measuring the separation of the maximums of each curve. On the data shown here, the separation of the peaks is 2.75 ±0.2 A,˚ giving the sum of

ZTe + 3Ti = 4343 ± 750 eV. The main contributor to this sum will be the product of the electron temperature with the average charge state Z.

We can use fits to the data taking advantage of scattered light form factors from kinetic plasma theory to get a better idea of individual temperatures. This fluid limit quantity will help constrain the range of the main contributor to this quantity, ZTe, as reasonable estimates should fall within the error bars on this directly measured quantity. Our form fitting calculation explicitly included account of the spectral resolution of the instrumentation.

Using form factor ﬁts to these peaks should give us a well-constrained estimate of the ion temperature and the product of the electron temperature and the average charge state. Comparing diﬀerent atomic models, which give the average charge state 105

Figure 6.4: Results from atomic models, giving Z and ZTe as a function of Te.

as a function of temperature, it is then possible to estimate the electron temperature

and average charge state individually. This was done using a Saha atomic model,

an average-atom model, and an analytic estimate also based on the Saha atomic

model. Shown in Figure 6.4 are results from these models, giving both Z and ZTe

as a function of Te. A straight line fit through the center of these values provides the estimates used to give separate results for average charge state and electron temperature from fits to the scattered light spectrum. The best fits in Figure 6.5a.

Combining information from the ﬂuid separation of the peaks, the data from the kinetic model ﬁt, and the temperature dependence from the ionization state models, we can conclude that in the plasma measured, Ti = 300 +200/-85 eV, Te = 250 ±

35 eV, and Z = 13.7 ± 0.5. Due to physical reasons, the ion temperature cannot be lower than the electron temperature, constraining the lower error bar on the ion temperature. Fits using the extreme values of the error bars, for comparison, are shown in Figure 6.5b and c. 106

(a)

(b)

(c)

Figure 6.5: Best fit and error bars to Thomson scattered data. a) Lineout from data (purple) and best fit to data (black), with Ti = 300 eV, Te = 250 eV, and Z = 13.7, based on average atom model. b) Lineout (purple, solid) and Te error bars from fluid limit. Dashed line is Ti = 300 eV, Te = 285 eV, Z = 14.2. Dotted line is Ti = 300 eV, Te = 215 eV, Z = 13.2. These lines obviously lie well outside the lineout of the data. c) Lineout (purple, solid) and Ti error bars from fitting the data. Dashed line is Ti = 500 eV, Te = 250 eV, and Z = 13.7, while the minimum of the ion temperature is the same as the minimum of the electron temperature. That curve does not lie significantly outside the data points. 107

Changes to the fit parameters (ZTe and Ti) change the shape of the fit in distinct ways that provide unique information. As stated above, the separation of the peaks is proportional to ZTe +3Ti. So, changes to Ti will move the peaks slightly, while small changes to Te or ZTe will have larger effects on the relative separation of the peaks.

However, changes to the ion temperature also aﬀect the depth of the trough between the two peaks and broadens or tightens the wings of the spectrum. This eﬀect is the result of the level of Landau damping, which corresponds to the ratio ZTe/Ti.

These characteristics of the fit can be seen in Figures 6.5 b and c. In Figure 6.5b, the uncertainty in the separation of the peaks is used to calculate the uncertainty on the electron temperature and average ionization state, as ZTe is the main contributor to that quantity. The extreme values of Te and Z are then plotted as a fit to the data, holding Ti at its best fit value, 300 eV. The fit with these values deviates from the data, with the peaks being too wide on the upper value (long dashes) and too narrow on the lower value (short dashes). Since it also affects the value of ZTe/Ti, the trough between the peaks is too low for the higher value (long dashes), and too high for the lower value (short dashes), as well as deviating slightly in the fit to the wings of the data. In Figure 6.5c, we use the deviation of the fit from the trough between the peaks as an indicator of the ion temperature uncertainty. Keeping Te

and Z at best ﬁt values, we let Ti increase until the trough height was well above

the data level. This variation had some eﬀect on the ﬁt to the wings of the data, but

this eﬀect is much less pronounced.

These results diﬀer from the predictions from 1D radiation hydrodynamic models,

which predict a peak electron temperature of Te = 200 eV, with Ti = 450 eV and Z

= 15.6 at the same position. This indicates that the shock may be initially stronger

than in the simulation, resulting in a higher initial ion temperature that transfers 108 more energy to the electrons in the plasma. The ion temperature prediction is within the large error bars given on that quantity. The average charge state is dependent on the model used, which was a Saha model in these simulations.

This measurement of average velocity at 20.1 ns and 3.7 mm from the initial position of the drive surface marks the latest measurement of position after the shock is launched. This may be signiﬁcant, as it raises the question as to how quickly the shock is decelerating at this point. The driven system depends on the momentum of the shocked beryllium slab continuing to drive the system forward.

At the probed point, 3.7 mm from the initial drive disk position, assuming all of the argon is swept up by the shock, the shocked gas mass is 1.05 µg. The beryllium piston mass inside the tube for a 20 µm thick drive disk is 10.0 µg, so the beryllium momentum is still significant compared to the momentum in the argon, assuming they are moving at the same speed. A rarefaction wave on the laser-incident side spreads out the beryllium plasma, and continues through the beryllium as the shock loses strength. When the shock has slowed significantly, the rarefaction wave moves completely through the beryllium slab, and begins to affect the dense, shocked gas.

This may aﬀect the shock speed, increasing the rate of deceleration.

What happens when a shock is no longer driven? If the shock were the only element of a system, a rarefaction wave would form on the side of the disturbance that was initially driven, moving at the sound speed of the shocked plasma. Eventually, it would overtake the shock front, and form a blast wave. In this system, a rarefaction wave begins to propagate through the beryllium slab as soon as the driving laser beams turn off. This rarefaction wave proceeds through the beryllium. However, radiation from the collapsed layer can ablate the backside of the beryllium slab, causing the material to flow in the opposite direction of the material affected by the 109 rarefaction wave at slightly supersonic speeds. It is only as the shock slows from the build up of shocked material in the collapsed layer that the rarefaction wave can proceed through the remaining beryllium, and into the collapsed layer. This will depend on how strongly the collapsed layer is radiating, and how much material is involved in the supersonic flow. CHAPTER VII

Radiation Hydrodynamic Simulations

7.1 One-Dimensional Hyades Simulations

The bulk of the simulation of this experiment was done using the 1-D version of the radiation hydrodynamics code, Hyades [31]. Hyades is a single-fluid, three- temperature Lagrangian code. This means the electrons and ions are treated as a single fluid instead of two separate fluids in the system, but the radiation temperature, electron temperature, and ion temperature are calculated and tracked sepa- rately. A Lagrangian code has zones that are initially assigned parcels of material, and the mass remains in the zone for the entire simulation; the zone moves to track the material as the experiment evolves, becoming more compressed or expanding as the material changes density. Hyades uses a multigroup, flux-limited diffusion scheme to account for radiation in the system. Multigroup means that photons are divided by wavelength into groups, and the appropriate opacities for each group of energy/wavelength are calculated. Hyades can also run with radiation transport off or in a greybody mode, where it is assumed that all radiation is at the same “grey” wavelength and uses a tabular opacity. Flux-limited diffusion means that radiation transport is approximated as a diffusion mechanism, which is fairly accurate for an optically thick system, limited by a physically acceptable limit for the amount of flux

110 111 which can propagate. At the extreme, this is the free-streaming limit for photons.

In hydrodynamic codes, the amount of thermal energy conducted by electrons can become unphysically high. This is because codes use a Spitzer-Harm model for heat

ﬂux, which can overpredict the heat ﬂow in systems with steep temperature gradients.

Here we use an electron heat ﬂux-limiter to reduce the heat ﬂux to physically sensible levels.

Hyades was used first for proof of principle in the experiment described in previous chapters, then later as a guide to experiment design. Simulations discussed in this section were done at a laser irradiance of 4.2 x 1014 W/cm2. This number is 42% of the highest irradiance ever used on an actual shot, 1.0 x 1015 W/cm2. The lower irradiance in the simulations are used to account for 2D energy transport effects in the laser irradiated surfaces, which has been confirmed in other laser-irradiated hydrodynamic experiments. Subsequent experiments were done at a lower irradiance.

In the section comparing simulation results to experiment results, simulations were performed at an irradiance of 42% of the lower laser irradiance, 3.36 x 1014 W/cm2.

This is discussed further in Section 7.3.

7.1.1 Production of a radiatively collapsed shock

The ﬁrst task put to Hyades was to show that a low-Z pusher launched via laser ablation pressure could produce a shock in a gas that collapsed higher mass density than would occur through strong shock compression. Recall, a strong shock in an ideal gas (γ = 5/3) compresses the shocked material by

ρ γ + 1 (7.1) f = = 4. ρo γ − 1

Processes that increase the internal degrees of freedom of a gas will lower the poly- 112 tropic index, and increase the initial compression seen in a plasma. In simulations of the experiment, where a 40 µm thick beryllium disk is launched into 6 mg/cm3 of xenon gas with no radiation transport, we see a shock compression to a maximum density of 0.06 g/cm3, or by factor of 10 over the initial density. This suggests that the polytropic index of the material as calculated by the SESAME equation of state table is γ = 11/9, or 1.22. After the initial shock compression of xenon gas, further compression occurs when radiation saps energy from the shocked gas, decreasing the temperature, and correspondingly increasing the density.

Figure 7.1: Two 1D hyades simulations of density. The solid line shows the density proﬁle of a beryllium-driven shock in xenon using a multigroup treatment of radiation. The vertical line shows the boundary between these two materials, with the xenon feature being the rightmost dense feature. The dashed line shows the same experimental setup in a Hyades run with radiation transport turned oﬀ. Again, the vertical line shows the boundary between the driving beryllium plasma and the xenon plasma.

In Figure 7.1, two density proﬁles at 16 ns from the start of the drive beams from Hyades runs are plotted. The dashed line is the simulation mentioned above, 113

where 40 µm of beryllium is launched via laser ablation pressure into 6 mg/cm3 of xenon gas, with the radiation transport in the system turned oﬀ. The laser launches a shock that moves from left to right. The boundary between the xenon and the beryllium is indicated by a vertical line, here labeled “contact surface”, with the beryllium to the left of the surface and the xenon to the right. In this simulation, we see that the beryllium has produced a region of shocked xenon in the simulation that is approximately 10 times as dense as the initial gas, and spans the extent of

200 µm. In this case, the boundary between the beryllium and xenon has moved about 1.85 mm from the initial position of the beryllium.

The solid curve in Figure 7.1 is a density proﬁle from an identical simulation to the one just described, except with a multigroup, diﬀusive radiative transport model to treat radiation. This simulation used 90 photon groups with group boundaries at the atomic transition energies. Most of these groups had an average energy of less than 10 keV. The maximum density of the xenon feature in this simulation is 0.2 g/cm3, more than 30 times the initial density of the xenon gas. The leading edge of this xenon feature is in approximately the same place as the leading edge of the xenon feature in the no-radiation case, but the thickness of the layer is only 80 µm. That is

2.5 times smaller than the thickness of the xenon layer with no radiation transport.

In this simulation, the boundary between the beryllium and the xenon has moved

2.0 mm from the initial beryllium position, 150 µm further than the boundary in the no-radiation simulation. The signiﬁcance of this diﬀerence will be discussed later in this chapter.

At the xenon density shown in the multigroup simulation of Figure 7.1, the dense collapsed layer should be observable via x-ray radiography, and motivated the use of xenon as the ﬁll gas for these experiments. From Chapters Four and Five, we know 114

0.100

500 ion ) 3 temperature T e m m c / density 400 p g ( e 0.001 r y a t i t u s r n e e 300

( D e

V s s )

a electron

M temperature 200 0.010

100

0 1.75 1.80 1.85 1.90 1.95 Position (mm)

Figure 7.2: Profile of radiatively collapsed layer in xenon gas. This simulation was done with a 20 µm beryllium drive disk in 1.1 ATM of xenon. The solid line is mass density, the dashed line is ion temperature, and the dotted line is electron temperature. The spike in ion temperature marks the position of the shock front. that the shocked layer is thin and dense, rather than extended with lower density, confirming that radiation plays a significant role in the dynamics of this shocked system.

Figure 7.2 shows a proﬁle of mass density (solid line), electron temperature (dotted line), and ion temperature (dashed line) as a function of position at 10 ns for a shock in xenon at 10 ns after the drive beams turn on. Compare this, for example, the the cartoon in Figure 2.1 in Chapter Two. The shock front is marked by a sharp increase in the ion temperature. Collisions with ions quickly heats electrons, which radiate energy away. The shocked gas is compressed to high density as the ions and elecrons cool.

A second question to answer before using precious laser time was how early the 115

1.000 1 ns 2 ns

3 ns

0.100 mass density (g/cc)

0.010

0 200 400 600 Distance (µm)

Figure 7.3: Formation of a collapsed shock in the ﬁrst few nanoseconds after the drive beams turn on. Note the diﬀerent peak density of collapsed plasma, which is the rightmost dense feature for each plotted curve.

shock could be imaged. If the shock did not collapse to a high enough density or

produce a thick enough shock, it would not be as obvious on the radiography images.

Early times in the multigroup simulation show the formation of the dense collapsed

layer in xenon using a 40 µm thick drive disk. In Figure 7.3, we see density proﬁles of multigroup simulations at 1, 2, and 3 ns after the laser beams turn on. In these curves we see a large beryllium feature on the left, followed by a burgeoning xenon feature to the right. Between 1 ns and 2 ns, we see the density of this feature increase. Between

2 and 3 ns, we see that the feature has reached the maximum density, and the feature becomes thicker. The density of the xenon feature at 3 ns actually decreases a little, and we see a growing gap between the xenon feature and the bulk of the beryllium. 116

This is indicative of signiﬁcant radiation from the xenon acting as a pressure source on the optically thick beryllium, causing a slight separation.

