Investigation of Gamma-Ray Time Shifts Caused by Capsule Areal

INVESTIGATION OF GAMMA-RAY TIME SHIFTS CAUSED BY CAPSULE AREAL DENSITY VARIATIONS IN INERTIAL CONFINEMENT FUSION EXPERIMENTS AT THE NATIONAL IGNITION FACILITY AND THE OMEGA FACILITY

by Elliot M. Grafil c Copyright by Elliot M. Grafil, 2015 All Rights Reserved A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Applied Physics).

Golden, Colorado Date

Signed: Elliot M. Graﬁl

Signed: Dr. Uwe Greife Thesis Advisor

Golden, Colorado Date

Signed: Dr. Jeﬀ Squier Professor and Head Department of Physics

ii ABSTRACT

This thesis describes work on Cherenkov based gamma detectors used as diagnostics at Inertial Confinement Fusion (ICF) facilities. The first part describes the calibration and commissioning of the Gamma Reaction History diagnostic which is a four cell Cherenkov detector array used to characterize the ICF implosion at the National Ignition Facility (NIF) by measuring the gamma rays generated during the fusion event. Two of the key metrics which the GRH measures are Gamma Bang Time (GBT) generated from the D(T, α)n thermonuclear burn and Ablator Peak Time (APT) caused by (n, n0)γ reactions in the surrounding capsule ablator. Simulations of ignition capsules predict that GBT and APT should be time synchronized. After GRH commissioning, the array was used during first year of NIF operation in the National Ignition Campaign. Contrary to expectations, time shifts between GBT and APT of order 10s of picoseconds were observed. In order to further investigate the possibility of these time shifts in view of testing both instrument and code credibility an ICF shot campaign at the smaller OMEGA facility in Rochester was devised. It was performed during two full shot days in April of 2013 and 2014 and confirmed in principle the viability of the Cherenkov detector approach but raised additional questions regarding the credibility of the simulation codes used to describe ICF experiments. Specifically the measurements show that the understanding of temporal be- havior of GBT vs APT may not be properly modeled in the DRACO code used at OMEGA. In view of the OMEGA results which showed no time shifts between GBT and APT, the readout and timing synchronization system of the GRH setup at the NIF was reevaluated in the framework of this thesis. Motivated by the results, which highlighted the use of wrong optical fiber diameters and possible problems with the installed variable optical attenuators, the NIF equipment has been updated over the recent months and new timing tests will be performed during the next years.

iii TABLE OF CONTENTS

ABSTRACT ...... iii

LIST OF FIGURES AND TABLES ...... vii

LIST OF SYMBOLS ...... xix

LIST OF ABBREVIATIONS ...... xx

ACKNOWLEDGEMENTS ...... xxii

DEDICATION ...... xxiii

CHAPTER 1 INTRODUCTION ...... 1

1.1 Nuclear Fusion ...... 2

1.2 Achieving ICF Through NIF ...... 4

1.2.1 The NIF Facility ...... 4

1.2.2 ICF Capsules ...... 10

1.2.3 ICF Process At The NIF ...... 13

1.3 Diagnostic Development ...... 14

1.4 Ablator Time Dependance ...... 17

CHAPTER 2 CHERENKOV DETECTION OF ELECTROMAGNETIC RADIATION 19

2.1 Cherenkov Radiation ...... 19

2.2 History Of Cherenkov Detectors At ICF Facilities ...... 23

2.3 Evolution Of The GRH Detector At NIF ...... 25

CHAPTER 3 CALIBRATION OF GRH ...... 32

3.1 Calibration Experiments At HIGS ...... 32

3.1.1 Translational Scan Charecterization ...... 39

iv 3.1.2 Pressure Scan ...... 40

3.2 Detailed Geometric Simulation Of GRH and Comparison With HIGS . . . . . 50

3.2.1 Geant4 Simulation ...... 50

3.2.2 HIGS Comparison ...... 52

3.2.3 Simulated GRH’s Gas IRF ...... 55

CHAPTER 4 GAMMA RAY TIMESHIFT BETWEEN D-T SIGNAL AND CAP- SULE ABLATOR ...... 60

4.1 Theory ...... 60

4.2 Simulations ...... 62

4.3 Ablator Timeshift Measurement At The National Ignition Facility ...... 69

4.3.1 GRH Diagnostic At The National Ignition Facility ...... 69

4.3.2 Timing Calibration At The National Ignition Facility ...... 79

4.3.3 Experimental Results At The National Ignition Facility ...... 81

4.3.4 Cross Cell Analysis Of GRH Diagnostic Data ...... 83

4.4 Veriﬁcation Experiments At OMEGA ...... 87

4.4.1 OMEGA Facility ...... 87

4.4.2 GRH System At the OMEGA Facility ...... 90

4.4.3 GCD System At OMEGA Facility ...... 99

4.4.4 Cross Timing Between The GRH And The GCD ...... 102

4.4.5 Measurement Of Gamma-Ray Time Shift Caused By Time Dependent Ablator Arial Density ...... 105

4.4.6 OMEGA Ablator Timeshift Experimental Results ...... 110

4.5 Potential Explanations For the Discrepancy Between NIF and OMEGA timing data ...... 114

v 4.5.1 Mach-Zehnder Data Acquisition System ...... 115

4.5.2 Monte-Carlo Error Analysis of Mach-Zehnder System ...... 124

4.5.3 Instrumental Timing Error At The NIF ...... 133

CHAPTER 5 SUMMARY AND CONCLUSION ...... 140

5.1 Issues With HYDRA And DRACO Simulations Of ICF Implosions . . . . . 140

5.2 Instrumental Error In The GRH At The NIF ...... 142

5.3 Conclusion ...... 144

5.4 Future Work ...... 146

REFERENCES CITED ...... 148

APPENDIX A - DERIVATION OF LAWSON CRITERION ...... 165

APPENDIX B - KINDLE GRH GEOMETRY DEFINITION ...... 168

APPENDIX C - KINDLE PMT GEOMETRY DEFINITION ...... 192

vi LIST OF FIGURES AND TABLES

Figure 1.1 The National Ignition Facility (NIF). Diagram shows the two laser bays containing a total of 192 beams routed to the target chamber (silver sphere), where inertial conﬁnement fusion (ICF) experiments take place [1]...... 1

Figure 1.2 One of forty-eight Preampliﬁer Modules (PAM) being inspected [2]...... 5

Figure 1.3 One of two laser bays that houses the ampliﬁers for 96 of the 192 laser beams [3]...... 6

Figure 1.4 The NIF target vacuum chamber. The Final Optics Assembly (FOA) attached to laser ports can be seen at the top and bottom. Unoccupied square aluminum laser ports meant for direct drive are seen in the center. Also in the center, circular diagnostic ports are visible. The blue borated concrete forms a protective layer around the aluminum vacuum chamber. Floors are removed digitally via Photoshop [4]...... 8

Figure 1.5 Cryogenic target positioning system (CryoTARPOS) holding the hohlraum (silver cylinder) and capsule inside the hohlraum. Five seconds before a shot, the triangle shrouds opens exposing the cryogenically cooled (<19 K) capsule to the target chamber environment [5]...... 9

Figure 1.6 The NIF hohlraum (a) Exploded schematic of the hohlraum and thermo- mechanical package. (b) Picture of a nominal NIF hohlraum [6]...... 10

Figure 1.7 X-ray image of a typical Cryo D-T capsule. The various layers that make up the capsule shell can be seen [7]...... 11

Figure 1.8 Monte Carlo N-Particle Transport Code simulation done by L. Dauﬀy of the photon spectrum for the National Ignition Facility. Simulated spectrum is of a Cryo D-T capsule composed of CH...... 16

Figure 1.9 The Gamma Reaction History array currently installed at the National Ignition Facility [8]...... 17

vii Figure 1.10 Measurement of the gamma rays produced from a single NIF ICF event performed on June 20th 2011 (shot N110620-002-999). The four GRH detectors were set at 2.86 MeV (red) dominated by signals from the capsule ablator, 5 MeV (green) dominated by signals from the hohlraum, 8 MeV (purple) and 10 MeV (blue) both of which are dominated by signals from the thermonuclear burn. According to theory, these peaks should be time aligned and not separated...... 18

Figure 2.1 Huygens’ Principle applied to Cherenkov radiation. A particle (red dot) that is traveling to the left is emitting an equally spaced in time wave. Due to the particle traveling faster then the wave, a wavefront (blue line) is formed which can be subsequently viewed as the emission source (blue arrows)...... 20

Figure 2.2 The angle θ that the Cherenkov wave front makes with respect to the par- c ticle velocity. Since vthreshold> n , vparticle is the hypotenuse of the triangle when Cherenkov radiation is formed...... 21

Figure 2.3 Plot of the Frank-Tamm formula for a variety of particle velocities. . . . . 23

Figure 2.4 Picture of the inside of the U.S. Geological Survey’s TRIGA Reactor located in the Denver Federal Center. The blue glow is caused by Cherenkov radiation generated by relativistic particles interacting with the surrounding water [9]...... 24

Figure 2.5 Schematic of the Gamma Cherenkov Detector. Gamma radiation enters from the right until it interacts with a Compton converter plate (red). There the gamma ray is converted into an electron which travels through a gas cell. Cherenkov light is emitted which is then focused onto the PMT through Cassegrain optics (green) [10]...... 24

Figure 2.6 The Gamma Cherenkov Detector undergoing preperations for deployment at the OMEGA facility...... 26

Figure 2.7 Data from the OMEGA Facility, taken on 04/16/13 by the Gamma Cherenkov Detector using a Mach-Zehnder data acquisition system. Once the system has been timed, a measurement of Gamma Bang Time can be performed. This is done by measuring the diﬀerence in time between the initial Cherenkov signal generated by the D-T reaction and a timing ﬁdu- cial(not shown). As the neutrons spread out they interact with some of the surrounding material generating gammas. This signal persists until the neutrons directly interact with the PMT, generating a spike in signal, until the neutron front passes through...... 27

viii Figure 2.8 Schematics of the Gamma Reaction History (GRH) Detector. (a) Side view of a entire GRH detector. (b) Internal optic components of a GRH detector [11]...... 28

Figure 2.9 Gamma Reaction History diagnostic deployed at the National Ignition Facility surrounded by the Gamma Reaction History group...... 29

Figure 2.10 Diagram of the Photek multi-channel plate based photo multiplier tube (PMT) used by Gamma Reaction History detector...... 30

Figure 2.11 Optical layout of a Gamma Reaction History detector...... 31

Figure 3.1 Overview of the Duke storage-ring free electron laser (FEL). Optical klystrons are seen in purple. The HIγS beam pickoﬀ is seen in the middle right [12]. 33

Figure 3.2 Partial layout of the HIγS facility. The left room contains beam collimation and shielding. The center room is the Upstream Target Room (UTR), which is where a GRH detector was installed. The remaining room is the Main Gamma-Vault [13]...... 34

Figure 3.3 High purity Germanium (HPGe) paddles placed parallel with the beam line. 35

Figure 3.4 Installation of the GRH detector in the Upstream Target Room. (a) The linear stage before being attached to the GRH allows movement horizontal to the beam axis. (b) Laser alignment of the GRH detector to center of the beam line...... 36

Figure 3.5 Photo of the inside of the PMT test can. 4 LED corresponding to red, green, blue and white are at the end of this tube. The PMT is placed inside and sealed. A LED is then powered on and the PMT’s output is recorded and then compared to previous calibrations...... 37

Figure 3.6 Stanford Research System Model PS350 High Voltage Power Supply which controlled the PMT voltage...... 38

Figure 3.7 (a) Tektronix DPO71254 Digital Phosphor Oscilloscope used to record counting mode data. (b) Overlay of multiple waveforms taken during the experimental campaign. The rising edge shows HPGe paddle signal. The negative going peak is the Cherenkov signal detected by the GRH. . . . . 38

Figure 3.8 Three angle (-39◦, 0◦ and 59◦) planes over which the 1 cm diameter pencil beam was moved across the Compton converter plate of the GRH detector. 39

ix Figure 3.9 HIγS data of a translational scan across the Compton converter plate of the GRH done with a 1 cm diameter 16.75MeV gamma ray pencil beam ◦ at 200 PSI SF6 at an angle of 0 ...... 42

Figure 3.10 Pressure scans done using a 1 cm diameter 4.4 MeV gamma ray pencil beam using SF6 gas. Data was obtained using the current mode acquisition method. (a) Plot of the pressure response. (b) Log plot of the pressure response showing a detectable sub threshold signal...... 43

Figure 3.11 Current Kindle based GEANT4 GRH simulation geometry. (a) Wireframe model of GRH. Displays mirror geometry (white) and PMT active area (blue). (b) Solid body model of the GRH. Domed end cap is hidden showing Compton converter plate (red)...... 52

Figure 3.12 Comparison of GEANT4 Monte Carlo Simulation (blue circle) to data taken at the HIγS facility (red triangle). HIγS data is of a translational scan across the Compton converter plate of the GRH done with a 1 cm 16.75 MeV gamma ray beam at 200 psi SF6. Simulation data has been normalized to show overall trend of data...... 53

Figure 3.13 Comparison of GEANT4 Monte Carlo Simulation (blue circle) to data taken at the HIγS facility (red triangle). HIγS data is of a pressure scan using SF6 in the GRH detector done with a 1 cm 4.4 MeV gamma ray beam pointed at the center of the converter plate. Simulation data has been normalized to real measured data at 215 psia following overall trend of data. (a) Plot of experimental compared to simulation. (b) Log plot of experimental compared to simulation...... 54

Figure 3.14 GRH detector simulated gas impulse response function to an incident gamma-ray. With an increase of pressure both the time delay and width of the produced signal increases...... 59

Figure 4.1 Plot of CH D-T capsule’s ablator radius (green) and fuel (black) vs time overlayed over the gamma rays production from the D-T burn (red) and (n, n0)γ reactions with the ablative material (blue) in an igniting capsule. The maximum neutron yield is achieved at peak compression resulting in the peak gamma production from the D(T,α)n reaction (GBT) and the 12C(n, n0)γ reaction (APT) being time aligned...... 62

x Figure 4.2 Plot of CH D-T capsule’s ablator radius (green) and fuel (black) vs time overlayed over the gamma rays production from the D-T burn (red) and (n, n0)γ reactions with the ablative material (blue) in a non-ignition capsule. Due to incorrect shock timing, the hot spot forms before peak compression is achieved. This results in the D(T,α)n reaction reaching its maximum before the capsule has completely converged. Since the 12C(n, n0)γ is dependent on both the ρRablator and the neutrons for the D-T burn, the peak of the gamma production from the ablator (APT) is oﬀset later in time then the D-T peak (GBT)...... 63

Figure 4.3 Density plot of a 2D DRACO simulation of an ICF capsule being compressed. The once smooth surface of the capsule now has multiple perturbations due to Rayleigh-Taylor instabilities [14]...... 66

γ Figure 4.4 HYDRA simulations showing DT ρR (black), CH ρR (green), DT s (red) 12 γ and C s (blue). (a) Nominal simulation with no perturbative eﬀects. Note how there is negligible shift between GBT and APT. (b) Simulation with ablator mix and shock mistiming eﬀects resulting in a shift between GBT and APT [15]...... 67

Figure 4.5 Scientist standing next to the Gamma Reaction History diagnostic at the National Ignition Facility. The GRH diagnostic is comprised of four GRH detectors. The PMT of each of these detectors is placed as close as physically possible to the other PMTs (center of the array) in order to ensure the background observed by each PMT is as identical as possible...... 70

Figure 4.6 The GRH diagnostic’s port cover attached to the NIF target chamber at 064-020. It serves to couple the NIF target camber to the four GRH detectors. Four holes are bored through the port cover and valves are attached allowing each GRH detector to have the minimum amount of mass in direct line of sight of the target chamber center while maintaining the target chamber’s vacuum...... 71

Figure 4.7 The GRH mounting bracket before being installed on the GRH port diagnostic cover. The stack of dark-grey metal at the center of the mounting bracket are multiple slabs of Tungsten used to shield the PMTs located directly behind them...... 72

Figure 4.8 Cabling schematic for a single GRH detector as installed at the National Ignition Facility...... 74

Figure 4.9 Inside the GRH diagnostic junction box which connects the the GRH diagnostic in the target chamber room to the data acquisition system in the Mezzanine level of the NIF building...... 75

xi Figure 4.11 One of the many Tektronix DPO71254 Digital Phosphor Oscilloscope used to record data from the GRH diagnostic...... 76

Figure 4.10 Inside one of the equipment racks used to control the GRH diagnostic. Starting from the bottom are the GRH diagnostic Mach-Zehnder bias controller (gold). The bias controller monitors the output of a Mach- Zehnder modulator and applies a DC signal in order to set the modulator to quadrature before an ICF experiment. On top of them are two ±15 V power supplies used to energize the photo receivers. Above the power supplies there are mounted four PS350 high voltage power supplies used to bias the four PMTs used by the GRH diagnostic. Above these power supplies lay the delay generators used by the GRH diagnostic to trigger the various components in the system...... 77

Figure 4.12 Optical ﬁducial diminishing pulse train recorded by GRH diagnostic cell D at the NIF. This diminishing pulse train is achieved by coupling a 2x2 splitter into itself...... 79

Figure 4.13 BC-422 scintillator in the process of being installed in a GRH detector replacing the Compton converter plate...... 80

Figure 4.14 Data recorded by a GRH detector from timing shot N110522. The diminishing ﬁducial train (left) is timed against the rising edge of the scintillator signal (right)...... 81

Figure 4.15 Diﬀerence in peak time of the GRH signal for a given threshold, as compared to the 8 MeV channel for a selection of CH ablator D-T ICF experiments at the NIF. The 8 MeV channel is assumed to be free of contamination from gamma-rays arising from the interaction of 14.1 MeV neutron with material surrounding the NIF capsule...... 82

Figure 4.16 Log plot of the Hohlraum/TMP impulse response function of a GRH detector at 4.5 MeV threshold. This IRF was generated from an MCNP simulation of the NIF Hohlraum/TMP completed by L. Dauﬀy at LLNL. . 84

Figure 4.17 Shows the forward ﬁt cross cell analysis across all four GRH detectors [16]. 85

Figure 4.18 Laboratory for Laser Energetics (LLE) OMEGA Facility. 60 beam lines seen on the right are focused to a single point in the target chamber seen on the left [40]...... 88

Figure 4.19 OMEGA facility laser bay [40]...... 89

Figure 4.20 Laser routing from Laser Bay to Target Chamber [42]...... 90

xii Figure 4.21 Omega target chamber [42]...... 91

Figure 4.22 (a) The GRH installed on the OMEGA target vacuum chamber. (b) OMEGA target vacuum chamber map [17]. The GRH is located at H8. . . 91

Figure 4.23 (a) The Mach-Zehnder system attached to the GRH’s PMT. (b) Stanford Research System Model PS350 High voltage power supply used to power the PMT, sitting on top of a Tektronix SCD...... 92

Figure 4.24 Schematic of GRH’s data acquisition setup at OMEGA...... 93

Figure 4.25 Handsome scientist standing next to the GRH’s data acquisition setup installed in LaCave...... 94

Figure 4.26 (a) Two 20 mW 1554 nm CW ThorLabs WDM Laser Diode modules mounted in a ThorLabs Pro800 chassis. Two PM ﬁbers (blue) are delivering the CW laser output to the Mach-Zehnder modulators mounted to the GRH. (b) Mach-Zehnder bias controller (gold) monitoring output from the Mach-Zehnder and delivering a bias signal to them...... 95

Figure 4.27 (a) Two NewFocus Photo Receivers converting the two optical signals from the Mach-Zehnder interferometers into electrical signals. (b) High Frequency splitter (gold) is used to mix the Mach-Zehnder signal and an electrically generated comb fiducial signal. A 10dB electrical attenuator (blue) is placed in line with the electrical comb fiducial signal to stop reflections caused by the Mach-Zehnder signal...... 96

Figure 4.28 Tektronix DPO71254 Digital Phosphor Oscilloscope used to record the signals generated from the two PR attached to it...... 97

Figure 4.29 (a) 1x6 optical splitter (beige) used to distribute an optical comb ﬁducial to multiple optical to electrical converters (black). The converters are used as an electrical ﬁducial for both the GRH and GCD. (b) Stanford Research System Model DG645 Digital Delay Generator used to delay and split a trigger signal for both the GRH and GCD oscilloscopes...... 97

Figure 4.30 Data taken by one GRH detector at OMEGA on April 16th 2013. Starting on the left is the optical comb ﬁducial followed by the Cherenkov signal. The Cherenkov signal is followed by gamma rays created from neutrons scattering oﬀ of diagnostic equipment placed near the target chamber center. The large ramp to the right of the plot are the neutrons generated from the D-T burn directly interacting with the PMT...... 98

xiii Figure 4.31 (a) GCD installed in a test TIM undergoing various safety checks. (b) GCD-2 and GCD-3 undergoing preparations to be installed in a TIM attached to the OMEGA chamber...... 99

Figure 4.32 (a) Si puck used for physical timing reference. Black marks are caused by laser scorching. (b) Puck holder which connects the Si puck to the GCD. 100

Figure 4.33 (a) Mach-Zehnder suitcase installed on the GCD. (b) Inside of the Mach- Zehnder suitcase [18]...... 101

Figure 4.34 (a) NewFocus Photo Receivers installed on the GCD oscilloscope. (b) Tek- tronix TDS6124C Digital Storage Oscilloscope used to record data generated by the GCD...... 102

Figure 4.35 Measurement of the electric fiducial relative to gamma bang time. (top) Measurement of GCD Fidu - GCD GBT. (bottom) Measurement of GRH Fidu - GRH GBT. Note that the 2nd set of fiducials is from the optically injected comb fiducial, which was illuminating the PMT of the GRH detector...... 103

Figure 4.36 (a) Electronic ﬁducial before time alignment. (b) Detected Cherenkov signal before time alignment...... 106

Figure 4.37 (a) Electronic ﬁducial after application of time alignment. (b) Detected Cherenkov signal after time alignment of the electronic ﬁducial...... 107

Figure 4.38 Detected Cherenkov signal after time alignment of the electronic ﬁducial and time oﬀsets using the GCD data have been applied. Dashed line shows zero time shift line. The 3 MeV GRH thresholds are time shifted later in time due to the higher index of refraction in the gas, which slows light traveling through the pressure cell...... 109

Figure 4.39 GRH signal produced from the neutrons generated from an ICF experiment at OMEGA interacting with an Si puck place 11.4 cm away from the ICF capsule...... 110

Figure 4.40 Measurement of the time shift between the 3 MeV threshold signal compared to the 8 MeV threshold signal using electric ﬁducial (blue), optical ﬁducial (green) and Si puck (red). The shaded area represents post shot DRACO simulations of the expected time shift between these two quantities...... 113

Figure 4.41 Mach-Zehnder modulator. (a) Internal schematic of the Mach-Zehnder Modulator. (b) Mach-Zehnder Modulator deployed at the NIF [19]. . . . 116

xiv Figure 4.42 Change in total light output IOut with respect to change of voltage at a speciﬁc voltage(interferometer leg phase diﬀerence). Due to the periodic nature of this function, this graph repeats for the V0 to Vπ interval. . . . 118

Figure 4.43 Mach-Zehnder transfer function. It shows where the maximum (IMax and minimum (IMin) output light intensity occurs relative to the voltage applied to the Mach-Zehnder modulator. Due to encoding sensitivity the ◦ modulator is typically biased at V π . This results in a 90 degree phase 2 oﬀset between the interferometer legs and is called the quadrature point. If VIn Vπ the signal will invert (”roll over”). If the input signal is large enough this inversion can occur multiple times due to the transfer function’s periodic nature...... 119

Figure 4.44 Three classes of Gaussian input signals coupled to the Mach-Zehnder modulator at quadrature. The blue signal is at the ideal amplitude, being between 60%-70% of V π of the modulator. The red signal’s amplitude is at 2 V π . Finally, the Green signal amplitude exceeds V π , which will cause the 2 2 signal to roll over once it has been encoded...... 122

Figure 4.45 Output of the Mach-Zehnder modulator to the three Gaussian signals in Figure 4.44. Note that this graph is of a negative going signal (lower levels equal more light) simulating the data recorded by the GRH. The red signal’s peak compression is due to the decrease in sensitivity near V π . 2 Since the Green signal amplitude exceeds V π , the top portion of the peak 2 has been inverted causing the double peak phenomenon...... 123

Figure 4.46 Applying 4.18 to the output of the Mach-Zehnder modulator to the three Gaussian signals. While both blue and red signals remain unchanged, the green signal is inverted at V π . The original waveform can be retrieved 2 either through manually editing the data by ﬂipping it at V π or by stitching 2 multiple Mach-Zehnder modulator data together...... 124

Figure 4.47 Record of a Mach-Zehnder optical signal transmitted by a GRH detector. Due to the oscilloscope’s configuration with the baseline (seen at -0.225 V) being at 10% of full scale, a large input signal that rolls over multiple times is cut off at the bottom going beyond the oscilloscope’s ability to record. The difference in measured maxima for the peaks formed during the roll over is caused by the frequency dependent IMin...... 126

xv Figure 4.48 Initial Gaussian input (red) before being folded with Mach-Zehnder transfer function. Final Gaussian output (black dots) after oscilloscope errors have been applied and unfolded using Mach-Zehnder transfer function. The output data was fitted (dashed blue) assuming a Gaussian peak. This fitted Gaussian parameters were compared to the original input Gaussian in order to determine the effects both the Mach-Zehnder and oscilloscope had on the recorded data...... 128

Figure 4.49 Histogram generated during Monte-Carlo error analysis showing peak position error. The histogram is for 70% Mach-Zehnder max amplitude at 100 mV FS...... 129

Figure 4.50 Histogram generated during Monte-Carlo error analysis showing relative FWHM error. The histogram is for 70% Mach-Zehnder max amplitude at 100mV FS...... 130

Figure 4.51 Histogram generated during Monte-Carlo error analysis showing relative amplitude error. The histogram is for 70% Mach-Zehnder max amplitude at 100 mV FS...... 131

Figure 4.52 Intermodal dispersion can result in the input Gaussian (red) being distorted due to temporal spread of diﬀerent modes of the detected signal (blue). If this temporal spread is large enough there is a possibility of detecting multiple peaks from a single signal (green)...... 133

Figure 4.53 Movements of light through different types of fiber. (a) Optical Single- Mode fiber supports only light traveling through the primary mode directly through the fiber. (b) Optical Multi-Mode fiber allows various modes to travel through the fiber. These modes are populated when the light enters at an angle not normal to the fiber core. Due to the beam having to travel a longer path to reach the end of the fiber, the beam exits the fiber with a time offset when compared to a normal incident beam...... 134

Figure 4.54 Intensity proﬁles of the lowest order propagation modes supported in a multi-mode ﬁber...... 135

Figure 4.55 GRH diagnostic fiducial fiber chain. The common 2ω fiducial is split four ways before passing through four variable optical attenuators. The four GRH detectors during nominal operations are set to a variety of PMT bias levels. Due to this the attenuation supplied by each variable optical attenuator is unique...... 138

xvi Figure 4.56 Variable Optical Attenuator based on Micro Electrical Mechanical Systems technology(VOA-MEMS). (a) Diagram showing how the VOA-MEMS operate. (b) Picture of the internal structure of the VOA-MEMS showing the platform and electrostatic motor (black) that tilts the optical mirror (silver disk) attenuating the light signal [20]...... 139

Figure 5.1 Comparison of experimental yield obtained at the NIF versus post-shot 1D simulated yield. Solid line shows where simulation is in agreement with experimental results [21]...... 141

Figure 5.2 Fiducial time shift caused by the MEMS-VOA for all four of the GRH detectors comprising the diagnostic array. The signiﬁcant shift between normal and timing shots for cell B and cell C (2.9 MeV and 4.5 MeV thresholds) is viewed as a physical shift in the observed Cherenkov signal. Since the ﬁducial is being shifted earlier in time, the Cherenkov signal has seemed to have moved later in time...... 145

Table 3.1 Experimental campaign to characterize the GRH detector’s transational response to gamma-rays...... 40

Table 3.2 SF6 Pressure scan experimental campaign at Eγ=16.86 MeV...... 44

Table 3.3 CO2 Pressure scan experimental campaign at Eγ=16.86 MeV...... 45

Table 3.4 SF6 Pressure scan experimental campaign at Eγ=10.0 MeV...... 46

Table 3.5 CO2 Pressure scan experimental campaign at Eγ=10.0 MeV...... 47

Table 3.6 SF6 Pressure scan experimental campaign at Eγ=4.4 MeV...... 48

Table 3.7 CO2 Pressure scan experimental campaign at Eγ=4.4 MeV...... 49

Table 3.8 Pressure and the associated refractive index for CO2 gas and SF6(λ=546 nm T=22◦C) [22] ...... 57

Table 3.9 Index of refraction for CO2 gas and SF6 gas at various wavelength [23]. . . 58

Table 4.1 1-D and 2-D HYDRA simulations showing the eﬀect of diﬀerent failure modes on key capsule metrics [15]...... 68

Table 4.2 Nominal threshold conﬁguration of the GRH diagnostic at NIF...... 81

Table 4.3 Comparison of deconvoluted data with a forward ﬁt cross cell analysis for CH capsules at the NIF [16]...... 86

xvii Table 4.4 Experimental results of cross timing GRH and GCD at 8MeV threshold. 104

Table 4.5 Experimental results of cross timing GRH and GCD at 8 MeV threshold. 111

Table 4.6 Experimental results of cross timing GRH and GCD at 8 MeV threshold. Shows timing diﬀerences between GCD data and the three timing methods used on the GRH...... 112

Table 4.7 Tektronix DPO71254C oscilliscope information [24]...... 132

Table 5.1 Threshold of each of the GRH system’s cells at the NIF during normal operations...... 143

Table 5.2 Applied voltage to VOA-MEMS during diﬀerent operating conditions. . . 143

xviii LIST OF SYMBOLS

Atomic number ...... Z

Cross section ...... σ

Energy of photon ...... Eγ

Mass of electron ...... me

Minimum threshold energy ...... Emin

d...... d

Refractive index of medium ...... n

Rest mass ...... m0

Speed of light ...... c

xix LIST OF ABBREVIATIONS

Ablator Peak Time ...... APT

Arbitrary Lagrangian-Eulerian ...... ALE

Atomic Weapons Establishment ...... AWE

Cherenkov Radiation ...... CR

Colorado School of Mines ...... CSM

Organisation Europ´ennepour la Recherche Nucl´eaire ...... CERN

Department Of Energy ...... DOE

Deuterium and Tritium ...... DT

Duke Free Electron Laser Laboratory ...... DFELL

Equations Of State ...... EOS

Free Electron Laser ...... FEL

Gamma Bang Time ...... GBT

Gamma Cherenkov Detector ...... GCD

Gamma Reaction History ...... GRH

High Intensity Gamma-Ray Source ...... HIGS

High Purity Germanium ...... HPGe

High Voltage ...... HV

High Voltage Power Supply ...... HVPS

Impulse Response Function ...... IRF

Inertial Conﬁnement Fusion ...... ICF

Laboratory for Laser Energetics ...... LLE

xx Lawrence Livermore National Laboratory ...... LLNL

Laser Plasma Interaction ...... LPI

Mach-Zehnder ...... MZ

Monte Carlo N-Particle Transport Code ...... MCNP

Micro Electrical Mechanical System Variable Optical Attenuator ...... MEMS-VOA

Multi Channel Plate ...... MCP

National Ignition Facility ...... NIF

Oﬀ-Axis Parabolic ...... OAP

Optical to Electrical ...... O/E

Photo Multiplier Tube ...... PMT

Photo Receiver ...... PR

Quantum Eﬃcency ...... QE

Rayleigh-Taylor ...... RT

Shock Timing ...... ST

Thermo-Mechanical Package ...... TMP

Upstream Target Room ...... UTR

Ultra Violet ...... UV

xxi ACKNOWLEDGEMENTS

This thesis was only made possible through the support of my colleagues, friends and wonderful family who devoted their time in helping me complete this endeavor. First I would like to thank my advisor Dr. Uwe Greife whose sagely advice proved critical in completing this thesis. Also I would like to thank the GRH Diagnostic Development Team. More specifically I would like to note Wolfgang Stoeffl for his critical input and insight who helped push me along in this endeavor and Hans W. Herrmann for his guidance. I would also like to mention Yong-Ho Kim for his continuous enthusiasm and help as well as Dan Sayer for our weekly discussions over burritos. Last but not least, I want to extend a thanks to my friends for the emotional support they gave me during the writing of the text. More specifically I would like to thank Jacob Lavinghouse for the midnight banana milk shake runs and Sandy Cavallaro for the baggies of vegetables. Finally I would like to thank my parents, David and Dasha for their continual support and encouragement through this process.

xxii To Linda Breder 1924 - 2010

xxiii CHAPTER 1 INTRODUCTION

The National Ignition Facility(NIF) located at Lawrence Livermore National Laboratory (LLNL) in Livermore, CA (see Figure 1.1) is currently aiming to become one of the premiere facilities for laser-based inertial conﬁnement fusion (ICF) research.