10 ns 15 ns 20 ns

0.100 mass density (g/cc)

0.010

0.001 1.0 1.5 2.0 2.5 Distance (mm)

Figure 7.4: Density proﬁles from multigroup simulation at three times for a shock launched with a 40 µm drive disk. Note that as the shock moves farther, the thickness of the shock increases, and the maximum density decreases slightly.

As the shock evolves at later time, we see the thickness of the shocked layer increasing as it moves through the xenon. Shown in Figure 7.4 are three density proﬁles from a shock launched with a 40 µm drive disk, shown from left to right at 10, 15, and 20 ns. The right-most dense feature is compressed xenon, while the feature to the left on each curve is the dense beryllium pusher. Here, you see that the maximum density of the shock decreases slightly as the beryllium pusher slows down, driving a weaker shock. The thickness of the collapsed layer increases signiﬁcantly over time, from a thickness of about 40 µm at 10 ns to a thickness of over 100 µm at 117

20 ns. A perfect side-on measurement of the collapsed layer via radiography should observe this diﬀerence. However, diﬃculties with exact side-on observation prevent a precise measurement of this feature. The measured and simulated shock thicknesses as a function of time are shown in Chapter Five.

7.1.2 Drive disk thickness variation

Once experiments verified the production of a collapsed shock in the nominal target configuration, we turned to the possibility of driving faster shocks to produce more dramatic radiative effects. As discussed in the Radiation Hydrodynamics chapter, when the ratio of radiative flux to energy flux carried by the material gets large

(deﬁned as the quantity Rrad), the system will radiate away energy to bring that ratio down. To produce more dramatic radiative eﬀects, one would seek to increase this

2 ratio in the experiment. Using the strong shock relation that tells us that Ti ∝ us, we remind the readers that

4 5 σT us (7.2) Rrad = ∝ . ρouscvT ρo

Shock velocity and initial mass density are both quantities we control in an experiment. To launch a faster shock, we can use the same laser intensity on a thinner beryllium disk. By using a thinner disk, the shock launched by the laser through the beryllium takes less time to pass through the whole disk. When all the beryllium is shocked, the laser pressure is a subsonic disturbance, which accelerates the whole disk. Since the disk is thinner, there is less material to accelerate, and the laser can push it to higher velocities. Also, because the shock passed through the material faster, the laser pulse is subsonic for longer, and therefore accelerates the material for a greater period of time. These combined eﬀects mean that a thinner drive disk 118 can launch a much faster driven shock in the xenon.

Shown in Figure 7.5 are three density proﬁles from multigroup Hyades simulations at 10 ns after the drive lasers turn on. These simulations were run with three diﬀerent drive disk thicknesses, from left to right, 40, 20, and 10 µm beryllium disks.

There are several things to note when examining this figure. The most obvious is the difference the drive disk makes on the shock velocity. The thinner the disk, the farther the shock has propagated in 10 ns. The second is the structure on the front (right) side of the dense xenon layer. On the profiles for the 40 and 20 µm disks, the rise in density looks smooth and sharp, all in one continuous step. The 10

µm curve shows more reﬁned structure, where one can see the initial density jump due to strong shock compression, followed by the further increase in density due to radiation loss. This structure is actually present on all three curves, but is not well enough resolved on the ﬁrst two to notice on this plot.

The third thing to notice is that the beryllium pusher in each case looks very different. As the beryllium drives the shock from left to right in these simulations, the beryllium is also expanding to the left now that the pressure source from the laser is gone. A rarefaction wave is causing some of the material on the left side of the beryllium (the laser driven side) to expand to the left as the bulk of the material moves to the right. It is the momentum in the beryllium driving a shock in xenon, enhanced by supersonic expansion of the beryllium towards the beryllium/xenon boundary. This supersonic flow is mainly driven by ablation of the beryllium by the radiation escaping from the collapsed layer. Because the rarefaction wave moves at the speed of sound, it cannot overtake the region of supersonic flow until the shock slows due to the effect of mass build up in the collapsed layer. When the shock slows, the rarefaction can overtake the rest of the beryllium driver, and proceed into the 119 collapsed gas layer. In Figure 7.5c, the rarefaction has moved into the xenon gas.

The density proﬁle at maximum density in the layer shows a tilt towards the left, as the gas begins to expand to the left. This late-time evolution is discussed more in the next section.

Figure 7.5: Density proﬁles from three multigroup simulations at the same time, 10 ns after the drive beams turn on. Each simulation used a diﬀerent thickness of drive disk, pictured from left to right on the plot, 40 µm, 20 µm, and 10 µm.

7.1.3 Late-time eﬀects

At some late time, the evolution of the system should change from that of a collapsed shock driven by a piston to that of an undriven system. As mass builds up in the shocked xenon layer, the beryllium piston slows by momentum conservation.

This simple picture is complicated by material backflow from the rarefying beryllium plasma, so that the piston does not slow as quickly as a piston would without backflow of material. This rarefaction wave moves at the speed of sound in the beryllium plasma. At the beryllium/xenon boundary, the beryllium is optically thick to the radiation from the xenon layer. This radiation source ablates material at that 120 boundary, causing it to flow to the right at a speed faster than the sound speed of the beryllium plasma, creating a lower-density gap between the bulk of the beryllium and the xenon layer. This is best seen in Figure 7.5a for a 40 µm drive disk. In this

ﬁgure, the boundary between the beryllium and the xenon is at the left edge of the dense xenon feature.

Figure 7.6: a) Density and b) velocity proﬁles at 6, 12, 18, and 24 ns after the drive lasers turn on for an experiment using a 20 µm thick beryllium drive disk.

As the shock moves through the xenon gas and the collapsed layer becomes thicker, momentum conservation slows the piston, and the rarefaction wave can eventually move through the region of ablated material at the beryllium/xenon boundary. The wave can then move into the collapsed xenon layer, causing the layer to expand. At this point, the beryllium plasma is no longer driving the shock in xenon.

A simulation showing this transition is presented in Figure 7.6. In Figure 7.6a, we show density profiles of a simulation of the experiment driven by a 20 µm thick drive disk at 6 ns intervals, up to 24 ns. While the xenon feature gets much thicker in time and slightly less dense, the beryllium expands towards the left of the figure. After 121 about 6 ns, the densest part of the beryllium is less dense than the xenon feature, and continues to decrease in time at all points in the beryllium. In Figure 7.6b, we show the velocity profiles at the same times. For the first 18 ns, the deceleration of the shock is roughly linear, as shown by the dotted line through the peak velocity through the first three times shown. However, at late time the velocity does not follow the linear decrease; in fact, it stays moving relatively fast. This may be the effect of expanding xenon now that the driving force of the beryllium no longer controls the velocity of the shock in xenon gas. Also note the effect of the rarefaction wave on the xenon layer at t = 24 ns in Figure 7.6a; the lower density at the left edge of the layer is due to the rarefaction wave. Free expansion of the xenon to the left in this figure would be hampered by the presence of the low-density beryllium plasma in a 1D simulation.

7.2 Two-Dimensional Simulations

Two-dimensional simulations were done of this experiment in xenon gas to ensure that lateral material and energy losses were not signiﬁcant. Hyades has a 2D package, but the strong shear near the walls of this experiment made the version of the code available at that time unusable. In this geometry, one must let the xenon move along the polyimide tube walls to contain the experiment. This led to zones along the walls folding over themselves, or “bowtie-ing”. The presence of these bowties slowed the code to a crawl. It was possible to pause the code, manually ﬁx the zone boundaries to untie them, and restart the code, but the bowtie-ing happened so quickly that not much ground was gained before the code slowed again. Therefore, other codes were tapped to help explore the 2D simulations of our experiment. 122

7.2.1 FCI

FCI-2 is a Lagrangian hydrodynamic code, also using single-fluid, three temperature treatment [11]. It treats radiation via a flux-limited multigroup diffusive transport model, and uses flux-limited electron-heat transport. In these respects, it is much like Hyades. However, FCI uses non-local-thermodynamic equilibrium model, where Hyades uses an average atom local-thermodynamic equilibrium model to calculate the relevant atomic physics.

Shown in Figure 7.7 is the 2D density proﬁle generated by FCI-2 at 8 ns, using a 40 µm beryllium driver, showing from the center of the tube to one edge. The shock is moving from left to right. Here, the color scheme reﬂects the compression of the material compared to the initial density of 0.006 g/cm3. This simulation also shows a thin, collapsed layer of xenon gas at a higher density than predicted by the

1D Hyades simulation. Peak compression of the xenon is 45 times the initial gas density, while Hyades predicted just over a factor of 30 compression. Here, we also see a low-density layer in between the dense xenon and the beryllium pusher, again due to the radiation from the xenon acting as a pressure source. While there is some curvature in the collapsed layer structure near the polyimide wall of the experiment tube, most of the front structure away from the walls is not very curved. Also, at this time, almost all of the xenon that has been shocked is contained in the collapsed layer; very little has escaped around the beryllium.

Using this 2D simulation, a radiograph can be simulated to check that the simulation results actually reﬂect the experimental ones. Using the density data from this simulation, and the opacity of beryllium and xenon at 5.2 keV from the NIST FFast

X-ray Database (online at http://physics.nist.gov/PhysRefData/FFast/Text/cover.html), transmission levels should be similar to those of a radiograph taken with a vanadium 123

Figure 7.7: Density simulation in two dimensions using the FCI-2 code at 8 ns after the drive beams turn on. The shock moves from left to right. The leftmost dense feature is the beryllium pusher, separated by a low-density region from the rightmost dense xenon feature. The coloring of the graph reﬂects the density expressed in units of the initial xenon gas density. Peak compression of the xenon gas is 45 times over initial density. backlighter. The cylindrical geometry of the target was taken into account, and noise and resolution information was taken from actual data. The simulated radiograph that resulted is shown in Figure 7.8.

From this simulation, we can also futher explore the eﬀects of a slight tilt in the line-of-sight of the diagnostic. From tilting the line of sight of this radiograph by 5 degrees, the imaged dense layer grew from 50 µm in thickness to over 90 µm in thickness, due to the 600 µm diameter of the polyimide tube containing the experiment.

This dramatic eﬀect shows how much even a small misalignment in the chamber or error in fabrication can make big diﬀerences on the data image.

7.2.2 Zeus

Zeus-2D is a Eulerian code (ﬁxed zone positions), using a single-ﬂuid, two temperature treatment of the material with gray radiation transport. As described in 124

240 63 Thin Xe 54 Layer 45 ) 160 36 m µ (

27 . s 18 d

r 80

o 9 o C

0 ρ / t ((aa)) e g ο

r 300 a T

n i

e 200 c n a t s i

D 100

(b) 700 800 900 Distance in Target Coords. (µm)

Figure 7.8: a) FCI-2 density profile at 8ns, shown also in Figure 7.7. b) Simulated radiograph from data in that 2D density profile. This simulated radiograph shows an image of the collapsed xenon layer slightly thicker than that shown in the simulation, approximately 50 µm thick. 125 his 2005 papers, Leibrandt et al. ([34], [33]) implemented a flux-limited diffusion radiation module, as well as a front-tracking module and a heuristic ionization model.

For simulations of the driven xenon experiment, the code used ideal gas equations of state and least-squares ﬁts of the SESAME opacities, described in more detail in this paper. This simulation also used a polystyrene drive disk at 1.05 g/cm3, at a thickness of 72 µm instead of a beryllium drive disk, However, at this density and thickness, the areal mass driven is the same as a 40 µm beryllium disk. Zeus-2D does not have a laser package, so the initial conditions are linearly interpolated from

Hyades at 1 ns, the instant when the lasers turn off. This time is also chosen because it is unlikely that 2D effects will have made significant impact on the system at this time.

The assumption of flux-limited diffusion introduces an assumption about the angular dependence of the radiation field. This eliminates the need to treat radiation discretely over angle, reducing computation time. This assumption is only really justified in optically thick systems. This paper is one of few to explore the validity of the flux-limited diffusion approximation in systems that are not inherently optically thick. By doing a convergence study on grid spacing and time steps in both one- and two-dimensional simulations, this study shows that the results of a flux-limited diffusion scheme do converge on the experimental values, but do not capture all the structure seen in the data.

In one dimension, grid spacing dominates the error in the measurements of early shocked-layer thickness, while it’s time rate of change depends more on the time step. As the experiment progresses and the shocked layer becomes thicker, time step errors take over. In two dimensions, the shock shows a curved structure, with trailing xenon visible along the walls, between the walls and the shocked drive disk. 126

7.3 Issues Between Simulation and Experiment

As has been documented for 2D simulations, the laser irradiance used in such 1D simulations must be reduced to give accurate results, because radial heat transport reduces the ablation pressure in the actual system. The irradiation in the present experiments is nearly identical to that used in previous work with two-layer, non- radiative, purely hydrodynamic targets, diﬀering only in these ways: a) the present experiments use SSD (Smoothing by Spectral Dispersion, see Chapter Three), b) the present experiments use an irradiance that is 80% of the value used previously, and c) the present experiments use 20 µm of Be, from which the shock emerges during the laser pulse, while the previous experiments used 150 µm of polyimide as a ﬁrst layer, so that the shock traversed only about half of this layer during the laser pulse. In the previous work we have extensively compared the results of Hyades simulations to measurements of the shock and interface positions. We found that the code reproduced the observations very well using an irradiance that was 42% of the actual value. This was the value scaled here.

Even after scaling the laser intensity to sensible levels in the 1D simulation, beryllium/xenon interface position data collected over several shots show a large discrepancy between the measured position of the interface and the predicted interface position from 1D simulations. The uppermost curve in Figure 7.9 is a 1D Hyades simulation run at the irradiance described above. This curve lies well above the experimental data, overpredicting the distance the interface has traveled by approximately 25%. The other curves on the plot show the eﬀect of decreasing the laser irradiance on the interface position. To obtain the observed trajectory of interface locations, the laser irradiance must be reduced to almost 70% of the nominal value. 127

While this represents a possible avenue for getting the correct interface position, it is an ad hoc adjustment to match the data that is not supported by our previous understanding.

Figure 7.9: Data points are experimentally measured positions of the beryllium/xenon interface for experiments using a 20 µm thick drive disk. The lines represent interface positions in simulations with full laser intensity and scaled laser intensities. The laser intensity must be reduced by approximately 25% to match the data.

The discrepancy just described might be a consequence of either the one-dimensional dynamics of the system or of two-dimensional effects. The potential physical issues that could create errors in the one-dimensional behavior include the equation of state of the Be, the effect of radiation in the Be as it is shocked and accelerated, and the effect of the radiation from the Xe on the Be as the shock evolves. The potential issues in two dimensions are the lateral flow of energy, presumably reducing the ab- 128 lation pressure during the laser pulse, and the lateral flow of matter after the laser pulse. We had only a limited ability to learn from two-dimensional simulations.

Simulations using the FCI code, which includes laser absorption and flux-limited, diffusive electron heat transport [43] exhibited a discrepancy similar to that seen in the 1D results. Simulations with FCI and with Zeus ([34], [33]) did not produce significant lateral mass flow. This motivated a more extensive exploration of the one-dimensional issues, described here.

Because the shock velocity and collapsed layer position in these experiments and simulations depend on the position of the driven surface, we ﬁrst undertook to examine the treatment of the beryllium in the simulations more closely to help explain the interface position discrepancy. We explored the possibility that errors in the Be equation of state (EOS) might be important by doing a sequence of simulations varying

γ. While this might fail to capture details associated with changes in compressibility as different electron shells open up in the material, it should show whether the behavior of the system is strongly sensitive to the EOS. In addition, for Be shocked to 50 Mbars it would be quite surprising to find subtle differences relating to the detailed structure of the equation of state. We found that variations in γ produced the expected increase or decrease of the Be density but led to only small changes in the interface velocity. This is not surprising as the ablation pressure and mass ablation rate due to the laser should be weakly affected by changes in compressibility, so that the main determinants of the velocity are the total impulse from the laser and the total areal mass of the target.

We proceeded to explore the impact of radiation on the simulated structures.

In simulations done with xenon gas, as shown in Figure 7.10, there is a distinct difference in the beryllium profile when radiation is turned off, which might or might 129

Figure 7.10: Simulations of laser driven beryllium into 0.006 g/cm3 helium gas. These simulations are identical to simulations done of the experimental setup described, except using a weakly radiating fluid. Solid lines are simulations with diffusive multigroup radiative transport, while the dotted lines are simulations with radiation artificially suppressed. Note the marked difference in the density profile of the beryllium at 10 ns between the two simulations. 130 not be due entirely to the xenon acting as a radiation source on the beryllium. The

first question to explore then was whether the radiation treatment of the simulation affected the density profile of the beryllium if such a radiation source were no longer present. To that end, we performed simulations identical to those described above, removing xenon gas and replacing it with helium gas at the same mass density,

0.006 g/cm3. Helium gas is not a strong radiation source, and therefore diﬀerences in the beryllium proﬁle would be caused only by radiation in the Be. Shown in

Figure 5 are the results of simulations over 10 ns with beryllium driven into helium gas, with multigroup radiation transport (solid line) and with radiation artificially suppressed (dashed line). The dense feature in both of these simulations is the beryllium. After 10 ns, the beryllium density profile in the radiative simulation is significantly different than in the non-radiative simulation. While the position and density of the beryllium/helium interface is approximately the same in the two simulations, the radiative case shows the beryllium extended farther backwards, at a peak density that is less than half the peak density in the non-radiative simulation.

Therefore, even in a weakly radiating fluid, the radiation treatment in the simulation has a significant effect on the beryllium behavior. However, the difference in the position of the interface between the Be and the He is negligible between these two cases, so the effect of the radiation within the Be during the laser pulse appears not to explain the discrepancy we are exploring.

The third issue we explored is the impact of the radiation from the xenon. In

Figure 7.11 we compare simulations using multigroup radiation transport in xenon gas (solid line) to those in helium gas (dashed line) over 10 ns. At 2.5 ns, the difference in the beryllium profile between these two simulations is minimal. But as the radiatively collapsed layer becomes more defined, the differences become more 131

Figure 7.11: Multigroup simulations of a beryllium disk driven into xenon (solid lines) and helium (dashed lines). At 2.5 ns, the difference in the beryllium structure and interface position between the two simulations is minimal. By 10 ns, the difference in the structure of the beryllium is quite different. At this time, the beryllium/xenon interface has moved 250 µm further than the beryllium/helium interface. The beryllium in the xenon simulation at this time also has significantly more material to the right of the density peak, suggesting flow of beryllium ablated by the xenon radiation source. 132

dramatic. At 10 ns, the peak density of the beryllium driven into xenon gas is less

than 1/3 that of the peak density of the beryllium driven into helium gas. Much

more beryllium is located to the right of the peak density in the xenon simulation,

suggesting that beryllium ablated by the radiating xenon layer is ﬂowing to the right

in this ﬁgure relative to the motion of the peak density of the beryllium. This is

conﬁrmed by examination of Figure 7.6, which shows a region of acceleration to the

right of the beryllium peak at 6 ns. Here, the position of the interface in the xenon

simulation is approximately 250 µm farther to the right than that in the helium

simulation. The interface position at this time in the helium simulation is located

at 1500 µm from the initial position of the drive disk; this interface position at this

time is about 10% farther than the experimentally measured interface position at

10 ns. The proﬁles to the left of the beryllium density peaks are the same in both

simulations.

7.4 One-Dimensional Simulations in Argon Gas

The bulk of the radiography data displayed in Chapter Four was imaged in xenon

gas, which motivated the focus of this chapter. Some early radiography data and

the Thomson scattering experiments were done with argon as a ﬁll gas. Argon is

less radiative than xenon, so the peak compression of the collapsed layer is slightly

lower in argon than in xenon. Shown below is a simulation of a 20 µm beryllium

disk launched into 1.1 ATM of argon gas (0.001 g/cm3 or 1.5 x 1019 atoms/cm3) at a simulated laser intensity of 3.36 x 1014 W/cm2, 42% of the laser intensity used in the experiments.

Figure 7.12 shows density proﬁles in argon gas at several times. Based on the time and the position that the Thomson scattered spectrum was collected, this simulation 133

5 ns 0.100 10 ns 15 ns 20 ns ) 3 m c / g (

y t i

s 0.010 n e D

s s a M

0.001

1.0 2.0 3.0 4.0 Position (mm)

Figure 7.12: Multigroup simulations of a 20 µm beryllium disk driven into argon gas at 1.1 ATM (1 mg/cm3). 134 overpredicts the shock position in the same way that the xenon simulations did, by about 25%. The argon structure here is more extended than the xenon structure.

After an initial density jump and plateau at 28 times the initial mass density, the argon begins to collapse again, to a ﬁnal density that is 80 times the initial density.

A small ablation driven gap separates the argon from the bulk of the beryllium, but it is not as distinct as in the xenon simulations. This is intuitively sensible, assuming that argon radiates less strongly than xenon. It also seems that the beryllium has spread out less at late times compared to similar xenon results, which are shown in

Figure 7.6.

density 0.100 ion temperature

300 T ) e 3 m m p c / e r g ( a

t y u t i r e s

200

n 0.010 ( e e electron V D

)

s temperature s a M

100

0.001

0 3.4 3.6 3.8 Position (mm)

Figure 7.13: Multigroup simulations of a 20 µm beryllium disk driven into argon gas at 1.1 ATM (1 mg/cm3), showing mass density, ion temperature, and electron temperature. 135

Figure 7.13 shows the simulated density (solid), electron temperature (dotted), and ion temperature (dashed) for a simulation in argon at 16 ns after the drive beams turn on, using a 20 µm beryllium drive disk. The position of the shock front at this time is the same as the position as the Thomson scattering volume described in Chapter Six. The shock front is marked by the spike in the ion temperature. The ion and electron maximum temperatures are both lower than in xenon, as is the maximum mass density. However, the ﬁnal compression is higher, because the initial gas mass density was lower in argon than in xenon.

Two-dimensional simulations were not done in argon gas. If more experiments are done in the future to examine the structure of the collapsed layer in argon, this may be useful for comparison.

7.5 Summary of Simulation Results

Hyades simulations in one dimension provided a useful tool for understanding and visualization of the important physical quantities. However, the limitations of the radiation treatment in one dimension prevent this from being a quantitative, predictive tool. In all the simulations shown, the position of the shock was overshot by up to 30%. As this experiment evolves, other physical quantities will be measured, quantifying the errors in the simulations of those quantities..

Detailed radiation treatment, especially in multi-dimensions, is computationally expensive, and unavailable to the author at the time this thesis was written. However, as more powerful lasers become available, more of the radiative ﬂux- and pressure- dominated will be accessible via experiment. It will be essential to have a computational tool capable of handling the physics of radiation hydrodynamics to model these experiments to help maximize the eﬃciency of these experimental campaigns. CHAPTER VIII

Conclusions and Future Directions

Side-on backlit x-ray radiography was successful both in targets that were area- backlit and imaged on to a 4-strip framing camera and for targets that were pinhole- backlit and imaged onto a single-strip framing camera. Using a single-strip framing camera yielded higher-contrast images than were ﬁrst obtained with four-strip images, after experimentation with target design resulted in a viable pinhole-backlighter target. Further smoothing of backlit pinhole images to minimize source and gain variation revealed a clumpy structure on some collapsed layers. Attempts to do both kinds of radiography on the same shot were unsuccessful, as high-energy noise from the area backlighter contaminated data on the single-strip framing camera, exposing the phosphor despite the gating mechanism.

VISAR diagnostics show that there is enough preheat of the unshocked material to partially ionize it, creating an inverse-bremsstrahlung barrier for the green probe beam from that diagnostic, even though the attempted novel use of the interferometer to see the changing electron density of the shocked plasma via fringe-shifting was not successful.

One- and two- dimensional simulations of this radiation hydrodynamic phenomena aided qualitative understanding of the formation and evolution of the driven system.

136 137

These simulations were very limited in their predictive ability, miscalculating the shock position in all simulations.

The use of the Thomson scattering diagnostic with a scattering volume within a driven shock front provided data about the temperature and ﬂow velocity of the shocked plasma. Fits to the spectra structure determined the ion and electron temperature in the small scattering volume, conﬁrming the temperature calculations of

1D simulations to within the error bars of the measurement.

8.1 Radiative Shocks in Astrophysics

At the 6th International High-Energy-Density Laboratory Astrophysics conference in March, 2006, John Castor mentioned in his invited talk that it is diﬃcult to pick an astrophysical system and model a radiative shock experiment after it.

However, he said, if you create a radiative shock in the laboratory, it was almost certainly possible to ﬁnd an astrophysical system with the same properties, due solely to the sheer number of radiative shocks in astrophysics [10]. I did not succeed in forming quantitative link between this experiment and any astrophysical shock during the course of this research. Perhaps a more extensive object search, along with more quantitative measures of the experimental system, would reveal an appropriate subject.

However, I did ﬁnd examples in astrophysics in the same fundamental regime as the shocks described in the previous chapters. Recall from Chapter Two that we can establish regimes of radiative shocks according to the optical depth upstream and downstream from the shock. In the case of the radiative shock experiments and of the astrophysical shocks discussed below, we explore shocks that are optically thin in the unshocked material (“upstream”) and optically thick in the shocked 138 material (“downstream”). This similarity in structure allows us to describe the systems with the same equations. This similarity also means that a code which can correctly reproduce the experimental radiative shock system, with known initial conditions, should also correctly describe these astrophysical radiative shocks in the same regime. The examples that I found are discussed below, where similarities between the example and the experiment are highlighted.

8.1.1 Shocks Emerging from Supernovae

The life of a large star is ended by a dramatic explosion, known as a core-collapse supernova, or Type II supernova. Fusion burning at the center of the star generates heat that provides a pressure source that hydrostatically counters the inward pull of gravity. Fusion of low-mass elements produces energy, and produces heavier and heavier elements until iron is produced. Since iron has the highest binding energy per nucleon, fusion is not energetically favored, and an iron core is produced. This core is supported by the degeneracy pressure of its electrons, and when the core exceeds a 1.4 solar masses, this pressure is no longer enough to carry the weight of the star.

The core collapses, and the star implodes.

In consequence of the core collapse of a large star, a powerful shock wave moves outward and blows the star apart, ejecting most of the stellar material. The process of shock breakout into the surrounding shell of circumstellar material takes on the order of a day, measured as the light curve rises to peak luminosity. The luminosity of the star rises greatly when the shock deposits energy in the optically thin outermost layers of the star. The deposited energy is radiated away, producing the so-called

“ultraviolet burst.” In this optically thin layer, it is possible for the shock to lose a signiﬁcant amount of energy through radiation loss [53].

As described in the Radiation Hydrodynamics chapter, loss of signiﬁcant amounts 139 of energy via radiation lowers the internal pressure of the shocked material, leading to increased density response in the form of compression. This compression continues until the gas has cooled via radiation to its postshock equilibrium temperature.

Simulations from Ensman and Burrows [17] show the formation of a cooling layer for parameters from the observations of nearby supernova 1987a. These simulations were done using the 1D code VISPHOT, which is a Lagrangian, two-temperature,

LTE radiation hydrodynamics code. This code solves the co-moving frame frequency- integrated moment equations of the radiative transfer equation. It does not make the assumption of isotropic radiation, nor does it require a ﬂux-limited diﬀusion scheme for proper treatment of radiation. The model used a 20 solar mass main sequence star with the outer layers removed to get the correct envelope mass for SN

1987a, which then was given an enhanced helium abundance in the envelope. This procedure gave a 17.6 solar mass progenitor star, with a radius of 3 ×1012 cm and a luminosity of 4.4 ×1038 ergs/sec. The optical depth profile for this system is given in Figure 8.1. This profile was calculated assuming blackbody radiation at effective temperatures calculated from the bolometric light curve.