Figure 1.1: The National Ignition Facility (NIF). Diagram shows the two laser bays containing a total of 192 beams routed to the target chamber (silver sphere), where inertial conﬁnement fusion (ICF) experiments take place [1].

The NIF is a unique ICF physics platform that is a key component to the Department of Energy’s (DOE) research into the fusion of Deuterium and Tritium (D-T)[25, 26]. By using lasers to heat and compress a capsule ﬁlled with fusion fuel (D-T), the fuel achieves the necessary conditions for the atoms to overcome the electric repulsion of the Coulomb barrier and combine in a T (D, n)α thermonuclear reaction (Q=17.6 MeV)[27]. Since the NIF is the only ICF facility theoretically capable of creating the temperatures and pressures necessary for a theoretically self-sustaining thermonuclear fusion reaction (fusion ignition), it can play

1 a pivotal role in furthering our understanding of thermonuclear reactions [28]. The current experimental and calibration campaigns being performed at the NIF are focused on increasing overall neutron yield by tuning capsule shock timing and how the capsule converges as it is being compressed [29–32]. The main point of this thesis will investigate ﬁndings of a potential timing diﬀerence between the peak of the T (D, n)α reaction and when the capsule achieves peak convergence as inferred from detected gamma rays produced by the ICF event.

1.1 Nuclear Fusion

The NIF facility is attempting to determine if laser based ICF is capable of exceeding the Lawson criterion and achieving fusion ignition. The Lawson criterion (see Equation 1.1, Appendix A for derivation) deﬁnes the minimum conditions needed for a fusion reactor to obtain a self sustaining fusion reaction[33].

12 k T n τ ≥ B (1.1) e E E σv

Where:

• ne is the electron density.

• τE is the electron conﬁnement time.

• E is the energy of the fusion products.

• kB is the Boltzmann constant.

• T is the ion temperature.

• σ is the fusion nuclear cross section.

• v is the average velocity of atoms.

2 By assuming an optimal D-T 50-50 mix, the equation is typically rearranged into the fusion triple product (see Equation 1.2). The triple product states the criteria in terms of

conﬁnement time (τE), ion temperature (T ) and particle density(n).

2 12 kBT nT τE ≥ (1.2) EDT hσDT vDT iT

Where:

• σDT is the temperature dependent DT fusion cross-section.

• vDT is the temperature dependent relative velocity of the DT ions.

Unlike magnetic conﬁnement fusion (such as Tokomak reactors) which attempt to exceed

the criteria by having a long conﬁnement time (τE ≈ 4s at the International Thermonuclear Experimental Reactor [34, 35]), the NIF hopes to surpass the criteria by achieving a high particle density over an extremely short time period (τE ≈0.1 ns - 1 ns[36–38]). Due to these short timescales the Lawson criterion can be rearranged in terms of the areal density (ρR)

of the D-T fuel inside the capsule. The conﬁnement time, τE, can be approximated as the time it takes for the ion to travel a distance (R) at the speed of sound through the material

(vs). R τE ≈ (1.3) vs q kB T Since vs = m , we substitute Equation 1.3 into Equation 1.2 and rearrange:

2 R 12 kBT nT q ≥≈ (1.4) kB T EDT hσDT vDT iT m

3 12 (kBT ) 2 nR ≥≈ 1 (1.5) EDT m 2 hσDT vDT iT

3 Since the mass density ρ = hnmi:

3 (k T ) 2 ρR ≥≈ B (1.6) hσDT vDT iT

Inserting the nominal values used in Lawson Criterion calculations:

mg ρR ≥≈ 1000 (1.7) cm2

Equation 1.7 serves as an approximate ρR necessary for alphas generated in the thermonuclear reaction to self-heat the capsule and initiate a theoretically self sustaining burn. Once this criterion is surpassed and the capsule becomes self sustaining, the capsule is said to have achieved ignition. In surpassing this criterion the NIF aims to determine the path of future fusion energy production in the U.S. By achieving a single ignition ICF event, the NIF would be able to study and understand the variables that aﬀect fusion reactions in an ICF environment. By supporting such research, the NIF may enable scientists to take another step towards achieving the goal of harnessing nuclear fusion as an energy source for power plants [1, 39].

1.2 Achieving ICF Through NIF

The NIF intends to exceed the Lawson Criterion by converging 192 lasers, with a total UV light energy of 1.8 MJ, onto a capsule ﬁlled with DT gas, compressing it and thereby producing the conditions required for large scale fusion reactions to occur [1, 39, 40].

1.2.1 The NIF Facility

The 192 laser beams are all initially generated from a single 1052.91 nm (referred to as 1ω) flash, produced by a two-stage Yb-doped fiber laser, which is located in the Master Oscillator Room (MOR) [41, 42]. Inside the MOR, the single pulse is split and smoothed into 48 separate beams which are fed into 48 Preamplifier Modules (PAMS), as seen in Figure 1.2

4 [41, 42].

Figure 1.2: One of forty-eight Preampliﬁer Modules (PAM) being inspected [2].

Inside the PAMs the laser beam passes through a two-stage amplification process taking the 1 nJ pulse from the MOR and amplifying it to <6 J, before it is spectrally smoothed [41, 42]. After amplification, the laser beams enter the Input Sensor Package (ISP). The ISP is used to measure and align the pulsed beam. The output of the ISP is then delivered to the Preamplifier Beam Transport System (PABTS). Each PABTS splits the delivered beam into 4 beams, referred to as a quad, turning the 48 lasers into 192. Besides splitting, PABTS also adjust timing (±250 ps), magnification, as well as isolate all the previous components from the main beam line [41, 42]. After being injected into the main beam line, seen in Figure 1.3, the pulsed beam is sent through a Plasma Electrode Pocket Cell (PEPC). PEPC acts as an optical switch, which traps the pulsed beam in an optical cavity. In the optical cavity, the pulsed beam is amplified via a series of 16 (a total of 3072 for the 192 beams) 42 kg neodymium-doped phosphate glass amplifiers. 7,680 Xenon flashlamps powered by a 422 MJ capacitor bank are used to

5 optically excite the amplifiers [43]. As the pulse travels through the amplifiers, the amplifiers release some of the energy stored via stimulated emission. The pulsed beam is sent through the amplifier a total of four times providing a boost in total power from 6 J to 4 MJ of inferred light [41, 42].

Figure 1.3: One of two laser bays that houses the ampliﬁers for 96 of the 192 laser beams [3].

After amplification is complete, the PEPC are switched to allow the pulsed beam to pass by and enter the main beam line, where it is routed to the target bay; a cylindrical concrete room that is 30 m high, with a radius of 15 m [44]. The target vacuum chamber where the ICF experiments take place is housed in the center of this room. Since the target needs to be illuminated from various directions (current indirect drive ICF configuration has lasers enter from the top and bottom of the target vacuum chamber), each beam needs to be delayed by a different amount, in order to ensure they arrive at the target at the exact same moment. During this routing, the 192 beams are focused and filtered to ensure a very uniform field.

6 Before the pulsed beam enters the target chamber, it passes through the Final Optics Assembly (FOA), where the pulsed beam traverses through two crystals of potassium dihydrogen phosphate, which converts the 1ω light to 3ω (351 nm) [45]. This conversion is necessary to the specific ICF approach taken at the NIF. But during this conversion process >50% of the laser energy is lost, bringing the total energy to 1.8 MJ [46]. Subsequently, the 3ω laser pulse is focused and passes through a vacuum window and two layers of debris shielding to enter the target vacuum chamber. There it interacts with a hohlraum (a hollow cylinder) containing a capsule filled with fusion fuel [45]. The target vacuum chamber itself is a 5 m radius sphere made out of 10 cm thick aluminum. On top of this aluminum, 0.4 m of borated concrete is used to form an outer shell, which is used to both thermalize neutrons, as well as capture low energy neutrons produced during experiments (see Figure 1.4) [47]. Anti-reflection stainless steel coats the inside chamber wall which absorbs reflected UV light and infrared light from the hohlraum [44]. Seventy-two 1.16 m square holes are drilled into the chamber that allow access for the laser quads. Also 118 diagnostic ports with a radius between 7.5 cm to 35 cm were installed allowing diagnostics a direct line of sight to the ICF experiment [44]. The ICF experiment, hohlraum and capsule, are positioned in the center of the target vacuum chamber using the cryogenic target positioning system (CryoTARPOS) or target positioning system (TARPOS), as seen in Figure 1.5. The CryoTARPOS/TARPOS system is not just used for target positioning but also for cooling, filling with fuel and characterization of the capsule [48]. In the case of the CryoTARPOS, additionally a D-T ice layer inside the capsule is formed. During the cryogenic process, the temperature differential between the D-T fuel reservoir and the capsule are used to fill the capsule via a fill tube. Once filled, the capsule is further cooled to its final temperature (<19 K), resulting in the formation of a D-T fuel ice layer [48]. During this entire process, the capsule is monitored using 3-axis x-ray imaging installed inside the CryoTARPOS. The process of filling, cooling, and forming

7 Figure 1.4: The NIF target vacuum chamber. The Final Optics Assembly (FOA) attached to laser ports can be seen at the top and bottom. Unoccupied square aluminum laser ports meant for direct drive are seen in the center. Also in the center, circular diagnostic ports are visible. The blue borated concrete forms a protective layer around the aluminum vacuum chamber. Floors are removed digitally via Photoshop [4].

8 the D-T ice layer, takes approximately 15 to 20 hours [48].

Figure 1.5: Cryogenic target positioning system (CryoTARPOS) holding the hohlraum (silver cylinder) and capsule inside the hohlraum. Five seconds before a shot, the triangle shrouds opens exposing the cryogenically cooled (<19 K) capsule to the target chamber environment [5].

The hohlraum as seen in Figure 1.6, is normally a 5.44 mm in diameter and 10.01 mm high cylinder primarily composed of gold or uranium [4]. Uranium provides an approximate 30% boost to the conversion of laser to x-ray over gold, however there are contamination issues utilizing this ﬁssionable material [40]. The hohlraum is attached to the CryoTAR- POS/TARPOS via Silicon ﬁngers, which are part of the thermo-mechanical package (TMP) [48]. The hohlraum itself is used to convert the laser energy into x-rays, as well as to smooth out the intensity of photons hitting the capsule. The reason for converting the 1ω light to 3ω is to better facilitate the laser to x-ray conversion process in the plasma environment that is formed by the lasers. The electrons in the plasma environment more readily absorb 1ω light then 3ω light thereby screening the 1ω light from the hohlraum. Therefore, the 3ω light is

9 better able to penetrate the plasma and couple to the hohlraum, resulting in more x-rays to compress the capsule [49]. The hohlraum is ﬁlled with He gas and contains a fusion capsule. Small windows are cut in the hohlraum wall to allow the ﬁlling of the capsule, as well as providing direct lines of sight to various neutron and x-ray imaging diagnostics [40].

(a) Schematic of a NIF Hohlraum (b) Hohlraum

Figure 1.6: The NIF hohlraum (a) Exploded schematic of the hohlraum and thermo- mechanical package. (b) Picture of a nominal NIF hohlraum [6].

1.2.2 ICF Capsules

The fusion fuel capsules (see Figure 1.7) inside the hohlraum are normally 2 mm in diameter with a 10 µm diameter ﬁll tube. The bulk of the capsule shell material can be composed of either CH, SiO2 or Be [40]. The capsule shell is usually composed of multiple layers with diﬀerent dopants, such as Cu, Ge or Xe. These dopants have a variety of uses. They can be used to change the properties of the capsule compression by changing the speed of sound of the material, absorb x-rays produced in the hohlraum to prevent pre-heating of the fuel or used as a diagnostic of the implosion via solid or gaseous radiochemistry sampling. Inside each capsule there is usually a mixture of fusion fuel using Tritium, Deuterium, and/or Hy-

10 drogen [40]. There are various types of ICF capsules tailored to the study of a particular eﬀect:

Figure 1.7: X-ray image of a typical Cryo D-T capsule. The various layers that make up the capsule shell can be seen [7].

Cryo D-T Speciﬁcally designed to reach ignition and sustained burn, these capsules have a projected energy production of over 10 MJ of energy. They are typically composed of a CH shell with a solid cryogenically frozen D-T fuel layer followed by D-T gas in the interior [50] (see Figure 1.7). Due to radioactive self-heating caused by the tritium,

11 the overall roughness of the ice surface is signiﬁcantly reduced, projected to improve the overall yield of the capsule [51]. The expected neutron yield from these capsules are of order 1013 − 1019 neutrons/shot [7, 50].

THD Nearly identical in design to the Cryo D-T capsules. However, they are designed to study the hydrodynamic assembly of the fuel. Due to the composition of the fuel layer (74% tritium, 24% hydrogen and 2% deuterium), α-heating is inhibited. Since α- heating is inhibited, ignition cannot occur which caps the expected maximum yield of the capsules to <1015 neutrons/shot. Since the capsule is hydrodynamically equivalent to a Cryo D-T capsule, it can be used as a surrogate. Therefore, diagnostics that would be normally blinded due to a large neutron yield can be ﬁelded to characterize the performance of capsule compression [7].

Symmetry Identical to Cryo D-T capsules except that the fuel and fuel ice layer is replaced by a hydrogen-helium gas mixture. The Symmetry capsules are designed to measure the shape of the capsule implosion via x-rays [7].

Exploding Pushers Driven directly without the use of a hohlraum, unlike the previous capsule designs. The targets are typically glass spheres filled with D-T gas. Instead of having a compression phase, half of the shell mass explodes away from the capsule sending a shock wave through the fuel D-T gas mixture towards the center. The converging shock heats the center of the fuel and initiates the thermonuclear reaction. Due to this capsule design anisotropy effects have less influence on fusion yields. These types of capsules are ideal for diagnostic calibrations due to the repeatability in capsule performance [7].

12 1.2.3 ICF Process At The NIF

The ICF process itself begins when the 192 lasers ﬁrst enter the hohlraum through the laser entrance holes (LEHs) at the top and bottom and begin heating the inside wall forming plasma [52]. Thermal conduction via electrons begins to heat the remaining hohlraum material to approximately 300 eV [52]. The hohlraum generates the bulk of the x-rays (via black body radiation), which are used to compress the capsule [53]. The hohlraum converts approximately 80% of the laser energy into x-rays. However, with solid angle coverage, only ≈3% of the x-rays are utilized to compress the capsule. This is due to the ratio of the hohlraum’s inner wall area to the capsules area, as well as x-rays escaping through the LEHs [53]. During this process, the plasma formed from hohlraum material mixes with the He gas that ﬁlled the hohlraum, forming a mixed plasma surrounding the capsule. As the lasers interact with this plasma, x-rays are generated via stimulated Brillouin scattering and stimulated Raman scattering. This processes is referred to as Laser Plasma Interaction (LPI) [54]. The x-rays from the hohlraum and LPI begin to heat and then ablate the outer shell of the capsule. The ablation of the outer shell results in the capsule’s rapid compression. Ahead of this compression, however, is a shockwave that travels through the capsule [54]. As the shock converges in the center of the capsule, a “hot spot” forms, where the fusion reaction initially begins. By carefully adjusting when and how much laser power is used to drive this system, the hot spot is formed and then the capsule with the rest of the D-T fuel isentropically compresses to >1000 g/cm3 around the hot spot[1, 28, 39]. When the shock wave generated during the ablative/compression process coalesces in the center of the capsule it is referred to as Shock Timing (ST) [40]. If the capsule reaches these high densities, the emission of a 3.5 MeV 4He nucleus from the T (D, n)α thermonuclear reaction is projected to heat the surrounding capsule material. This heating is referred to as alpha bootstraping, since it boosts the amount of thermonuclear

13 reactions in the assembled D-T fuel capsule [1, 28, 39, 55]. Once the thermonuclear reaction becomes self-sustaining via this alpha bootstrapping, the capsule is said to have ignited, i.e. ignition has occurred in the capsule. While the theory of reaching ignition is thought to be understood, there are various perturbative effects that hinder the isentropic compression of the capsule. Rayleigh-Taylor instabilities, an instability resulting from a less dense fluid pushing on a more dense fluid, play a key role in impeding the capsule compression [39, 40]. Also, capsule roughness and defects in the uniformity of the D-T fuel layer play a role in preventing a capsule from igniting [54]. The NIF is currently targeting its research to minimize or remove these obstructions.

1.3 Diagnostic Development

Since NIF is attempting to achieve a break-even point with ICF, diagnostic devices are needed to determine fusion yields as well as both quantitatively and qualitatively describe each ICF shot. While the primary diagnostics will be based on neutrons emerging from the ICF shots (such as the NIF NTOF[56]), these methods can only provide a partial picture of the physical processes that fuel capsule underwent. Additional to neutron yield and ion temperature from neutron detectors [56–58], it would be beneficial to gain information on the temporal development of the burn over a wide range of flux levels as well as determine specifics on the movement of the collapsing shell. One proposed method to achieve this goal is to utilize the various gamma rays given off during an ICF event. The excited 5He∗ composite nucleus formed from the T (D, n)α fusion reaction itself has a chance to produce two distinct high energy gamma rays. A small fraction (4 × 10−5) of the gamma ray producing 5He∗ compound nucleus decays by the emission of a 16.75 MeV gamma ray and subsequent emission of a low energy neutron (instead of a 14.1 MeV neutron) [59].

14 The 5He∗ can de-excite through the following processes [59]:

5He∗ → 4He +1 n (1.8)

5 ∗ 5 He → He + Eγ(16.75MeV ) (1.9)

5 ∗ 5 ∗ He → He + Eγ(13.5MeV ) (1.10)

The neutron generated by the T (D, n)α also interacts with the surrounding capsule material (C,Si,O) and hohlraum producing a variety of (n,x) reactions. Of particular interest due to their intensity are [60–63]:

12 1 12 1 0 C + n → C + n + Eγ(4.43MeV ) (1.11)

16 1 16 1 0 O + n → O + n + Eγ(6.129MeV ) (1.12)

28 1 28 1 0 Si + n → Si + n + Eγ(6.88MeV ) (1.13)

By energetically isolating these various lines in the ICF gamma spectrum, a variety of quantitative measurements can be made. Figure 1.8 is a Monte Carlo N-Particle Transport Code (MCNP) simulation done by L. Dauﬀy, estimating the photon spectrum produced at NIF using a CH shell capsule and surrounding bulk material. By measuring the arrival time of the broad spectrum of 13.5 MeV and 16.75 MeV gamma rays, one can measure the duration of the thermonuclear reaction, as well as measure when the reaction takes place in relation to the initial laser pulse [59]. By isolating and measuring the lower energy gamma rays produced by the surrounding capsule material, the various ablator areal density (ρRC , ρRO) can be found and the total ablator areal density of the imploding ablator can be inferred [64, 65]. In order to isolate these important gamma lines a time resolved, thresholded gamma ray diagnostic needed to be constructed.

15 DT -3 D 10 C Au Al Si Total 10-4

10-5 Rays Per Neutron -

10-6 Gamma

10-7 0 5 10 15 20 Gamma-Ray Energy MeV

Figure 1.8: Monte Carlo N-Particle Transport Code simulationH L done by L. Dauﬀy of the photon spectrum for the National Ignition Facility. Simulated spectrum is of a Cryo D-T capsule composed of CH.

In order to achieve these goals an array of time resolved, threshold Cherenkov radiation detectors was built. By utilizing the Compton effect, the various gamma rays produced during the ICF event are converted into electrons whose maximum energy is bounded by the energy of the incident gamma ray. These Compton electrons can then be sent through an optically translucent medium. If the electron is traveling faster then the local speed of light in the medium, optical photons are emitted promptly via a process called Cherenkov effect [66]. The production of Cherenkov radiation is dependent on both the electron’s speed and the refractive index of the medium. Therefore, by varying the material properties of the medium, the electron energy (and therefore gamma ray energy) required to produce photons can be set. By having an array of Cherenkov detectors, each containing a gas at a different refractive index, the different gamma rays produced during the NIF ICF event can be discriminated by their energy [67]. Furthermore, since the temporal resolution of Cherenkov radiation is extremely fine (<1 ps [68]) the response time of the equipment is the limiting factor for

16 temporal data acquisition. This line of reasoning led to the development of the Gamma Reaction History (GRH) diagnostic seen in Figure 1.9.

Figure 1.9: The Gamma Reaction History array currently installed at the National Ignition Facility [8].

This thesis presents work on test experiments in the commissioning phase of the ICF Cherenkov detectors aimed at understanding and calibrating the system through comparisons to detector simulations. Due to operational time pressures this process was still ongoing after the GRH’s installation at the NIF, where the diagnostic has been used in many of the important NIF attempts to achieve ignition.

1.4 Ablator Time Dependance

The data gathered by the GRH diagnostic since its installation at NIF has returned startling results. According to the basic theory, as the ICF capsule achieves maximum compression, neutron production due to the T (D, n)α reaction would reach its peak. However, as seen in Figure 1.10, the gamma rays due to the the de-excitation of the 5He∗ produced by the T (D, n)α (8 MeV and 10 MeV threshold) seem to occur earlier then the gamma rays produced by the capsule material (2.86 MeV and 5 MeV threshold). This data suggests that

17 the fusion event occurred well before the capsule had arrived at peak convergence.

Figure 1.10: Measurement of the gamma rays produced from a single NIF ICF event performed on June 20th 2011 (shot N110620-002-999). The four GRH detectors were set at 2.86 MeV (red) dominated by signals from the capsule ablator, 5 MeV (green) dominated by signals from the hohlraum, 8 MeV (purple) and 10 MeV (blue) both of which are dominated by signals from the thermonuclear burn. According to theory, these peaks should be time aligned and not separated.

If this data is accurate, it would help to potentially explain why the ICF Ignition campaign at NIF covered during this work failed to achieving ignition. This thesis describes the work completed, and calibrations performed to understand this new set of Cherenkov Detec- tors built for use at the National Ignition Facility. This body of work aims at explaining the diﬀerence in timing between D-T and ablator material signal as measured by the Gamma Reaction History diagnostic at the NIF.

18 CHAPTER 2 CHERENKOV DETECTION OF ELECTROMAGNETIC RADIATION

Over the last century there have been multiple methods developed to convert gamma radiation into an easily quantized electrical signal which can then be recorded. Due to the short timescales present during an ICF event (<1 ns), a technique to detect the gamma radiation which preserves the temporal component of the signal was needed. These timing constraints resulted in the rejection of traditional measuring methods such as scintillation because of its relatively long decay tails. This led to the development of multiple time resolved detectors that rely upon Cherenkov radiation in order to convert the gamma ﬂash into a usable electrical signal.

2.1 Cherenkov Radiation

Cherenkov Radiation is the spontaneous emission of photons caused by a charged particle traveling through a medium at velocities exceeding the phase velocity of light in the medium. Cherenkov radiation was ﬁrst experimentally discovered by Pavel A. Cherenkov in 1934 [66], and a formal theory was formed by Ilya Frank and Igor Tamm in 1937 [69]. It was observed that in order to generate Cherenkov radiation a particle needs to exceed the local phase velocity of light in a medium. The index of refraction of a medium, n, is a ratio of the speed of light, c, and the phase velocity as light propagates through the medium,

vphase, as seen in Equation 2.1 [66].

c n = (2.1) vphase

Since a particle needs to exceed vphase of light in a medium, the threshold velocity (vthreshold) that it needs to exceed is: c v = (2.2) threshold n

19 For typical materials, the index of refraction ranges from 1-2.5. Therefore, Cherenkov radiation is usually observed only in the presence of relativistic particles. Utilizing relativistic

kinematics the threshold velocity can be rewritten in terms of the minimum energy, Emin, a

particle with rest mass, m0, needs to have in order to generate Cherenkov radiation as seen in Equation 2.3

2 m0c Emin = (2.3) q c 2 ( n ) 1 − c2 Since Cherenkov radiation only occurs when the wave source (particle) exceeds the velocity of the wave it emits, the characteristics of this eﬀect can be explained through Huygens’

Principle [67]. As illustrated in Figure 2.1, a particle (red dot) traveling with velocity, vparticle, continuously emits wave pulses in equal space intervals. If the particle’s velocity exceeds the velocity of the waves it emits, a wave front (blue line) is formed. Due to Huygens’ Principle this wave front can then be seen as the source of emission (blue arrows).

Figure 2.1: Huygens’ Principle applied to Cherenkov radiation. A particle (red dot) that is traveling to the left is emitting an equally spaced in time wave. Due to the particle traveling faster then the wave, a wavefront (blue line) is formed which can be subsequently viewed as the emission source (blue arrows).

20 As seen in Figure 2.2, using simple trigonometry we can characterize the angle at which this wave front is formed with respect to the particles velocity vector. Over a period of

time, t, the particle travels a distance xparticle = vparticlet. During this time period the wave

c c generated by the particle travels xwave = n t. Since vparticle> n the angle of the light cone is:

c cos(θ) = (2.4) nvparticle

c t n

Θ vParticlet

Figure 2.2: The angle θ that the Cherenkov wave front makes with respect to the parti- c cle velocity. Since vthreshold> n , vparticle is the hypotenuse of the triangle when Cherenkov radiation is formed.

While this explains the observed light cone generated by Cherenkov radiation, it does not explain why a particle exceeding the local speed of light would emit radiation. In order to explain this one must picture a charged particle passes through a dielectric material. As this

21 particle moves through the material it momentarily polarizes the nearby surrounding atoms inducing a momentary dipole. At low velocities this polarization is perfectly symmetrical around the charged particle. Due to this symmetry, there is no net electric field. Therefore as the particle continues to move and the polarization collapses there is no radiation generated [67]. However, at higher speeds this symmetry is broken along the axis of the charged particle’s movement. The distribution of polarized atoms no longer looks like a sphere but a cone with the apex along the axis of the charge particle’s movement. Therefore an electrical field in the form of a single dipole is established in the dielectric material. As each atom returns to its previous unpolarized state, the energy from the electric field is then converted into emitted Cerenkov radiation [67, 70]. Due to the speed at which this change of state occurs, the generation of Cherenkov radiation can be viewed as nearly instantaneous. Of particular interest is what spectrum the Cherenkov radiation is emitted as. The work done on this issue by both Frank and Tamm resulted in the formulation of the Frank-Tamm formula [70]: dN 2παZ2 1 = (1 − ) (2.5) dxdλ λ2 β2n2

Where:

• N is the number of photons generated.

• x is the path length traveled by a particle.

• λ is the wavelength of a particle.

1 • α is the ﬁne structure constant α ≈ 137 .

• Z is the charge of the particle.

v • β is the ratio of the particle velocity to c. β = c

• n is the index of refraction of the medium the particle is traveling through.

22 Both Ilya Frank and Igor Tamm were awarded the Nobel Prize in Physics in 1958 due to this discovery [69]. The Frank-Tamm formula, plotted in Figure 2.3, shows that the spectrum

1 generated by a charged particle with constant velocity has a simple λ2 dependence. Due to this the characteristic blue glow of Cherenkov radiation as seen in Figure 2.4 is easily explained. While Cherenkov radiation generates a full spectrum of light, the most dominant frequency is at the UV end of the visible spectrum. L arb. units H Λ dN dx d

200. 300. 400. 500. 600. 700. 800. Wavelength nm

Figure 2.3: Plot of the Frank-Tamm formulaH forL a variety of particle velocities.

Using the knowledge of how to generate Cherenkov radiation, a variety of radiation detectors have been built to detect high energy gamma rays and particles.

2.2 History Of Cherenkov Detectors At ICF Facilities

Previously Cherenkov detectors have already been ﬁelded at ICF facilities. The most notable is the Gas Cherenkov Detector (GCD) [59, 71, 72] built by Los Alamos National Labs (LANL) and deployed at the Omega facility at the Laboratory for Laser Energetics (LLE) in Rochester, NY. The GCD seen in Figure 2.5 and Figure 2.6 uses a Beryllium converter foil to transform gamma radiation to Compton electrons. These Compton electrons travel

23 Figure 2.4: Picture of the inside of the U.S. Geological Survey’s TRIGA Reactor located in the Denver Federal Center. The blue glow is caused by Cherenkov radiation generated by relativistic particles interacting with the surrounding water [9].

through a simple gas ﬁlled pressure vessel. By controlling both the gas type (CO2 and C2F6) and pressure, diﬀerent energy thresholds can be set for the production of Cherenkov light.

Figure 2.5: Schematic of the Gamma Cherenkov Detector. Gamma radiation enters from the right until it interacts with a Compton converter plate (red). There the gamma ray is converted into an electron which travels through a gas cell. Cherenkov light is emitted which is then focused onto the PMT through Cassegrain optics (green) [10].

The Cherenkov light, produced by relativistic electrons in the gas, then travels through the pressure vessel until it hits the Cassegrain optics. The Cassegrain optics serves to focus

24 Cherenkov light onto the PMT. The Cassegrain optics allows a Tungsten shield to be placed in front of the PMT. This shield serves to attenuate the unconverted gamma rays that could directly impact the PMT [59, 71, 72]. The GCD at the Omega facility has been highly successful at measuring the time between the impinging of laser light on the fusion target and the peak fusion reactivity. This is referred to as Gamma Bang Time (GBT), as seen in Figure 2.7. However, it was believed that a new detector could be built that would signiﬁcantly enhance the ability to accurately measure GBT, and additionally measure the width of the fusion burn, referred to as Gamma Burn Width (GBW) [73]. The need to measure the GBT and GBW of an ICF event in order to get the diagnostic information necessary to optimize NIF shots towards ignition led to the development of the Gamma Reaction History detector.