Simulations of shock breakout show a spike in ion temperature just behind the hydrodynamic shock front, followed by a rapid increase in mass density. Even at large radii, this layer remains physically thin. This is similar to the density and temperature proﬁles from 1-D simulations of the shock wave, described in the Radiation

Hydrodynamics Simulations chapter, and shown again in Figure 8.2. There, we see a similar dense region that is thin compared to the distance it travels from where the shock is launched. We also see a spike in temperature at the shock front (as one will see at all shock fronts), with rapid cooling behind the shock front. Also in both cases, the ﬁnal post-shock temperature is approximately the same temperature as 140 1992ApJ...393..742E

Figure 8.1: Optical depth and mass proﬁles from 1D simulation of the supernova explosion of 1987a Most of the mass is within the inner 350 zones. Optical depth is calculated from the surface (zone 500) inward, and 22 zones are at an optical depth less than 1. The rise in optical depth in zone 40 marks the location of the shock front. From Ensman and Burrows, 1992.

that of the unshocked material.

In Figure 8.2a, the collapsed layer is almost four magnitudes higher in density than

the unshocked gas, and is extremely thin. These two features from the simulation

suggest an enhancement in the density jump at the shock front from radiative cooling.

If strong shock compression alone was responsible for the enhancement in density,

the polytropic index of the shocked gas would have been approximately γ = 1.0002, which is a very small value. Also, while all shocks have a spike in ion temperature, not all shocks have such a fast drop of the ion temperature. Here, both the fast cooling and thin, dense feature are eﬀects of radiative collapse of the shocked gas.

This process is physically identical to the radiative collapse of the shocked gas in the experiment presented here. Simulation results from the experiment are shown in Figure 8.2b for comparison. While the shocks are not identical (with diﬀerent initial densities, shock speeds, compositions, and total radiative ﬂuxes), the physics 141

Figure 8.2: Temperature and mass density profiles from (a) Ensman and Burrows, 1992 and (b) 1D radhydro simulations of driven radiative shock experiment in xenon. While the scales are different, both the density and temperature profiles are qualitatively similar. Note the spike in temperature, followed by rapid cooling and a significant increase in the density in a thin layer. This similarity will last until the supernova shock moves into a regime where the material behind the shock becomes optically thin, farther away from the exploding star. describing the process is the same. Therefore, any simulation that can correctly describe the experimental system, which has well known initial conditions, should be able to describe this type of shock in an astrophysical system, such as SN 1987a.

This would be subject to the ability of the code to treat the diﬀerent materials and radiation mechanisms that may be present in the two systems.

8.1.2 Cooling of Stellar Atmospheres

Stationary shocks, ubiquitous in many astrophysical systems, also exist within the atmosphere surrounding large stars. These shocks in the low-density atmosphere can cool radiatively. In this scenario, the star will be optically thick downstream of the shock, while the unshocked low density atmosphere upstream from the shock will be optically thin to radiation, similar to the experimental scenario explained in other chapters. Fokin, Massacrier, and Gillet [18] attempt to model the radiative wake structure in a shocked stellar atmosphere by assessing iron line and continuum radiative cooling. The treatment presented in this paper is oﬀered as a general solution for shocks in low-density atmospheres. As an example, the model is applied 142

to shocks in diﬀerent types of pulsating stars.

As explained in Fokin, 2004, most of the radiation cooling will happen just behind

the shock front in what they call the “radiative wake structure”. This structure is

shown in Figure 8.3. The model of the wake adopted for the study by Fokin et. al

is shown by the solid lines in the ﬁgure.

Figure 8.3: Shock structure from computational analysis of a radiative shock in a stellar atmosphere. The solid line structure was adopted for analysis of the temperature and density structure in the radiative wake. From Fokin et. al, 2004.

Shown in Figure 8.4 are 1D simulation results of the temperature and density

structure behind a radiative shock with a velocity of 50 km/sec in a stellar atmosphere

with an unshocked gas temperature of 5000 K (or 0.43 eV), an initial density of

2 × 10−12 g/cm−3, and an with the initial temperature just behind the shock front of 10000 K (or 0.86 eV) . Note that the density at the shock front in Figure 8.4 is approximately 4 × 1010 g/cm3, two orders of magnitude higher than the initial density quoted.

Because the optical depth proﬁle in the system studied by Fokin et al. is similar to 143

ρ 1.5 10 [g/mol] T µ µ 9

1.0 8 T [1000K] 7

0.5 6 -10 3 ρ [10 g/cm ] 5

107 106 105 4.104 2.104 0 ∆r [cm]

Figure 8.4: Temperature, mean molecular weight, and mass density proﬁle of a stationary shock in a stellar atmosphere. The x-axis is the distance from the shock front. The vertical line marks a change in scale, as quantities change more slowly farther from the shock front. From Fokin et. al, 2004. that of the experiment described in previous chapters, we can undertake to compare them a little more closely. Figure 8.4 shows the temperature, mean molecular weight, and density proﬁle of the shocked system discussed in the reference. Simulations of typical Population I and Population II type stars show that much of the cooling comes from iron line radiation, with a non-negligible contribution from continuum radiation of hydrogen transitions. In an LTE calculation, the authors undertook the task of performing a detailed calculation of the thermal radiative wake structure.

Figure 8.5 shows the contributions to the cooling of the shocked gas from several of the main contributors. The solid line in the ﬁgure shows the total cooling rate of the gas. The short dashed line shows the contribution from the Fe I line. The long dashed line shows the contribution to the cooling rate from the Fe II line. Note that this line actually heats the system at some distance from the shock front. The dotted line shows the continuum contribution, from hydrogen series transitions.

We used simulations of the experiment described in the Computational Support 144

Figure 8.5: Effect on cooling rates from different contributions. This log plot gives both heating and cooling of the system, with zero on the y-scale corresponding to no heating or cooling. From Fokin et. al, 2004. chapter to back out a similar cooling rate profile from thermal radiation from the shocked xenon, shown in Figure 8.6. The opacity of xenon was taken from fits to the sesame tables calculated in Leibrandt et al.[33]. The beryllium opacity was taken from minimum values in the online NIST FFast Database. This shows the cooling rate is significant in the optically thin transition region just behind the shock. As the xenon becomes more dense, cooler, and more optically thick, the cooling slows quickly, and then levels off and some much slower rate. The maximum cooling rate is more than 3 orders of magnitude higher than this final level. This final downstream xenon cooling rate is lower than the cooling rate calculated for the unshocked xenon, which is the material to the right of zero in Figure 8.6. Figure 8.6a is the cooling profile over the extent of the experiment in xenon, and Figure 8.6b is a close-up of the cooling layer near the shock front.

As you can see in Figure 8.6, the total cooling rate does not go to zero far away 145

Figure 8.6: Calculated cooling rate from experiment in xenon. Radiation was assumed to be thermal radiation from the cooling layer in the shocked plasma. This plot is in similar units to the cooling rate of Fokin, with cooling rates reported as negative. a) Cooling proﬁle of most of the experiment, including beryllium driver. b) Cooling proﬁle of just xenon, near the shock front. from the shock, as it does in the astrophysical example, and as shown in Figure

??. However, further examination of the cooling times for this system show that the smallest cooling rates correspond to cooling times of approximately 50 ns, which is more than twice the duration of the experiment. At the highest cooling rates

(just behind the shock), the cooling time is approximately 100 picoseconds, which is reasonable based on simulations of the experiment.

In Fokin et al., the authors placed an emphasis on the incomplete nature of modeling radiative transfer in such a complicated environment. They cited several works with questionable results due to insufficient modeling of the radiation, and offered their solution with several caveats. They also state in the text, “we have no way of directly proving our main hypothesis, i.e. that the region between our “front” and the viscous shock front is effectively transparent for all iron lines.” While the experiment in the present thesis described does not provide a testbed for measurement of spectral lines relevant to stellar atmospheres, it does provide a vehicle through 146 which this hypothesis might be tested in the future, using a higher-powered laser and a relevant gas mixture.

8.2 Applications

In addition to providing a vehicle that may lead over time to further understanding of certain astrophysical shocks, this experiment has direct relevance to a new type of directly-driven laser fusion target. This target is called a laser-driven dynamic hohlraum, or LDDH. This type of target combines the smooth radiation source from a traditional gold hohlraum, with the more efficient convergent geometry of a traditional directly-driven fusion fuel capsule. In this geometry, a fusion fuel pellet is surrounded by a layer of high-Z gas in addition to the normal spherical ablative and driving layers. Xenon was used in early tests. Lasers irradiate the outer layers, launching them radially inward. This drives a shock in the gas, which undergoes radiative collapse. The radiation from this gas, in addition to the centrally converging material, compresses the central fuel with a smooth radiation source from the collapsed shock in the gas. This approach combines the major attractions of both direct and indirect drive into one target. Unfortunately, these assets are combined into a target that is difficult to make. The compression of the central fuel in a fusion target must be as symmetric as possible to maximize the yield of the fusion explosion. These gas-filled LDDH must have a fill tube to pump gas into the target, which then must be attached in a way that keeps the target gas-tight. This requires a significant amount of glue, creating a large irregularity on the outside of the target and a spot that cannot be driven by lasers. 147

8.3 Future Directions

This experiment can beneﬁt from being diagnosed in a more quantitative way.

Measurements of the temperature of shocked plasma as well as the warm precursor would be useful in quantitative comparison of the shock in this experiment to other radiative shocks, as well as to radiation hydrodynamics codes. In the past year, initial experiments were performed to do just that, as well as to improve the current radiography diagnostic.

8.3.1 Flux Measurements

A natural measurement of a system with signiﬁcant radiation would be a radiation temperature measurement with a ﬂux-collecting diagnostic. Initial experiments have been designed and executed for experiments utilizing both a soft-x-ray detector

(the DANTE diagnostic), and a soft-UV detector (the Streaked Optical Pyrometer diagnostic) at the Omega Laser Facility. These experiments should work with either

fill gas used in previous experiments (argon and xenon), but initial experiments used xenon gas. These diagnostics would measure the effective radiation temperature of different parts of the experiments by fitting the collected radiation flux to a blackbody curve. The Streaked Optical Pyrometer would probe the unshocked, preheated material, which VISAR measurements estimate to be at least a few eV. The DANTE diagnostic would be more sensitive to the soft x-ray emission from the shocked material itself, which 1D and 2D simulations predict to be a few hundred eV. This number is supported by the Thomson-scattering measurements in argon gas. Initial results were promising for the use of this diagnostic in future experiments. 148

8.3.2 Short-Pulse Backlighters and Ungated Imaging Diagnostics

The experiment that tested the viability of the flux measuring techniques for this experiment also incorporated advances in radiography techniques. Other experiments done in this research group have successfully used an ungated x-ray collection diagnostic, with excellent results. Ungated diagnostics have intrinsically less noise than gated diagnostics, as there are no voltage pulses or microchannel plates to in- troduce any gain variation. This ungated diagnostic actually uses the length of the backlighter pulse as the “gating” mechanism to image onto a piece of x-ray film shielded only with beryllium. This unprotected piece of film is also susceptible to x-rays generated by the lasers and laser-irradiated sources other than the backlighter.

These other sources may expose the ﬁlm and lower the contrast on the data image, and so extreme shielding measures are taken to protect the ﬁlm from these sources.

A large acrylic shield with gold wedges pointing towards the diagnostic protected the x-ray film from high-energy photons produced in the driving pulse. The target design also afforded protection from a laser beam used to blast an opening in the back end of the target to afford a direct line of sight to the xenon plasma to the diagnostics described above. A shadowed image of the target in the target chamber is shown in Figure 8.7.

For slow moving shocks like those in previous successful experiments, backlighter pulses of the length used for the gated experiment described in previous chapters,

1 ns, are appropriate. However, the radiative shocks move at well over 100 km/sec, and so an image with a backlighter source lasting 1 ns would smear the image over

100 µm. Therefore, in the most recent experiment, a 100 ps backlighter was used for the ﬁrst time. This pulse length is at the lower edge of what is currently possible for an Omega beam. Initial attempts to use this diagnostic were successful. 149

Figure 8.7: Targets for new generation of radiative shock experiments. Targets are gas tight with view up the back end of the target into cylinder. A large acrylic shield with gold wedges facing the diagnostics surrounds the drive surface. a) Three-D CAD image of target. b) Shadowed image of target prototype roughly positioned in the Omega chamber.