2.3 Evolution Of The GRH Detector At NIF

A single Gamma Reaction History detector, as seen in Figure 2.8, was initially designed to measure GBT to an accuracy of <50 ps and GBW to an accuracy of <10 ps over a D-T neutron yield range of 1014 to 1016 [74]. As previously mentioned, there are multiple gammas produced in the ICF environment at the NIF that need to be isolated in order to thoroughly characterize the capsule implosion. For this reason, the complete GRH diagnostic, as deployed now at the NIF, is not composed of a single Cherenkov detector but instead it is comprised of four identical GRH Cherenkov detectors as seen in Figure 2.9[74, 75]. The GRH detects gamma rays when the gammas hit a 63.12 mm radius, 9.52 mm thick aluminum converter plate. At the converter plate the gammas transform through the Comp- ton effect into Compton electrons. As these Compton electrons exit the converter plate they pass into a tube portion of a pressure cell that contains Cherenkov gas. Traveling through this tube, the electrons generate Cherenkov radiation. The Cherenkov photons travel up to 600 mm in the tube until they hit and are reflected off of a 63.50 mm radius, 90◦ degree Off- Axis Parabolic (OAP) mirror with a 355.60 mm focal length. This OAP mirror is mounted

25 Figure 2.6: The Gamma Cherenkov Detector undergoing preperations for deployment at the OMEGA facility.

26 35

DT Signal Scatter Direct Neutron Interaction 30

Voltage (V) 15

Bang Time 10

0 115 120 125 130 135 140 145 Time (ns)

Figure 2.7: Data from the OMEGA Facility, taken on 04/16/13 by the Gamma Cherenkov Detector using a Mach-Zehnder data acquisition system. Once the system has been timed, a measurement of Gamma Bang Time can be performed. This is done by measuring the diﬀerence in time between the initial Cherenkov signal generated by the D-T reaction and a timing ﬁducial(not shown). As the neutrons spread out they interact with some of the surrounding material generating gammas. This signal persists until the neutrons directly interact with the PMT, generating a spike in signal, until the neutron front passes through.

in place and is not adjustable. The photons continue to travel 200.42 mm through the pressure cell until they reach a 62.50 mm radius flat adjustable turning mirror angled at 45◦ degrees. After being reflected, the photons then travel 142.00 mm where they hit a 29.845 mm radius, 5 mm thick sapphire window with a 1.755 refractive index. The sapphire window is placed in a flange with a 20.066 mm radius opening that serves as an aperture. After the photons pass through the sapphire window they exit the pressure chamber and enter a chamber filled with air. Traveling 195 mm further the photons encounter a non-adjustable 50.80 mm radius, 90◦ degree OAP mirror with a 152.4 mm focal length. This OAP mirror is tilted 33◦ degrees

27 (a) Gamma Reaction History side view (b) Gamma Reaction History internal optics

Figure 2.8: Schematics of the Gamma Reaction History (GRH) Detector. (a) Side view of a entire GRH detector. (b) Internal optic components of a GRH detector [11].

with respect to the plane that the first OAP mirror and flat mirror lay on. At this point the photons continue to travel 311.10 mm to the last mirror: a 33.02 mm radius, 90◦ degree non-adjustable OAP mirror with a 38.10 mm focal length. Further on, the photons travel 33.45 mm to the Photek PMT face. The PMT’s (seen in Figure 2.10) face location is variable due to the ability to shim the PMT to a more optimal position. The PMT has a 5.30 mm deep, 60◦ degree tapered cylindrical opening with minor radius of 6.0 mm that leads to a 5.60 mm thick glass window. The photons then hit a multi- channel plate (MCP) detector, where they are converted into electrons and are measured as a voltage pulse at the PMT output. Figure 2.11 shows the complete optical layout. The reason for this complex optical layout is to separate in time the Cherenkov photons of interest from gamma rays directly interacting with the PMT. This design intended to achieve a significant improvement over the GCD in terms of accuracy of GBT measurements. However, this increased resolution has come at the cost of sensitivity, which has limited the GRH’s effective D-T neutron yield range to be higher than

28 Figure 2.9: Gamma Reaction History diagnostic deployed at the National Ignition Facility surrounded by the Gamma Reaction History group. the GCD. Due to the unique physical environment (lacking reproducibility and predictability) present at the NIF an extensive experimental campaign to calibrate the GRH was performed mostly elsewhere in order to separate the various components of the signal (capsule, D-T, hohlraum). The following chapter describes the eﬀorts used to calibrate the instrument in experiments performed at Duke University’s HIGS facility, and in-situ at the National Ignition Facility.

29 Figure 2.10: Diagram of the Photek multi-channel plate based photo multiplier tube (PMT) used by Gamma Reaction History detector.

30 Figure 2.11: Optical layout of a Gamma Reaction History detector.

31 CHAPTER 3 CALIBRATION OF GRH

In order to properly interpret data obtained from the GRH diagnostic at the NIF, the impulse response function (IRF) of the detector needed to be measured. The IRF allows the instrument response to be deconvolved from the recorded data enabling the original signal observed by the detector to be extracted. Given the unique radiation environment present at NIF, direct measurements of the GRH diagnostics’ gas IRF was deemed experimentally unfeasible. Therefore, an experimental campaign focused on benchmarking computational models of a GRH detector was performed. The gas IRFs generated from these models were then convolved with experimentally measured IRFs of the GRH diagnostics’ subsystems (Photo multiplyer tube and Mach-Zehnder) obtaining a total system IRF for the GRH diagnostic. The following sections discuss the calibration and simulation eﬀorts put forth in order to generate the the GRH’s IRF as well as calibration of the system.

3.1 Calibration Experiments At HIGS

A GRH detector was brought for two weeks to the High Intensity Gamma-ray Source (HIγS) located at the Duke Free Electron Laser Laboratory (DFELL) in Durham, North Carolina. It was used to characterize the overall detector response to translational scans across the surface of the detector, as well as to test the detector’s response to changes in the refractive index of the Cherenkov medium. These measurements would then be used to both calibrate and verify the accuracy of computational models. Free electron lasers (FEL) convert the kinetic energy of electrons into a coherent beam of photons. Electrons are initially accelerated to relativistic speed in vacuum before passing through a periodic magnetic wiggler ﬁeld inside an optical cavity. Since the magnetic ﬁeld accelerates the electrons, photons are produced via Bremsstrahlung [12]. The Duke storage-

32 ring FEL (see Figure 3.1) is capable of producing wavelengths of UV light that is tunable. The photon wavelength is determined by the energy of the electron beam as well as the magnetic ﬁeld produced by the optical klystrons [13, 76, 77].

Figure 3.1: Overview of the Duke storage-ring free electron laser (FEL). Optical klystrons are seen in purple. The HIγS beam pickoﬀ is seen in the middle right [12].

The HIγS facility utilizes the FEL photons via intra-cavity Compton backscattering in order to produce linear polarized gamma-ray beams of 2 MeV to 60 MeV with intensities

5 γ 7 γ of 10 s − 10 s [77]. This makes it an ideal facility to test the response of a GRH detector to the gamma-ray energy range of interest (3.0 MeV - 16.75 MeV) at the NIF. Figure 3.2 shows the layout of the HIγS facility. A GRH detector was installed in the HIγS Upstream Target Room (UTR), where calibrations took place. Before a GRH detector was set up at the HIγS facility, calibrations of gamma ﬂux levels were performed. The gamma beam was powered up and a measurement of the absolute ﬂux was made using a Sodium Iodide (NaI(Tl)) crystal located in the Main Gamma-Vault.

33 Figure 3.2: Partial layout of the HIγS facility. The left room contains beam collimation and shielding. The center room is the Upstream Target Room (UTR), which is where a GRH detector was installed. The remaining room is the Main Gamma-Vault [13].

In tandem with this measurement, flux levels were measured using high purity Germanium (HPGe) paddles placed parallel with the beam in the Upstream Target Room (UTR) as seen in Figure 3.3. After the NaI crystal determined the absolute gamma flux, a ratio was taken between this number and the number of gammas detected by the HPGe paddles. This enabled the HPGe paddles to be used to monitor the gamma flux without obstructing the beam path. After the HPGe paddles were calibrated, a single GRH detector was installed at the HIGS facility in the UTR. The GRH detector was placed on a linear stage (allowing translational movement (see Figure 3.4(a))), which was then mounted on an aluminum table. Alignment of the GRH to the center of the gamma beam line was performed using laser levels pre-installed in the UTR. Before installation of the Photek PMT into the GRH detector, measurements of the PMT’s response to various wavelengths of light were completed using a PMT test can.

34 Figure 3.3: High purity Germanium (HPGe) paddles placed parallel with the beam line.

The PMT test can (see Figure 3.5) is a light tight cylinder with LED emitters of diﬀerent wavelengths. It enables one to measure the PMTs response to calibrated light sources and thereby track the degradation of the PMTs Q value (Quantum eﬃciency). This measurement was done at various bias voltages (4.4 kV - 4.9 kV in 0.1 kV increments) and was repeated each day to measure the degradation of the PMT during the experimental campaign. After the PMT had been installed in the GRH detector, high voltage (HV) and PMT read out lines were run out of the UTR. Due to issues with accessibility and concerns with radiation all electronic equipment was placed outside the UTR behind shielding. The HV lines were connected to a Stanford Research System Model PS350 High Voltage Power Supply (HVPS) seen in Figure 3.6. The PMT was supplied with a 4.9 kV bias voltage via the HVPS throughout the entire experiment. The PMT readout was connected to either an electrometer or an oscilloscope, depending on which mode of data acquisition the GRH was operated in. In current mode the PMT

35 (a) Linear Stage (b) Laser Alignment of GRH

Figure 3.4: Installation of the GRH detector in the Upstream Target Room. (a) The linear stage before being attached to the GRH allows movement horizontal to the beam axis. (b) Laser alignment of the GRH detector to center of the beam line. was attached to a Keithley Model 6514 Programmable Electrometer measuring the current detected by the PMT over a 45 second interval. However, given the nature of the data produced at the NIF, a single pulse, data needed to be acquired in counting mode where each pulse could be assessed. In counting mode the signal from the PMT was fed into a Tektronix DPO71254 Digital Phosphor Oscilloscope (4 channel, 12.5 GHz bandwidth, 50 GigaSamples/s) seen in Fig- ure 3.7. The facility provided a timing pulse, which signals when gamma rays are injected into the UTR. This signal was delayed using a Stanford Research System Model DG645 Digital Delay Generator and used to gate the PMT signal recorded by the scope. For each data point, approximately 23,000 waveforms produced by the PMT were saved, which were analyzed at a later time. Using both of these methods, two classes of characterization scans were made on the GRH detector. The ﬁrst was a translational scan across the Compton converter plate while varying the gamma-ray energy. The second was a pressure scan using two diﬀerent Cherenkov gases

(CO2 and SF6) at a ﬁxed gamma-ray energy.

36 Figure 3.5: Photo of the inside of the PMT test can. 4 LED corresponding to red, green, blue and white are at the end of this tube. The PMT is placed inside and sealed. A LED is then powered on and the PMT’s output is recorded and then compared to previous calibrations.

37 Figure 3.6: Stanford Research System Model PS350 High Voltage Power Supply which controlled the PMT voltage.

(a) Digital phosphor oscilloscope (b) Counting mode data

Figure 3.7: (a) Tektronix DPO71254 Digital Phosphor Oscilloscope used to record counting mode data. (b) Overlay of multiple waveforms taken during the experimental campaign. The rising edge shows HPGe paddle signal. The negative going peak is the Cherenkov signal detected by the GRH.

38 3.1.1 Translational Scan Charecterization

During the translational scan, both a 4.4 MeV and 16.75 MeV 1 cm diameter pencil

beam were applied to the GRH detector ﬁlled with CO2 or SF6 gas at a multitude of discrete pressures (gamma-ray energy thresholds). The pencil beam was moved across the area that houses the Compton converter plate. This was done in 1 cm increments which was dropped to 0.5 cm during transitional areas. Due to the GRH detector’s non-symmetric design the translational scan was performed multiple times rotating the GRH detector about the center axis of the Compton converter plate. The GRH detector was rotated at an angle of -39◦, 0◦ and 59◦ as seen in Figure 3.8.

PMT

+51°

0° + -

-39°

Figure 3.8: Three angle (-39◦, 0◦ and 59◦) planes over which the 1 cm diameter pencil beam was moved across the Compton converter plate of the GRH detector.

Table 3.1 lists the performed HIγS experimental campaigns to characterize the GRH detector’s response to these gamma-rays. Note that in many of the translational scans, the

39 data was taken multiple times using diﬀerent options for the GRH such as adding Tungsten shielded rings or placing various collimators in the beam line.

Table 3.1: Experimental campaign to characterize the GRH detector’s transational response to gamma-rays. Gas Pressure (psi) Threshold (MeV) Mode Range (cm) Angle (deg) SF6 37.3 16.75 Counting -10 to 10 0 CO2 65 16.75 Current -10 to 10 0 CO2 65 16.75 Counting -9 to 9 0 CO2 65 16.75 Current -9 to 9 -39 CO2 65 16.75 Current -9 to 9 51 SF6 200 4.4 Current -10 to 10 -39 SF6 200 4.4 Current -10 to 10 51 SF6 200 4.4 Current -10 to 10 0 SF6 200 4.4 Counting 9 to 9 0

Figure 3.9 shows the response of the GRH detector to one of the translational scans. Note that the response is not axial symmetric across the converter plate. This lack of symmetry is believed to be caused by scatter into the gas Cherenkov cell. As the pencil beam is translated to a higher negative number, the beam begins to enter the gas cell situated after the ﬁrst OAP mirror slightly boosting the observed Cherenkov light. A comparison of the translational scan data gathered at HIGS compared to the GEANT4 simulation is found in Section 3.2.2.

3.1.2 Pressure Scan

In order to verify the thresholding eﬀects of the gases used at the NIF and observe the GRH detector’s response to a change of pressure an experimental campaign was completed where a GRH detector’s pressure was varied. This pressure scan of the GRH detector was performed using a 1 cm diameter pencil beam with gamma ray energies of 4.4 MeV, 10.0

MeV and 16.75 MeV. The two gases used, CO2 and SF6, were varied in pressure between 0 psia and 200 psia. During this pressure scan the gamma ray pencil beam was targeted directly at the center of the GRH detector’s Compton converter plate. Due to the large

40 change in signal amplitude generated by the GRH over these pressure ranges, it was decided to attenuate the gamma ray beam using a copper mass of known thickness upstream of the HPGe paddle counters. This allowed for the GRH Detector PMT bias levels to remain constant throughout the pressure scan. A measurement was made at the same pressure before and after an attenuation change allowing the current measurement to be anchoring to the previous measurement. The following tables outline the experimental campaign to characterize the GRH detector’s response to a change of pressure for SF6 (Eγ=16.86 MeV Table 3.2, Eγ=10.0 MeV

Table 3.4, Eγ=4.4 MeV Table 3.6) and CO2 (Eγ=16.86 MeV Table 3.3, Eγ=10.0 MeV Ta- ble 3.5, Eγ=4.4 MeV Table 3.7).

Figure 3.10 shows the pressure response of the GRH detector with SF6 gas to a 4.4 MeV gamma beam using the current mode acquisition method. A comparison of the pressure scan data gathered at HIGS compared to the GEANT4 simulation is found in Section 3.2.2. Both methods of data acquisition (counting and current mode) produce roughly the same trends in both translation and pressure scans. However, there is an unexplained discrepancy in amplitude by a factor of 0.7 between the current mode data and counting mode data. While various theories have been put forth such as inaccuracies in dark current measurements of the PMT, there has been no resolution to the cause of this discrepancy. Also, surprisingly, in the pressure scan there seems to be a sub-threshold Cherenkov signal. While initially this sub-threshold signal was thought to be transition radiation, it is now thought to be caused by high energy >60 MeV Bremsstrahlung radiation produced by the FEL which contaminated the near mono-energetic beam. Further investigations would need to be performed in order to verify this theory which are, however, outside of the scope of this thesis.

41 L H Arb Intensity

-10 -5 0 5 10 Displacement From Center cm

Figure 3.9: HIγS data of a translational scan across the Compton converter plate of the GRH done with a 1 cm diameter 16.75MeV gamma ray pencil beam at 200 PSI SF6 at an angle of 0◦. H L

42 0.06

0.05

0.04

0.03

0.02

0.01 Photons per Gamma 0.00 0 50 100 150 200 SF6 Pressure psia

(a) SF6 Pressure Scan Plot -1 10 H L

10-2

10-3 Photons per Gamma 10-4 0 50 100 150 200 SF6 Pressure psia

(b) SF6 Pressure Scan Log Plot

Figure 3.10: Pressure scans done using a 1 cm diameterH 4.4 MeVL gamma ray pencil beam using SF6 gas. Data was obtained using the current mode acquisition method. (a) Plot of the pressure response. (b) Log plot of the pressure response showing a detectable sub threshold signal.

43 Table 3.2: SF6 Pressure scan experimental campaign at Eγ=16.86 MeV. Eγ (MeV) Attenuation (cm) Gas Pressure (psia) Threshold (MeV) Orientation (deg) Translation (cm) 16.86 16.0 SF6 215.0 2.9 0 0 200.0 3.0 128.0 4.0 100.0 4.6 12.9 87.4 5.0 8.0 57.9 6.3 37.4 8.0 16.0 8.0 17.2 12.0 2.45 15.0 .0 13.0 .0 12.9 14.0 11.6 .0 10.5 .0 9.8 16.0 9.2 .0 8.4 .0 7.9 18.0 6.4 20.0 0.6 ∞ 0.0 0.6 ∞ 8.0 0.4 ∞

44 Table 3.3: CO2 Pressure scan experimental campaign at Eγ=16.86 MeV. Eγ (MeV) Attenuation (cm) Gas Pressure (psia) Threshold (MeV) Orientation (deg) Translation (cm) 16.86 16.0 CO2 215.0 4.16 0 0 200.0 4.33 155.0 5.0 100.0 6.36 12.9 65.0 8.0 8.0 12.9 42.4 10.0 8.0 8.0 29.9 12.0 4.9 22.2 14.0 19.4 15.0 0.0 17.1 16.0 16.1 16.5 15.2 17.0 14.4 17.5 13.6 18.0 11.0 20.0

45 Table 3.4: SF6 Pressure scan experimental campaign at Eγ=10.0 MeV. Eγ Attenuation (cm) Gas Pressure (psia) Threshold (MeV) Orientation (deg) Translation (cm) 10.0 10.45 SF6 215.0 2.9 0 0 12.9 200.0 3.0 128.0 4.0 100.2 4.6 87.4 5.0 8.0 87.4 5.0 57.8 6.3 37.3 8.0 0.0 30.0 9.0 27.0 9.5 25.8 10.0 22.4 10.5 20.4 11.0 17.4 12.0 12.8 14.0 6.4 20.0 2.9 30.0 0.4 ∞ 0.2 ∞

46 Table 3.5: CO2 Pressure scan experimental campaign at Eγ=10.0 MeV. Eγ (MeV) Attenuation (cm) Gas Pressure (psia) Threshold (MeV) Orientation (deg) Translation (cm) 10.0 8.0 CO2 214.06 4.16 0 0 199.8 4.33 155.2 5.0 99.8 6.36 8.0 64.8 8.0 0.0 52.0 9.0 46.8 9.5 42.4 10.0 38.8 10.5 29.9 12.0

22.2 14.0 11.0 20.0 5.0 30.0 0.4 ∞

47 Table 3.6: SF6 Pressure scan experimental campaign at Eγ=4.4 MeV. Eγ W Attenuation (cm) Gas Pressure (psia) Threshold (MeV) Orientation (deg) Translation (cm) 4.4 10.45 SF6 215.0 2.9 0 0 8.0 4.9 2.54 0.0 200.0 3.0 160.0 3.5 128.0 4.0 105.0 4.5 96.0 5.0 58.0 6.3 37.0 8.0 25.8 10.0

48 Table 3.7: CO2 Pressure scan experimental campaign at Eγ=4.4 MeV. Eγ (MeV) Cu Attenuation (cm) Gas Pressure (psia) Threshold (MeV) Orientation (deg) Translation (cm) 4.4 0.0 CO2 200.0 4.3 0 0 105.0 4.5 155.0 5.0 100.0 6.3 64.5 8.0 42.4 10.0 11.0 20.0

49 3.2 Detailed Geometric Simulation Of GRH and Comparison With HIGS

The experimental data obtained in Section 3.1, was used as a benchmark in order to calibrate the various computational simulations developed of the GRH. A total of three diﬀerent Monte-Carlo simulations of the GRH were produced. Two GRH simulations were constructed in Geant4, one by the author of this thesis and another by the British Atomic Weapons Establishment (AWE)[78]. A third simulation of the GRH was done in ACCEPT by LANL [78]. These simulations, once calibrated, were used to develop a deeper understanding of the GRH’s detection characteristics and more importantly to produce an IRF for diﬀerence in gas type and pressure. The following sections will discuss the Geant4 model built by CSM and its calibration against the data obtained in Section 3.1.

3.2.1 Geant4 Simulation

GEANT4 (Geometry and Tracking) is a C++ based Monte-Carlo physics toolkit developed at the Organisation Europeénnepour la Recherche Nucléaire(CERN) [79]. GEANT4 tracks the passage of particles through constructed geometries. It also gives the user the flexibility to add or remove physical processes to a simulated particle, allowing not only for accurate modeling of physical processes, but also enables the user to quickly isolate the cause of an observable. Initially, the GEANT4 toolkit was designed for use in high-energy physics [80]. However, after extensive modification and testing, it has been extended to accurately model lower energy particles and photons. In CSM’s GRH simulation, GEANT4 was utilized to track the gamma-rays that have left the capsule environment and were heading towards a detector, where the gamma rays interact producing Compton electrons. GEANT4 then generates and tracks Cherenkov photons produced by the relativistic electrons, until the photons either interact with a surface that is defined as a detector or exit the simulation area.

50 While GEANT4 handled the underlying physics, the construction of the GRH geometry was done under Sapphire/Kindle, a set of specialized software developed at CSM. Sapphire is a C++ based general GEANT4 framework, initially developed by Luke Erikson, which enables the rapid construction and testing of a GEANT4 application. Instead of having to hard code various components such as a particle manager, a Sapphire based GEANT4 program can call various Sapphire libraries, which contain prebuilt generalized functions. One of Sapphire’s greatest strengths is that geometry, particle gun, and material properties are not defined in the compiled program source code, but are defined using human readable macro files. Below is an example of the human readable code, it defines a thin aluminum cylinder.

1 # Converter: Aluminum target

2 # ------

3 cylinder

4 name Converter

5 radius 63.1190 mm

6 innerRadius 0.0000 mm

7 length 8.9916 mm

8 material ConverterMetal

9 position 0.0000 0.0000 -9.4958 mm

10 color 0.50 0.00 0.50

11 parent World

12 end

Kindle is the Sapphire based simulation of the GRH detector. Engineer drawings and schematics of the GRH were used to produce macro files that define the GRH geometry. Furthermore, material properties, such as the properties of the Cherenkov medium, are defined in Kindle. Kindle collects these files and uses Sapphire to process them. Sapphire then uses GEANT4 to actually track the particles through the detailed geometry and reports the

51 results in a human readable format. Figure 3.11 shows the current GRH model. Appendix B and Appendix C shows the Kindle code used to generate said models.

(a) Kindle Simulation GRH Wireframe (b) Kindle Simulation GRH Exterior

Figure 3.11: Current Kindle based GEANT4 GRH simulation geometry. (a) Wireframe model of GRH. Displays mirror geometry (white) and PMT active area (blue). (b) Solid body model of the GRH. Domed end cap is hidden showing Compton converter plate (red).

3.2.2 HIGS Comparison

A full set of simulations were done along the experimental campaign performed at the HIγS facility. A comparison of the data gathered at HIγS versus the GEANT4 simulation found that while the trends in the data were the same, the overall amplitude of the simulation was large by a factor of 1.6 when compared to experiment. This amplitude diﬀerence between simulation and reality can be accounted for by considering a variety of physical eﬀects not modeled in the simulation. One possible explanation for the systematic drop in detected amplitude is oxidization of the bare aluminum mirrors that are part of the GRH optics. Figure 3.12 shows a GEANT4 simulation of a translational scan over-layed on top of data taken at HIγS facility. The data has been normalized to actual data at 0 cm displacement.

52 The simulations show an overall good agreement with the data obtained at HIγS across all gamma ray energies and pressures. The wings on the observed data, (<-8 cm and >8 cm displacement) is caused by scattering of gamma rays from the surrounding air directly interacting with the PMT or entering the Cherenkov cell. This explains the larger signal detected on one side as well as the lack of signal observed by simulation (direct interactions are not recorded, only optical photons are counted). L H Arb Intensity

-10 -5 0 5 10 Displacement From Center cm

Figure 3.12: Comparison of GEANT4 Monte Carlo Simulation (blue circle) to data taken at the HIγS facility (red triangle). HIγS data is of a translational scan across the Compton converter plate of the GRH done with a 1 cm 16.75 MeV gammaH rayL beam at 200 psi SF6. Simulation data has been normalized to show overall trend of data.

Figure 3.13 is a comparison of the GEANT4 simulation to the pressure scan data obtained at HIγS facility. The data has been normalized to actual data at 215 psia. The overall trend and thresholding characteristics match the measured data. However, the observed signal below threshold was not reproduced by the simulation. This signal is believed to be the result of high energy gamma-ray contamination of the ”mono-energetic” beam and thus not observed in the simulation.

53 0.06

0.05

0.04

0.03

0.02

0.01 Photons per Gamma 0.00 0 50 100 150 200 SF6 Pressure psia

(a) SF6 Pressure Scan Plot Vs Simulation -1 10 H L

10-2

10-3 Photons per Gamma 10-4 0 50 100 150 200 SF6 Pressure psia

(b) SF6 Pressure Scan Log Plot Vs Simulation

Figure 3.13: Comparison of GEANT4 Monte Carlo SimulationH L (blue circle) to data taken at the HIγS facility (red triangle). HIγS data is of a pressure scan using SF6 in the GRH detector done with a 1 cm 4.4 MeV gamma ray beam pointed at the center of the converter plate. Simulation data has been normalized to real measured data at 215 psia following overall trend of data. (a) Plot of experimental compared to simulation. (b) Log plot of experimental compared to simulation.

54 The GEANT4 simulation is capable of reproducing the overall response observed in both pressure and translation to a variety of incident gamma ray beams. Since this simulation has been calibrated against these measurements and been validated, the GEANT4 simulation of the GRH detector and the scaling factors observed can be used to simulate the gas IRF that cannot be measured directly.

3.2.3 Simulated GRH’s Gas IRF

The threshold at which the GRH detector produces Cherenkov light is set via changing the refractive index of the gas. This change of refractive index is accomplished by increasing or decreasing the pressure in the gas cell. While the use of gas allows the GRH detector to easily change the energy threshold at which it detects gamma-rays, the change in refractive index also affects the speed at which the produced Cherenkov photons arrive at the PMT. This shift in the phase velocity of the produced light is perceived as a shift in timing of the measured signal. Therefore an accurate model of where the Cherenkov light is produced, and the pressure dependent index of refraction is needed in order to obtain when the gamma rays arrived at the detector. Without these models, the effect that the change of gas has on the produced signal, the IRF of the gas, could not be understood. The gas IRF is necessary to accurately compare the signals from GRH detectors that are set to different thresholds. At low pressures the Compton electrons needed for Cherenkov light generation are nearly all produced in the Compton converter plate or the surrounding aluminum structure of the GRH detector. However, as the gas pressure increases, the gas itself becomes the main producer of Compton electrons from incident gamma-rays. Due to this effect, the entire gas cell itself needs to be considered as a volumetric light source for Cherenkov radiation. This results in a complex system where at low pressure (higher speed of light) the Cherenkov photons are more localized and produced farther away from the PMT. At higher pressures (slower speed of light) the Cherenkov photons are produced over a larger volume but closer to the PMT. This complex pressure dependent system is what drove the creation of the

55 Monte-Carlo GEANT4 simulation of the GRH detector. In order to properly characterize the eﬀect of the gas, the simulation needs accurate data on the index of refraction of the two gases used, CO2 and SF6. The index of refraction of gas is set in the simulation using a pressure and wavelength dependent polynomial ﬁt to multiple empirical data sets. In gas the refractive index is linearly dependent on the average density of the gas as seen in Equation 3.1 [81].

n − 1 = κρ (3.1)

Where:

• n is the index of refraction of a gas.

• κ is a gas speciﬁc scaling constant relating to the density.

• ρ is the average density of the gas.

For the pressure ranges that a GRH detector typically runs at (0 psi - 200 psi for both CO2 and SF6), the density varies linearly with pressure. Therefore the refractive index of the gas can be written in terms of the pressure, P , of the gas and a gas speciﬁc pressure scaling constant κ0 as seen in Equation 3.2 [81].

n − 1 = κ0P (3.2)

Attempts at applying a linear fit to the empirical data seen in Table 3.8 found that while a linear fit served as a good approximation the data could be better characterized by applying a 3rd order polynomial fit. Equation 3.3 is the 3rd order polynomial fit to the data for the pressure dependent refractive index for CO2.

−3 −4 2 −8 3 −4 nCO2 (P ) = 1 + (9.22 × 10 + 0.28P + 1.03 × 10 P + 6.88 × 10 P ) × 10 (3.3)

56 Equation 3.4 is the 3rd order polynomial ﬁt for the SF6 data.

−4 −6 2 −10 3 −4 nSF6 (P ) = 1 + (1.22 − 8.97 × 10 P + 1.26 × 10 P − 6.24 × 10 P ) × 10 (3.4)

4 (n-1)×10 CO2 Pressure(psi) SF6 Pressure(psi) 5.38 19.1 – 10.75 37.8 22.1 16.13 56.4 33.0 21.5 74.6 43.8 26.88 92.7 54.2 32.26 110.4 64.4 37.63 127.9 74.5 43.01 145.1 84.4 48.39 162.2 94.1 53.76 178.9 103.6 59.14 195.5 112.9 64.51 211.7 121.9 69.89 227.7 130.9 75.27 243.5 139.7 80.64 259.1 148.2 86.02 274.5 156.6 91.4 289.7 164.8 96.77 304.7 172.8 102.15 – 180.6 107.52 – 188.2 112.9 – 195.7 118.28 – 203.2 129.03 – 217.1 139.78 – 230.5 150.53 – 243.2 161.29 – 255.2 172.04 – 266.8 182.79 – 276.4 193.54 – 286.7

Table 3.8: Pressure and the associated refractive index for CO2 gas and SF6(λ=546 nm T=22◦C) [22]

While the index of refraction is primarily dependent on the density of the material, there is a component that depends on the frequency of light that passes through it. This frequency

57 dependent component of the refractive index is called the dispersion of the material [82]. This eﬀect is typically observed by passing white light through a glass prism and seeing a spectrum

1 of colors produced. Since Cherenkov light is generated with a λ2 spectrum (see Frank-Tamm formula, Equation 2.5), and not at a single frequency of light, dispersion serves to widen the observed signal. An empirical formula for dispersion was calculated doing a 3rd order polynomial ﬁt to the data found in Table 3.9. Given the common reference point of 546 nm between the pressure and dispersion data sets, the ﬁtted polynomial was normalized at 546 nm. This resulted in a function that represented the percent change of the refractive index given a wavelength.

Equation 3.5 is the derived percentage dispersion formula for CO2.

−4 −6 2 −10 3 DCO2 (λ) = 1.2162 − 8.9697 × 10 λ + 1.2586 × 10 λ − 6.2422 × 10 λ (3.5)

Equation 3.6 is the derived percentage dispersion formula for SF6.

−4 −7 2 −10 3 DSF6 (λ) = 1.1164 − 4.7127 × 10 λ + 6.3479 × 10 λ − 2.9676 × 10 λ (3.6)

4 4 λ(nm) CO2 n-1×10 SF6 n-1×10 644.024 4.0720 6.9939 546.225 4.0976 7.0158 508.723 4.1113 7.0284 480.125 4.1245 7.0412 435.956 4.1492 7.0647

Table 3.9: Index of refraction for CO2 gas and SF6 gas at various wavelength [23].

Over the pressure range of interest it was assumed that this percentage based dispersion remained ﬁxed and did not vary with pressure. Due to this the wavelength and pressure dependent index of refraction for both CO2 and SF6 is simply a multiplication of the percentage dispersion formula and pressure dependent index of refraction seen in Equation 3.7.

58 n(λ, P ) = D(λ) × n(P ) (3.7)

With an empirical based index of refraction folded into the GEANT4 simulation a variety of impulse response functions were generated using pressure settings typically deployed at the NIF. Figure 3.14 is a comparison of some of the generated impulse response functions that can be used to remove the eﬀects that pressure has on the recorded GRH signal.

Figure 3.14: GRH detector simulated gas impulse response function to an incident gamma- ray. With an increase of pressure both the time delay and width of the produced signal increases.

With the above calibration work done, the shifts in timing caused by instrument response can in principle be separated from shifts caused by physical eﬀects. The following chapters describe the experimental data obtained at NIF, and my analysis to determine if the data has physical signiﬁcance as implied by simulations of the NIF implosion.

59 CHAPTER 4 GAMMA RAY TIMESHIFT BETWEEN D-T SIGNAL AND CAPSULE ABLATOR

At the NIF, the GRH diagnostic is used to quantitatively measure the timing of the gamma ray ﬂash produced during an ICF event. Two key measurements made by the GRH diagnostic are the Gamma Bang Time (GBT), which is generated from the D(T, α)n thermonuclear burn and the Ablator Peak Time (APT) caused by (n, n0)γ reactions occurring in the compressed capsule ablator. For ideally performing capsules both theory and computational models predicted that these two measurements would be time synchronized. However, current GRH diagnostic measurements of both GBT and APT at the NIF show that APT is observed after GBT typically by 40 ps - 70 ps. In the succeeding sections, a theory backed by computational models is presented to explain the apparent time shift between GBT and APT observed at the NIF. An overview will be given of the GRH diagnostic used to observe the time shift and the two techniques used to measure the shift between GBT and APT will be described. In order to conﬁrm this shift between GBT and APT an experimental campaign was completed at a sister ICF facility, OMEGA. The results from this experimental campaign will be reviewed and potential ways to reconcile the data measured at NIF, OMEGA and computational simulations will be described.

4.1 Theory

In an ideally performing ICF capsule, the thermonuclear burn occurs when the capsule shell has completely converged and stagnates at its peak compression. During this stagnation phase the gaseous D-T fuel inside the ICF capsule fuses producing an excited 5He nucleus [83]. The 5He nucleus releases this energy through one of three processes: decomposition into a 3.5 MeV α and 14.1 MeV neutron through a D(T,α)n reaction, de-excitation through emission of either a 16.75 MeV gamma-ray, or emission of a broad gamma-ray distribution

60 centered at 13.5 MeV [59]. Measurements of this gamma to neutron branching ratio has found a branch of (4.2 ± 2.0) × 10−5 [59]. These gamma rays can be used to determine when the D-T burn occurred relative to laser beam on target, known as Gamma Bang Time, and can be used to measure the reaction history of the D-T burn, known as Gamma Burn Width [84]. The neutrons generated in the D(T,α)n reaction proceed to escape the D-T fuel and pass through the capsule shell material. A small fraction of these neutrons are captured or inelasticly scattered by the surrounding capsule ablator material through (n, γ) and (n, n0)γ reactions. These ablator gamma rays

can be used to not only measure the total ablator areal density (ρRablator) of the capsule,

but can in principle be used to determine the time dependent ρRablator over the D-T burn [64, 65, 85, 86]. Current theoretical models predict that the peak time of these capsule ablator gamma rays, known as Ablator Peak Time, should be time synchronous with the GBT as seen in Figure 4.1. This is due to the short distance the generated neutrons need to travel before interacting with the capsule ablator, as well as the fast decay time associated with the dominant gamma emitting state of the ablator material currently deployed at the NIF. In

12 0 the case of CH ablator material a bright 4.4 MeV gamma-ray ( C(n, n )γ, T 1 = 42 fs) is 2 28 0 produced, for SiO2 capsules a 6.88 MeV gamma-ray ( Si(n, n )γ,T 1 = 33 fs). 2 In the case of non-igniting capsules (failures), it is believed that GBT should occur before APT. As the lasers impinge on the ablator material and compress the capsule, the shocks waves prematurely form a hot spot at the center of the capsule. Due to the premature formation of the hot spot the D(T,α)n reaction takes place as the capsule material continues to compress and increase in ρR. The energy released from the D-T reaction begins to counteract the force applied from the lasers driving the capsule compression. This results in a reduced yield compared to the theoretical predicted yield. Since the D-T yield peaks

(GBT) before the maximum ρRablator is achieved (minimum ablator radius), the APT, which is a convolution of the neutrons from the D(T,α)n reaction and the ρRablator, is believed to

61 Figure 4.1: Plot of CH D-T capsule’s ablator radius (green) and fuel (black) vs time overlayed over the gamma rays production from the D-T burn (red) and (n, n0)γ reactions with the ablative material (blue) in an igniting capsule. The maximum neutron yield is achieved at peak compression resulting in the peak gamma production from the D(T,α)n reaction (GBT) and the 12C(n, n0)γ reaction (APT) being time aligned.

be oﬀset later in time than GBT as seen in Figure 4.2. While this simple picture can explain the oﬀset currently seen at the NIF, advanced hydrodynamic simulations of the capsule implosion were performed in order to quantify the magnitude of this shift as well as further the understanding of the physical events taking place during an ICF experiment.

4.2 Simulations

Due to the exotic physics involved, most of our inferred knowledge about an ICF event comes from 30 years of advanced hydrodynamic simulations of plasmas [87]. Two simulation programs are of particular importance in the understanding of this potential time shift between GBT and APT. The software programs are HYDRA developed at LLNL and used

62 Figure 4.2: Plot of CH D-T capsule’s ablator radius (green) and fuel (black) vs time overlayed over the gamma rays production from the D-T burn (red) and (n, n0)γ reactions with the ablative material (blue) in a non-ignition capsule. Due to incorrect shock timing, the hot spot forms before peak compression is achieved. This results in the D(T,α)n reaction reaching its maximum before the capsule has completely converged. Since the 12C(n, n0)γ is dependent on both the ρRablator and the neutrons for the D-T burn, the peak of the gamma production from the ablator (APT) is oﬀset later in time then the D-T peak (GBT).

primarily to simulate the NIF ICF experiments [87], and DRACO developed by LLE used to simulate OMEGA capsule implosions [88]. HYDRA, at its core is a multi-dimensional hydrodynamic code that models the time dependent Navier-Stokes equations for viscous and incompressible material [87]. Unlike its predecessors, HYDRA discretizes space using Arbitrary Lagrangian-Eulerian (ALE) formulation. ALE allows the polygonal spatial grid to move with the material over time [87, 88]. By discretizing space in this fashion, there is no need to calculate convective terms (Eu- lerian formulation, a spatially ﬁxed grid), without degrading the accuracy of the material movement (Lagrangian formulation, grid attached to material boundary) [87, 88]. Overall this reduces the computational complexity of simulations and makes the rezoning (choos-

63 ing a better mesh) and remaping process (interpolating fluid variables) less computationally intensive [87, 88]. Besides tracking the movement of a capsule as it is compressed, HYDRA incorporates various Monte-Carlo models in order to track both neutron transportation as well as charged particle transportation. This, combined with HYDRA’s ability to simulate the various radiation generation/interactions, allows HYDRA to simulate the thermonuclear burn occurring inside an ICF capsule [46, 89]. Due to the inclusion of the various physical packages, this multi-physics code forms a solid foundation on which to simulate the ICF experiments con- ducted at the NIF. Due to the incredible amount of physical processes HYDRA simulates, a full 3D simulation of a single ICF experiment can take upwards of three months on a 8192 processor super computer. Therefore, these full 3D simulations are typically reserved for post-shot simulations of previous ICF experiments. A combination of both 2D and 1D HYDRA simulations are used to drive capsule/experiment design at the NIF as well as to explore the potential effects various physical processes that are believed to occur during the evolution of a capsule [21]. While these 2D and particularly 1D simulations can be done on a single workstation, they fail to capture the full effects of the instabilities that occur during the compression of a capsule. In particular, the 2D and 1D simulations are incapable of accurately representing the effects of Rayleigh-Taylor instabilities [14, 89–92]. Rayleigh-Taylor instabilities occur between the interface to fluids of different densities when a force is applied. This typically results in ”fingers” of more dense fluid entering into the less dense fluid. Due to these fingers the force applied is no longer uniform across the surface boundary which promotes further growth of these instabilities [14, 89]. In the case of a capsule the dense fluid is the capsule ablator. As the capsule is compressed, perturbations form on both the surface and inside of the capsule as seen in Figure 4.3. These perturbations have a detrimental effect on the shock used to form the hot spot at the

64 center of the capsule where the D-T burn occurs. As the perturbations continue to grow as the capsule is compressed, portions of cold dense ablator material can enter the hot spot region further reducing the neutron yield. This issue of mass entering the hot spot of the capsule is called ”ablator mix”. While HYDRA is used to simulate ICF experiments at the NIF, various hydrodynamic codes have been developed to tackle this complex problem for other experiments. Of particular importance is DRACO, a multidimensional radiation hydrodynamics code developed by LLE[88]. DRACO also uses ALE formulation to solve the hydrodynamic equation of states [88]. On top of this, various physics modules that track things such as laser-energy deposition and radiation transport are applied to the simulation in an attempt to simulate the capsule implosion occuring at OMEGA [88]. From both HYDRA and DRACO, the gamma spectrum produced during an ICF experiment can be extracted and compared to the experimental results obtained by a GRH detector. In order to explain the time shift observed in the NIF data, multiple HYDRA simulations were performed by C. Cerjan at LLNL. Table 4.1 list the results of various 1D and 2D HYDRA simulations where the eﬀects of both shock mistiming and ablator mix were varied. The data generated by the simulations strengthen the claim to validity of the theoretical models used to explain the time shift observed between GBT and APT. For an ideal igniting capsule, both APT and GBT should be time aligned as seen in Figure 4.4(a). While the initial burn begins near peak compression, due to alpha heating the D-T fuel ignites which pushes both GBT and APT further back in time when compared to the maximum fuel and ablator ρR. In order to separate GBT and APT various failure modes need to be introduced into the simulation. With the introduction of issues with ablator mix and shock mistiming, the D-T fuel burn occurs before the fuel and ablator have reached max density as seen in Figure 4.4(b). By including these failure modes not only does GBT and APT separate by the magnitude observed by the GRH diagnostic, these failure modes also reduced the neutron

65 Figure 4.3: Density plot of a 2D DRACO simulation of an ICF capsule being compressed. The once smooth surface of the capsule now has multiple perturbations due to Rayleigh- Taylor instabilities [14]. yield to levels currently obtained at the NIF. According to simulations this shift might be a direct indicator of ablator mix and shock mistiming present in the current ICF experiments performed at the NIF. If this is true, it would give experimentalists at the NIF a quantifiable measurement indicating the fitness of an ICF experiment. Therefore, an intensive analysis was performed on the data obtained from the GRH diagnostic at the NIF. This was then followed up by a verification experiment at OMEGA where DRACO simulations showed that the same effect seen at the NIF should be present.

66 (a) Nominal (b) Mix and Mistiming

γ 12 Figure 4.4: HYDRA simulations showing DT ρR (black), CH ρR (green), DT s (red) and C γ s (blue). (a) Nominal simulation with no perturbative eﬀects. Note how there is negligible shift between GBT and APT. (b) Simulation with ablator mix and shock mistiming eﬀects resulting in a shift between GBT and APT [15].

67 Table 4.1: 1-D and 2-D HYDRA simulations showing the eﬀect of diﬀerent failure modes on key capsule metrics [15].

1D 2D Nominal Mix Mix & Timing Nominal Mix & Timing Asymmetric Asymmetric & Mix 17 15 13 13 13 14 13 Yneutron 7.244x10 1.256x10 5.904x10 5.175x10 6.058x10 7.835x10 5.543x10 TIon(keV) 15.27 2.80 1.77 1.52 1.70 2.84 1.52 15 12 11 10 11 12 11 Y12C 3.796x10 8.571x10 2.866x10 3.447x10 3.066x10 3.193x10 3.471x10 −3 −3 −3 −4 −3 −3 −3 Normalized Y12C 5.24x10 6.82x10 4.85x10 6.66x10 5.06x10 4.07x10 6.26x10 GBW (ps) 50 130 300 220 305 120 245 APT-GBT (ps) -2.5 12.7 42.7 7.4 32.3 12.5 32.4

68 4.3 Ablator Timeshift Measurement At The National Ignition Facility

The Gamma Reaction History diagnostic has been deployed at the National Ignition Facility since 2010. It has been in continuous operation collecting data across multiple experimental campaigns, recording data from almost every single high neutron yield ICF event at the NIF. The GRH diagnostic at the NIF has been tasked with measuring the arrival time of gamma rays from both the thermonuclear burn (GBT), and the ablator gamma rays (APT). Besides gathering data on these ICF metrics the GRH has also been tasked with recording the thermonuclear burn duration and shape, which is known as the reaction history of the ICF event. Typically the reaction history is characterized by the width of the thermonuclear burn known as the Gamma Bang Width (GBW). These metrics are needed in order to characterize the ICF event at the NIF and help diagnose the NIF’s current failure to achieve their goal of capsule ignition. It was initially expected that GBT and APT would be time synchronous. However, the trend in current data obtained at the NIF shows an offset with APT happening 20 ps to 70 ps after GBT. The simulations seen in Section 4.2, show that if this time offset is real and not an instrumental effect, the lower than expected neutron yields when compared to simulations can be explained as issues with both shock timing during capsule convergence and ablator mix. Not only would these metrics give an explanation for the low neutron yield, but it would give scientists a parameter to tune both lasers and capsule design.

4.3.1 GRH Diagnostic At The National Ignition Facility

In order to properly measure these metrics, a total of four GRH detectors comprise the overall Gamma Reaction History diagnostic at the NIF (as seen in Figure 4.5). These four detectors allow for four concurrent measurements of any ICF implosion event. Due to this, the GRH diagnostic is capable of isolating the gammas resulting from the thermonuclear burn as well as neutron interacting with the capsule ablator on a single shot.

69 Figure 4.5: Scientist standing next to the Gamma Reaction History diagnostic at the Na- tional Ignition Facility. The GRH diagnostic is comprised of four GRH detectors. The PMT of each of these detectors is placed as close as physically possible to the other PMTs (center of the array) in order to ensure the background observed by each PMT is as identical as possible.

The GRH diagnostic itself is mounted at the entrance of a port hole on the NIF target chamber at the chamber coordinate 064-020 . The port hole itself is covered by a 1.890 inch thick, 31.00 inch diameter aluminum port diagnostic cover as seen in Figure 4.6. This cover has a total of four holes, one for each GRH detector, bored through it. These holes allow the GRH to have an unobstructed line of sight to the target chamber center (TCC) located 5.9 m away. On top of each hole, a computer controlled valve is installed in order to maintain the vacuum integrity of the NIF target chamber. Attached to this port cover is an aluminum mounting bracket seen in Figure 4.7. This mounting bracket holds all four of the GRH detectors in place as well as distributes the load across the port diagnostic cover. The mounting bracket serves as the only external location

70 Figure 4.6: The GRH diagnostic’s port cover attached to the NIF target chamber at 064- 020. It serves to couple the NIF target camber to the four GRH detectors. Four holes are bored through the port cover and valves are attached allowing each GRH detector to have the minimum amount of mass in direct line of sight of the target chamber center while maintaining the target chamber’s vacuum. to place Tungsten radiation shielding. The core of the mounting bracket contains multiple Tungsten inserts which reduce both direct particle interactions and LPI x-rays from arriving at the four PMTs positioned behind it. However, there is no shielding to reduce scattering from secondary sources surrounding the GRH diagnostic. Therefore, at lower neutron yields (<5 × 1014) an appreciable background caused by LPI x-rays is observed underneath the detected Cherenkov signal. The GRH detectors are installed on the mounting bracket in a four leaf clover arrangement with PMT and ﬁnal stage optics positioned behind the center of the bracket. Due to the varying light intensity levels expected when measuring the Cherenkov light for each threshold, two types of PMTs are deployed at the NIF. Two single stage micro-channel plate based PMT developed by Photek were installed in two of the GRH detectors, These PMTs are meant

71 Figure 4.7: The GRH mounting bracket before being installed on the GRH port diagnostic cover. The stack of dark-grey metal at the center of the mounting bracket are multiple slabs of Tungsten used to shield the PMTs located directly behind them. to cover the lower threshold range (<8 MeV). The detectors are designated GRH Cell A and B. For the higher threshold type (8 MeV and 10 MeV) two double stage micro-channel plate based PMT from Photek are installed in the remaining two GRH detectors. These two detectors are labeled GRH Cell C and D. For each GRH detector, the output of the PMT is connected via SMA cabling to a high speed 80:20 SMA splitter as seen in Figure 4.8. For cells A and B an additional 6dB attenuator is placed in line on the 20% leg resulting in the split becoming an 80:10 splitter. For cells C and D a 6dB attenuator is placed between the PMT and splitter resulting in the splitter becoming a 40:10 splitter. Every single output of the splitters are then coupled to their own Mach-Zehnder modulator, converting the PMT’s electrical signal into an optical one. The modulator attached to the large signal is designated MZ1, while the modulator attached to the smaller signal output is designated as MZ2. The reason for this split is to

72 increase the dynamic range of the Mach-Zehnder encoding without having the signal ”roll over” as explained in Section 4.5.1. The cabling necessary to run the Mach-Zehnder modulator (polarization maintaining fiber for input, SMA cable for a DC bias and single mode optical fiber carying the encoded signal) are bundled with the PMT high voltage cable and routed through an EMI shielded umbilical cord to a junction box seen in Figure 4.9. This junction box routes all the cables from each GRH detector to a data acquisition system located approximately a little over 100 ft away in a separate room on the Mezzanine level of the NIF building. This long distance is necessary due to the unique radiation environment present at the NIF. As higher neutron yields are achieved, issues due to volumetric radiation contamination and radiation induced currents would render the data acquisition system inoperable if placed near the target chamber. By distancing the setup and placing it behind multiple concrete barriers these issues are eliminated. The Mezzanine level stores the equipment necessary to run the Mach-Zehnder modulators, data acquisition system and distribution system for an optical timing fiducial used by each of the four GRH detectors. In order to run the Mach-Zehnder modulators, a bank of eight 20.0 mW 1554 nm CW ThorLab Pro8 laser diodes are used. The output from these lasers is coupled into eight 50 µm polarization-maintaining fiber which are then routed to the target chamber room where the Mach-Zehnder modulator is installed. The optical output of each Mach-Zehnder module is coupled into a 9 µm single mode SMF-28e fiber which is routed back to the Mezzanine level. There the optical signal is inserted into a specially designed Mach-Zehnder bias controller. The Mach-Zehnder bias controller, seen in Figure 4.10, is specially designed to apply a DC bias to the Mach-Zehnder modulator setting one leg of the interferometer at a 90◦ phase offset (Quadrature) before an ICF experiment. This is achieved by forming a feedback loop with the Mach-Zehnder modulator. An analog SMA cable is routed from the Mezzanine to the Mach-Zehnder modulator in the target bay. This cable transmits a DC offset signal as well as

73 iue48 aln ceai o igeGHdtco sisalda h ainlIgnition National the at installed as detector GRH single a for Facility. schematic Cabling 4.8: Figure

Mach Zehnder Target Bay 1 80%

80:20 SMA 6dBm Mach Zehnder PMT Splitter 20% 2

Mezzanine High Voltage Channel 2 Channel 1 1554nm ThorLabs Power Supply Pro800 Laser PS350 NIF Bias Controller

1x5 50:50 SMA 74 MEMS VOA Photo Receiver CH 1 Splitter Splitter

CH 2

50:50 SMA Photo Receiver CH 3 DPO Splitter 71254C 2x2 Oscilloscope Splitter CH 4

Delay Generator Aux DG535 In

NIF Facility Legend

High Voltage Multi Mode Fiber GRH Optical Fidu NIF Ref. Trigger SMA Single Mode Fiber BNC Polarize Maintaining Fiber Figure 4.9: Inside the GRH diagnostic junction box which connects the the GRH diagnostic in the target chamber room to the data acquisition system in the Mezzanine level of the NIF building.

75 a modulated 1 kHz triangle wave. The bias controller monitors the Mach-Zehnder modulator output for this wave and adjusts the DC bias level accordingly. Once the modulator has been properly biased it is ready to encode the electrical signal into an optical one. After leaving the Mach-Zehnder bias controller, the optical signal is fed into a NewFocus photo receiver which converts the optical signal into an electrical one. The electrical signal is then split using a high speed 50:50 SMA splitter. These outputs are then routed to one of four Tektronix DPO71254 Digital Phosphor Oscilloscopes (4 channel, 12.5 GHz bandwidth, 50 GigaSamples/s) seen in Figure 4.11, one for each of the four GRH detectors. The two electrical outputs from MZ1 are attached to channel 1 and 2 on the oscilloscope, with the output from MZ2 using the remaining two channels. The oscilloscopes are triggered by a Stanford Research System Model DG645 Digital Delay Generator. The delay generator is triggered by a facility wide timing trigger generated from the Integrated Timing System used to synchronize all of the NIF’s 192 laser beams.

Figure 4.11: One of the many Tektronix DPO71254 Digital Phosphor Oscilloscope used to record data from the GRH diagnostic.

76 Figure 4.10: Inside one of the equipment racks used to control the GRH diagnostic. Starting from the bottom are the GRH diagnostic Mach-Zehnder bias controller (gold). The bias controller monitors the output of a Mach-Zehnder modulator and applies a DC signal in order to set the modulator to quadrature before an ICF experiment. On top of them are two ±15 V power supplies used to energize the photo receivers. Above the power supplies there are mounted four PS350 high voltage power supplies used to bias the four PMTs used by the GRH diagnostic. Above these power supplies lay the delay generators used by the GRH diagnostic to trigger the various components in the system.

77 After the oscilloscopes have been triggered and the data from the ICF experiment has been collected, the data is automatically archived on an Oracle database. The data is then sent to the Shot Data Analysis Engine. The Shot Data Analysis Engine then attempts to analyze the collected data for the metrics of interest such as GBT and GBW. This is achieved by stitching the data from each of the four channels of an oscilloscope together, applying the Mach-Zehnder unfold function, which deconvolves out the impulse response function of both the installed PMT and gas pressure, before finally fitting the recorded peaks. In order to stitch all four channels of the oscilloscope together, an optical timing fiducial is flashed onto the PMT before the arrival of the Cherenkov signal. The optical fiducial itself is a 527 nm Gaussian pulse delivered by the NIF facility. This pulse is sent through a 3 µm 2x2 splitter with one of the outputs fed back into the input side. This results in multiple pulses spaced apart that diminish in amplitude with each pulse as seen in Figure 4.12. This fiducial pulse train is then routed using 3 µm fiber into a 1x4 splitter which fans out the signal to the four GRH detectors. After being split, each signal is sent through a 6 µm fiber to a micro electrical mechanical system variable optical attenuator (MEMS-VOA). The MEMS-VOA attenuates the light signal by bouncing it off an electrostatically driven tilting mirror. This mirror shifts the light beam into or out of an output fiber, thereby reducing the light coupled into the output fiber. After being attenuated the signal is sent through a 6 µm fiber to the target chamber room where it is fed into the GRH detector. The light itself is inserted into the GRH detector at the 2nd OAP mirror facing directly into the PMT. In order to avoid spot degradation of the PMT at the end of the fiber a graded-index lens is mounted. By using this shared diminishing fiducial train, not only can the GRH detectors be timed directly against when the NIF lasers are fired (t0) but high precision cross timing between GRH detectors is achievable.

78 6 L V H 4 Voltage 2

0 -2 0 2 4 6 8 10 12 Time ns

Figure 4.12: Optical ﬁducial diminishing pulse train recorded by GRH diagnostic cell D at the NIF. This diminishing pulse train is achievedH byL coupling a 2x2 splitter into itself.

4.3.2 Timing Calibration At The National Ignition Facility

Two types of timing calibrations are performed on the GRH diagnostic. The ﬁrst is an absolute timing calibration to when lasers impinge on the capsule, needed for a direct measurement of peak time of the various thresholds. The second is a relative timing measurement between the GRH detectors which enables the detected signal to be decomposed into its constituent signals. For absolute timing, each of the GRH diagnostic gas cells is evacuated, then purged with air until it is at room pressure. Each of the four GRH detectors is then opened and a 3 mm thick plastic x-ray scintillator (BC-422) is installed, replacing the Compton converter plate as seen in Figure 4.13. Due to its incredibly fast rise time (<20 ps) when excited by x-rays, this scintillator can be used to measure when lasers impinge upon a target positioned at the center of the NIF target chamber. During an absolute timing shot a target coated with silver or gold is placed at the target chamber center. The NIF lasers are ﬁred at the target producing a large x-ray signal. These

79 Figure 4.13: BC-422 scintillator in the process of being installed in a GRH detector replacing the Compton converter plate. x-rays then excite the plastic scintillator installed in the GRH and the resulting scintillation photons that are recorded by the GRH’s PMT. During this shot the typical diminishing fiducial train which is generated from firing the NIF lasers is triggered and then recorded by the PMT. The fiducial can then be timed against the rising edge of the scintillator signal as seen in Figure 4.14. This results in the fiducial being absolutely timed to the NIF laser system enabling an absolute measurement of a Cherenkov signal against the fiducial. For a cross cell timing shot all the GRH detectors are set to an 8 MeV threshold. A D-T exploding pusher is then imploded and all four GRH detectors measure the D-T signal. Since all four detectors are observing the same physical phenomenon, the observed Cherenkov peak can be used as a reference for when the diminishing fiducial train arrives at each detector. This measurement provides a table of temporal offsets that are applied to each channel once the signal has been aligned by the fiducial. If absolute timing is not needed, this method is preferred over the scintillator timing method due to the inherent precision of the fitting

80 7

5 L V H 4

3 Voltage 2

0 0 10 20 30 40 50 60 Time ns

Figure 4.14: Data recorded by a GRH detector from timing shot N110522. The diminishing ﬁducial train (left) is timed against the rising edgeH ofL the scintillator signal (right).

method. Using these two high precision methods of timing, the temporal component of the data obtained by the four detectors comprising the GRH diagnostic can be compared.

4.3.3 Experimental Results At The National Ignition Facility

During nominal high yield operation the GRH diagnostic is conﬁgured with the following gamma energy thresholds seen in Table 4.2. Since the GRH’s deployment on the NIF target chamber it has been steadily recording data for every ICF experiment when the neutron yield was expected to exceed 1013.

Table 4.2: Nominal threshold conﬁguration of the GRH diagnostic at NIF. Setting Cell A Cell B Cell C Cell D

Threshold (MeV) 10.0 2.9 4.5 8

81 Therefore, a substantial historical data set has been gathered observing the gamma ray signals at these thresholds. Figure 4.15 shows the relative peak timing diﬀerence for a given threshold when it is compared to the 8 MeV threshold for a selection of CH ablator D-T ICF experiments at the NIF. This relative peak timing diﬀerence was calculated based on the absolute timing method relying on the measurements of the BC-422 scintillator.

100 ó æà æ N111215 ps L ì N111112 H 80 ìç à ì N111103 æ ò ò N111029 60 ô N110914 àò ô ç N110908 á N110904 40 ó í N110826 8 MeV Peak ò ó N110620 - 20 ç ì 0 ìæçàáòôóí á á

Peak Time àô æí ô -20 2 4 6 8 10ó 12í Threshold MeV

Figure 4.15: Diﬀerence in peak time of the GRHH signalL for a given threshold, as compared to the 8 MeV channel for a selection of CH ablator D-T ICF experiments at the NIF. The 8 MeV channel is assumed to be free of contamination from gamma-rays arising from the interaction of 14.1 MeV neutron with material surrounding the NIF capsule.

The 8 MeV threshold was picked as the reference condition since it was assumed to be free of contamination from the gamma rays generated from the interaction of 14.1 MeV neutron with material surrounding the NIF ICF capsule. Therefore, the 8 MeV threshold should be a direct measurement of the GBT. The lower thresholds are not a clean signal of just the (n, n0)γ occurring in the ablator, but a mix of the ablator signal as well as signals from the hohlraum and TMP. Both the holhraum and TMP are comprised of Au, Al and Si which generated a detectable gamma

82 ray signal when hit by 14.1 MeV neutrons. Because of the spatial distance the hohlraum and TMP have from the thermonuclear burn it was expected that the 4.5 MeV and 2.9 MeV thresholds to be pushed back in time relative to GBT. However, due to the ρR of the ablator and the relative brightness of the 4.4 MeV gamma ray from 12C(n, n0)γ reaction, the majority of the signal comprising the 2.9 MeV threshold should originate from gammas generated from the CH ablator. If there was no time offset between GBT and APT, the 2.9 MeV threshold should arrive slightly later then the 8 MeV channel (due to the effects of the holhraum and TMP signal). However, the time delay observed in the 2.9 MeV threshold (see Figure 4.15) cannot solely be explained by the effects of the hohlraum and TMP. The data indicates that the APT must have an appreciable delay when compared to the GBT. These experimental results fall within the predictions made by HYDRA for ICF capsules that failed to achieve ignition. These results not only point to the reason why the ICF capsules failed to achieve ignition, but also explain the discrepancy between predicted and achieved neutron yields. In order to strengthen the argument put forth by HYDRA simulations, that a shift between GBT and APT indicates both ablator mix and shock timing issues, an analysis technique to decompose the data into its various source signals was developed. Using this method a direct measurement of the time difference between GBT and APT can be achieved.

4.3.4 Cross Cell Analysis Of GRH Diagnostic Data

In order to decompose the data obtained by the GRH diagnostic into its aggregate source signals, an analytical method using the physical constraints of the system was developed by the GRH group [86]. This method relies on forward ﬁtting the 8 MeV and 10 MeV threshold using the GRH cell PMT and gas IRF in order to retrieve the full D-T reaction history. This reaction history, is then convolved with a threshold dependent hohlraum and TMP IRF generated from MCNP simulations, as seen in Figure 4.16. This produced the response

83 of the hohlraum and TMP over the D-T burn at each threshold.

Au Al 10-6 Si Total

10-7 Cherenkov Photons Per Neutron 10-8 0.00 0.05 0.10 0.15 0.20 0.25 Time ns

Figure 4.16: Log plot of the Hohlraum/TMP impulseH L response function of a GRH detector at 4.5 MeV threshold. This IRF was generated from an MCNP simulation of the NIF Hohlraum/TMP completed by L. Dauﬀy at LLNL.