It is anticipated that future students will employ these techniques mentioned above, as well as Thomson scattering, and very likely other diagnostics to develop a much more detailed understanding of these shocks and their structure. APPENDICES

150 151

APPENDIX A

“Observation of collapsing radiative shocks in laboratory experiments,” [43]. 152

PHYSICS OF PLASMAS 13, 082901 ͑2006͒

Observation of collapsing radiative shocks in laboratory experiments A. B. Reighard, R. P. Drake, K. K. Dannenberg, D. J. Kremer, M. Grosskopf, E. C. Harding, and D. R. Leibrandt Department of Atmospheric Oceanic and Space Sciences, University of Michigan, Ann Arbor, Michigan 48109 S. G. Glendinning, T. S. Perry, B. A. Remington, and J. Greenough Lawrence Livermore National Laboratory, Livermore, California 94551 J. Knauer and T. Boehly Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623 S. Bouquet Département de Physique Théorique et Appliquée (DPTA), CEA-DIF, BP 12, 91680 Bruyères-le-Châtel, France L. Boireau Département de Physique Théorique et Appliquée (DPTA), CEA-DIF, BP 12, 91680 Bruyères-le-Châtel, France, and LUTH, Observatoire de Paris, Paris, France M. Koenig and T. Vinci Laboratoire pour l’Utilisation des Lasers Intenses, Ecole Polytechnique, 91128 Palaiseau, France ͑Received 27 March 2006; accepted 21 June 2006; published online 3 August 2006͒ This article reports the observation of the dense, collapsed layer produced by a radiative shock in a laboratory experiment. The experiment uses laser irradiation to accelerate a thin layer of solid-density material to above 100 km/s, the ﬁrst to probe such high velocities in a radiative shock. The layer in turn drives a shock wave through a cylindrical volume of Xe gas ͑at ϳ6mg/cm3͒. Radiation from the shocked Xe removes enough energy that the shocked layer increases in density and collapses spatially. This type of system is relevant to a number of astrophysical contexts, providing the potential to observe phenomena of interest to astrophysics and to test astrophysical computer codes. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2222294͔

I. INTRODUCTION gime but can reach the regime of large radiative fluxes just described. Radiative shocks are a type of radiative hydrodynamic Achieving both high enough temperature and sufficient phenomenon. Shock waves heat the material they pass optical depth simultaneously requires the use of high-energy- through, and first become radiative shocks when the radiative density facilities. Little laboratory data exist on radiative flux from the hot material becomes energetically significant. shocks, as they are difficult to establish under controlled con- Radiative shocks abound in the universe, but their study in ditions. If the region on either side of the shock is “optically the laboratory is relatively new. Creation of these systems thin” ͑easily allows the passage of the thermal radiation from requires temperatures of tens of electron volts or more, suf- the shocked matter͒, the density of the shocked layer can 3,4 ficient to create ionized matter in which at minimum radia- increase greatly as it cools by radiating away its energy. tive energy fluxes locally can exceed material energy fluxes. The thickness of the shocked layer correspondingly de- In any radiative shock there is an “optically thin” region creases, so the shock can be said to collapse. Here we report ͑having small optical depth͒ where radiative effects are large, a laboratory experiment to observe, for the first time, the collapsed layer produced by a radiative shock. near the density jump. Here by “optical depth” we refer to Radiation and radiative collapse both play important the number of e-foldings of attenuation of thermal radiation. roles in astrophysical shock waves. The shock wave emerg- The optical depth of the entire system on each side of the ing from a supernova passes through a regime in which the density jump corresponding to the shock determines the de- 1,2 shocked layer collapses in space because of radiative energy tailed properties of radiative shocks, including the extent losses.5 Similar dynamics can occur at the accretion shocks of the region over which radiative effects are large. In ex- produced during star formation,6–8 and at the reverse shock periments on radiative shocks, the optical depth, for the ther- in a supernova remnant formed from a star with a dense mal radiation from the shocked matter, must be adequate to stellar wind9 or preexisting dense material as in supernova allow significant energy exchange between matter and radia- 1987A.10,11 Stratified ionization states form in a radiative tion on the time scale of the experiment. There is also in precursor of a Herbig-Haro object with a radiative cooling principle a regime of very high temperature and very large layer.12 There is more generally a radiative cooling zone be- optical depth in which the radiation pressure can exceed the hind most astrophysical shocks. Collapse of an existing material pressure.1 Current experiments cannot reach this re- shocked layer can occur in some cases, as, e.g., in aging

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082901-2 Reighard et al. Phys. Plasmas 13, 082901 ͑2006͒

supernova remnants in which the shocked layer is no longer driven.13 One can organize the prior laboratory work on radiating shock waves by the strength of the radiative effects that were present, which scale very strongly with shock velocity, 14 us. Experiments discussed by Edwards et al. produced ϳ us 8 km/s in a cylindrical blast wave, and observed radiative cooling effects that resulted from heating of the shocked FIG. 1. Target diagram. In this view the backlighter plate would sit directly ͑ gas by electron heat conduction. At higher us, experiments behind target, below the plane.. When the VISAR velocity interferometer can exceed the threshold15 for the formation of a thermal system for any reflector͒ diagnostic was used ͑see the text for reference͒, additional arms were added to hold a quartz window and a mirror for the radiative precursor, in which thermal radiation from matter VISAR laser, and shielding was added behind the drive disk and to the left heated by the shock itself heats the matter ahead of ͑“up- of the arms to reduce preheating of the gas in the arms. When a point stream” of͒ the shock. Radiative precursors have been ob- backlighter was used, its line of sight was in the same direction as the served in experiments by Bozier et al.,16 Grun et al.,17 Keiter VISAR line of sight. et al.,15 Bouquet et al.,18 Koenig et al.,19,20 and Vinci.21 The experiment of Grun et al.17 produced a quasispherical radiative blast wave, in which radiation during the shock transi- 22 tion is calculated to play a key role. tube to evacuate the target and then fill it with xenon. The The present experiment is the first in planar geometry to xenon pressure was measured for each experiment, and was exceed the threshold for radiative collapse by formation of a 1.1 ͑±10%͒ atm for the cases of interest here corresponding postshock cooling layer, and to detect the material that has to ␳ =6 mg/cm3 or to 2.7ϫ1019 atoms/cm3. The drive disk been shocked and cooled. Following the shock, which heats 0 was either 51 ␮m of polyimide ͑±3% and at 1.41 g/cm3͒ ions primarily, the ions and electrons equilibrate rapidly overcoated with 20 ͑+5/−10͒ ␮m of polyvinyl at 1 g/cm3, compared to the rate of radiative cooling. The resulting, ini- or 20 ␮mor40␮m ͑±7%͒ of Be. We focused ten laser tial postshock electron and ion temperature for a strong 4 beams of wavelength 0.35 ␮m onto a 1 mm spot centered on shock, T ,is init the ϳ2.5 mm diameter drive disk in a square, 1 ns flat-top 2 2 u pulse, with the midpoint of the rising edge defining time T = s , ͑1͒ init ͑␥ ͒2 ഛ +1 cv t=0. The total energy was 4000 J. Distributed phase plates ͑DPPs͒ created super-Gaussian focal spots of 720 or 820 ␮m in which ␥ is the polytropic index appropriate to the shock diameter ͑full width at half-maximum͒, with small-scale transition and c is the specific heat at constant volume of the v structure which fluctuated via smoothing by spectral disper- postshock material, equal to 3͑Z+1͒k /͑2Am ͒ for a fully B p sion ͑SSD͒. The resulting laser irradiance was up to ionized gas. ͑Here k is the Boltzmann constant, m is the B p 1015 W/cm2. The pressure from laser ablation first shocked proton mass, and Z and A are the average ionization and and then accelerated the drive disk, launching it into the atomic mass numbers, respectively.͒ In a material like xenon, xenon and driving a shock. c and ␥ both should include the effects of ionization. A v X-ray radiography was the principal diagnostic, using postshock cooling layer must form when the energy flux due two types of x-ray sources called “backlighters.” The laser to thermal radiative losses from the shocked material exceeds beams producing the x rays were of the same wavelength and the energy flux entering the shocked material. This natural normalization of the fluid energy equation in an optically laser pulse as given previously, at a nominal energy of thick system gives a threshold for significant radiative cool- 450 J/beam, without SSD and usually without DPPs. Some ing as R Ͼ1, where shots included an “area backlighter,” in which such laser r beams were focused to a ϳ1 mm spot on a vanadium foil ͑␥ ͒ ␴ 4 ␴ 5 +1 4 Tinit 64 us several square millimeters in area and 5 ␮m thick, to pro- R = = , ͑2͒ r ␥ ␳ 3 ␥͑␥ ͒7 4 ␳ ϳ 0us +1 cv 0 duce K-shell emission at 5.2 keV. This millimeter-sized source was placed 4±0.25 mm from the target, and imaged ␴ ␳ in which is the Stefan-Boltzmann constant and 0 is the onto a framing camera24 through pinholes. A “backlit pin- mass density of the unshocked, upstream material. The cor- hole” was also used on some shots, where the laser beams responding threshold velocity23 in xenon, at 10 mg/cm3,is were focused to a 400 ␮m spot on a 5 ␮m thick V foil, approximately 50 km/s. If the optical depth of the region spaced by 100 ␮m of CH behind an 80 ␮m thick Ta sub- behind the shock decreases, decreasing the emissivity of the strate with a 20 ␮m through hole, covered by 100 ␮mof shocked material, the value of R required to see large radia- r CH. This small x-ray source was located 12±0.1 mm from tive effects increases. the target, and projected a radiograph of the target onto a framing camera located ϳ229 mm beyond it. Due to vignett- II. EXPERIMENT ing, the effective source size for this measurement was We drive a planar, radiative shock through a xenon-filled ϳ15 ␮m. A gold grid was placed on the target to calibrate target and observe the structure of the shocked xenon layer. the location and magnification of the image. A velocity in- Figure 1 shows a target schematic. The inside diameter ͑i.d.͒ terferometer system for any reflector ͑VISAR͒ diagnostic of the gas cell was either 600 or 912 ␮m. We used the fill ͑see Fig. 1͒ was also used in some cases.

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082901-3 Observation of collapsing radiative shocks¼ Phys. Plasmas 13, 082901 ͑2006͒

FIG. 2. ͑Color online͒ Radiography image from an area backlighter, at FIG. 3. ͑Color online͒ Radiography image from a point-projection back- 13.5 ns, from an experiment with a polyimide drive disk attached to a poly- lighter, or a “backlit pinhole,” from an experiment with a 20 ␮m drive disk imide tube of 912 ␮m i.d., irradiated with SSD at 9.3ϫ1014 W/cm2 onto a attached to a polyimide tube of 575 ␮m i.d., irradiated with SSD at 4.8 720 ␮m laser spot. The illumination was by x rays from V produced by ϫ1014 W/cm2 onto an 820 ␮m laser spot, again using a V backlighter. The overlapping six laser beams. The grid with a fiducial feature establishing an same type of fixed spatial fiducial is present, as are the tube walls. The shock absolute location is evident in the lower part of the figure. The wall of the is tilted in the plane of the image, but some evidence of trailing xenon along tube can be seen near the upper edge. the tube walls is present.

III. EXPERIMENTAL RESULTS data image shows a compression of approximately 35 in the xenon layer. If the line of sight was not exactly side on, the Radiography of the shock in xenon shows clear indica- true compression would be higher. One-dimensional ͑1D͒ tions of a thin, dense shock. On a range of experiments, we and 2D simulations discussed in the following provide fur- have seen dense shocked layers with thicknesses ranging be- ther support of the creation of a radiatively collapsed shock. tween 45 and 80 ␮m. In the plane of the radiograph, some layers were tilted with respect to the target axis by as much IV. SIMULATION RESULTS as 10°. We show the thinnest of these layers in Fig. 2, taken at 13.5±0.3 ns, with the region of highest opacity being One can gain further insight into the impact of radiation 45 ␮m thick. One can see the center of the shock ͑which is on the experiment through simulations. We first discuss the moving to the right͒ at approximately 1600 ␮m from the results of simulations of this system using the 1D, Lagrang- 27 initial driven surface, with indications of a trailing layer of ian, single-fluid-three-temperature code HYADES, run using dense xenon along the wall of the tube. The velocity aver- multigroup, diffusive radiation transport with 90 photon aged over the first 13.5 ns is 118 km/s. Figure 3 shows a groups, adjusted to resolve the edges in the xenon opacity at typical radiograph with a thicker layer, from an experiment up to 6 keV. The equation of state of xenon was the with a 22 ␮m drive disk and a 10% lower drive irradiance. SESAME table.28 In the regime of this experiment, the poly- In this image, the center of the layer has moved 1150 ␮min tropic index ͑␥͒ inferred from the table is in the range of 8.0±0.3 ns, where its thickness is 65 ␮m. The average ve- 1.2–1.3, as is appropriate for an ionizing medium that is locity of the shock until this time is ϳ140 km/s. dense enough that collisional recombination is dominant.23 It When the VISAR diagnostic was used,25 fringe patterns is worth noting that the effective ␥ of xenon can be signifi- from the VISAR diagnostic ceased before the drive laser shut cantly smaller, e.g., in lower-density media in ͑more or less͒ off. We attribute this to collisional absorption in the Xe gas, coronal equilibrium, which is the case for the experiments heated to a few eV by radiative preheat.26 Later, a thin fea- with blast waves in gases.22,29 The xenon was modeled using ture appeared, showing no fringes and nonuniform in space an average-atom, local-thermodynamic-equilibrium ͑LTE͒ and duration. We attribute this signal to reflection of the in- description. One would expect this description and the radia- terferometer beam from the edge of the shock front. The tion transport model to be qualitatively accurate but not fully shock velocity inferred from this is consistent with that de- predictive. As has been thoroughly documented through 2D termined from the radiographic data. simulations,30 the laser irradiance used in such 1D simula- Even without any input from computer simulations, the tions must be reduced to give accurate results, because radial data provide strong evidence that there is a shock that has heat transport reduces the ablation pressure in the actual sys- significantly collapsed. Assuming that two-dimensional ͑2D͒ tem. Here it was adjusted to the level required to match the lateral flow is small, which is supported by the limited layer behavior of relevant purely hydrodynamic experiments. of absorbing material along the tube wall in the image and The solid curve in Fig. 4͑a͒ shows the above-mentioned also by the simulations discussed below, the thickness of the radiative simulation results, whereas the dashed curve shows layer corresponds directly to the amount of compression in results of a simulation in which radiation is artificially sup- the shock. For the thinnest observed thickness of 45 ␮m, pressed. The shock transition is the right-most increase in assuming the line of sight to be exactly side on and given the density, which is moving to the right into preheated matter. instrumental resolution of 10 ␮m, one concludes that the The shocked xenon layer is just to the left of the shock tran-

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082901-4 Reighard et al. Phys. Plasmas 13, 082901 ͑2006͒

FIG. 4. ͑a͒ Density vs position from two Hyades simulations, at 16 ns, for experiments at a laser intensity of 1015 W/cm2. The boundaries between the drive plasma, in this case Be, and the xenon are shown, labeled “contact surfaces.” The solid line shows the result for multigroup, diffusive radiation transport, whereas the dashed line shows the result for a nonradiative sys- FIG. 5. ͑Color online͒͑a͒ Density proﬁle at 7 ns, from a 2D simulation of tem. When radiation is suppressed ͑dashed line͒, a collapsed layer does not the experiment, using the FCI code. The shock is moving to the right. The form. ͑b͒ Density and temperature vs position from the Hyades simulation color bar calibrates the density as a ratio to the initial gas density. ͑b͒ with radiation transport at 16 ns. The solid line is mass density, the dashed Simulated radiograph, using density data from ͑a͒. Poisson noise and a line is ion temperature, and the dash-dotted line is electron temperature. point-spread function from data are included. Note the difference in scales between ͑a͒ and ͑b͒.

low-Z material behind the shock is heated, and has separated sition. In the radiative case one can see the postshock density from the xenon layer. This separation is clearly seen in Fig. increase due to cooling. This density increase is well re- 5͑a͒, but not in radiography, because of the low absorption of solved in this Lagrangian calculation, and shows a maximum the diagnostic x rays by low-Z material. compression of a factor of 35 over the initial gas density, Figure 5͑b͒ is a simulated radiograph based on the den- compared to a maximum compression of 13 in the radiation- sity profile shown in Fig. 5͑a͒ and the experimental resolu- suppressed case. To the left of the contact surface is a more- tion. The boundary between xenon and beryllium is at the structured layer of low-Z material. The structure in this layer left edge of the right-most dense feature, whereas the dense has been established during the laser pulse, when there is feature at the top of the image is the plastic wall. Mass ab- shock reverberation in the driving material. The radiation has sorption coefficients for beryllium and xenon at 5.4 keV two effects. First, it narrows the shocked xenon layer by were taken from the National Institute for Standards and increasing its density. This is the primary effect one can de- Technology FFAST database.34 The source-induced broaden- tect using radiography. Second, it heats the low-Z material ing is 250 ␮m at the microchannel plate. Poisson noise esti- that is driving the shock and causes the xenon layer to sepa- mated from representative experimental data is included, and rate from it. As the xenon layer radiates, radiation-driven the image is smoothed based on the instrumental smoothing ablation creates a distinct, low-density region between the 31 determined from grid edges in data. This assumes also that dense driver material and the dense collapsed layer. In Fig. the shock is observed from exactly side-on; if the shock were ͑ ͒ 4 b one can see the effects of radiative heating ahead of the tilted by 5° from edge-on, a 50 ␮m thick, 600 ␮m diameter shock, of the cooling that accompanies the density increase layer would appear almost 90 ␮m thick. Therefore, this in the cooling layer, and of the radiative heating and ablation method of detection gives an upper limit on the actual thick- of the beryllium. 32,33 ness of the layer, and thereby the density of the collapsed We also ran 2D simulations using the code FCI, a material. Lagrangian, one-fluid, three-temperature code with multigroup diffusive radiation transport, an average atom non- V. CONCLUSIONS AND FUTURE DIRECTIONS LTE treatment of materials, and flux-limited electron heat transport. Figure 5͑a͒ shows the calculated profile of mass The layer of xenon produced by a nonradiative shock, density at 7 ns for a case with a 600 ␮m gas cell and an with an effective ␥ of 1.2-1.3, would be from 140 to 220 ␮m 820 ␮m laser spot. The density in most of the shocked layer thick at the location seen in Fig. 4, and the observed layer is is about 45 times the initial density, and there has been very 45 ␮m. Thus, one might suggest that the density has in- little radial flow of mass out of the shocked layer. In the 2D creased another factor of 3–4 in consequence of radiative simulations, the decrease of temperature ahead of the shock losses, reaching a total of ϳ40 times the initial xenon den- is more rapid than in 1D simulations, as one would expect sity. The inferred density increase would be reduced to what- due to the inclusion of radial radiation losses. Again, the ever extent material has left the shocked region by flowing

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082901-5 Observation of collapsing radiative shocks¼ Phys. Plasmas 13, 082901 ͑2006͒

radially, although the 2D simulations find this to be small. 6N. Calvet and E. Gullbring, Astrophys. J. 509, 802 ͑1998͒. 7 ͑ ͒ However, this line-of-sight measurement will have a strong A. Hujeirat and J. C. B. Papaloizou, Astron. Astrophys. 340,593 1998 . 8S. A. Lamzin, Astrophys. Space Sci. 261, 137 ͑1999͒. tendency to overestimate the thickness of the shocked layer, 9R. A. Chevalier and C. Fransson, Astrophys. J. 420, 268 ͑1994͒. due to any tilt, curvature, or rippling of the shock front. A 10K. J. Borkowski, J. M. Blondin, and R. McCray, Astrophys. J. 477,281 perfectly aligned measurement of the density profile shown ͑1997͒. in Fig. 3͑a͒, with the resolution of the pinhole used, would 11K. J. Borkowski, J. M. Blondin, and R. McCray, Astrophys. J. Lett. 476, ͑ ͒ produce a layer from 30 to 40 ␮m thick. Thus, it appears 31 1997 . 12B. Reipurth and J. Bally, Annu. Rev. Astron. Astrophys. 39,403͑2001͒. reasonable to conclude that we have observed a thin layer of 13J. M. Blondin, E. B. Wright, K. J. Borkowski et al., Astrophys. J. 500, shocked xenon whose density has been increased signifi- 342 ͑1998͒. cantly by radiative losses. 14M. J. Edwards, A. J. MacKinnon, J. Zweiback et al., Phys. Rev. Lett. 87, 0850041 ͑2001͒. Future experiments can work in several worthwhile di- 15 rections. They can examine the structure of the shocked layer P. A. Keiter, R. P. Drake, T. S. Perry et al., Phys. Rev. Lett. 89, 165003 ͑2002͒. in more detail, can assess how it scales with parameters such 16J. C. Bozier, G. Thiell, J. P. Le-Breton et al., Phys. Rev. Lett. 57, 1304 as shock velocity and initial gas density, and can attempt to ͑1986͒. devise diagnostic approaches that can directly measure the 17J. Grun, J. Stamper, C. Manka et al., Phys. Rev. Lett. 66, 2738 ͑1991͒. 18 properties of the shocked layer. In addition, by watching the S. Bouquet, C. Stéhlé, M. Koenig et al., Phys. Rev. Lett. 92, 225001 ͑2004͒. long-term evolution of the shocked layer, such experiments 19M. Koenig, A. Benuzzi-Mounaix, N. Grandjouan et al., Shock Compres- might observe the onset of hydrodynamic instabilities like sion of Condensed Matter-2001 ͑2001͒, p. 1367. 35 those discussed by Vishniac and Ryu. Beyond such work, 20M. Koenig, T. Vinci, A. Benuzzi-Mounaix et al., Astrophys. Space Sci. this system could be developed as a radiation source for ex- 298,69͑2005͒. 21 ͑ ͒ periments to examine other issues such as radiation transport. T. Vinci, Phys. Plasmas 13, 010702 2006 . 22J. M. Laming and J. Grun, Phys. Rev. Lett. 89, 125002 ͑2002͒. 23R. P. Drake and A. B. Reighard, AIP Conf. Proc. 1,1417͑2006͒. ACKNOWLEDGMENTS 24K. S. Budil, D. M. Gold, K. G. Estabrook et al., Astrophys. J., Suppl. Ser. 127, 261 ͑2000͒. The authors acknowledge the vital contributions of the 25L. M. Barker and J. Hollenback, J. Appl. Phys. 43, 1669 ͑1972͒. Omega technical staff, the target fabrication staff at 26A. B. Reighard, R. P. Drake, K. K. Dannenberg et al.,inProceedings of Lawrence Livermore National Laboratory, Erika Roesler, Inertial Fusion Science and Applications Conference ͑American Nuclear Rebecca Gabl, and Peter Susalla, as well as for useful dis- Society, Inc., Monterey, CA, 2003͒, Vol. 1, p. 950. 27 cussions with Dmitri Ryutov and Russell Wallace. J. T. Larsen and S. M. Lane, J. Quant. Spectrosc. Radiat. Transf. 51,179 ͑1994͒. This work is supported by the National Nuclear Security 28SESAME: The Los Alamos National Laboratory Equation of State Data- Agency under DOE Grant Nos. DE-FG03-99DP00284 and base, LA-UR-92–3407 ͑1992͒. DE-FG03-00SF22021, and by other grants and contracts. 29E. Liang and K. Keilty, Astrophys. J. 533, 890 ͑2000͒. 30D. G. Braun ͑private communication͒. 31 ͑ ͒ 1R. P. Drake, High Energy Density Physics: Foundations of Inertial Fusion M. Herrmann private communication . 32 ͑ and Experimental Astrophysics ͑Springer, New York, 2006͒. R. Dautray and J.-P. Watteau, La Fusion Thermonucleaire par Laser Ey- 2D. Mihalas and B. Weibel-Mihalas, Foundations of Radiation Hydrody- rolles, Paris, 1993͒. 33 namics ͑Dover, Mineola, NY, 1999͒. G. Schurtz, in La Fusion Thermonucleaire Inertielle par Laser, edited by 3F. H. Shu, The Physics of Astrophysics: Gas Dynamics ͑University Science R. Dautray ͑Eyrolles, Paris, France, 1994͒, Vol. 2, p. 1055. Books, Mill Valley, CA, 1992͒. 34C. T. Chantler, K. Olsen, R. A. Dragoset et al. ͑National Institute of 4R. P. Drake, Astrophys. Space Sci. 298,49͑2005͒. Standards and Technology, 2005͒. 5L. Ensman and A. Burrows, Astrophys. J. 393, 742 ͑1992͒. 35E. T. Vishniac and D. Ryu, Astrophys. J. 337, 917 ͑1989͒.

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APPENDIX B

“Thomson scatttering from a shock front,” [44]. 158

REVIEW OF SCIENTIFIC INSTRUMENTS 77, 10E504 ͑2006͒

Thomson scattering from a shock front A. B. Reighard, R. P. Drake, T. Donajkowski, M. Grosskopf, and K. K. Dannenberg Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, Michigan 48109 D. Froula, S. Glenzer, J. S. Ross, and J. Edwards Lawrence Livermore National Laboratory, Livermore, California 94551 ͑Received 8 May 2006; presented on 8 May 2006; accepted 29 May 2006; published online 22 September 2006͒ We have obtained a Thomson scattering spectrum in the collective regime by scattering a probe beam from a shock front, in an experiment conducted at the Omega laser at the Laboratory for Laser Energetics. The probe beam was created by frequency converting a beamline at Omega to a 2 ns pulse of 0.263 ␮m light, focused with a dedicated optical focusing system. The diagnostic system included collecting optics, spectrometer, and streak camera, with a scattering angle of 101°. The target included a primary shock tube, a 20-␮m-thick beryllium drive disk, 0.3-␮m-thick polyimide windows mounted on a secondary tube, and a gas ﬁll tube. Detected acoustic waves propagated parallel to the target axis. Ten laser beams irradiated the beryllium disk with 0.351 ␮m light at 5 ϫ 14 2 ␳ 10 W/cm for 1 ns starting at to, driving a strong shock through argon gas at o =1 mg/cc. The 200 J probe beam ﬁred at t=19 ns for 2 ns, and at t=20.1 ns a 0.3 ns signal was detected. We attribute this signal to scattering from the shocked argon, before the density increased above critical due to radiative collapse. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2220069͔

Thomson scattering measurements use an optical laser periments described in Reighard et al.,7,8 and fabricated at ͑␭ ͒ ͑ ͒ with some initial wavelength and wave number o and ko to the University of Michigan. A three-dimensional 3D elastically scatter from electron density fluctuations with a computer-aided design ͑CAD͒ drawing of the experimental given wave vector ͑k͒.1,2 Over the last 40 years, experiments geometry in the target chamber is shown in Fig. 1. have used Thomson scattering to extract fundamental plasma To create a driven shock that may radiatively collapse, a properties from the scattered frequency spectrum, and it is low-Z, planar disk was launched by laser ablation pressure now widely used as a diagnostic in fusion research.3–5 into a cylindrical volume filled with argon gas. This disk was Thomson scattering probes individual electrons in the fashioned from beryllium, 20±3 ␮m thick, 2.0±0.1 mm in noncollective regime, when light is scattered from plasma diameter. The disk was mounted on a polyimide tube, inside fluctuations ͑of wave number k͒ with wavelengths shorter diameter ͑i.d.͒ 575 ␮m, outside diameter ͑o.d.͒ 600 ␮m. The ͑ ␭ Ͼ ͒ than a Debye length k De 1 . Resonant plasma fluctua- target package was gas tight, and fitted at the back end with tions in the collective regime, in the form of probed collec- a hypodermic tube through which the target was evacuated ͑ ͒ tive ion-acoustic wave features of wave number kiaw , are of air and filled with argon. The argon pressure was mea- observed when the probed electrons follow the motion of the sured for each experiment, and was 1.1 ͑±10%͒ atm for the ͑ Ͼ ␭ ␳ 3 ions ZTe /Ti kiaw De, where Z is ionization state, Te is elec- cases of interest here, corresponding to o =1 mg/cm or to ͒ ϫ 19 3 tron temperature, and Ti is ion temperature . In this regime 2.7 10 atoms/cm . the electrons move to screen the potential created by ion To allow for probe entrance and Thomson-scattered- fluctuations.6 To probe electrons in the collective regime of a light-exit holes, another polyimide tube of larger diameter driven shock wave in gas, we have applied Thomson- was fitted over the main target tube, creating an arm at a 45° scattering techniques to a radiatively collapsed shock wave angle to the shock propagation axis, pointing towards the 4␻ in argon gas. probe beam location when properly aligned. This polyimide The experiment conducted for this purpose created a tube was 725 ␮m i.d., 875 ␮m o.d., and totaled approxi- driven shock in argon with shock velocity high enough to mately 3 mm long. This arm served two main purposes. cause radiative collapse. Thomson-scattered light was then First, it acted as a guide to drill an entrance hole into the collected from the shocked gas, and an attempt was made to main target body, clearing a path to what would be the scat- image the dense, postshock gas using x-ray radiography. To tering volume on the shock axis. Second, it provided a flat accomplish this, the targets were designed to form a laser- surface onto which a thin film of polyimide could be affixed, driven piston that drove the shock, and the target body was sufficiently far from the target axis that plastic plasma would structured to create unobstructed paths for the probe entrance not mix with argon plasma on the shock axis, providing at and scattered light exit paths. Beam timing was specified to least a 2 mm offset from the center of the main target tube. allow for x-ray radiography of the shock, using an indepen- This thin film was 3000 Å thick, and provided a gas tight dently positioned backlighter target. The target for these ex- barrier. Design calculations showed that the plastic plasma periments was based on those for driven radiative shock ex- produced in the destruction of this film cleared from the

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10E504-2 Reighard et al. Rev. Sci. Instrum. 77, 10E504 ͑2006͒