After time aligning all four detectors of the GRH diagnostic using the cross cell timing method, a forward fit is made to retrieve D-T reaction history, hohlraum and TMP response, LPI x-ray background and an ablator response confined by the D-T reaction history. By letting the amplitude of these signals float an attempt is made to fit the data from all four GRH detectors as seen in Figure 4.17. This cross cell analysis enables the measured signal to be decomposed into the source terms and allows for the isolation of the ablator signal. With the ablator signal isolated, the APT can be measured. Table 4.3 compares the peak time of the deconvolved 2.9 MeV threshold relative to the 8 MeV threshold with the cross cell analysis forward fit to the APT relative to GBT. After removing the contribution of the hohlraum on the overall time shift observed on the 2.9 MeV threshold, there remains an unaccounted for 30 ps shift when comparing the signal derived

84 Figure 4.17: Shows the forward ﬁt cross cell analysis across all four GRH detectors [16].

from the carbon ρR to the gammas from the D-T burn. This shift is in good agreement with HYDRA simulations for capsules expected to have both mix and shock timing issues. Given the capsule’s lower then predicted ideal neutron yield, this time shift could be an indicator as to why the experimental shots failed. In order to ascertain if the time shift observed in the 2.9 MeV and 4.5 MeV threshold channels is a true physical eﬀect, an experimental campaign using the GRH and another Cherenkov detector, the Gamma Cherenkov Detector, was performed at the NIF sister facility, OMEGA. The experimental campaign to investigate this eﬀect was proposed by the author of this thesis.

85 Table 4.3: Comparison of deconvoluted data with a forward ﬁt cross cell analysis for CH capsules at the NIF [16]. Deconvolved Forward Fit NIF Shot Diﬀerence (ps) 2.9 MeV - 8 MeV (ps) C Peak - D-T Peak (ps) N111103 82 45 -37 N111112 56 34 -22 N111215 80 32 -48 N120126 72 30 -42 N120131 61 29 -32 N120205 53 21 -32 N120219 80 10 -70 N120316 56 24 -32 N120321 50 18 -32 N120417 72 21 -51 N120716 68 22 -46 N120802 105 45 -60 N120920 93 27 -66 Average 71 28 -44

86 4.4 Veriﬁcation Experiments At OMEGA

On April 16th, 2013 an experimental campaign was performed at the OMEGA facility located at the Laboratory for Laser Energetics (LLE) in Rochester, New York. This experimental campaign was to see if cross timing between the GRH and GCD detectors was technically feasible and to develop techniques to measure the time shift caused by the ablator areal density. A subsequent experimental campaign occurred on April 8th, 2014 to directly measure the shift between GBT and APT in order to verify the results obtained at NIF.

4.4.1 OMEGA Facility

The OMEGA facility (see Figure 4.18), much like the NIF, is a platform for the study of ICF physics. However, there are two key differences between OMEGA and the NIF. The first key difference is that the laser power provided at OMEGA is 30 kJ vs the NIF’s 1.8 MJ [93]. The second is that the lasers are positioned to do direct drive ICF while NIF is configured for indirect drive ICF [93]. Due to these differences, the OMEGA facility can reach a maximum neutron yield in the low 1014 neutrons/shot. But, due to the lower strain on laser optics, a larger volume of shots (>12) can be fired in a day. This provides a valuable tool to address fundamental physics questions, as well as calibrate the NIF’s ICF diagnostics. The OMEGA facility uses its 60 lasers to perform direct drive ICF experiments by compressing a capsule filled with fusion fuel inside a 1.5 m radius vacuum target chamber [94]. The 60 lasers initially start as a 1053 nm 1.0 nJ laser pulse produced by a Koheras Yb:FBG fiber master oscillator housed in the Oscillator Room [94]. This pulse is transmitted to the Pulse-Generation Room where the laser pulse is substantially modified. This room provides three options to seed the OMEGA beam line: “Main”, “SSD” and “Backlighter”. The Main configuration produces a basic laser pulse without heavy filtering, which is meant for mostly indirect drive ICF experiments [94]. SSD which stands for smoothing by spectral dispersion, is a two-dimensional smoothness applied to the laser beam and is used for the bulk of shots done. Backligher, while similar to Main, allows for up to 20 of the 60 beams to have a

87 Figure 4.18: Laboratory for Laser Energetics (LLE) OMEGA Facility. 60 beam lines seen on the right are focused to a single point in the target chamber seen on the left [40].

different arrival time and pulse shape [94]. Once an option has been selected, the pulse travels to one of three large-aperture ring amplifiers (LARA) located in the laser bay as seen in Figure 4.19. LARA spatially filters and then propagates the beam to the stage-A beam splitter, where the single laser beam is split three ways. This is done via polarization-control wave plates, a standard used for all splits at OMEGA. The three beams each pass through Nd-doped phosphate glass laser rods (64 mm diameter by 370 mm), which amplify the laser pulse [94]. These rod amplifiers, like all the laser amplifiers in the laser bay, are optically excited by Xenon flashlamps. Once excited the rod amplifiers amplify the laser beam by releasing some of the energy stored via stimulated emission [94]. After this amplification, each beam passes through the stage-B splitter that splits each beam five ways, producing a total of 15 beams. These 15 beams are passed through another set of 64 mm diameter rod amplifiers. The 15 beams are then expanded and enter stage-C

88 Figure 4.19: OMEGA facility laser bay [40].

where the beams pass through 90 mm diameter rod amplifiers before each one is split two ways resulting in a total of 30 beams with a total power around 1.5 kJ. 15 of the beams are routed to the North end of the laser bay, while the remaining 15 beams are routed to the South, where both sets enter stage-D as seen in Figure 4.20 [94]. In stage-D the 30 beams are split into the final 60 beams. During this process, the path length of the 60 beams are adjusted in order to compensate for any difference in arrival time to the center of the target vacuum chamber. The beams are then routed towards the target chamber, where they are amplified again through 90 mm diameter rod amplifiers. The lasers then pass into stage-E, where they are amplified by disk amplifiers. The disk amplifiers, like the rod amplifiers, are comprised of Nd-doped phosphate glass that is excited via Xenon flashlamps. Each disk is 3 cm thick, with a total of 4 disks per amplifier. For stage-E, the diameter of these amplifiers is 150 mm. The beams then enter stage-F, where the beam is amplified via a 200 mm diameter disk amplifier. At this point the total laser power has been amplified to 60 kJ [94].

89 Figure 4.20: Laser routing from Laser Bay to Target Chamber [42].

Right before the lasers enter the target bay the 1054 nm light is converted to 351 nm via the frequency-conversion crystal (FCC) subsystem. Much like NIF, OMEGA uses two crystals of potassium dihydrogen phosphate that convert the light, resulting in a large amount of energy loss [94]. After exiting the FCC the beam enters the target chamber bay, where two mirrors per beam are used to route the 60 laser beams into the target vacuum chamber as seen in Figure 4.21. At this point, the lasers impinge on the fuel capsule resulting in ICF.

4.4.2 GRH System At the OMEGA Facility

Since early 2009, a GRH detector was deployed at the OMEGA facility to characterize the detector response to true ICF conditions, as well as shed light on poorly understood ICF physics [95]. The GRH detector was installed on the OMEGA target chamber at H8 (see Figure 4.22). Before installing the Photek PMT into the GRH, measurements of the PMT’s response to various wavelengths of light were completed using a PMT test can. This measurement was done at various bias voltages (4.1 kV- 4.9 kV in 0.1k V increments) and was completed before and after each experimental campaign in order to measure the degradation and quantum eﬃciency of the PMT.

90 Figure 4.21: Omega target chamber [42].

(a) GRH at OMEGA (b) OMEGA chamber map

Figure 4.22: (a) The GRH installed on the OMEGA target vacuum chamber. (b) OMEGA target vacuum chamber map [17]. The GRH is located at H8.

After the PMT had been installed in the GRH detector, the PMT output was split into two Mach-Zehnder (MZ) modulators (see Figure 4.23(a)), which are part of a multi-stage system that transforms the analog electrical signal into an analog optical signal [95, 96]. The reason for this split is that on one leg of the split a 6dB attenuator is attached allowing one

91 of the Mach-Zehnder modulators to cover more dynamic range. HV cable were run from the Stanford Research System Model PS350 HVPS (See Figure 4.23(b)) sitting inside LaCave, an experimental area located directly underneath the OMEGA target chamber, to the PMT. See Figure 4.24 for a schematic of the GRH data acquisition setup. Figure 4.25 is the GRH’s DAQ installed in LaCave.

(a) Mach-Zehnder (b) HVPS

Figure 4.23: (a) The Mach-Zehnder system attached to the GRH’s PMT. (b) Stanford Research System Model PS350 High voltage power supply used to power the PMT, sitting on top of a Tektronix SCD.

In order to set up this MZ fiber-optic link, two 20 mW 1554 nm CW ThorLabs WDM Laser Diode modules were deployed in LaCave (See Figure 4.26(a)). The laser light was transmitted to the GRH Mach-Zehnder modulators using a 50 µm PM fiber. From there the output of the Mach-Zehnder modulators were transmitted back to LaCave using duplex 9 µm SM fiber (SMF-28e). This output was inserted into a Mach-Zehnder bias controller developed by Kirk Miller from NSTec (See Figure 4.26(b)). The MZ bias controller generates a 1 kHZ triangle wave which is sent to the MZ interferometers via an analog SMA cable. It then monitors the output of the MZ interferometers for the 1 kHZ wave and changes the bias voltage (and thereby the path length) on the one of the two legs of the interferometer. By measuring both the negative and positive going

92 iue42:Shmtco R’ aaaqiiinstpa OMEGA. at setup acquisition data GRH’s of Schematic 4.24: Figure

Mach Zehnder Target Bay 1 80%

PMT 50-50 SMA 4:1 SMA 6dBm Mach Zehnder #210-416 Splitter Splitter 20% 2

40 ft LaCave High Voltage Laser A Laser B Channel 1 Channel 2 Power Supply 1554nm ThorLabs NIF Bias Controller PS350 (GPIB 1/6) Pro800 Laser

Optical N-Type to 12 ft Replaceable Photo Receiver 93 CH 4 Attenuator SMA Attenuator SCD-3 #4467

Photo Receiver 50-50 SMA CH 2 #4468 Splitter O/E 12 ft DPO 10dBm Converter 71254C +49.919 μs Oscilloscope

1x6 Optical Delay Generator +50.0 μs Aux In Splitter DG535 4 ft

Omega Facility Legend High Voltage LANL Ref. Trigger Multi Mode Fiber GRH Optical Fidu GCD Optical Fidu SMA (LaCave/Slot7/Ch2) BNC Single Mode Fiber ΔT=4950.3462μs Foam Flex Polarize Maintaining Fiber Figure 4.25: Handsome scientist standing next to the GRH’s data acquisition setup installed in LaCave. signals of the triangle wave, the bias controller attempts to set the MZ interferometer at the midway point of complete destructive interference. Since this baseline point is continuously measured, and the location of the baseline is known on the transfer function, any deviation from the baseline (due to a signal from the PMT) can be translated into voltage generated by the PMT. Further discussion on how the MZ system works can be found in Section 4.5.1. After exiting the Mach-Zehnder bias controller, the optical signals generated by the Mach-Zehnder interferometers are transmitted to NewFocus Photo Receivers (PR, see Fig- ure 4.27(a)). The PR takes the optical signal and converts it to an electrical one. Before being connected to the oscilloscope, the most sensitive Mach-Zehnder interferometer signal (one without attenuation) is mixed with an electrically generated comb like structure ﬁducial signal via a high frequency splitter (See Figure 4.27(b)). The two Mach-Zehnder interferom-

94 (a) GRH DAQ setup (b) GRH DAQ schematic

Figure 4.26: (a) Two 20 mW 1554 nm CW ThorLabs WDM Laser Diode modules mounted in a ThorLabs Pro800 chassis. Two PM ﬁbers (blue) are delivering the CW laser output to the Mach-Zehnder modulators mounted to the GRH. (b) Mach-Zehnder bias controller (gold) monitoring output from the Mach-Zehnder and delivering a bias signal to them.

eter signals are then transmitted to a Tektronix DPO71254 Digital Phosphor Oscilloscope (4 channel, 12.5 GHz bandwidth, 50 GigaSamples/s) seen in Figure 4.28. Two signals are provided by the OMEGA facility. One is an electrical trigger signal as well as the already understood 526 nm optical comb fiducial signal. Both signals are picked off from the main laser beam that impacts the ICF target. This enables the equipment to be timed with the laser pulse. The optical comb fiducial is split upstream by the facility and delivered via 50 µm multi-mode fiber. One of these optical fiducials passes through an screw adjusted variable optical attenuator before being routed to the GRH detector and injected into the GRH cell. This signal is pointed towards the PMT which is then detected by it. It serves as a timing reference which is unaffected by changes in the PMT bias voltage.

95 (a) NewFocus Photo Receivers (b) Electrically Injected Fidu

Figure 4.27: (a) Two NewFocus Photo Receivers converting the two optical signals from the Mach-Zehnder interferometers into electrical signals. (b) High Frequency splitter (gold) is used to mix the Mach-Zehnder signal and an electrically generated comb fiducial signal. A 10dB electrical attenuator (blue) is placed in line with the electrical comb fiducial signal to stop reflections caused by the Mach-Zehnder signal.

The second optical fiducial is further split using a 1x6 optical splitter seen in Fig- ure 4.29(a). The split signal is then injected into a high frequency Optical to Electrical (O/E) converter (See Figure 4.29(a)) which transforms the optical comb into an electrical comb. One of these electrical comb fiducials is sent to the GRH system, where a second one is sent to the GCD system. Before being electrically mixed into the PR signal using a high frequency splitter, a 10 dB electrical attenuator is used in order to damp electrical reflections. In the case of the electrical trigger signal, it is delayed by the facility by 4950.3462 µs before being delivered to the GRH DAQ setup. There it is inserted into a Stanford Research System Model DG645 Digital Delay Generator (See Figure 4.29(b)). The trigger signal is split, one for the GRH system and one for the GCD system. A delay is applied to the GRH leg of 50.0 µs before being sent to the oscilloscope to be used as a trigger signal to record the data produced by the GRH. Figure 4.30 shows the typical signal resulting from an ICF implosion of a D-T exploding pusher as recorded by the GRH detector.

96 Figure 4.28: Tektronix DPO71254 Digital Phosphor Oscilloscope used to record the signals generated from the two PR attached to it.

(a) Optical Fiducial 1x6 Splitter (b) DG645 Delay Generator

Figure 4.29: (a) 1x6 optical splitter (beige) used to distribute an optical comb ﬁducial to multiple optical to electrical converters (black). The converters are used as an electrical ﬁdu- cial for both the GRH and GCD. (b) Stanford Research System Model DG645 Digital Delay Generator used to delay and split a trigger signal for both the GRH and GCD oscilloscopes.

97 35

Optical Cherenkov Scatter Direct Neutron 30 Fidu Signal Interaction

Voltage (V) 15

100 110 120 130 140 150 160 170 Time (ns)

Figure 4.30: Data taken by one GRH detector at OMEGA on April 16th 2013. Starting on the left is the optical comb ﬁducial followed by the Cherenkov signal. The Cherenkov signal is followed by gamma rays created from neutrons scattering oﬀ of diagnostic equipment placed near the target chamber center. The large ramp to the right of the plot are the neutrons generated from the D-T burn directly interacting with the PMT.

98 4.4.3 GCD System At OMEGA Facility

Unlike the GRH, the GCD diagnostics are directly inserted into the target chamber by installing it in a ten-inch manipulator(TIM) (See Figure 4.31). The TIM serves as a transport shuttle for a GCD allowing it to be precisely positioned near the center of the target chamber.

(a) GCD installed in a test TIM (b) TIM on OMEGA target chamber

Figure 4.31: (a) GCD installed in a test TIM undergoing various safety checks. (b) GCD- 2 and GCD-3 undergoing preparations to be installed in a TIM attached to the OMEGA chamber.

During the experimental campaign two GCDs were deployed at OMEGA, GCD-1 and GCD-2, in TIM-5 and TIM-1 respectively. While GCD-1 was used for data acquisition, the other GCD served as a precision retractable mount for a Si puck (See Figure 4.32) to be place 11.4 cm away from the target chamber center. The Si puck was installed to serve as an extra physical timing reference to relate the capsule Cherenkov signal to during the experimental

99 campaign.

(a) Si puck (b) Si puck attatched to puck holder

Figure 4.32: (a) Si puck used for physical timing reference. Black marks are caused by laser scorching. (b) Puck holder which connects the Si puck to the GCD.

The GCD-1 uses a very similar data acquisition system as the GRH. However before installing a Photek PMT into the GCD-1, measurements of the PMT’s response to various wavelengths of light were completed using a PMT test can. This measurement was done at various bias voltages (4.1 kV- 4.9 kV in 0.1 kV increments) and was completed before and after each experimental campaign in order to measure the degradation and quantum eﬃciency of the PMT. Like the GRH, the GCD-1’s PMT was coupled to a Mach-Zehnder system. The signal is then split into two with one leg having a 6 dB attenuator. These two electronic signals are then sent into a Mach-Zehnder “suitcase” placed directly next to the detector in the

100 target bay. Unlike the GRH which had separate modules for the diode lasers, Mach-Zehnder interferometers and bias controller, all of these modules are condensed into a single box (See Figure 4.33). Internally this suitcase performs all the functions similarly to the GRH’s Mach-Zehnder system and is the next evolution of the Mach-Zehnder system.

(a) MZ suitcase (b) MZ suitcase internals

Figure 4.33: (a) Mach-Zehnder suitcase installed on the GCD. (b) Inside of the Mach- Zehnder suitcase [18].

The optical output from this suitcase is coupled into a duplex 9 µm SM fiber. This fiber takes the optical signal and transmits it to LaCave located directly underneath target vacuum chamber, where they are coupled into a pair of NewFocus PR(See Figure 4.34(a)). Like in the GRH’s DAQ setup, the most sensitive MZ interferometer signal is mixed with an electrically generated comb fiducial signal via a high frequency splitter with a 10 dB attenuator in line (See Figure 4.27(b)). The two MZ interferometer signals are then transmitted to a Tektronix TDS6124C Digital Storage Oscilloscope (4 channel, 12 GHz bandwidth, 40 GigaSamples/s) seen in Figure 4.34(b).

101 (a) NewFocus GCD photo receivers (b) Tektronix TDS6124C

Figure 4.34: (a) NewFocus Photo Receivers installed on the GCD oscilloscope. (b) Tektronix TDS6124C Digital Storage Oscilloscope used to record data generated by the GCD.

4.4.4 Cross Timing Between The GRH And The GCD

In order to measure the peak time shift caused by the capsule ablator’s time dependent ρR, high precision cross timing needed to be achieved between the GRH and the GCD detectors. By obtaining accurate cross timing between the detectors, the GCD can be used as a reference to when GBT has occurred relative to the ablator signal detected by the GRH. The fiducials that were provided by the LLE facility enabled the GRH and GCD to be time synchronized. Both the GRH and the GCD were set to an 8 MeV threshold in order to exclusively observe only the gammas generated by the D-T burn (GBT). Multiple shots were then taken with the detectors in this state. A measurement of the distance between the fiducial and the GBT on both detectors was then made as seen in Figure 4.35. Taking the difference between these two numbers, the variance in when the ICF implosion happens is removed and the overall shot to shot jitter between the detectors was measured. Table 4.4 lists the results. The results in Table 4.4 support that this method of cross timing the detectors exceeds (jitter approximatly ±4 ps) the required precision needed to detect the theoretical time shift (>20ps) caused by a change in the ablator pR during the D-T burn. The 6ps shift measured

102 10 Shot #69397 GCD 8MeV DT(10)SiO2[2.3] 8

4 Voltage (V) 2 GCD Fidu - GBT

0 20 40 60 80 100 120 6 Shot #69397 GRH 8MeV DT(10)SiO2[2.3] 5

2 GRH Fidu - GBT Voltage (V) 1

20 40 60 80 100 120 ns

Figure 4.35: Measurement of the electric fiducial relative to gamma bang time. (top) Measurement of GCD Fidu - GCD GBT. (bottom) Measurement of GRH Fidu - GRH GBT. Note that the 2nd set of fiducials is from the optically injected comb fiducial, which was illuminating the PMT of the GRH detector. after shot 69396 and 69397 were primarily due to a change in the PMT bias levels. Increasing the bias levels causes the photoelectrons generated at the photocathode to be accelerated through a greater potential difference. This results in the photoelectrons arriving earlier in time. This observed time shift is in agreement with previous measurements performed on a Photek PMT by AWE. Due to this effect, once timing has been established between the detectors, the PMT bias voltage cannot be changed.

103 Table 4.4: Experimental results of cross timing GRH and GCD at 8MeV threshold.

Shot # OMEGA RID Capsule Neutron Yield GRH PMT Bias(V) (GRH Fidu-GBT)-(GCD Fidu-GBT) (ns) 13 69385 43716 DT(10)SiO2[2.2] 1.8x10 4000 1.033 13 69389 43717 DT(10)SiO2[2.4] 2.5x10 4000 1.029 13 69393 43718 DT(10)SiO2[2.2] 1.8x10 4000 1.033 13 69396 43719 DT(10)SiO2[2.4] 2.6x10 4175 1.024 13 69397 43720 DT(10)SiO2[2.3] 2.1x10 4175 1.026

104 4.4.5 Measurement Of Gamma-Ray Time Shift Caused By Time Dependent Ablator Arial Density

Measurement of the gamma ray time shift was performed using two methods. The ﬁrst method relies upon using the GCD as a timing reference for when the neutrons and D-T gammas are generated in the thermonuclear burn. Both the GRH and GCD are set to an 8 MeV threshold in order to obtain cross timing between the two detectors. Once cross timing is achieved between the GCD and GRH, the GRH is dropped to 3 MeV threshold

and capsules comprised of a thin shell (2.0 µm - 2.5 µm) SiO2 are used. By using these thin shelled capsules, the spectrum above the 3 MeV threshold is primarily comprised of the D-T gammas (>95%), with the gammas generated from both Si and O only

being a minor contaminant of the signal due to the low ρRSiO2 . However, due to the increase of pressure in the GRH cell, the index of refraction of the gas is increased. This results in a time delay of the GRH signal. This delay is then measured over subsequent ICF shots and compared with both Geant4 simulations and calculations using the GRH geometry. Once this delay has been characterized, the capsules are then switched over to thick (15.0 µm - 20.0 µm) CH capsules. Due to the increase of mass in the thicker shells, as well as the

larger σn,γ for carbon, between 50%-70% of the 3 MeV signal is expected to be from the CH

ablator. Using the data from the SiO2 and CH capsules from both the GRH and GCD the

time shift caused by the time dependent ρRC in the CH capsules can be determined. The data reduction process is done by taking the raw data (a sample seen in Figure 4.36) and aligning it using the fiducial. Figure 4.37 shows the data being aligned using the electrical fiducial as the timing reference. After alignment to the fiducial has been completed a reference shot (8 MeV cross timing) is chosen. The Cherenkov signal measured by the GCD for each shot is then fitted. A timing offset is applied to the GCD data generated from each shot shifting the Cherenkov signal so that it is time aligned with the reference shot. These offsets are then applied on a shot by shot basis to the data obtained by the GRH. Thereby the shot to shot variation in ICF

105 5 Shot #69397 GCD 8MeV DT(10)SiO2[2.3] Shot #69404 GCD 8MeV DT(10)SiO2[2.3] 4 Shot #69408 GCD 8MeV DT(18)CH[15.3] 3

2 Voltage (V) 1

18 19 20 21 22 23 24 5 Shot #69397 GRH 8MeV DT(10)SiO2[2.3] Shot #69404 GRH 3MeV DT(10)SiO2[2.3] 4 Shot #69408 GRH 3MeV DT(18)CH[15.3]

2 Voltage (V) 1

20 21 22 23 24 25 26 ns (a) Raw electric ﬁducial

10 Shot #69397 GCD 8MeV DT(10)SiO2[2.3] Shot #69404 GCD 8MeV DT(10)SiO2[2.3] 8 Shot #69408 GCD 8MeV DT(18)CH[15.3]

4 Voltage (V) 2

0 118 119 120 121 122 123 124 20 Shot #69397 GRH 8MeV DT(10)SiO2[2.3] Shot #69404 GRH 3MeV DT(10)SiO2[2.3] 15 Shot #69408 GRH 3MeV DT(18)CH[15.3]

10 Voltage (V) 5

0 122 123 124 125 126 127 128 ns (b) Raw cherenkov signal

Figure 4.36: (a) Electronic ﬁducial before time alignment. (b) Detected Cherenkov signal before time alignment.

106 5 Shot #69397 GCD 8MeV DT(10)SiO2[2.3] Shot #69404 GCD 8MeV DT(10)SiO2[2.3] 4 Shot #69408 GCD 8MeV DT(18)CH[15.3]

2 Voltage (V) 1

18 19 20 21 22 23 24 5 Shot #69397 GRH 8MeV DT(10)SiO2[2.3] Shot #69404 GRH 3MeV DT(10)SiO2[2.3] 4 Shot #69408 GRH 3MeV DT(18)CH[15.3]

2 Voltage (V) 1

20 21 22 23 24 25 26 ns (a) Electric ﬁducial yime aligned

10 Shot #69397 GCD 8MeV DT(10)SiO2[2.3] Shot #69404 GCD 8MeV DT(10)SiO2[2.3] 8 Shot #69408 GCD 8MeV DT(18)CH[15.3]

4 Voltage (V)

0 118 119 120 121 122 123 124 20 Shot #69397 GRH 8MeV DT(10)SiO2[2.3] Shot #69404 GRH 3MeV DT(10)SiO2[2.3] Shot #69408 GRH 3MeV DT(18)CH[15.3] 15

10 Voltage (V) 5

0 122 123 124 125 126 127 128 ns (b) Cherenkov signal time aligned

Figure 4.37: (a) Electronic ﬁducial after application of time alignment. (b) Detected Cherenkov signal after time alignment of the electronic ﬁducial.

107 implosion timing is removed from the data. Finally, the diﬀerence in timing between the GRH and GCD Cherenkov signal for the reference shot is subtracted from all the GRH data as seen in Figure 4.38.

At this point the Cherenkov signals from the 3 MeV threshold SiO2 and CH can be directly compared. However, the 3 MeV GRH thresholds are time shifted later in time due to the higher index of refraction in the gas compared to the 8 MeV GRH threshold. Therefore, the IRF of the gas needs to be taken out in order to compare these signals to the reference timing shot. The second method to measure the gamma ray time shift relies on the use of a large mass placed near the ICF implosion. Typically, a puck that is comprised of a single element is placed centimeters away from the ICF event. By judiciously choosing the puck’s location, the gamma ray signal generated from (n, n0)γ reactions can be placed into a region with little to no background. The signal generated from the puck (as seen in Figure 4.39) can be used as a timing reference for when the neutrons generated during the D-T burn interact with the puck. By using this puck as a physical timing reference, a measurement can be made between

the observed Cherenkov peak produced by a low ρR capsule (the thin shelled SiO2) and a capsule with appreciable ρR. Since this measurement encodes when the ICF event occurred, both the GBT and APT can be measured using a single detector. While this method removes the need of both a second detector and shifts in pressure, the accuracy of the measurement can be aﬀected by any nonrecurring background signal or from minor movements of the puck. Movement of the puck is a severe concern due to the adverse environment inside an ICF chamber. Since the puck signal is generate primarily from 14.1 MeV neutrons interacting with the puck, a change of 1 mm will result in a measured shift of approximately 20 ps.

108 10 Shot #69397 GCD 8MeV DT(10)SiO2[2.3] 8 Shot #69404 GCD 8MeV DT(10)SiO2[2.3] Shot #69408 GCD 8MeV DT(18)CH[15.3] 6

4 Voltage (V) 2

0 118 119 120 121 122 123 124 20 Shot #69397 GRH 8MeV DT(10)SiO2[2.3] Shot #69404 GRH 3MeV DT(10)SiO2[2.3] Shot #69408 GRH 3MeV DT(18)CH[15.3] 15

10 Voltage (V) 5

0 118 119 120 121 122 123 124 ns (a) GCD time aligned

10 Shot #69397 GCD 8MeV DT(10)SiO2[2.3] 8 Shot #69404 GCD 8MeV DT(10)SiO2[2.3] Shot #69408 GCD 8MeV DT(18)CH[15.3] 6

4 Voltage (V) 2

0 119.6 119.8 120.0 120.2 120.4 120.6 120.8 121.0 20 Shot #69397 GRH 8MeV DT(10)SiO2[2.3] Shot #69404 GRH 3MeV DT(10)SiO2[2.3] Shot #69408 GRH 3MeV DT(18)CH[15.3] 15

10 Voltage (V) 5

0 119.6 119.8 120.0 120.2 120.4 120.6 120.8 121.0 ns (b) Zoomed view of Cherenkov signal

Figure 4.38: Detected Cherenkov signal after time alignment of the electronic ﬁducial and time oﬀsets using the GCD data have been applied. Dashed line shows zero time shift line. The 3 MeV GRH thresholds are time shifted later in time due to the higher index of refraction in the gas, which slows light traveling through the pressure cell.

109 12 Shot #69408 3MeV DT(18)CH[15.3]

6 Voltage (V)

125.0 125.2 125.4 125.6 125.8 126.0 126.2 ns

Figure 4.39: GRH signal produced from the neutrons generated from an ICF experiment at OMEGA interacting with an Si puck place 11.4 cm away from the ICF capsule.

4.4.6 OMEGA Ablator Timeshift Experimental Results

On April 8th, 2014, using the above measurement methods, an experimental campaign was performed to measure both GBT and APT to see if there was a time shift between these two quantities observable in the compact setup at Omega. Table 4.5 shows the measurements obtained by the two detectors. Note that the following quantities are measurements of the GBT - 3 MeV threshold peak. Therefore, a more negative number represents the 3 MeV threshold signal being detected later in time relative to GBT. Using the electrical ﬁducial cross timing method, the overall time shift was measured to be -1.2 ps± 5.9 ps. Using the optical ﬁducial cross timing method, the time shift was measured at -0.8 ps ± 8.6 ps. Finally, using the Si puck as a timing reference the time shift was found to be -4.2 ps ± 7.8 ps, all results clearly compatible with 0. The shot by shot data comparison can be seen in Figure 4.40 and Table 4.6.

110 Table 4.5: Experimental results of cross timing GRH and GCD at 8 MeV threshold. GRH GCD Shot OMEGA Capsule Neutron Peak-Opt.Fidu Peak-Elec.Fidu Peak-Si Puck Peak-Elec.Fidu # RID Type Yield (ns) (ns) (ns) (ns) 13 72887 43716 DT(10)SiO2[2.6] 3.36x10 100.686 18.055 N/A 92.957 13 72890 43717 DT(10)SiO2[2.6] 3.30x10 100.658 18.027 -1.311 92.925 72892 43718 DT(16.2)CD[19.90] 7.78x1012 102.392 19.760 -1.299 94.664 72894 43719 DT(16.2)CD[19.89] 5.47x1012 102.265 19.629 -1.311 94.534 72897 43720 DT(16.2)CD[19.80] 8.93x1012 102.377 19.743 -1.306 94.639 72899 43719 DT(16.8)CH[19.81] 4.99x1012 102.281 19.656 -1.303 94.543 72901 43720 DT(16.2)CD[20.00] 9.45x1012 101.607 18.970 -1.311 93.882 72903 43720 DT(16.8)CH[19.62] 8.97x1012 101.488 18.859 -1.303 93.755 72904 43720 DT(16.2)CD[20.00] 8.20x1012 101.631 19.004 -1.308 93.898

111 Table 4.6: Experimental results of cross timing GRH and GCD at 8 MeV threshold. Shows timing differences between GCD data and the three timing methods used on the GRH. Shot OMEGA Capsule Neutron Opt.Fidu Diff. Elec.Fidu Diff. Si Puck Diff. # RID Type Yield (ps) (ps) (ps) 72892 43718 DT(16.2)CD[19.90] 7.78x1012 4 3 -9 72894 43719 DT(16.2)CD[19.89] 5.47x1012 5 0 0 72897 43720 DT(16.2)CD[19.80] 8.93x1012 -4 -7 -5 72899 43719 DT(16.8)CH[19.81] 4.99x1012 -13 -7 -8 72901 43720 DT(16.2)CD[20.00] 9.45x1012 12 6 0 72903 43720 DT(16.8)CH[19.62] 8.97x1012 -4 -2 -8 72904 43720 DT(16.2)CD[20.00] 8.20x1012 -6 -2 -3 Average: -0.8 -1.2 -4.2

112 20

L 0 ps H

-10 Time Shift

-20

Draco Simulation

-30

72892 72894 72897 72899 72901 72903 72904 Shot ð

Figure 4.40: Measurement of the time shift between the 3 MeV threshold signal compared to the 8 MeV threshold signal using electric ﬁducial (blue), optical ﬁducial (green) and Si puck (red). The shaded area represents post shot DRACO simulations of the expected time shift between these two quantities.