FIG. 2. Imaged spectrum from successful Thomson scattering experiment. Scattered light signal begins at 20.1±0.25 ns after drive beams turn on, about halfway through the 2 ns duration of the probe beam. The Thomson scattered light duration was 300±12 ps. Timing and velocity measurements FIG. 1. 3D CAD rendering of experimental geometry, with beam directions. were consistent from scattering within the driven shock transition layer, as Beam timings and properties are discussed in the text. The gas fill tube was the gas collapses due to radiation loss. attached to plastic hose through a voltage transducer to measure target gas pressure. In addition, alignment wires used for metrology and rotational alignment were positioned at two separate places on the target. A dotted probe-beam spot size was 100 ␮m, and with an energy of circle outlines the location of the scattering volume on the target axis. 200 J. The collection diagnostic was an imaging UV spectrometer located in the TIM 2 ͑ten-inch manipulator͒ port ͑␪=79.19, ␾=90.0͒ of the Omega chamber, with a 250 ␮m probe beam path sufficiently quickly such that it did not slit. In this geometry, the scattering angle was 101°. The interfere with the propagation of the probe beam. The align- target axis ͑␪=69.6, ␾=241.5͒ was chosen such that the ion- ment of this tube was checked during target metrology to acoustic waves probed via Thomson scattering were parallel ensure a clear path to the shock propagation axis, as this was to the shock propagation direction. The scattering volume in sensitive to mounting angle and both rotational and transla- the target was 3.7±0.1 mm from the drive surface of the tional alignment of the target in the chamber. Another hole target. The volume was determined by the overlap of the was drilled in the main target body that faced the scattered 100 ␮m spot size from the probe beam and the slit from the light diagnostic when the target was properly positioned in spectrometer. the target chamber. This opening was approximately 400 ␮m The spectrometer used was an f /8.7, 1 m imaging UV in diameter, drilled through a flat surface fashioned from spectrometer with a grating with 3600 grooves/mm. The epoxy, and was also covered with a 3000-Å-thick polyimide spectrometer dispersion was calibrated with lines from mer- film. This provided an unobstructed path for scattered light cury lamp near 0.310 ␮m, with a standard adjustment to towards the diagnostic when this film was destroyed in the make the measurement appropriate for the 4␻ probe beam experiment. wavelength of 0.263 ␮m. The central wavelength, ␭=0.263, We focused ten laser beams of wavelength 0.35 ␮m onto was confirmed by measuring stray 4␻ light on an experiment a 1 mm spot centered on the beryllium drive disk in a square, in the same week. Spectra were imaged on a streak camera, 1 ns flat-top pulse, with the midpoint of the rising edge de- with a wavelength dispersion of 0.036 Å/pixel in a 5 ns win- fining time t=0. The total energy was ഛ4000 J. Distributed dow, with 6 ps/pixel dispersion in time. phase plates ͑DPPs͒ created super-Gaussian focal spots with In addition to Thomson scattering, we performed x-ray a diameter of 820 ␮m ͓full width at half maximum radiography of the target, using an x-ray framing camera ͑FWHM͔͒, with small-scale structure which fluctuated via opposite the backlighter target. Point projection radiography smoothing by spectral dispersion ͑SSD͒. The resulting laser of the shock proved unsuccessful, as an L-shell backlighter irradiance was up to 1015 W/cm2. The pressure from laser proved too dim to effectively image the absorption features ablation first shocked and then accelerated the drive disk, at that low an irradiance. launching it into the argon and driving a shock in the argon A double-peaked scattered-light spectrum was detected gas. At 16.0±0.25 ns after the drive beams turned on, a at 20.1±0.25 ns after the drive beams turned on, 1.1 ns after single destroyer beam with an energy of 400 J and a spot the probe beam turned on, about halfway through the dura- size of 400 ␮m fired on the film facing the UV spectrometer tion of the probe beam. The signal lasted 300±12 ps. The diagnostic in a 2 ns flat-topped pulse with no beam smooth- peaks were Doppler shifted by +1.41±0.2 Å by the plasma ing, clearing the path to this diagnostic. At 19.0±0.25 ns velocity of the gas in the scattering volume, corresponding to after the drive beams turned on, the probe beam turned on at a plasma velocity of 110±8 km/sec. The timing of the sig- 200 J in a 100 ␮m spot with no beam smoothing, in a 2 ns nal, along with the measured plasma velocity, suggests the flat-topped pulse, which first exploded the film on the arm probe beam was scattered off of shocked plasma in the tran- facing this beam, as described above. This beam was aligned sition region of the radiatively shocked gas in argon, before to target chamber center first using a frequency doubled the gas density increased above critical for this geometry. beam, then confirmed in an alignment shot prior to the ex- The imaged spectrum is shown in Fig. 2. Further data analy- periment. The alignment shot used the 4␻ beam shooting a sis is discussed in Reighard et al.9 vanadium disk positioned at target chamber center. This shot also checked the successful propagation of the scattered light The authors would like to thank the University of Michi- onto the UV spectrometer slit through target chamber center. gan target fabrication team, including Mark Taylor, Christine The probe beam came from port P9 ͑␪=116.57, ␾ Krauland, Donna Marion, and Douglas Kremer. The authors =234.0͒ in the Omega chamber, and was a frequency qua- would also like to thank the technical staff at the Omega drupled component of the main beam, at ␭=0.263 ␮m. The laser facility. This work is supported by the National Nuclear

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10E504-3 TS from a shock front Rev. Sci. Instrum. 77, 10E504 ͑2006͒

Security Agency under DOE Grant Nos. DE-FG03- Glenzer, and C. Rousseaux, Phys. Rev. Lett. 95, 195005 ͑2005͒. 4 ͑ ͒ 99DP00284 and DE-FG03-00SF22021, and by other grants S. H. Glenzer et al., Phys. Rev. Lett. 82,97 1999 . 5 S. H. Glenzer et al., Phys. Rev. Lett. 79, 1277 ͑1997͒. and contracts. 6 J. Shefﬁeld Plasma Scattering of Electromagnetic Radiation ͑Academic, New York, 1975͒. 1 H.-J. Kunze, E. Fuenfer, B. Kronast, and W. H. Kegel, Phys. Lett. 11,42 7 A. B. Reighard et al., Proceedings of the Third Inertial Fusion Science ͑1964͒. and Applications, edited by B. A. Hammel, D. D. Meyerhofer, J. Meyer- 2 A. A. Offenberger, W. Blyth, E. Dangor, A. Djaoui, M. H. Key, Z. Naimu- ter-Vehn, and H. Azechi ͑American Nuclear Society, Inc., 2004͒. din, and J. S. Wark, Phys. Rev. Lett. 71, 3983 ͑1993͒. 8 A. B. Reighard et al., Phys. Plasmas ͑to be published͒. 3 D. H. Froula, P. Davis, L. Divol, J. S. Ross, N. Meezan, D. Price, S. H. 9 A. B. Reighard et al., Phys. Rev. Lett. ͑in preparation͒.

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APPENDIX C

Shot data, diagnostics, and metrology tolerances

The purpose of this appendix is to collect all the relevant shot information that was not suitable to include in the text. Table C.1 gives a summary of the diagnostics

fielded on each shot day. Tables C.2 through C.10 give a list of all shots taken on each shot day, with relevant laser and target information, as well as a list of the data collected. Table C.11 gives the metrology tolerances for the targets for each shot day, and was also listed in Chapter Three. Finally Table C.12 gives the meaning of all the acronyms used in these tables. 162 163 able C.1: Table of facility setup at the Omega laser T facility for each shot day. 164 SFC N/A N/A N/A S mode Failure possible mistimed BL too dim mispointing mispointing, S SFC SFC SFC T none none Data S S S collected SFC SFC SFC SFC SFC SFC , S , S S S S S S S Primary T T Diagnostics 1.10 1.13 1.19 1.14 1.12 1.03 (ATM) Gas fill pressure (V) 1.16 1.189 1.246 1.193 1.174 1.084 Gas fill voltage PH BL (W/cm2) 1.338E+14 1.318E+14 1.304E+14 1.344E+14 1.015E+14 1.301E+14 Irradiance BL (J) 1020 1308 on PH target 1344.8 1325.2 1310.8 1350.8 Energy V V V V Sn Sn BL material ) 2 Total 4.74E+14 4.82E+14 (W/cm 4.857E+14 4.854E+14 4.887E+14 4.803E+14 Irradiance (J) 3813 3721 3810 3836 3770 3784 Total drive energy 14.6 20.6 17.1 10.6 13.6 13.6 (ns) total delay PH BL 0.6 0.6 0.6 0.6 0.6 0.6 (ns) gate delay PH BL -3 -3 -3 -3 -3 -3 (ns) delay PH BL driver -17 -23 -13 -16 -16 (ns) Main -19.5 driver advance m) 26 46 26 25 23 24 ! ( thickness Measured drive disk / disk 20 Be 40 Be 20 Be 20 Be 20 Be 20 Be Drive material thickness Sn V V V V A05- A05- A05- A05- A05- A05- Sn S S S S S S T T T T T T ------PH6- PH5- PH4- PH2- name Target PH8- PH10- ABR ABR ABR ABR ABR ABR Backlighter U05- U05- U05- U05- A05- A05- A A A A S S T T S S S S ------20-4 40-3 20-3 20-1 20-3 20-2 Main name Target ABR ABR ABR ABR ABR ABR able C.2: Summary of all shots taken on the August, 2005 shot day. See table of acronyms for more details. T RID Shot Form 18596 18595 18594 18593 18592 18591 Request Shot 40707 40706 40705 40703 40702 40700 Number 165 ed ed N/A N/A N/A N/A mode Failure unresolv unresolv SFC SFC SFC SFC none none Data S S S S collected SFC SFC SFC SFC SFC SFC S S S S S S Primary Diagnostics 1.10 1.08 1.11 1.11 1.13 1.30 (ATM) Gas fill pressure (V) 1.37 1.156 1.138 1.169 1.162 1.183 Gas fill voltage PH BL 2.89E+14 (W/cm2) 2.989E+14 2.923E+14 2.919E+14 2.858E+14 2.899E+14 Irradiance (J) 1696 1640 1622 target 1658.4 1656.4 1644.8 Energy on PH BL V V V V V V BL material ) 2 Total (W/cm 4.792E+14 4.794E+14 3.999E+14 3.961E+14 4.827E+14 4.894E+14 Irradiance (J) 3762 3763 3789 3842 Total drive 3139.2 3109.5 energy 9.6 4.6 8.1 20.6 14.6 9.75 (ns) total delay PH BL 0.6 0.6 0.6 0.6 0.6 0.75 (ns) gate delay PH BL 0 0 0 0 0 0 (ns) delay PH BL driver -9 -4 -9 -20 -14 -7.5 (ns) Main driver advance m) 11 47 24 11 24 47 ! ( thickness Measured drive disk 40 Be 20 Be 20 Be 40 Be 10 Be 10 Be material Drive disk thickness/ SM05- SM05- SM05- SM05- SM05- SM05------PH8 PH7 PH4 PH3 PH9 PH1 name BL Target ABR ABR ABR ABR ABR ABR SM05- SM05- SM05- SM05- SM05- SM05------10-3 40-1 20-2 10-2 20-1 40-1 Main name Target ABR ABR ABR ABR ABR ABR able C.3: Summary of all shots taken on the May, 2005 shot day. See table of acronyms for more details. T Shot 18267 18266 18265 18264 18263 18262 Request Form RID Shot 39929 39928 39927 39925 39924 39922 Number 166 m m N/A noise/ noise/ mispointing mispointing mispointing/di mispointing/di Failure mode SFC none none none none Data S collected SFC S S/4SFC S/4SFC T T SFC/4SFC SFC/4SFC Primary S S Diagnostics 1.04 1.14 1.01 0.96 1.11 (ATM) Gas fill pressure (V) 1.088 1.202 1.062 1.008 1.168 Gas fill voltage ) 2 N/A Area BL (W/cm 1.825E+14 1.838E+14 1.738E+14 1.446E+14 Irradiance (J) N/A 2321.4 2338.2 2211.6 1840.2 Energy on Area BL target ) 2 N/A N/A PH BL (W/cm Irradiance 5.6012E+14 5.3684E+14 5.1425E+14 (J) N/A N/A target 1626.8 1559.2 1493.6 Energy on PH BL V V V BL Sn Sn material Total (W/cm2) Irradiance 4.79618E+14 4.74777E+14 4.76561E+14 4.78599E+14 4.31847E+14 (J) 3765 3727 3741 3757 3390 drive Total energy N/A 18.7 18.7 12.7 12.7 (ns) total delay Area BL 0.2 0.2 0.2 0.2 N/A (ns) gate delay Area BL 3 3 -3 -3 N/A (ns) delay driver Area BL N/A N/A 15.7 15.7 15.7 (ns) total delay PH BL 0.2 0.2 0.2 N/A N/A (ns) gate delay PH BL 0 0 0 N/A N/A delay (ns) PH BL driver (ns) -15.5 -15.5 -15.5 -15.5 -15.5 advance Main driver m) 25 25 19 25 25 ! ( thickness Measured drive disk disk 20 Be 20 Be 20 Be 20 Be 20 Be Drive -F05- -F05- -F05- N/A N/A PH4 PH2 PH3 name ABR ABR ABR BL Target SF05- SF05- SF05- SF05- T T - - - - D25 20-2 20-1 20-4 20-2 Main name Target ABR ABR ABR ABR able C.4: Summary of all shots taken on the February, 2005 shot day. See table of acronyms for more details. T RID Shot Form 17696 17695 17694 17700 17699 Request Shot 38983 38982 38981 38976 38975 Number 167 y y y y y y aph aph aph aph aph aph adiogr adiogr adiogr adiogr adiogr adiogr mistimed mistimed mistimed mistimed mistimed mistimed ashout/4SFC ashout/4SFC ashout/4SFC ashout/4SFC ashout/4SFC ashout/4SFC w w w w w w Failure mode dual r dual r dual r dual r dual r dual r none none none none none none Data collected SFC/4SFC SFC/4SFC SFC/4SFC SFC/4SFC SFC/4SFC SFC/4SFC Primary S S S S S S Diagnostics 1.08 1.11 1.07 1.24 0.57 1.11 (ATM) Gas fill pressure (V) 1.13 1.12 1.166 1.301 0.595 1.169 Gas fill voltage ) 2 Area BL (W/cm Irradiance 4.0234E+14 4.0508E+14 4.0027E+14 4.0678E+14 3.6943E+14 3.6943E+14 2577 2559.6 2546.4 2587.8 2350.2 2350.2 Area BL target (J) Energy on ) 2 PH BL 2.23E+15 (W/cm 2.414E+15 2.433E+15 2.449E+15 2.458E+15 2.318E+15 Irradiance (J) 1576 target 1706.4 1719.6 1731.2 1737.6 1638.4 Energy on PH BL V V V V V V BL material Total (W/cm2) 4.775E+14 4.813E+14 4.651E+14 4.794E+14 4.713E+14 4.799E+14 Irradiance (J) 3748 3778 3651 3763 3700 3767 Total drive energy 7.7 8.2 9.2 12.2 15.7 24.2 (ns) total delay Area BL 0.2 0.2 0.2 0.2 0.2 0.2 (ns) gate delay Area BL 3 4 3 3.5 2.5 2.5 (ns) delay driver Area BL 9.2 5.2 5.7 6.2 12.2 19.2 (ns) total delay PH BL 0.2 0.2 0.2 0.2 0.2 0.2 (ns) gate delay PH BL 0 0 0 0 0 -1 (ns) delay PH BL driver -9 -5 -6 -12 -20 -5.5 (ns) Main driver advance m) 9 24 41 23 23 24 ! ( thickness Measured drive disk disk 20 Be 40 Be 20 Be 20 Be 20 Be Drive 10 Be BL PH-29 PH-27 PH-24 PH-17 PH-14 PH-13 name Target D8 D19 D22 D23 D24 D13 Main name Target RID Shot Form 16440 16439 16438 16445 16444 16443 Request Shot 37043 37041 37040 37039 37038 37037 Number (see Chapter Four). See table of acronyms for more details. able C.5: Summary of all shots taken on the August, 2004 shot day. Much of the data on this shot day were victim to dual radiography washout T 168 SFC 4SFC S noise noise mode Failure mistimed, mispointed none Data 4SFC 4SFC collected SFC/4SFC SFC/4SFC SFC/4SFC Primary S S S Diagnostics 1.10 0.97 1.06 (ATM) Gas fill pressure (V) 1.156 1.023 1.117 Gas fill voltage ) 2 Area BL (W/cm Irradiance 4.2248E+14 4.1945E+14 4.3733E+14 2687.7 2668.4 2782.2 Area BL target (J) Energy on ) 2 PH BL (W/cm Irradiance 2.36964E+15 2.34913E+15 2.63886E+15 1675 PH BL 1660.5 1865.3 target (J) Energy on V V V BL material ) 2 Total (W/cm 5.436E+14 4.824E+14 4.867E+14 Irradiance (J) Total drive 4269.4 3788.7 3822.2 energy -8.8 -6.8 -6.8 (ns) total delay Area BL 0.2 0.2 0.2 (ns) gate delay Area BL 3 3 3 (ns) delay driver Area BL 12.2 10.2 10.2 (ns) total delay PH BL 0.2 0.2 0.2 (ns) gate delay PH BL 0 0 0 (ns) delay PH BL driver -12 -10 -10 (ns) Main driver advance m) ! N/M N/M N/M ( thickness Measured drive disk disk 40 Be 80 PE 40 Be Drive -1 BL PH-3 PH-4 name Target RADBL Be-7 Be-5 Main name 2 mil 9 Target RID Shot Form 15853 15854 15851 Request Shot 35840 35839 35838 Number Chapter Four). See table of acronyms for more details. able C.6: Summary of all shots taken on the April, 2004 shot day. Much of the data on this shot day were victim to dual radiography washout (see T 169 target target target target target mode timing, timing, timing, timing, timing, Failure pointing, pointing, pointing, pointing, pointing, construction construction construction construction construction none none none none none Data collected SFC/4SFC SFC/4SFC SFC/4SFC SFC/4SFC SFC/4SFC Primary S S S S S Diagnostics 1.13 1.10 1.11 1.14 1.14 (ATM) Gas fill pressure (V) 2.138 2.091 2.106 2.174 2.161 Gas fill voltage ) 2 Area BL (W/cm 4.948E+14 4.932E+14 4.922E+14 4.855E+14 4.956E+14 Irradiance BL (J) target 3147.9 3137.4 3131.1 3088.4 3152.8 Energy on Area ) 2 PH BL 4.87E+14 (W/cm Irradiance 4.8507E+14 5.3232E+14 5.2726E+14 4.7494E+14 (J) 1576 1616 target 1609.6 1766.4 1749.6 Energy on PH BL V V V V V BL material Total (W/cm2) Irradiance 4.8293E+14 4.75159E+14 4.89554E+14 4.86752E+14 4.78089E+14 (J) 3730 3843 3821 3791 3753 Total drive energy 8.2 8.2 13.2 18.2 11.2 (ns) total delay Area BL 0.2 0.2 0.2 0.2 0.2 (ns) gate delay Area BL 3 4 3 3 4 (ns) delay driver Area BL 5.2 5.2 7.2 10.2 14.2 (ns) total delay PH BL 0.2 0.2 0.2 0.2 0.2 (ns) gate delay PH BL 0 0 0 0 0 (ns) delay PH BL driver -5 -5 -7 -10 -14 (ns) Main driver advance m) ! N/M N/M N/M N/M N/M ( thickness Measured drive disk disk Drive 1 mil PE 2 mil PE 1 mil PE 1 mil PE 2 mil PE BL PH13 PH-15 PH-18 PH-19 PH-21 name Target Main name Target 1-mil-3 2-mil-2 1-mil-6 1-mil-2 2-mil-3 RID Shot Form 14930 14929 14928 14927 14926 Request Shot 34046 34045 34044 34043 34042 Number details. able C.7: Summary of all shots taken on the November, 2003 shot day. This shot day produced no usable data. See table of acronyms for more T 170 a aming apnel hit mode camer fr Failure pointing pointing pointing pointing pointing pointing not known shr construction, construction, construction, construction, construction, construction, none none none none none none none none Data collected SFC SFC SFC 4SFC 4SFC 4SFC 4SFC S S S no data Primary Diagnostics N/A N/M N/M N/M N/M N/M N/M (ATM) Gas fill 0.963415 pressure N/A (V) N/M N/M N/M N/M N/M N/M 1.975 Gas fill voltage ) 2 N/A N/A N/A no data Area BL (W/cm 4.349E+14 4.257E+14 4.198E+14 4.256E+14 Irradiance (J) N/A N/A N/A 2708 2766.4 2670.9 2707.6 no data Energy on Area BL target ) 2 N/A N/A N/A N/A N/A PH BL (W/cm 9.782E+14 9.564E+14 9.267E+14 Irradiance BL (J) N/A N/A N/A N/A N/A on PH target 1229.3 1201.9 1164.5 Energy V V V V V V V V BL material N/A Total no data (W/cm2) 6.314E+14 Irradiance 6.1547E+14 6.2962E+14 6.0818E+14 6.0033E+14 6.1776E+14 (J) N/A 4945 4959 4715 Total drive 4833.9 4776.6 4851.9 no data energy N/A N/A N/A -8.6 (ns) total -10.6 -18.6 -24.6 -21.6 delay Area BL 0.4 0.4 0.4 0.4 0.4 N/A N/A N/A (ns) gate delay Area BL 0 0 0 0 0 N/A N/A N/A (ns) delay driver Area BL 0.9 N/A N/A N/A N/A N/A 10.1 12.1 (ns) total delay PH BL 0.9 0.9 0.9 N/A N/A N/A N/A N/A (ns) gate delay PH BL 0 0 0 N/A N/A N/A N/A N/A (ns) delay PH BL driver -9 -11 -19 -25 -22 -11 -13 (ns) none Main driver advance m) ! N/M N/M N/M N/M N/M N/M N/M none ( thickness Measured drive disk disk none 75 PE 75 PE 75 PE 75 PE 75 PE 75 PE 75 PE Drive BL BL2 BL1 none none none none none BL14 name Target P2 P1 M4 W6 W1 W3 none Main name Target RID Shot Form 14217 14216 14215 14214 12149 14213 14118 14103 Request Shot 32355 32354 32352 32347 32346 32345 32344 32343 Number of Michigan. See table of acronyms for more details. able C.8: Summary of all shots taken on the July, 2003 shot day. This shot day produced no usable data, and was the first day that used University T 171 mode Failure mistimed/ mistimed/ mistimed/ absorption absorption absorption absorption absorption mispointed/ none none none none Data 4SFC collected AR AR AR AR AR Primary 4SFC/VIS 4SFC/VIS 4SFC/VIS 4SFC/VIS 4SFC/VIS Diagnostics 1.08 1.22 1.02 1.06 1.10 (ATM) Gas fill pressure (V) 1.639 1.846 1.548 1.601 1.667 Gas fill voltage ) 2 Area BL (W/cm 4.431E+14 Irradiance 3.5707E+14 4.2743E+14 6.4295E+14 4.4975E+14 BL (J) target 2271.6 2719.2 4090.3 2818.9 2861.2 Energy on Area Sn Sn Sn Sn Sn BL material Total (W/cm2) 5.176E+14 6.005E+14 Irradiance 5.6354E+14 5.7396E+14 5.4279E+14 (J) 4426 Total drive 4065.2 4507.9 4263.1 4716.3 energy 4.7 4.7 11.2 18.2 18.2 (ns) total delay Area BL 0.2 0.2 0.2 0.2 0.2 (ns) gate delay Area BL 11 18 18 4.5 4.5 (ns) delay driver Area BL 0 0 0 0 0 (ns) Main driver advance disk 50 Be 50 Be 50 Be 50 Be 50 Be Drive S- S- S- S- S- 48 44 47 45 46 Main name Target TEMEA TEMEA TEMEA TEMEA TEMEA O O O O O RID Shot Form 12956 12954 12955 12953 12952 Request Shot 29937 29936 29935 29934 29932 Number table of acronyms for more details. able C.9: Summary of all shots taken on the December, 2002 shot day. Though the fill gas was xenon on this day, a tin backlighter was used. See T 172 mode Failure mistimed/ mistimed/ absorption absorption absorption mispointed AR none none Data 4SFC VIS collected AR AR AR AR Primary 4SFC/VIS 4SFC/VIS 4SFC/VIS 4SFC/VIS Diagnostics 0.65 1.09 1.10 1.08 (ATM) Gas fill pressure (V) 0.968 1.642 1.652 1.614 Gas fill voltage ) 2 N/A N/A N/A N/A Area BL (W/cm Irradiance BL (J) N/A N/A N/A N/A target Energy on Area Sn Sn Sn Sn BL material ) 2 N/A N/A N/A N/A Total (W/cm Irradiance (J) N/A N/A N/A N/A Total drive energy 4.7 4.7 12.2 10.2 (ns) total delay Area BL 0.2 0.2 0.2 0.2 (ns) gate delay Area BL 12 10 4.5 4.5 driver Area BL delay (ns) 0 0 0 0 (ns) Main driver advance disk 50 Be 50 Be 50 Be 50 Be Drive S-38 S-40 S-41 S-39 name TEMEA TEMEA TEMEA TEMEA O O O O Main Target Shot 12322 12321 12320 12253 Request Form RID Shot 28388 28386 28382 28380 information both in an online archive and personal notes is unavailable. See table of acronyms for more details. Number able C.10: Summary of all shots taken on the August, 2002 shot day. This was the first shot day for the radiative gas experiments. Laser energy T 173

Table C.11: Target feature tolerances as a function of shot day. Items listed as unknown were either not measured (if built at U. MI) or had no measured details on the document accompanying ﬁnished targets (if built at LLNL).

Experiments TS Thomson Scattering

RadGas Radiative Shock in Gas Supernova Rayleigh- SNRT Taylor Diagnostics Four Strip Framing 4SFC Camera

FXI Framed X-ray Imager NRL High-Energy X-ray HENEX Spectrometer

PFM Pulse-Forming Matrix

SSC X-ray Streak Camera Single Strip Framing SSFC Camera

Velocity Interferometer System for Any VISAR Reflector

XRPHC X-ray Pinhole Camera

XRFC X-ray Framing Camera Lasers

DPP Distributed Phase Plate Smoothing by Spectral SSD Dispersion Misc. Not available or Not N/A applicable N/M Not measured

Table C.12: Acronyms used to describe radiative shock experiments, both in the above tables and in the text. BIBLIOGRAPHY

174 175

BIBLIOGRAPHY

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Collapsing Radiative Shock Experiments on the Omega Laser

Amy B. Reighard

Chair: R. Paul Drake and Fred C. Adams

Radiative shocks are notoriously diﬃcult to produce in a laboratory setting, due to the extreme demands of the production of relatively high temperatures over suﬃcient extent for radiation and matter to interact. This dissertation describes a fundamental radiation hydrodynamics experiment, using a low-Z piston to drive a strong shock through low density gas, creating a driven, radiatively collapsed shock.

Using 10 beams of the 60-beam Omega Laser facility at the University of Rochester, a low-Z disk is irradiated with an intensity of approximately 5 × 1014 W/cm2 in a

1 ns square pulse over a 1 mm spot size. The laser disturbance ﬁrst shocks then accelerates the disk via laser ablation pressure, achieving velocities well over 200 km/sec. This accelerated piston drives a shock into gas, usually xenon. The strong shock heats the gas to several hundred eV, which then radiates away a signiﬁcant amount of energy, leading the shocked plasma to collapse to very high compression.

This experiment is compared to astrophysical systems with similar optical depth 1 proﬁles. Radiative shocks are common in astrophysical settings, where it is easy to generate fast shocks in low-density media. This experiment has applications to laser- driven dynamic hohlraums, which would take advantage of the radiative shock as a smooth implosion source while still reaping the beneﬁts of a converging geometry.