Unlike the NIF, OMEGA does not use a hohlraum since it utilizes a direct drive ICF approach. Due to this and the conﬁguration of mass near TCC, the signal produced by the GRH in the initial Cherenkov peak contains only two source terms, the gamma rays produced by the D-T burn, and the gammas produced by neutrons interacting with the ablator material. Since the 3 MeV threshold is comprised of these two signals it should theoretically be possible to separate the two and isolate the ablator signal. Unlike the ICF experiments at the NIF, where the D-T gamma signal is a small fraction of the 3 MeV threshold signal, 20%- 50% of the 3 MeV threshold signal at OMEGA originates from the D-T gammas because of the low ablator ρR at OMEGA. Therefore, the 3 MeV signal should not be taken as an absolute measurement of APT. Currently, there is no measured IRF for the PMT installed in the GRH at OMEGA. Without this IRF there is no way to easily transform the measured D-T signal from the

113 GCD into its equivalent signal if observed on the GRH detector. Attempts have been made to use the data obtained when both detectors were at the 8 MeV threshold to simulate the IRF. However, when using this IRF with a deconvolution technique to separate the ablator signal from the D-T gamma signal, the propagated errors in the measurement exceeded the scale of the shift to be measured. While there is no direct measurement of the APT, the experimental data is in complete disagreement with the predicted 3 MeV threshold signal timing shift in DRACO simulations. Furthermore, given the small time shift measured between GBT and the 3 MeV signal(-1.2 ps for electrical, -0.8 ps for optical) coupled with the femtosecond decay time of the excited C atom, there is no foreseeable way to produce a 10 ps shift in the APT, let alone the shift predicted by simulation. Due to this reasoning one can infer that in this specific case, the peak time of the 3 MeV signal can be directly translated into a measurement of the APT even though there is a large contribution from the D-T signal. Therefore, one can conclude that the experimental campaign done at OMEGA failed to reproduce the shift between the 3 MeV and 8 MeV thresholds observed by the GRH diagnostic at the NIF. Thereby it was not able to confirm the time offsets found between GBT and APT at the NIF or calculated via DRACO simulations for the OMEGA experiments and used in HYDRA simulations at NIF to explain shot failure.

4.5 Potential Explanations For the Discrepancy Between NIF and OMEGA timing data

This section discusses potential ways to resolve the discrepancy between the data obtained at NIF and OMEGA as well as the HYDRA and DRACO modeling. Due to speculation on the possible perturbative eﬀects of the Mach-Zehnder data encoding method, an investigation into the Mach-Zehnder data acquisition system was performed in the framework of this thesis. While the investigation found the chance for potential timing issues due to peak suppression and long term hysteresis, it was concluded that during nominal operations these issues had

114 a minimal effect on the data gathered. While the Mach-Zehnder data acquisition system was ruled out as a potential reason for the discrepancy, the timing accuracy of the data gathered at the NIF has been called into question. It was found that the current timing fiducal used by the GRH diagnostic at NIF is sent through fibers with an incorrect core diameter resulting in the potential for temporal shift through intermodal dispersion. The type of variable optical attenuators used at the NIF are believed to select a specific mode of light resulting in an attenuation dependent time offset. If this systematic effect is removed it has the potential to remove the time offset between the 3 MeV and 4.5 MeV thresholds when compared to the 8 MeV and 10 MeV thresholds, bringing the data in line with the measurements made at OMEGA. It should be noted that after installation of the GRH system at NIF, access to the equipment was very restricted, making typical test approaches impossible.

4.5.1 Mach-Zehnder Data Acquisition System

Due to the unique radiation environment present at NIF, a novel method for recording electrical signals generated from the GRH’s PMT was required. The signal generated in an ICF implosion needed to be encoded and then transported away from the target bay in less than 100 ns before the 14.1 MeV neutrons begin to bombard the detector and disrupt the recording electronics. In order to achieve these strict time requirements a method for recording the analog data was developed by coupling the PMT signal to a Mach-Zehnder modulator. The Mach-Zehnder modulator seen in Figure 4.41, uses a guided-wave Mach-Zehnder interferometer to modulate the intensity of the light output by inducing a phase diﬀerence via electro-optical induction [97]. This is achieved by taking the input light and splitting it in two. These two beams then travel an equal distance before being recombined. If these beams are perfectly in phase with one another the output intensity of light is equal to the input minus some intensity loss due to the split. If the beams are 180◦ out of phase, when

115 Input Output

VPMT VBias

(a) Schematic (b) Modulator use at the NIF

Figure 4.41: Mach-Zehnder modulator. (a) Internal schematic of the Mach-Zehnder Mod- ulator. (b) Mach-Zehnder Modulator deployed at the NIF [19].

they recombine there will be total destructive interference and there is no light output. A phase shift is introduced to one of the legs of the Mach-Zehnder interferometer by

passing one of the beams through a birefringent material, such as Lithium Niobate(LiNbO3), and then applying a variable electric field to the crystal. Due to the Pockels electro-optic effect, the birefringence of the material changes linearly with the electric field [98]. Since the birefringence (the polarization dependent index of refraction) is modified, the speed at which the beam transverses the leg is adjusted. This can be viewed as an increase in the length of the interferometer leg, which results in a phase shift of the light [97]. The phase shift is highly dependent on the polarity of the input beam. Therefore, the Mach-Zehnder modulator requires a stable polarized optical light source, as well as polarization maintaining fiber to transport the light from the source to the Mach-Zehnder modulator [97]. Since the phase shift changes linearly with the applied electric field, one can couple the output light to an electric signal such as the one generated by a PMT. While this phase shift changes linearly with voltage, the intensity of the output light does not. For an ideal interferometer the electric field at the output of the device is [97]:

EIn EIn E = eiβ1L + eiβ2L (4.1) Out 2 2

Where:

• EOut is the electric ﬁeld at the output of the interferometer.

116 • EIn is the electric ﬁeld at the input of the interferometer.

• β1 and β2 are the respective propagation constants in each of the interferometer legs.

• L is the length of an interferometer leg.

¯ Substituting ∆β = (β1 − β2)/2 and β = (β1 + β2)/2:

iβL¯ EOut = EIn cos(∆βL)e (4.2)

Using Equation 4.2, the ratio of intensity of the output light, IOut, to the input light, IIn can then be calculated [97]: 2 IOut |EOut| = 2 (4.3) IIn |EIn|

2 iβL¯ EIn cos(∆βL)e IOut = 2 (4.4) IIn |EIn|

I Out = cos2(∆βL) (4.5) IIn

The term ∆βL can be expressed in terms of the applied electrical signal, VIn, the wavelength,

λ, and a wavelength dependent crystal geometry and birefringent material constant, Kλ:

πV ∆βL = In (4.6) 2λKλ

The intensity of the output light can therefore be written as:

2 πLVIn IOut = IIn cos ( ) (4.7) 2λKλ

Due to the diﬃculty of measuring Kλ directly (it is unique for each Mach-Zehnder modulator), the above equation is typically expressed in terms of the voltage, Vπ, required to change

117 the modulator’s output light intensity from its maximum to its minimum intensity. Since:

λK V = λ (4.8) π L

Equation 4.7 becomes:

2 πVIn IOut = IIn cos ( ) (4.9) 2Vπ

By varying the input voltage, VIn, inside the periodic function found in Equation 4.9, the voltage dependent sensitivity of the modulator can be determined as seen in Figure 4.42. L Arb. H

V0 V Π V Π V 3 Π VΠ 4 2

Change In Light Output Per Voltage Change 4 Input Voltage

Figure 4.42: Change in total light output IOut with respect to change of voltage at a speciﬁc voltage(interferometer leg phase diﬀerence). Due to the periodic nature of this function, this graph repeats for the V0 to Vπ interval.

In order to maximize the system’s response to a small change of voltage (VIn << Vπ), a

V DC bias voltage, V , should be applied to the modulator so that V = π = V π . Once Bias Bias 2 2 π the modulator is biased at a 2 phase oﬀset, the modulator is said to be in quadrature [97].

At quadrature the output intensity, I π , is in between the maximum output intensity, I 2 Max

118 and the minimum output intensity, IMin, as seen in Figure 4.43.

IMax

Roll Over IBias Quadrature Roll Over Region Region Light Output

IMin

V0 V Π V Π V 3 Π VΠ 4 2 4 Phase Shift

Figure 4.43: Mach-Zehnder transfer function. It shows where the maximum (IMax and minimum (IMin) output light intensity occurs relative to the voltage applied to the Mach- Zehnder modulator. Due to encoding sensitivity the modulator is typically biased at V π . 2 This results in a 90◦ degree phase oﬀset between the interferometer legs and is called the quadrature point. If VIn < V0 or VIn > Vπ the signal will invert (”roll over”). If the input signal is large enough this inversion can occur multiple times due to the transfer function’s periodic nature.

As voltage is applied to the modulator, a linear approximation of the output light is encoded using this transfer function. If the negative or positive going signal amplitude exceeds V π , the signal inverts and enters into the ”roll over” region of the transfer function. 2 Since this transfer function is periodic in nature, the Mach-Zehnder allows a dynamic range limited only by breakdown inside the birefringent crystal. However, due to the loss of sensitivity near the critical roll over points (V0 and Vπ) there is the potential for data loss and distortion. This is due to the fact that in an ideal modulator there is perfect deconstructive interference, i.e. IMin = 0. However, realistically IMin has some non-zero value. Further complicating the retrieval of the applied voltage from the measured light is that both IMin

119 and IMax have some partial dependence on the frequency of the input signal.

Therefore, in order to retrieve the time dependent input signal from the PMT, VPMT (t), we write out Equation 4.9 for a realistic Mach-Zehnder modulator:

2 πVIn(t) I(t) = (IMax − IMin) cos ( ) + IMin (4.10) 2Vπ

2 1 Using the half angle formula, cos (θ) = 2 (1 + cos(2θ)):

(IMax − IMin) πVIn(t) I(t) = [1 + cos( )] + IMin (4.11) 2 Vπ

In our speciﬁc case the input voltage VIn(t) is comprised of two signals. The output of the

PMT, VPMT (t) plus the bias voltage, VBias.

(IMax − IMin) π(VPMT (t) + VBias) I(t) = [1 + cos( )] + IMin (4.12) 2 Vπ

Since the bias voltage tries to bring the modulator’s baseline intensity to half the maximum

◦ Vπ intensity (a 90 phase oﬀset), we know that VBias = 2 :

(IMax − IMin) πVPMT (t) π I(t) = [1 + cos( + )] + IMin (4.13) 2 Vπ 2

π Using the phase shift identity cos(θ + 2 ) = −sin(θ):

(IMax − IMin) πVPMT (t) I(t) = [1 − sin( )] + IMin (4.14) 2 Vπ

The light intensity range spanned by the modulator, IMax − IMin, can be expressed in terms of the intensity at the midway point, I π . Since V is set to produce this light intensity, 2 Bias

I = I π . Therefore: Bias 2

(I − I ) = 2(I π − I ) = 2(I − I ) (4.15) Max Min 2 Min Bias Min

120 Subbing the above into Equation 4.14:

πVPMT (t) I(t) = (IBias − IMin)[1 − sin( )] + IMin (4.16) Vπ

Rearranging the equation to collect light intensities on the right side:

πV (t) I(t) − I sin( PMT ) = 1 − Min (4.17) Vπ IBias − IMin

Taking the arcsine of both sides of the equation and solving for VPMT (t):

Vπ −1 I(t) − IMin VPMT (t) = sin (1 − ) (4.18) π IBias − IMin

Using Equation 4.18, we can unfold the signal delivered by the Mach-Zehnder modulator and retrieve the voltage output from the PMT. By assuming that the modulator can achieve perfectly deconstructive interference between each leg (IMin = 0) only three pieces of information are needed to retrieve the voltage measured by the PMT:

◦ • The voltage, Vπ, needed to shift the phase of a leg by 180 degrees. This is measured before the modulator is installed in the system.

◦ • The intensity of light, IBias, when the modulator is biased so that one leg is shifted 90 degrees out of phase. This is measured by taking the average light level over a period of time without any detectable signal on the PMT.

• The time dependent light signal, I(t), which is recorded by the oscilloscope.

Using this information the data recorded by the oscilloscope can be unfolded and the input signal on the Mach-Zehnder modulator can be retrieved. Figure 4.44 shows the start of this process with three Gaussian waves with diﬀerent amplitude applied to the Mach- Zehnder modulator at quadrature.

121 L V Π 2 PMT V H

V Π PMT Voltage 4

0 Time

Figure 4.44: Three classes of Gaussian input signals coupled to the Mach-Zehnder modulator at quadrature. The blue signal is at the ideal amplitude, being between 60%-70% of V π of 2 the modulator. The red signal’s amplitude is at V π . Finally, the Green signal amplitude 2 exceeds V π , which will cause the signal to roll over once it has been encoded. 2

Figure 4.45 shows the eﬀect of the intensity of light generated by the Mach-Zehnder modulator to the input signals from Figure 4.44. While the blue signal seems to be an accurate representation of the original input, the red signal’s peak appears to be compressed. This compression is caused by the loss of sensitivity of the Mach-Zehnder modulator near

the critical roll over point V . Note that a bias voltage of V π is applied, so an additional π 2

signal of V π places the Mach-Zehnder modulator at V . Since the green signal exceeds V π , it 2 π 2 has entered the roll over region of the transfer function resulting in the top portion inverting and producing the double peak phenomenon. Figure 4.46 presents the results of taking the data from Figure 4.45 and applying the Mach-Zehnder unfold equation 4.18. Both the green and red input signals are accurately reproduced. However in the case of the green signal, the top portion of the peak remains inverted. The original peak can be retrieved by manually editing the data and ﬂipping it at the discontinuity.

122 0 IMin L t H Light Intensity I

IBias Time

Figure 4.45: Output of the Mach-Zehnder modulator to the three Gaussian signals in Figure 4.44. Note that this graph is of a negative going signal (lower levels equal more light) simulating the data recorded by the GRH. The red signal’s peak compression is due to the decrease in sensitivity near V π . Since the Green signal amplitude exceeds V π , the top portion 2 2 of the peak has been inverted causing the double peak phenomenon.

Figure 4.46 shows an ideal case. In practice, as a signal reaches or exceeds the roll over point, the retrieved peak can be distorted due to incomplete information. In the case of a signal nearing the roll over point, the uncertainty of the frequency dependent IMax and

IMin can lead to suppression of the peak amplitude. Typically, the unfold function IMin is assumed to be zero causing the unfolded wave to be suppressed. For high frequency signals that roll over, the technique of ﬂipping at the discontinuity is error prone due to the limited sampling of the inputted signal. Due to these issues the accuracy of the data obtained by the GRH using this Mach-Zehnder encoding system can been called into question. Since the Mach-Zehnder encoding seems to only distort signals near the roll over region, a variety of setups have been constructed in order to mitigate theses issues. One such setup is splitting the signal into two Mach-Zehnder modulators that are 90◦ degrees out of phase with one another [99]. This allows the Mach-Zehnder modulators to hand oﬀ to one another as they enter the increased data error region. In the case of the GRH at both NIF and OMEGA, the signal is sent to two Mach-Zehnder modulators, one with a small Vπ and another with a

123 L V Π 2 PMT V H

V Π PMT Voltage 4

0 Time

Figure 4.46: Applying 4.18 to the output of the Mach-Zehnder modulator to the three Gaussian signals. While both blue and red signals remain unchanged, the green signal is inverted at V π . The original waveform can be retrieved either through manually editing the 2 data by ﬂipping it at V π or by stitching multiple Mach-Zehnder modulator data together. 2

large Vπ. In this setup the Mach-Zehnder modulators are ”stacked”, allowing the small Vπ modulator to accurate record smaller signals before handing the data acquisition oﬀ to the larger Vπ modulator [96]. While this setup does not allow for accurate reproduction across an unlimited dynamic range, it does allow for retrieval of signals that would have been lost using traditional data recording methods. In order to access the eﬀects that this novel data encoding system has on the measurements performed at NIF, a Monte-Carlo Error Analysis was done of the Mach-Zehnder system.

4.5.2 Monte-Carlo Error Analysis of Mach-Zehnder System

In order to ascertain the eﬀects that the Mach-Zehnder DAQ system has on the data acquired at the NIF, a Monte-Carlo error analysis was performed by the author of this thesis. Since the Mach-Zehnder system was coupled directly to the oscilloscopes it was decided to compare the eﬀects of the combination of Mach-Zehnder system and oscilloscope

124 to just the error caused by the oscilloscopes in order to determine the adverse eﬀects the Mach-Zehnder system has on our overall data acquisition. The simulation ﬁrst generated a normalized Gaussian signal in the form of:

2 1 − (x−µ) √ e 2σ2 (4.19) σ 2π where σ is the standard deviation, µ the mean and x position. The standard deviation was set by looking at historical data generated by the GRH diagnostic at the NIF. A 150 ps full width half max(σ = FWHM√ ) was chosen to be the representative case. The mean, µ 2ln2 was set to zero and the equation was multiplied by various test amplitudes (20%,45%,70%

Vπ of the Mach-Zehnder maximum amplitude ( 2 )) for each of the GRH oscilloscope settings used. The amplitudes were picked based upon where the data is normally stitched together (i.e. handed oﬀ to another Mach-Zehnder modulator). During nominal shot operations the Mach-Zehnder data is recorded using only 80% (baseline is set to 10% of the oscilloscopes full scale(FS) where the maximum is set to 90% of FS) of the available scope trace as seen in Figure 4.47. At this point a modiﬁed Mach-Zehnder fold transfer function (as seen in Equation 4.20) was applied to simulated signal:

2 π(Sig(t) + VBias) I(t) = A cos ( ) + IExt (4.20) 2Vπ

Where:

• I(x) is the simulated light output of a Mach-Zehnder modulator.

• A is the amplitude of light of the simulated Mach-Zehnder modulator. I.e. A =

IMax − IMin.

• Sig(t) is the simulated Gaussian signal.

125 Figure 4.47: Record of a Mach-Zehnder optical signal transmitted by a GRH detector. Due to the oscilloscope’s configuration with the baseline (seen at -0.225 V) being at 10% of full scale, a large input signal that rolls over multiple times is cut off at the bottom going beyond the oscilloscope’s ability to record. The difference in measured maxima for the peaks formed during the roll over is caused by the frequency dependent IMin.

• Vπ is the required voltage to change the simulated modulators outputted light intensity from its maximum to its minimum intensity.

• VBias is the bias voltage applied to the simulated Mach-Zehnder modulator to achieve

Vπ half the maximum light intensity. VBias = 2 .

• IExt is the extinction light intensity. It is the diﬀerence between the minimum achieved

light output and no light output. IExt = IMin.

This transfer function simulates the greatest source of error in the Mach-Zehnder encoding system, the uncertainty in IExt caused by the failure of the Mach-Zehnder modulator to achieve perfect deconstructive interference when combining the two legs of the interferometer.

Additionally, attempts by this author to characterize the IExt for the EOSpace Mach-Zehnder

126 modules used on the GRH using a separate Mach-Zehnder encoding system has found IExt to be frequency dependent. The measurements performed showed that it varies between

Vπ the ideal output of zero light and 8% of 2 . When applying this transfer function to the simulated Gaussian signal, IExt was randomly picked between these two extremes using a flat distribution. At this point the effects of the oscilliscope were applied when sampling the output of the Mach-Zehnder fold transfer function. The oscilloscopes used at the NIF to record data from the Mach-Zehnder system are Tektronix DPO71254C. Table 4.7 shows the sampling error characteristics of the DPO oscilloscope [24]. Using these characteristics, as the function was sampled, the errors caused by DC offsets, aperture uncertainty (sample time jitter), time base, least significant bit error and random noise were applied. Note that frequency dependent non linearity caused by attenuation at higher frequencies were not applied (a scope with 1GHz bandwith means at 1GHz the input signal is attenuated by 3dB). The sampled function was then unfolded using Equation 4.21. Figure 4.48 shows an example comparison of the initial Gaussian to the unfolded Gaussian generated by this analysis.

Vπ −1 I(t) VPMT (t) = sin (1 − ) (4.21) π IBias

During the unfolding process IExt was assumed to be ideal (IExt = IMin = 0) and represents the nominal assumptions during the data analysis performed at the NIF. A ﬁt was applied to the resulting data assuming a Gaussian and the quantities of amplitude, peak position and FWHM were compared to the original simulated input. This process was done 50,000 times for each of the amplitude/oscilloscope setting pairs. Histograms were then generated and used to evaluate the maximum peak ﬁtting error associated with using the currently deployed combinations of Mach-Zehnder system and GRH oscilloscopes. Figure 4.49, Figure 4.50 and Figure 4.51 show a sample of one set of the generated histograms.

127 æ 60 æ æ

50 æ

æ 40

L æ mV H æ 30

æ Amplitude 20 æ

æ 10 æ æ æ æ æ æ æ æ 0æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ

-400 -200 0 200 400 Time ps

Figure 4.48: Initial Gaussian input (red) beforeH beingL folded with Mach-Zehnder transfer function. Final Gaussian output (black dots) after oscilloscope errors have been applied and unfolded using Mach-Zehnder transfer function. The output data was fitted (dashed blue) assuming a Gaussian peak. This fitted Gaussian parameters were compared to the original input Gaussian in order to determine the effects both the Mach-Zehnder and oscilloscope had on the recorded data.

While these simulations give us an estimate of the error in the precision of measuring a single peak, the roughly Gaussian Cherenkov signal is always measured against an injected Gaussian ﬁducial signal. In order to determine the timing error, the error from ﬁtting both peaks is added in quadrature. The systematic error due to the time base accuracy caused by the distances separating both signals is also added as seen in Equation 4.22. This generates the estimated timing pk-pk error of a single cell.

q 2 2 Errorpk−pk = ErrorMCpk + ErrorMCpk + T imeBaseAccuracy∆tpk−pk (4.22)

128 Peak Position Error

2000

1500

Count 1000

500

0 -1 0 1 2 Time Shift ps

Figure 4.49: Histogram generated during Monte-CarloH L error analysis showing peak position error. The histogram is for 70% Mach-Zehnder max amplitude at 100 mV FS.

Using this method the Errorpk−pk caused by the oscilloscope in a worse case scenario is

Errorpk−pk ≈2.3 ps. The combination of oscilliscope and Mach-Zehnder DAQ is Errorpk−pk ≈5.4 ps. This analysis assumes that the data acquired from the Mach-Zehnder system remains

Vπ in the linear regime (between 0%-70% 2 ). As the measured voltage gets closer to IExt, error caused by both noise and LSB ﬂipping become larger and larger. This larger error in

amplitude results in a broadening of the peak positioning error. Also near IExt, the effects of MZ peak suppression can be observed causing the peak position to be offset from its true value. This analysis shows that while the MZ system does affect the overall error, it can not be used to explain the observed time shift seen at the NIF.

129 % FWHM Error FWHM Real FWHM Ideal

1400 H L 1200

1000

800 Count 600

400

200

0 0.94 0.95 0.96 0.97 0.98 0.99 1.00 % Error

Figure 4.50: Histogram generated during Monte-Carlo error analysis showing relative FWHM error. The histogram is for 70% Mach-Zehnder max amplitude at 100mV FS.

130 % Amplitude Error A Real A Ideal

1500 H L

1000 Count

500

0 0.93 0.94 0.95 0.96 0.97 0.98 % Error

Figure 4.51: Histogram generated during Monte-Carlo error analysis showing relative amplitude error. The histogram is for 70% Mach-Zehnder max amplitude at 100 mV FS.

131 Table 4.7: Tektronix DPO71254C oscilliscope information [24]. Number of bits: 8 bits DC measurement accuracy: ±( 2% —reading- net offset— + 0.35%—offset—+1.5mV + 0.014 FS) Offset accuracy: ±( 0.35% —net offset— + 1.5mV + 1% FS ) Time base accuracy: ±1.5ppm Aperture uncertainty: <4ps

132 4.5.3 Instrumental Timing Error At The NIF

During the construction and commissioning of the NIF, a timing error specification for the NIF drive laser was set to ±50 ps. The NIF facility wide timing fiducial is generated as a pick off from these drive lasers. The 1ω (1053nm) timing fiducials are distributed on 6 µm single mode fiber to all diagnostics. The NIF Facility also provides a 2ω (527 nm) and 3ω (351nm) timing fiducial. However, due to both the error specification and cost of ordering proper fibers for these other wavelength, the same 6 µm fiber is used to distribute these signals. Since the incorrect wavelength was transported through these fibers, both the 2ω and and 3ω timing fiducials used by the GRH are susceptible to timing distortions due to intermodal dispersion (see Figure 4.52). Amplitude

Time

Figure 4.52: Intermodal dispersion can result in the input Gaussian (red) being distorted due to temporal spread of diﬀerent modes of the detected signal (blue). If this temporal spread is large enough there is a possibility of detecting multiple peaks from a single signal (green).

Intermodal dispersion occurs when an optical signal is passed through a waveguide using multiple propagation modes [100]. The lowest order mode propagates the optical signal

133 through the waveguide on a direct path, parallel to the center line of the waveguide (see Figure 4.53(a)). Higher order modes route the optical signal over a longer distance by reflecting it off the boundaries of the waveguide (see Figure 4.53(b)). Since these modes propagate the signal through the waveguide at different apparent velocities, the exiting optical signal will be distorted.

Cladding

Core Light Ray

Cladding

(a) Single-Mode Fiber

Cladding Acceptance Core Cone Light Ray

Cladding Time Offset

(b) Multi-Mode Fiber

Figure 4.53: Movements of light through different types of fiber. (a) Optical Single-Mode fiber supports only light traveling through the primary mode directly through the fiber. (b) Optical Multi-Mode fiber allows various modes to travel through the fiber. These modes are populated when the light enters at an angle not normal to the fiber core. Due to the beam having to travel a longer path to reach the end of the fiber, the beam exits the fiber with a time offset when compared to a normal incident beam.

For fiber optics wave guides are categorized by their ability to maintain multiple propagation modes at a specific wavelength [100, 101]. If the fiber can support a single mode, the fiber is designated as a Single-Mode (SM) fiber. In the case of the fiber supporting multiple modes, it’s moniker is Multi-Mode (MM) fiber. In the case of a MM fiber, the higher order modes (see Figure 4.54) are typically populated by injecting the optical signal into the fiber

134 at an angle or by curving the ﬁber multiple times, which is done in a mode mixer.

Figure 4.54: Intensity proﬁles of the lowest order propagation modes supported in a multi- mode ﬁber.

When the GRH diagnostic was initially constructed, the 6 µm fiber provided by the facility was believed to be SM for the 2ω fiducial signal. Therefore, the GRH detectors were constructed using ThorLabs HI1060-J9 6 µm fibers. Midway through construction of the GRH diagnostic these fibers were found to be the incorrect fiber diameter and the correct fiber diameters cables (3 µm) were installed in various places. However, due to cost associated with laying fiber in the facility the 6 µm fiber remained in the system. Due to this error in correct fiber diameter, a calculation of both the number of modes present in the 6 µm fiber and the theoretical maximum timing shift needed to be completed.

135 In order to estimate the number of modes present in a step-index ﬁber, one needs to ﬁrst calculate the normalized frequency parameter, V , by using the Equation 4.23 [102].

2πrq V = n2 − n2 (4.23) λ core cladding

Where:

• λ is the wavelength of light.

• r is the radius of the ﬁber core.

• ncore is the index of refraction of the core.

• ncladding is the index of refraction of the core.

For the 6 µm ﬁber deployed at the NIF, the normalized frequency parameter for a 527 nm signal is: V = 12.6 (4.24)

From V , the number of modes, Nm, for a ﬁber with a large V can be approximated as [102]:

4 M ≈ V 2 (4.25) π2

Therefore for the 6 µm ﬁber deployed at the NIF the number of modes present in the ﬁber is: M ≈ 60 (4.26)

Since the 6 µm ﬁber have more then one mode present they are susceptible to intermodal dispersion issues when transporting the 2ω ﬁducial signal. Using Equation 4.27, one can

determine the time, tL, it takes for a light pulse to travel a distance, L, through a ﬁber which the light enters at angle θ [102].

n L t = core (4.27) L c cos(θ)

136 Using the above expression, the pulses temporal delay(τL) due to intermodal dispersion can be calculated by taking the diﬀerence in time needed for a light pulse entering the ﬁber at the

◦ two critical angles; the angle normally incident on the ﬁber core (θ0 = 0 ) and at the critical angle (θ = cos−1( ncladding )) where total internal reﬂection no longer happens. Calculating c ncore

τL [102]:

τL = tc − t0 (4.28)

ncoreL ncoreL τL = − (4.29) c cos(θc) c cos(θ0)

n L n L τ = core − core (4.30) L c ncladding c ncore

ncoreL ncore τL = ( − 1) (4.31) c ncladding

Using Equation 4.31, an estimation of the potential time shift can be performed. However, this time shift should appear as a systematic offset to the timing data moving both GBT and APT from their true value. This effect should not result in a temporal spread of GBT when compared to APT as observed at the NIF. In order for this time offset to be an instrumental effect, this shift needs to occur only when the GRH diagnostic changes modes from timing calibrations (8 MeV cross timing and absolute timing using scintillators) to its nominal data gathering configuration. If the fiducial fiber chain was completely static, intermodal dispersion could be easily ruled out as a cause for the time shift. However, in the fiducial fiber chain, as seen in Figure 4.55, the GRH diagnostic uses four Variable Optical Attenuators based on Micro Electrical Mechanical Systems (VOA-MEMS). The fiducial after being split passes through these VOA-MEMS. When the GRH diagnostic is set up for either a cross timing shot or an absolute timing shot using scintillators, the PMT bias voltage is changed to accommodate the

137 change in light intensity. Due to this change in PMT bias voltage and therefore amplification, the VOA-MEMS attenuation level is modified. When compared to nominal operations the attenuation provided by the VOA-MEMS attached to the 2.9 MeV and 4.5 MeV channels are dramatically altered. If the VOA-MEMS affects what modes are passed down the fiber to the GRH cell, a time shift would be expected to show up in the 2.9 MeV and 4.5 MeV threshold data when compared to the 8 MeV and 10 MeV threshold data.

Target Bay

U A A U

U U Mezzanine NIF Facility

1x4 2x2 527 nm VOA-MEMS U U U U 3 μm Splitter 3 μm Splitter Optical Fiducial

Other GRH Legend A APC 3 μm Fiber U UPC 6 μm Fiber

Figure 4.55: GRH diagnostic fiducial fiber chain. The common 2ω fiducial is split four ways before passing through four variable optical attenuators. The four GRH detectors during nominal operations are set to a variety of PMT bias levels. Due to this the attenuation supplied by each variable optical attenuator is unique.

The VOA-MEMS, seen in Figure 4.56, attenuates the input light signal by changing the amount of light coupled into the output fiber. This is achieved via reflecting the input signal onto a mirror mount connected to electrostatic actuators. The mirror is initially aligned so that the input signal is reflected directly into the center of the output fiber [103]. In response to an external applied voltage these actuators tilt the mirror by a small degree. This tilt causes the mirror to shift the input signal so it is illuminating the fiber off center and some of the light is lost, attenuating the signal[103].

138 (a) VOA-MEMS Diagram (b) VOA-MEMS Internal Structure

Figure 4.56: Variable Optical Attenuator based on Micro Electrical Mechanical Systems technology(VOA-MEMS). (a) Diagram showing how the VOA-MEMS operate. (b) Picture of the internal structure of the VOA-MEMS showing the platform and electrostatic motor (black) that tilts the optical mirror (silver disk) attenuating the light signal [20].

Since the VOA-MEMS’s attenuation is caused by changing the angle (mirror tilting) in which the light enters the output fiber core, any change in attenuation level also results in changing the modes that are populated for the 2ω fiducial signal. Since the VOA-MEMS are the only thing that changes in the fiducial chain between timing mode and nominal operations, the time shift due to modal dispersion should only matter between the VOA- MEMS and the fiducial injection into a GRH detector. Looking at Figure 4.55 and using Equation 4.31 the estimated maximum shift is 1500 ps which is an amount larger by an order of magnitude to the currently observed GBT to APT time shift seen at the NIF.

139 CHAPTER 5 SUMMARY AND CONCLUSION

In these previous chapters we have discussed the extensive work performed in order to give credence to the experimental results showing time differences of order 10’s of ps between GBT and APT in ICF shots at the NIF. Attempts at another ICF environment to observe this type of timing difference between the gammas generated by the T (D, n)α reaction and those produced by the capsule ablator undergoing (n, n0)γ did not show the effect. While simulation work performed at both the NIF and OMEGA support the results obtained at the NIF, this chapter will discuss why the author of this thesis concludes that there is probably no time shift between GBT and APT.

5.1 Issues With HYDRA And DRACO Simulations Of ICF Implosions

Both HYDRA and DRACO have gone through extensive verification and validation as- sessments. Also they have been bench-marked against one another and showed no significant deviation in simulated results. However, due to the complexity of the system being modeled, the bulk of all simulation work performed in either code is using 1-D or 2-D models of an ICF implosion [21]. While these simplified models allow for the trend of various parameters to be mapped, they do not capture all of the physics present in the system. Figure 5.1 compares the NIF ICF experimental results to post shot 1-D HYDRA simulations. It is known that without a full 3D simulation, the growth of the capsule shell perturbations due to Rayleight-Taylor (RT) instability cannot be accurately modeled as the shell is being accelerated [53, 90, 91]. Without the 3D effects of RT instability, many of the parameters of interest such as neutron yield and capsule areal density are affected and in most cases they are overestimated. However, even with the inclusion of such 3D effects, this current generation of hydrodynamic codes do not model all of the known physics present in an ICF implosion.

140 Figure 5.1: Comparison of experimental yield obtained at the NIF versus post-shot 1D simulated yield. Solid line shows where simulation is in agreement with experimental results [21].

While the hydrodynamic codes simulate the hydrodynamics, laser propagation, as well as radiation transfer present in the ICF enviroment, many smaller perturbative effects such as magnetic and electric fields generated in the plasma are not [87, 88]. Besides these issues with the equations of state (EOS) not describing the system accurately, another area of simulation deficiency is the accuracy of the material properties table. The hydrodynamic simulations require experimentally verified data tables listing key material properties such as material opacity and speed of sound. However, due to both funding as well as the system’s enormous pressures and temperatures, data on these material properties is incomplete and has been sourced from a variety of data tables such as astronomical measurements [87, 88].

141 While considerable effort has gone into extrapolating the data set to cover the experimental regime the NIF is in, this leaves the simulations vulnerable. Given the known large divergence between simulation and current ICF experimental results, the issues with the EOS and incomplete material properties table, any divergence between these simulations and the results obtained at OMEGA (and NIF) are not suspect, but expected. Since it is expected that there will be a deviation between the simulated neutron yield and ρRablator, in comparison with experimental reality, these simulations cannot be used as an argument to favor one experimental data set over another. Just to reiterate, given the current state of these simulations, and its vulnerability, these simulations can probably not be reliably used to to discuss finer details of an ICF implosion (i.e. the small timing offsets observed) although they might describe trend in experimental results. Due to the above reasoning the question remains as to whether given the null result achieved at OMEGA, the data observed at the NIF reflects reality or is an instrumental error.

5.2 Instrumental Error In The GRH At The NIF

Section 4.5.3 outlined how the VOA-MEMS could potentially affect the cell to cell timing of the system at the NIF. Due to the issue revolving around SF6 recovery and potential contamination of the D-T scrubing system employed at the NIF, it was decided to only change the gas and pressure in each GRH cell when those changes were absolutely required (absolute timing and inter-cell cross timing). Operationally this meant that each threshold the GRH is set to at typical operations is tied directly to a single cell. Table 5.1 lists each GRH cell and its associated pressure. Since each threshold is tied to a single cell any systematic offset (at normal operational pressure) between cells will show up as an offset between thresholds. In order to perform inter-cell cross timing each of the four GRH cells are pressurized with CO2 gas to an 8 MeV threshold and an ICF implosion event is recorded. While this technique should take care

142 Table 5.1: Threshold of each of the GRH system’s cells at the NIF during normal operations. Setting Cell A Cell B Cell C Cell D Gas Type CO2 SF6 CO2 CO2 Pressure (psia) 42.4 215.0 187.0 64.4 Threshold (MeV) 10.0 2.9 4.5 8

of any and all systematic offsets, as we change the cell’s threshold back to it’s normal shot operation pressure we have to change in the current readout system both the PMT and VOA-MEMS settings. While the PMT has a small effect on timing (estimated to be <5 ps), the VOA-MEMS have been identified as possible sources of timing error. As seen in Table 5.2, Cell B (2.9 MeV) & C (4.5 MeV) have the potential for a time shift when compared to their timing measured during inter-cell cross timing calibration due to the significant difference in voltage applied to them.

Table 5.2: Applied voltage to VOA-MEMS during diﬀerent operating conditions. Cell A Cell B Cell C Cell D

Normal 1.94 - 2.13 V 0.0 V 0.0 V 1.69 - 1.91 V Cross Cell Timing 2.04 V 2.69 V 2.3 V 2.29 V Absolute Timing 2.13 V 2.1 - 2.69 V 1.7 - 2.21 V 1.91 - 2.2 V

One question to answer would be how large of a shift is present in the 2.9 MeV and 4.5 MeV threshold. Due to limited access we cannot determine the shift at this time but we can speculate about the direction of the time shift. Does the VOA-MEMS shift the timing fiducial earlier in time thereby making the Cherenkov signal seem later after time alignment has been performed (as observed in shots)? If the VOA-MEMS are a mode selecting device, it stands to reason that at the minimum light attenuation (0.0 V on a VOA-MEMS) we are propagating the primary modes of light, i.e. the ones that travel the fastest through the fiber. Therefore any attenuation will make the timing fiducial appear later in time making

143 the detected Cherenkov signal appear earlier. Using this reasoning and looking at Table 5.2, we can conclude that the fiducials for all cells were shifted later in time during both timing procedures. During nominal operations only the fiducial for cells A and D associated with the higher thresholds (8 MeV and 10 MeV) maintained this delay. The fiducial for the cells B and C (2.9 MeV and 4.5 MeV thresholds) were significantly shifted earlier in time as seen in Figure 5.2. However, the analysis uses the previously determined delays measured during the timing shots. Assuming that the time between the fiducial and signal is the same in each detector, the analysis shifts the Cherenkov signal later in time for cells B and C. Therefore, when comparing the 2.9 MeV and 4.5 MeV thresholds to the 8 MeV and 10 MeV thresholds, the Cherenkov signals from 2.9 MeV and 4.5 MeV thresholds should appear delayed to the 8 MeV and 10 MeV threshold. This is the direction of the time shift observed in the shot sequences at the NIF. Unfortunately, determining the true time shift in-situ at the NIF due to the VOA-MEMS is currently experimentally impossible due to the restricted access to the equipment controlled by the NIF management. The extremely small timing difference believed to be caused by the VOA-MEMS means we cannot use an external trigger or timing source due to the inherent timing jitter present in the devices. We are required to pick off part of the laser pulse. However, by inserting a fiber splitter into the fiducial chain, the splitter would change what modes are propagated and at what angle the light arrives into the VOA-MEMS thereby changing the propagation speed down the rest of the system.

5.3 Conclusion

Due to the unresolved timing issue caused by the VOA-MEMS and the inability to assess how small or major the timing shift is, the current time shift between GBT and APT observed at the NIF is suspect. While there might be a shift between the GBT and APT, it is likely smaller than the initial data suggested. Attempts to observe this shift at the NIF sister ICF facility OMEGA showed no measurable shift between GBT and APT. While simulation

144 Figure 5.2: Fiducial time shift caused by the MEMS-VOA for all four of the GRH detectors comprising the diagnostic array. The signiﬁcant shift between normal and timing shots for cell B and cell C (2.9 MeV and 4.5 MeV thresholds) is viewed as a physical shift in the observed Cherenkov signal. Since the ﬁducial is being shifted earlier in time, the Cherenkov signal has seemed to have moved later in time.

145 results from both the NIF (HYDRA) and OMEGA (DRACO) both can produce a time shift, the poor predictive quality of the simulations for other parameters does not instill confidence in their results. By contemplating the magnitude of time shifts possibly produced by the VOA-MEMS, the experimental results showing negligible GBT and APT time difference at OMEGA and the list of requirements necessary in HYDRA and DRACO simulations in order to produce an appreciable time shift, it is the opinion of the author of this thesis that there is likely no measurable time shift present between GBT and APT at the NIF. Definitely, the GRH diagnostic results should not be used as timing parameters for shot improvements as no reliable effect-cause relationship can be established.

5.4 Future Work

However, due to experimental (and time) limitations at this point no deﬁnitive conclusion can be made about the time shift present at the NIF. While there are some indicators that point to the lack of or smaller than measured time shift, there are still areas that need to be investigated before this time shift can be deﬁnitively ruled as either a real physical phenomenon or detector artifact. Due to operational restrictions as well as the scope of this thesis, the following lists these areas as well as future work that needs to be completed in order to arrive at a more robust conclusion. Due to the poor accuracy of the current generation of hydrodynamic simulations, a large amount of work is needed before they can be used as a foundation for more quantitative arguments. Some of the areas that need further work are:

1. The Hydrodynamic codes attempt to extrapolate using data taken at much lower neutron yields. This results in large discrepancies between model neutron yields and simulation neutron yields. More ICF experiments dedicated to verifying simple test cases need to be performed at the NIF.

2. Oversimpliﬁcation of simulations due to limited computational capacity results in many

146 important perturbing eﬀects being ignored. Full 3D simulations of post-shot ICF experiments need to be completed as well as simulations of these potential failure modes.

3. Gamma spectra produced by materials near TCC are in some cases poorly measured or completely unknown. There should be a concentrated eﬀort to place mono-isotopic samples in a 14.1 MeV neutron beam line and record the produced gamma spectrum.

4. The index of refraction for CO2 and SF6 gas is tabulated at pressure/wavelength combinations that are not relevant to Cherenkov production done at the NIF. By using a percentage based dispersion a correction is applied to the pressure dependent index of refraction. However, it is assumed that there is no pressure dependence to this correction. An experiment to measure both the pressure and wavelength dependent index of refraction for these speciﬁc gases should be performed.

The following lists future work needed speciﬁcally on the GRH detector:

1. Disagreement between counting and current mode data generated at HIγS needs to be resolved.

2. Due to volumetric contamination caused by the neutron radiation, the PMT impulse response function is only measured once at the NIF. It is unknown how much this impulse response function changes due to neutron bombardment and PMT aging.

3. The fiducial fiber and VOA-MEMS attenuators used by the GRH diagnostic at the NIF need to be replaced with single mode fibers appropriate for the 527 nm fiducial. This would result in the elimination of the a potential large timing shift.

Once the majority of these issues are addressed, the measurements provided by the GRH diagnostic coupled with the intensive simulation work will hopefully shed light on the physics that is occurring inside the ICF capsule as it undergoes compression and thermonuclear burn.

147 REFERENCES CITED

[1] George H. Miller, Edward I. Moses, and Craig R. Wuest. The national ignition facility: enabling fusion ignition for the 21st century. Nuclear Fusion, 44(12):S228, December 2004. ISSN 0029-5515. doi: 10.1088/0029-5515/44/12/S14. URL http://iopscience.iop.org/0029-5515/44/12/S14.

[2] Lawrence Livermore National Labs. Along the laser beampath - preampliﬁer module, . URL https://lasers.llnl.gov/media/photo-gallery/laser-beam&id= 5&category=laser-beam.

[3] Lawrence Livermore National Labs. Along the laser beampath - NIF laser bay, . URL https://lasers.llnl.gov/media/photo-gallery/laser-beam&id=8.

[4] Lawrence Livermore National Labs. In the target area - NIF target chamber, . URL https://lasers.llnl.gov/media/photo-gallery/target-area&id=10&category= target-area.

[5] NNSA Public Aﬀairs. NNSA and LLNL announce ﬁrst successful integrated experiment at NIF, October 2010. URL https://www.llnl.gov/news/ nnsa-and-llnl-announce-first-successful-integrated-experiment-nif.

[6] Lawrence Livermore National Labs. In the target area - NIF hohlraum, . URL https://lasers.llnl.gov/media/photo-gallery/target-area&id=8&category= target-area.

[7] Lawrence Livermore National Labs. National ignition campaign: Target fabrication, NIF & photon science, . URL https://lasers.llnl.gov/programs/nic/target_fabrication.php.

[8] Breanna Bishop. Physics world names national ignition facility fuel gain top 10 breakthrough of the year, December 2014. URL https://www.llnl.gov/news/ physics-world-names-national-ignition-facility-fuel-gain-top-10-breakthrough-year.

[9] Timothy M. DeBey. Personal communication.

[10] Mike Rubery. Personal communication, December 2014.

[11] Hans W. Herrmann. Personal communication.

148 [12] G. S. Edwards, S. J. Allen, R. F. Haglund, R. J. Nemanich, B. Redlich, J. D. Simon, and W-C. Yang. Applications of free-electron lasers in the biological and material sciences. Photochemistry and Photobiology, 81(4):711–735, July 2005. ISSN 0031-8655. doi: 10.1562/2004-11-08-IR-363R.1. URL http://www.bioone.org/doi/abs/10.1562/2004-11-08-IR-363R.1.

[13] H.R. Weller. HIGS - a new gamma-ray facility for nuclear physics. In Chiral Dynamics, volume Volume 11 of Proceedings from the Institute for Nuclear Theory, pages 466–467. WORLD SCIENTIFIC, December 2001. ISBN 978-981-02-4723-2. URL http://www.worldscientific.com/doi/abs/10.1142/9789812810977_0098.

[14] V. A. Smalyuk, S. X. Hu, J. D. Hager, J. A. Delettrez, D. D. Meyerhofer, T. C. Sangster, and D. Shvarts. Rayleigh-taylor growth measurements in the acceleration phase of spherical implosions on OMEGA. Physical Review Letters, 103(10):105001, September 2009. doi: 10.1103/PhysRevLett.103.105001. URL http://link.aps.org/doi/10.1103/PhysRevLett.103.105001.

[15] Charlie Cerjan. Personal communication.

[16] Dan Sayer. Personal communication.

[17] J. A. Frenje, C. K. Li, F. H. Se´guin,D. G. Hicks, S. Kurebayashi, R. D. Petrasso, S. Roberts, V. Yu. Glebov, D. D. Meyerhofer, T. C. Sangster, J. M. Soures, C. Stoeckl, C. Chiritescu, G. J. Schmid, and R. A. Lerche. Absolute measurements of neutron yields from DD and DT implosions at the OMEGA laser facility using CR-39 track detectors. Review of Scientiﬁc Instruments, 73(7):2597, 2002. ISSN 00346748. doi: 10.1063/1.1487889. URL http://www.academia.edu/6788539/Absolute_ measurements_of_neutron_yields_from_DD_and_DT_implosions_at_the_OMEGA_ laser_facility_using_CR-39_track_detectors.

[18] E. Kirk Miller. Personal communication.

[19] EOSPACE – low-loss LiNbO3 products 2013, . URL http://www.eospace.com/.

[20] MEMS — santec, . URL http://www.santec.com/en/about/coretechnology/mems.

[21] D. E. Hinkel, M. J. Edwards, P. A. Amendt, R. Benedetti, L. Berzak Hopkins, D. Bleuel, T. R. Boehly, D. K. Bradley, J. A. Caggiano, D. A. Callahan, P. M. Celliers, C. J. Cerjan, D. Clark, G. W. Collins, E. L. Dewald, T. R. Dittrich, L. Divol, S. N. Dixit, T. Doeppner, D. Edgell, J. Eggert, D. Farley, J. A. Frenje, V. Glebov, S. M. Glenn, S. W. Haan, A. Hamza, B. A. Hammel, C. A. Haynam, J. H.

149 Hammer, R. F. Heeter, H. W. Herrmann, D. Ho, O. Hurricane, N. Izumi, M. Gatu Johnson, O. S. Jones, D. H. Kalantar, R. L. Kauﬀman, J. D. Kilkenny, J. L. Kline, J. P. Knauer, J. A. Koch, A. Kritcher, G. A. Kyrala, K. LaFortune, O. L. Landen, B. F. Lasinski, T. Ma, A. J. Mackinnon, A. J. Macphee, E. Mapoles, J. L. Milovich, J. D. Moody, D. Meeker, N. B. Meezan, P. Michel, A. S. Moore, D. H. Munro, A. Nikroo, R. E. Olson, K. Opachich, A. Pak, T. Parham, P. Patel, H.-S. Park, R. P. Petrasso, J. Ralph, S. P. Regan, B. A. Remington, H. G. Rinderknecht, H. F. Robey, M. D. Rosen, J. S. Ross, R. Rygg, J. D. Salmonson, T. C. Sangster, M. B. Schneider, V. Smalyuk, B. K. Spears, P. T. Springer, E. Storm, D. J. Strozzi, L. J. Suter, C. A. Thomas, R. P. J. Town, E. A. Williams, S. V. Weber, P. J. Wegner, D. C. Wilson, K. Widmann, C. Yeamans, A. Zylstra, J. D. Lindl, L. J. Atherton, W. W. Hsing, B. J. MacGowan, B. M. Van Wonterghem, and E. I. Moses. Progress toward ignition at the national ignition facility. Plasma Physics and Controlled Fusion, 55(12): 124015, December 2013. ISSN 0741-3335. doi: 10.1088/0741-3335/55/12/124015. URL http://iopscience.iop.org/0741-3335/55/12/124015.

[22] J.A. Niederer. Index of refraction and dispersion of several gases in cerenkov counter use. Technical report, Brookhaven National Lab, December 1961.

[23] H. E. Watson and K. L. Ramaswamy. The refractive index dispersion and polarization of gases. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 156(887):144–157, August 1936. ISSN 0080-4630. doi: 10.1098/rspa.1936.0140. URL http://rspa.royalsocietypublishing.org/content/156/887/144.

[24] Tektronix. MSO70000c, DSA70000c/d, DPO70000c/d, DPO7000c, MSO5000, and DPO5000 series oscilloscopes speciﬁcations and performance veriﬁcation technical reference. Technical report.

[25] T. C. Sangster, R. L. McCrory, V. N. Goncharov, D. R. Harding, S. J. Loucks, P. W. McKenty, D. D. Meyerhofer, S. Skupsky, B. Yaakobi, B. J. MacGowan, L. J. Atherton, B. A. Hammel, J. D. Lindl, E. I. Moses, J. L. Porter, M. E. Cuneo, M. K. Matzen, C. W. Barnes, J. C. Fernandez, D. C. Wilson, J. D. Kilkenny, T. P. Bernat, A. Nikroo, B. G. Logan, S. Yu, R. D. Petrasso, J. D. Sethian, and S. Obenschain. Overview of inertial fusion research in the united states. Nuclear Fusion, 47(10):S686, October 2007. ISSN 0029-5515. doi: 10.1088/0029-5515/47/10/S17. URL http://iopscience.iop.org/0029-5515/47/10/S17.

[26] Mark Herrmann. Plasma physics: A promising advance in nuclear fusion. Nature, 506(7488):302–303, February 2014. ISSN 0028-0836. doi: 10.1038/nature13057. URL http://www.nature.com/nature/journal/v506/n7488/full/nature13057.html.

150 [27] Joseph A. Angelo. Nuclear Technology. Greenwood Publishing Group, January 2004. ISBN 9781573563369.

[28] Edward I. Moses. Ignition and inertial conﬁnement fusion at the national ignition facility. Journal of Physics: Conference Series, 244(1):012006, August 2010. ISSN 1742-6596. doi: 10.1088/1742-6596/244/1/012006. URL http://iopscience.iop.org/1742-6596/244/1/012006.

[29] T. R. Dittrich, O. A. Hurricane, D. A. Callahan, E. L. Dewald, T. D¨oppner,D. E. Hinkel, L. F. Berzak Hopkins, S. Le Pape, T. Ma, J. L. Milovich, J. C. Moreno, P. K. Patel, H.-S. Park, B. A. Remington, J. D. Salmonson, and J. L. Kline. Design of a high-foot high-adiabat ICF capsule for the national ignition facility. Physical Review Letters, 112(5):055002, February 2014. doi: 10.1103/PhysRevLett.112.055002. URL http://link.aps.org/doi/10.1103/PhysRevLett.112.055002.

[30] H.-S. Park, O. A. Hurricane, D. A. Callahan, D. T. Casey, E. L. Dewald, T. R. Dittrich, T. D¨oppner,D. E. Hinkel, L. F. Berzak Hopkins, S. Le Pape, T. Ma, P. K. Patel, B. A. Remington, H. F. Robey, J. D. Salmonson, and J. L. Kline. High-adiabat high-foot inertial conﬁnement fusion implosion experiments on the national ignition facility. Physical Review Letters, 112(5):055001, February 2014. doi: 10.1103/PhysRevLett.112.055001. URL http://link.aps.org/doi/10.1103/PhysRevLett.112.055001.

[31] John Lindl, Otto Landen, John Edwards, Ed Moses, and N. I. C. Team. Review of the national ignition campaign 2009-2012. Physics of Plasmas (1994-present), 21(2): 020501, February 2014. ISSN 1070-664X, 1089-7674. doi: 10.1063/1.4865400. URL http: //scitation.aip.org/content/aip/journal/pop/21/2/10.1063/1.4865400.

[32] E. I. Moses and the NIC Collaborators. The national ignition campaign: status and progress. Nuclear Fusion, 53(10):104020, October 2013. ISSN 0029-5515. doi: 10.1088/0029-5515/53/10/104020. URL http://iopscience.iop.org/0029-5515/53/10/104020.

[33] J. D. Lawson. Some criteria for a power producing thermonuclear reactor. Proceedings of the Physical Society. Section B, 70(1):6, January 1957. ISSN 0370-1301. doi: 10.1088/0370-1301/70/1/303. URL http://iopscience.iop.org/0370-1301/70/1/303.

[34] Chris Llewellyn Smith and Steve Cowley. The path to fusion power. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 368(1914):1091–1108, March 2010. ISSN 1364-503X,

151 1471-2962. doi: 10.1098/rsta.2009.0216. URL http://rsta.royalsocietypublishing.org/content/368/1914/1091. The promise, status and challenges of developing fusion power are outlined. The key physics and engineering principles are described and recent progress quantiﬁed. As the successful demonstration of 16 MW of fusion in 1997 in the Joint European Torus showed, fusion works. The central issue is therefore to make it work reliably and economically on the scale of a power station. We argue that to meet this challenge in 30 years we must follow the aggressive programme known as the ‘Fast Track to Fusion’. This programme is described in some detail.

[35] F. Wagner, Sanae-I. Itoh, Shigeru Inagaki, Masako Shindo, and Masatoshi Yagi. The physics basis of ITER conﬁnement. pages 31–53. AIP, 2009. doi: 10.1063/1.3097319. URL http://adsabs.harvard.edu/abs/2009AIPC.1095...31W.

[36] Carlos Andres Barrera. Experimental Component Characterization, Monte Carlo-based Image Generation and Source Reconstruction for the Neutron Imaging System of the National Ignition Facility. ProQuest, 2007. ISBN 9780549530114.

[37] David Hafemeister. Physics of Societal Issues: Calculations on National Security, Environment, and Energy. Springer Science & Business Media, December 2013. ISBN 9781461492726.

[38] Mordecai D. Rosen. The physics issues that determine inertial conﬁnement fusion target gain and driver requirements: A tutorial. Physics of Plasmas (1994-present), 6 (5):1690–1699, May 1999. ISSN 1070-664X, 1089-7674. doi: 10.1063/1.873427. URL http://scitation.aip.org/content/aip/journal/pop/6/5/10.1063/1.873427.

[39] Edward I. Moses. Ignition on the national ignition facility: a path towards inertial fusion energy. Nuclear Fusion, 49(10):104022, October 2009. ISSN 0029-5515. doi: 10.1088/0029-5515/49/10/104022. URL http://iopscience.iop.org/0029-5515/49/10/104022.

[40] Siegfried H. Glenzer, Brian K. Spears, M. John Edwards, Ethan T. Alger, Richard L. Berger, Darren L. Bleuel, David K. Bradley, Joseph A. Caggiano, Debra A. Callahan, Carlos Castro, Daniel T. Casey, Christine Choate, Daniel S. Clark, Charles J. Cerjan, Gilbert W. Collins, Eduard L. Dewald, Jean-Michel G. Di Nicola, Pascale Di Nicola, Laurent Divol, Shamasundar N. Dixit, Tilo D¨oppner,Rebecca Dylla-Spears, Elizabeth G. Dzenitis, James E. Fair, Lars Johan Anders Frenje, M. Gatu Johnson, E. Giraldez, Vladimir Glebov, Steven M. Glenn, Steven W. Haan, Bruce A. Hammel, Stephen P. Hatchett Ii, Christopher A. Haynam, Robert F. Heeter, Glenn M. Heestand, Hans W. Herrmann, Damien G. Hicks, Dean M. Holunga, Jeﬀrey B. Horner, Haibo Huang, Nobuhiko Izumi, Ogden S. Jones, Daniel H. Kalantar, Joseph D. Kilkenny, Robert K. Kirkwood, John L. Kline, James P. Knauer, Bernard

152 Kozioziemski, Andrea L. Kritcher, Jeremy J. Kroll, George A. Kyrala, Kai N. LaFortune, Otto L. Landen, Douglas W. Larson, Ramon J. Leeper, Sebastien Le Pape, John D. Lindl, Tammy Ma, Andrew J. Mackinnon, Andrew G. MacPhee, Evan Mapoles, Patrick W. McKenty, Nathan B. Meezan, Pierre Michel, Jose L. Milovich, John D. Moody, Alastair S. Moore, Mike Moran, Kari Ann Moreno, David H. Munro, Bryan R. Nathan, Abbas Nikroo, Richard E. Olson, Charles D. Orth, Arthur Pak, Pravesh K. Patel, Tom Parham, Richard Petrasso, Joseph E. Ralph, Hans Rinderknecht, Sean P. Regan, Harry F. Robey, J. Steven Ross, Jay D. Salmonson, Craig Sangster, Jim Sater, Marilyn B. Schneider, F. H. Séguin,Michael J. Shaw, Milton J. Shoup, Paul T. Springer, Wolfgang Stoeffl, Larry J. Suter, Cliff Avery Thomas, Richard P. J. Town, Curtis Walters, Stephen V. Weber, Paul J. Wegner, Clay Widmayer, Pamela K. Whitman, Klaus Widmann, Douglas C. Wilson, Bruno M. Van Wonterghem, Brian J. MacGowan, L. Jeff Atherton, and Edward I. Moses. First implosion experiments with cryogenic thermonuclear fuel on the national ignition facility. Plasma Physics and Controlled Fusion, 54(4):045013, April 2012. ISSN 0741-3335. doi: 10.1088/0741-3335/54/4/045013. URL http://iopscience.iop.org/0741-3335/54/4/045013.

[41] Peter J. Wisoﬀ, Mark W. Bowers, Gaylen V. Erbert, Donald F. Browning, and Donald R. Jedlovec. NIF injection laser system. volume 5341, pages 146–155, 2004. doi: 10.1117/12.538466. URL http://dx.doi.org/10.1117/12.538466.

[42] Mark Bowers, Scott Burkhart, Simon Cohen, Gaylen Erbert, John Heebner, Mark Hermann, and Don Jedlovec. The injection laser system on the national ignition facility. volume 6451, pages 64511M–64511M–20, 2007. doi: 10.1117/12.700478. URL http://dx.doi.org/10.1117/12.700478.

[43] Christopher J. Stolz. The national ignition facility: the path to a carbon-free energy future. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 370(1973):4115–4129, August 2012. ISSN 1364-503X, 1471-2962. doi: 10.1098/rsta.2011.0260. URL http://rsta.royalsocietypublishing.org/content/370/1973/4115. The National Ignition Facility (NIF), the world’s largest and most energetic laser system, is now operational at Lawrence Livermore National Laboratory. The NIF will enable exploration of scientiﬁc problems in national strategic security, basic science and fusion energy. One of the early NIF goals centres on achieving laboratory-scale thermonuclear ignition and energy gain, demonstrating the feasibility of laser fusion as a viable source of clean, carbon-free energy. This talk will discuss the precision technology and engineering challenges of building the NIF and those we must overcome to make fusion energy a commercial reality.

[44] Dennis Eimerl. Science and technology review september 1999, September 1999. URL https://e-reports-ext.llnl.gov/pdf/236351.pdf.

153 [45] Alan K. Burnham, Lloyd A. Hackel, Paul J. Wegner, Thomas G. Parham, Lawrence W. Hrubesh, Bernie M. Penetrante, Pamela K. Whitman, Stavros G. Demos, Joseph A. Menapace, Michael J. Runkel, Michael J. Fluss, Michael D. Feit, Michael H. Key, and Thomas A. Biesiada. Improving 351-nm damage performance of large-aperture fused silica and DKDP optics. volume 4679, pages 173–185, 2002. doi: 10.1117/12.461712. URL http://dx.doi.org/10.1117/12.461712.

[46] D. C. Eder, A. E. Koniges, O. S. Jones, M. M. Marinak, M. T. Tobin, and B. J. MacGowan. Late-time simulation of national ignition facility hohlraums. Nuclear Fusion, 44(7):709, July 2004. ISSN 0029-5515. doi: 10.1088/0029-5515/44/7/003. URL http://iopscience.iop.org/0029-5515/44/7/003.

[47] R. W. Wavrik, J. R. Cox, and P. J. Fleming. National ignition facility target chamber. Technical report, Lawrence Livermore National Lab., Livermore, CA (United States). Funding organisation: US Department of Energy (United States), 2000. URL http://inis.iaea.org/Search/search.aspx?orig_q=RN:37040942.

[48] T. Malsbury, B. Haid, C. Gibson, D. Atkinson, K. Skulina, J. Klingmann, J. Atherton, E. Mapoles, B. Kozioziemski, and E. Dzenitis. Fielding the NIF cryogenic ignition target. Technical report, Lawrence Livermore National Lab., Livermore, CA (United States). Funding organisation: US Department of Energy (United States), 2008. URL http://inis.iaea.org/Search/search.aspx?orig_q=RN:40020968.

[49] J. L. Kline, S. H. Glenzer, R. E. Olson, L. J. Suter, K. Widmann, D. A. Callahan, S. N. Dixit, C. A. Thomas, D. E. Hinkel, E. A. Williams, A. S. Moore, J. Celeste, E. Dewald, W. W. Hsing, A. Warrick, J. Atherton, S. Azevedo, R. Beeler, R. Berger, A. Conder, L. Divol, C. A. Haynam, D. H. Kalantar, R. Kauﬀman, G. A. Kyrala, J. Kilkenny, J. Liebman, S. Le Pape, D. Larson, N. B. Meezan, P. Michel, J. Moody, M. D. Rosen, M. B. Schneider, B. Van Wonterghem, R. J. Wallace, B. K. Young, O. L. Landen, and B. J. MacGowan. Observation of high soft x-ray drive in large-scale hohlraums at the national ignition facility. Physical Review Letters, 106 (8):085003, February 2011. doi: 10.1103/PhysRevLett.106.085003. URL http://link.aps.org/doi/10.1103/PhysRevLett.106.085003.

[50] Lawrence Livermore National Labs. Capsule implosions: NIF & photon science, . URL https://lasers.llnl.gov/for_users/experimental_capabilities/ capsule_implosions.php.

[51] A. J. Mackinnon, J. L. Kline, S. N. Dixit, S. H. Glenzer, M. J. Edwards, D. A. Callahan, N. B. Meezan, S. W. Haan, J. D. Kilkenny, T. D¨oppner,D. R. Farley, J. D. Moody, J. E. Ralph, B. J. MacGowan, O. L. Landen, H. F. Robey, T. R. Boehly, P. M. Celliers, J. H. Eggert, K. Krauter, G. Frieders, G. F. Ross, D. G. Hicks, R. E.

154 Olson, S. V. Weber, B. K. Spears, J. D. Salmonsen, P. Michel, L. Divol, B. Hammel, C. A. Thomas, D. S. Clark, O. S. Jones, P. T. Springer, C. J. Cerjan, G. W. Collins, V. Y. Glebov, J. P. Knauer, C. Sangster, C. Stoeckl, P. McKenty, J. M. McNaney, R. J. Leeper, C. L. Ruiz, G. W. Cooper, A. G. Nelson, G. G. A. Chandler, K. D. Hahn, M. J. Moran, M. B. Schneider, N. E. Palmer, R. M. Bionta, E. P. Hartouni, S. LePape, P. K. Patel, N. Izumi, R. Tommasini, E. J. Bond, J. A. Caggiano, R. Hatarik, G. P. Grim, F. E. Merrill, D. N. Fittinghoff, N. Guler, O. Drury, D. C. Wilson, H. W. Herrmann, W. Stoeffl, D. T. Casey, M. G. Johnson, J. A. Frenje, R. D. Petrasso, A. Zylestra, H. Rinderknecht, D. H. Kalantar, J. M. Dzenitis, P. Di Nicola, D. C. Eder, W. H. Courdin, G. Gururangan, S. C. Burkhart, S. Friedrich, D. L. Blueuel, l. A. Bernstein, M. J. Eckart, D. H. Munro, S. P. Hatchett, A. G. Macphee, D. H. Edgell, D. K. Bradley, P. M. Bell, S. M. Glenn, N. Simanovskaia, M. A. Barrios, R. Benedetti, G. A. Kyrala, R. P. J. Town, E. L. Dewald, J. L. Milovich, K. Widmann, A. S. Moore, G. LaCaille, S. P. Regan, L. J. Suter, B. Felker, R. C. Ashabranner, M. C. Jackson, R. Prasad, M. J. Richardson, T. R. Kohut, P. S. Datte, G. W. Krauter, J. J. Klingman, R. F. Burr, T. A. Land, M. R. Hermann, D. A. Latray, R. L. Saunders, S. Weaver, S. J. Cohen, L. Berzins, S. G. Brass, E. S. Palma, R. R. Lowe-Webb, G. N. McHalle, P. A. Arnold, L. J. Lagin, C. D. Marshall, G. K. Brunton, D. G. Mathisen, R. D. Wood, J. R. Cox, R. B. Ehrlich, K. M. Knittel, M. W. Bowers, R. A. Zacharias, B. K. Young, J. P. Holder, J. R. Kimbrough, T. Ma, K. N. La Fortune, C. C. Widmayer, M. J. Shaw, G. V. Erbert, K. S. Jancaitis, J. M. DiNicola, C. Orth, G. Heestand, R. Kirkwood, C. Haynam, P. J. Wegner, P. K. Whitman, A. Hamza, E. G. Dzenitis, R. J. Wallace, S. D. Bhandarkar, T. G. Parham, R. Dylla-Spears, E. R. Mapoles, B. J. Kozioziemski, J. D. Sater, C. F. Walters, B. J. Haid, J. Fair, A. Nikroo, E. Giraldez, K. Moreno, B. Vanwonterghem, R. L. Kauffman, S. Batha, D. W. Larson, R. J. Fortner, D. H. Schneider, J. D. Lindl, R. W. Patterson, L. J. Atherton, and E. I. Moses. Assembly of high-areal-density deuterium-tritium fuel from indirectly driven cryogenic implosions. Physical Review Letters, 108(21):215005, May 2012. doi: 10.1103/PhysRevLett.108.215005. URL http://link.aps.org/doi/10.1103/PhysRevLett.108.215005.

[52] S. H. Glenzer, B. J. MacGowan, N. B. Meezan, P. A. Adams, J. B. Alfonso, E. T. Alger, Z. Alherz, L. F. Alvarez, S. S. Alvarez, P. V. Amick, K. S. Andersson, S. D. Andrews, G. J. Antonini, P. A. Arnold, D. P. Atkinson, L. Auyang, S. G. Azevedo, B. N. M. Balaoing, J. A. Baltz, F. Barbosa, G. W. Bardsley, D. A. Barker, A. I. Barnes, A. Baron, R. G. Beeler, B. V. Beeman, L. R. Belk, J. C. Bell, P. M. Bell, R. L. Berger, M. A. Bergonia, L. J. Bernardez, L. V. Berzins, R. C. Bettenhausen, L. Bezerides, S. D. Bhandarkar, C. L. Bishop, E. J. Bond, D. R. Bopp, J. A. Borgman, J. R. Bower, G. A. Bowers, M. W. Bowers, D. T. Boyle, D. K. Bradley, J. L. Bragg, J. Braucht, D. L. Brinkerhoﬀ, D. F. Browning, G. K. Brunton, S. C. Burkhart, S. R. Burns, K. E. Burns, B. Burr, L. M. Burrows, R. K. Butlin, N. J. Cahayag, D. A. Callahan, P. S. Cardinale, R. W. Carey, J. W. Carlson, A. D. Casey, C. Castro, J. R. Celeste, A. Y. Chakicherla, F. W. Chambers, C. Chan, H. Chandrasekaran, C. Chang, R. F. Chapman, K. Charron, Y. Chen, M. J.

155 Christensen, A. J. Churby, T. J. Clancy, B. D. Cline, L. C. Clowdus, D. G. Cocherell, F. E. Coffield, S. J. Cohen, R. L. Costa, J. R. Cox, G. M. Curnow, M. J. Dailey, P. M. Danforth, R. Darbee, P. S. Datte, J. A. Davis, G. A. Deis, R. D. Demaret, E. L. Dewald, P. Di Nicola, J. M. Di Nicola, L. Divol, S. Dixit, D. B. Dobson, T. Doppner, J. D. Driscoll, J. Dugorepec, J. J. Duncan, P. C. Dupuy, E. G. Dzenitis, M. J. Eckart, S. L. Edson, G. J. Edwards, M. J. Edwards, O. D. Edwards, P. W. Edwards, J. C. Ellefson, C. H. Ellerbee, G. V. Erbert, C. M. Estes, W. J. Fabyan, R. N. Fallejo, M. Fedorov, B. Felker, J. T Fink, M. D. Finney, L. F. Finnie, M. J. Fischer, J. M. Fisher, B. T. Fishler, J. W. Florio, A. Forsman, C. B. Foxworthy, R. M. Franks, T. Frazier, G. Frieder, T. Fung, G. N. Gawinski, C. R. Gibson, E. Giraldez, S. M. Glenn, B. P. Golick, H. Gonzales, S. A. Gonzales, M. J. Gonzalez, K. L. Griffin, J. Grippen, S. M. Gross, P. H. Gschweng, G. Gururangan, K. Gu, S. W. Haan, S. R. Hahn, B. J. Haid, J. E. Hamblen, B. A. Hammel, A. V. Hamza, D. L. Hardy, D. R. Hart, R. G. Hartley, C. A. Haynam, G. M. Heestand, M. R. Hermann, G. L. Hermes, D. S. Hey, R. L. Hibbard, D. G. Hicks, D. E. Hinkel, D. L. Hipple, J. D. Hitchcock, D. L. Hodtwalker, J. P. Holder, J. D. Hollis, G. M. Holtmeier, S. R. Huber, A. W. Huey, D. N. Hulsey, S. L. Hunter, T. R. Huppler, M. S. Hutton, N. Izumi, J. L. Jackson, M. A. Jackson, K. S. Jancaitis, D. R. Jedlovec, B. Johnson, M. C. Johnson, T. Johnson, M. P. Johnston, O. S. Jones, D. H. Kalantar, J. H. Kamperschroer, R. L. Kauffman, G. A. Keating, L. M. Kegelmeyer, S. L. Kenitzer, J. R. Kimbrough, K. King, R. K. Kirkwood, J. L. Klingmann, K. M. Knittel, T. R. Kohut, K. G. Koka, S. W. Kramer, J. E. Krammen, K. G. Krauter, G. W. Krauter, E. K. Krieger, J. J. Kroll, K. N. La Fortune, L. J. Lagin, V. K. Lakamsani, O. L. Landen, S. W. Lane, A. B. Langdon, S. H. Langer, N. Lao, D. W. Larson, D. Latray, G. T. Lau, S. Le Pape, B. L. Lechleiter, Y. Lee, T. L. Lee, J. Li, J. A. Liebman, J. D. Lindl, S. F. Locke, H. K. Loey, R. A. London, F. J. Lopez, D. M. Lord, R. R. Lowe-Webb, J. G. Lown, A. P. Ludwigsen, N. W. Lum, R. R. Lyons, T. Ma, A. J. MacKinnon, M. D. Magat, D. T. Maloy, T. N. Malsbury, G. Markham, R. M. Marquez, A. A. Marsh, C. D. Marshall, S. R. Marshall, I. L. Maslennikov, D. G. Mathisen, G. J. Mauger, M. Y. Mauvais, J. A. McBride, T. McCarville, J. B. McCloud, A. McGrew, B. McHale, A. G. MacPhee, J. F. Meeker, J. S. Merill, E. P. Mertens, P. A. Michel, M. G. Miller, T. Mills, J. L. Milovich, R. Miramontes, R. C. Montesanti, M. M. Montoya, J. Moody, J. D. Moody, K. A. Moreno, J. Morris, K. M. Morriston, J. R. Nelson, M. Neto, J. D. Neumann, E. Ng, Q. M. Ngo, B. L. Olejniczak, R. E. Olson, N. L. Orsi, M. W. Owens, E. H. Padilla, T. M. Pannell, T. G. Parham, R. W. Patterson, G. Pavel, R. R. Prasad, D. Pendlton, F. A. Penko, B. L. Pepmeier, D. E. Petersen, T. W. Phillips, D. Pigg, K. W. Piston, K. D. Pletcher, C. L. Powell, H. B. Radousky, B. S. Raimondi, J. E. Ralph, R. L. Rampke, R. K. Reed, W. A. Reid, V. V. Rekow, J. L. Reynolds, J. J. Rhodes, M. J. Richardson, R. J. Rinnert, B. P. Riordan, A. S. Rivenes, A. T. Rivera, C. J. Roberts, J. A. Robinson, R. B. Robinson, S. R. Robison, O. R. Rodriguez, S. P. Rogers, M. D. Rosen, G. F. Ross, M. Runkel, A. S. Runtal, R. A. Sacks, S. F. Sailors, J. T. Salmon, J. D. Salmonson, R. L. Saunders, J. R. Schaffer, T. M. Schindler, M. J. Schmitt, M. B. Schneider, K. S. Segraves, M. J. Shaw, M. E. Sheldrick, R. T. Shelton, M. K. Shiflett, S. J. Shiromizu, M. Shor, L. L. Silva, S. A. Silva, K. M.

156 Skulina, D. A. Smauley, B. E. Smith, L. K. Smith, A. L. Solomon, S. Sommer, J. G. Soto, N. I. Spaﬀord, D. E. Speck, P. T. Springer, M. Stadermann, F. Stanley, T. G. Stone, E. A. Stout, P. L. Stratton, R. J. Strausser, L. J. Suter, W. Sweet, M. F. Swisher, J. D. Tappero, J. B. Tassano, J. S. Taylor, E. A. Tekle, C. Thai, C. A. Thomas, A. Thomas, A. L. Throop. Demonstration of ignition radiation temperatures in indirect-drive inertial conﬁnement fusion hohlraums. Physical Review Letters, 106(8):085004, February 2011. doi: 10.1103/PhysRevLett.106.085004. URL http://link.aps.org/doi/10.1103/PhysRevLett.106.085004.

[53] M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan. Three-dimensional HYDRA simulations of national ignition facility targets. Physics of Plasmas (1994-present), 8(5):2275–2280, May 2001. ISSN 1070-664X, 1089-7674. doi: 10.1063/1.1356740. URL http://scitation.aip.org/content/aip/journal/pop/8/5/10.1063/1.1356740.

[54] V. N. Goncharov, J. P. Knauer, P. W. McKenty, P. B. Radha, T. C. Sangster, S. Skupsky, R. Betti, R. L. McCrory, and D. D. Meyerhofer. Improved performance of direct-drive inertial conﬁnement fusion target designs with adiabat shaping using an intensity picket. Physics of Plasmas (1994-present), 10(5):1906–1918, May 2003. ISSN 1070-664X, 1089-7674. doi: 10.1063/1.1562166. URL http: //scitation.aip.org/content/aip/journal/pop/10/5/10.1063/1.1562166.

[55] R. A. Lerche, M. D. Cable, and P. G. Dendooven. ICF burn-history measurments using 17-MeV fusion gamma rays. Technical report, Lawrence Livermore National Lab., CA (United States). Funding organisation: USDOE, Washington, DC (United States), 1995. URL http://inis.iaea.org/Search/search.aspx?orig_q=RN:27049546.

[56] V. Yu Glebov, T. C. Sangster, C. Stoeckl, J. P. Knauer, W. Theobald, K. L. Marshall, M. J. Shoup, T. Buczek, M. Cruz, T. Duffy, M. Romanofsky, M. Fox, A. Pruyne, M. J. Moran, R. A. Lerche, J. McNaney, J. D. Kilkenny, M. J. Eckart, D. Schneider, D. Munro, W. Stoeffl, R. Zacharias, J. J. Haslam, T. Clancy, M. Yeoman, D. Warwas, C. J. Horsfield, J.-L. Bourgade, O. Landoas, L. Disdier, G. A. Chandler, and R. J. Leeper. The national ignition facility neutron time-of-flight system and its initial performance (invited). The Review of Scientific Instruments, 81(10):10D325, October 2010. ISSN 1089-7623. doi: 10.1063/1.3492351.

[57] C. B. Yeamans, D. L. Bleuel, and L. A. Bernstein. Enhanced NIF neutron activation diagnostics. The Review of Scientiﬁc Instruments, 83(10):10D315, October 2012. ISSN 1089-7623. doi: 10.1063/1.4739230.

[58] D. T. Casey, J. A. Frenje, M. Gatu Johnson, F. H. S´eguin,C. K. Li, R. D. Petrasso, V. Yu Glebov, J. Katz, J. P. Knauer, D. D. Meyerhofer, T. C. Sangster, R. M.

157 Bionta, D. L. Bleuel, T. D¨oppner,S. Glenzer, E. Hartouni, S. P. Hatchett, S. Le Pape, T. Ma, A. MacKinnon, M. A. McKernan, M. Moran, E. Moses, H.-S. Park, J. Ralph, B. A. Remington, V. Smalyuk, C. B. Yeamans, J. Kline, G. Kyrala, G. A. Chandler, R. J. Leeper, C. L. Ruiz, G. W. Cooper, A. J. Nelson, K. Fletcher, J. Kilkenny, M. Farrell, D. Jasion, and R. Paguio. Measuring the absolute deuterium-tritium neutron yield using the magnetic recoil spectrometer at OMEGA and the NIF. The Review of Scientiﬁc Instruments, 83(10):10D912, October 2012. ISSN 1089-7623. doi: 10.1063/1.4738657.

[59] Y. Kim, J. M. Mack, H. W. Herrmann, C. S. Young, G. M. Hale, S. Caldwell, N. M. Hoffman, S. C. Evans, T. J. Sedillo, A. McEvoy, J. Langenbrunner, H. H. Hsu, M. A. Huff, S. Batha, C. J. Horsfield, M. S. Rubery, W. J. Garbett, W. Stoeffl, E. Grafil, L. Bernstein, J. A. Church, D. B. Sayre, M. J. Rosenberg, C. Waugh, H. G. Rinderknecht, M. Gatu Johnson, A. B. Zylstra, J. A. Frenje, D. T. Casey, R. D. Petrasso, E. Kirk Miller, V. Yu Glebov, C. Stoeckl, and T. C. Sangster. D-t gamma-to-neutron branching ratio determined from inertial confinement fusion plasmasa). Physics of Plasmas (1994-present), 19(5):056313, May 2012. ISSN 1070-664X, 1089-7674. doi: 10.1063/1.4718291. URL http: //scitation.aip.org/content/aip/journal/pop/19/5/10.1063/1.4718291.

[60] F. Ajzenberg-Selove. Energy levels of light nuclei a = 11-12. Nuclear Physics A, 506 (1):1–158, January 1990. ISSN 0375-9474. doi: 10.1016/0375-9474(90)90271-M. URL http://www.sciencedirect.com/science/article/pii/037594749090271M.

[61] D. R. Tilley, H. R. Weller, and C. M. Cheves. Energy levels of light nuclei a = 16–17. Nuclear Physics A, 564(1):1–183, November 1993. ISSN 0375-9474. doi: 10.1016/0375-9474(93)90073-7. URL http://www.sciencedirect.com/science/article/pii/0375947493900737.

[62] L. C. Thompson and J. R. Risser. Gamma rays from the inelastic scattering of 14-mev neutrons in ${\mathrm{C}}ˆ{12}$ and ${\mathrm{O}}ˆ{16}$. Physical Review, 94(4):941–943, May 1954. doi: 10.1103/PhysRev.94.941. URL http://link.aps.org/doi/10.1103/PhysRev.94.941.

[63] D. Rochman, R. C. Haight, J. M. O’ Donnell, M. Devlin, T. Ethvignot, and T. Granier. Neutron-induced reaction studies at FIGARO using a spallation source. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 523(1–2):102–115, May 2004. ISSN 0168-9002. doi: 10.1016/j.nima.2003.12.026. URL http://www.sciencedirect.com/science/article/pii/S0168900204000427.

[64] N.M. Hoffman, H.W. Herrmann, Y.H. Kim, H.H. Hsu, C.J. Horsfield, M.S. Rubery, D.C. Wilson, W. W. Stoeffl, C.S. Young, J.M. Mack, E.K. Miller, E. Grafil, S.C.

158 Evans, T.J. Sedillo, V.Yu. Glebov, and T. Duﬀy. In situ calibration of the gamma reaction history instrument using reference samples (“pucks”) for areal density measurements. EPJ Web of Conferences, 59:13019, 2013. ISSN 2100-014X. doi: 10.1051/epjconf/20135913019. URL http://www.epj-conferences.org/articles/ epjconf/abs/2013/20/epjconf_ifsa2011_13019/epjconf_ifsa2011_13019.html.

[65] N. M. Hoffman, D. C. Wilson, H. W. Herrmann, and C. S. Young. Using gamma-ray emission to measure areal density of inertial confinement fusion capsules. The Review of Scientific Instruments, 81(10):10D332, October 2010. ISSN 1089-7623. doi: 10.1063/1.3478690.

[66] P. A. Cerenkov.ˇ Visible radiation produced by electrons moving in a medium with velocities exceeding that of light. Physical Review, 52(4):378–379, August 1937. doi: 10.1103/PhysRev.52.378. URL http://link.aps.org/doi/10.1103/PhysRev.52.378.

[67] Blair Ratcliﬀ and Jochen Schwiening. Cherenkov counters. In Claus Grupen and Ir`eneBuvat, editors, Handbook of Particle Detection and Imaging, pages 453–471. Springer Berlin Heidelberg, 2012. ISBN 978-3-642-13270-4, 978-3-642-13271-1. URL http: //link.springer.com/referenceworkentry/10.1007/978-3-642-13271-1_18.

[68] S. Majewski, A. Margaryan, and L. Tang. Proposal for cherenkov time of ﬂight technique with picosecond resolution. arXiv:physics/0508040, August 2005. URL http://arxiv.org/abs/physics/0508040.

[69] Boris M. Bolotovskii. Vavilov – cherenkov radiation: its discovery and application. Physics-Uspekhi, 52(11):1099, November 2009. ISSN 1063-7869. doi: 10.3367/UFNe.0179.200911c.1161. URL http://iopscience.iop.org/1063-7869/52/11/R03.

[70] I. Frank and Ig Tamm. Coherent visible radiation of fast electrons passing through matter. In Professor Dr Boris M. Bolotovskii, Professor Dr Victor Ya Frenkel, and Professor Rudolf Peierls, editors, Selected Papers, pages 29–35. Springer Berlin Heidelberg, 1991. ISBN 978-3-642-74628-4, 978-3-642-74626-0. URL http://link.springer.com/chapter/10.1007/978-3-642-74626-0_2.

[71] J. M. Mack, S. E. Caldwell, S. C. Evans, T. J. Sedillo, D. C. Wilson, C. S. Young, C. J. Horsfield, R. L. Griffith, and R. A. Lerche. Multiplexed gas cherenkov detector for reaction-history measurements. Review of Scientific Instruments, 77(10):10E728, October 2006. ISSN 0034-6748, 1089-7623. doi: 10.1063/1.2351912. URL http: //scitation.aip.org/content/aip/journal/rsi/77/10/10.1063/1.2351912.

159 [72] C. J. Horsfield, S. E. Caldwell, C. R. Christensen, S. C. Evans, J. M. Mack, T. Sedillo, C. S. Young, and V. Yu Glebov. γ-ray ‘bang-time’ measurements with a gas-cherenkov detector for inertial-confinement fusion experiments. Review of Scientific Instruments, 77(10):10E724, October 2006. ISSN 0034-6748, 1089-7623. doi: 10.1063/1.2352736. URL http: //scitation.aip.org/content/aip/journal/rsi/77/10/10.1063/1.2352736.

[73] A. M. McEvoy, H. W. Herrmann, C. J. Horsfield, C. S. Young, E. K. Miller, J. M. Mack, Y. Kim, W. Stoeffl, M. Rubery, S. Evans, T. Sedillo, and Z. A. Ali. Gamma bang time analysis at OMEGA. The Review of Scientific Instruments, 81(10): 10D322, October 2010. ISSN 1089-7623. doi: 10.1063/1.3485083.

[74] Hans W. Herrmann, Joseph M. Mack, Carlton S. Young, Robert M. Malone, Wolfgang Stoeffl, and Colin J. Horsfield. Cherenkov radiation conversion and collection considerations for a gamma bang time/reaction history diagnostic for the NIF. The Review of Scientific Instruments, 79(10):10E531, October 2008. ISSN 1089-7623. doi: 10.1063/1.2979868.

[75] R. M. Malone, H. W. Herrmann, W. Stoeffl, J. M. Mack, and C. S. Young. Gamma bang time/reaction history diagnostics for the national ignition facility using 90 degrees off-axis parabolic mirrors. The Review of Scientific Instruments, 79(10): 10E532, October 2008. ISSN 1089-7623. doi: 10.1063/1.2969281.

[76] Henry R. Weller. A free-electron laser generated gamma-ray beam for nuclear physics. Acta Physica Hungarica Series A, Heavy Ion Physics, 14(1-4):405–414, January 2001. ISSN 1219-7580, 1588-2675. doi: 10.1556/APH.14.2001.1-4.38. URL http://link.springer.com/article/10.1556/APH.14.2001.1-4.38.

[77] H.R. WELLER. The HIGS facility: A free-electron laser generated gamma-ray beam for research in nuclear physics. In Electromagnetic Interactions in Nuclear and Hadron Physics, pages 227–246. WORLD SCIENTIFIC, June 2002. ISBN 978-981-238-044-9. URL http://www.worldscientific.com/doi/abs/10.1142/9789812777218_0023.

[78] M. S. Rubery, C. J. Horsfield, H. Herrmann, Y. Kim, J. M. Mack, C. Young, S. Evans, T. Sedillo, A. McEvoy, S. E. Caldwell, E. Grafil, W. Stoeffl, and J. S. Milnes. Monte carlo validation experiments for the gas cherenkov detectors at the national ignition facility and omega. Review of Scientific Instruments, 84(7):073504, July 2013. ISSN 0034-6748, 1089-7623. doi: 10.1063/1.4812572. URL http: //scitation.aip.org/content/aip/journal/rsi/84/7/10.1063/1.4812572.

[79] J. Allison, K. Amako, J. Apostolakis, H. Araujo, P.A. Dubois, M. Asai, G. Barrand, R. Capra, S. Chauvie, R. Chytracek, G.A.P. Cirrone, G. Cooperman, G. Cosmo,

160 G. Cuttone, G.G. Daquino, M. Donszelmann, M. Dressel, G. Folger, F. Foppiano, J. Generowicz, V. Grichine, S. Guatelli, P. Gumplinger, A. Heikkinen, I. Hrivnacova, A. Howard, S. Incerti, V. Ivanchenko, T. Johnson, F. Jones, T. Koi, R. Kokoulin, M. Kossov, H. Kurashige, V. Lara, S. Larsson, F. Lei, O. Link, F. Longo, M. Maire, A. Mantero, B. Mascialino, I. McLaren, P.M. Lorenzo, K. Minamimoto, K. Murakami, P. Nieminen, L. Pandola, S. Parlati, L. Peralta, J. Perl, A. Pfeiﬀer, M.G. Pia, A. Ribon, P. Rodrigues, G. Russo, S. Sadilov, G. Santin, T. Sasaki, D. Smith, N. Starkov, S. Tanaka, E. Tcherniaev, B. Tome, A. Trindade, P. Truscott, L. Urban, M. Verderi, A. Walkden, J.P. Wellisch, D.C. Williams, D. Wright, and H. Yoshida. Geant4 developments and applications. IEEE Transactions on Nuclear Science, 53(1):270–278, February 2006. ISSN 0018-9499. doi: 10.1109/TNS.2006.869826.

[80] Bryan Bednarz, Gty Chen, Harald Paganetti, Bin Han, Aiping Ding, and X. George Xu. COMPARISON OF PARTICLE-TRACKING FEATURES IN GEANT4 AND MCNPX CODES FOR APPLICATIONS IN MAPPING OF PROTON RANGE UNCERTAINTY. Nuclear Technology, 175(1):2–5, July 2011. ISSN 0029-5450.

[81] George W. Walker. On the dependence of the refractive index of gases on temperature. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 201:435–455, January 1903. ISSN 0264-3952. URL http://www.jstor.org/stable/90905.

[82] Max Born and Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diﬀraction of Light. Cambridge University Press, October 1999. ISBN 9780521642224.

[83] Kenneth S. Krane. Introductory Nuclear Physics. Wiley, New York, 3 edition edition, October 1987. ISBN 9780471805533.

[84] H. W. Herrmann, C. S. Young, J. M. Mack, Y. H. Kim, A. McEvoy, S. Evans, T. Sedillo, S. Batha, M. Schmitt, D. C. Wilson, J. R. Langenbrunner, R. Malone, M. I. Kaufman, B. C. Cox, B. Frogget, E. K. Miller, Z. A. Ali, T. W. Tunnell, W. Stoeﬄ, C. J. Horsﬁeld, and M. Rubery. ICF gamma-ray reaction history diagnostics. Journal of Physics: Conference Series, 244(3):032047, August 2010. ISSN 1742-6596. doi: 10.1088/1742-6596/244/3/032047. URL http://iopscience.iop.org/1742-6596/244/3/032047.

[85] George R. Labaria, Judith A. Liebman, Daniel B. Sayre, Hans W. Herrmann, Essex J. Bond, and Jennifer A. Church. Multi-objective optimization for the national ignition facility’s gamma reaction history diagnostic. page 86020C, February 2013. doi: 10.1117/12.2009047. URL http://spie.org/Publications/Proceedings/Paper/10.1117/12.2009047.

161 [86] D. B. Sayre, L. A. Bernstein, J. A. Church, H. W. Herrmann, and W. Stoeﬄ. Multi-shot analysis of the gamma reaction history diagnostica). Review of Scientiﬁc Instruments, 83(10):10D905, October 2012. ISSN 0034-6748, 1089-7623. doi: 10.1063/1.4729492. URL http: //scitation.aip.org/content/aip/journal/rsi/83/10/10.1063/1.4729492.

[87] M. A. Christon. Hydra, a ﬁnite element computational ﬂuid dynamics code: User manual. Technical Report UCRL-MA–121344, Lawrence Livermore National Lab., CA (United States), June 1995. URL http://www.osti.gov/scitech/biblio/109508.

[88] D. Keller, T. J. B. Collins, J. A. Delettrez, P. W. McKenty, P. B. Radha, R. P. J. Town, B. Whitney, and G. A. Moses. DRACO—a new multidimensional hydrocode. In APS Division of Plasma Physics Meeting Abstracts, volume -1, November 1999. URL http://adsabs.harvard.edu/abs/1999APS..DPP.BP139K.

[89] Jim Rathkopf. Science and technology review, December 2004. URL https://str.llnl.gov/str/December04/pdfs/12_04.3.pdf.

[90] Daniel S. Clark and Max Tabak. Acceleration- and deceleration-phase nonlinear rayleigh-taylor growth at spherical interfaces. Physical Review E, 72(5):056308, November 2005. doi: 10.1103/PhysRevE.72.056308. URL http://link.aps.org/doi/10.1103/PhysRevE.72.056308.

[91] Y.Y. Lau, M.R. Weis, and R.M. Gilgenbach. A property of the rayleigh-taylor instability. In 2013 Abstracts IEEE International Conference on Plasma Science (ICOPS), pages 1–1, June 2013. doi: 10.1109/PLASMA.2013.6633345.

[92] M. J.-E. Manuel, C. K. Li, F. H. S´eguin,J. Frenje, D. T. Casey, R. D. Petrasso, S. X. Hu, R. Betti, J. D. Hager, D. D. Meyerhofer, and V. A. Smalyuk. First measurements of rayleigh-taylor-induced magnetic ﬁelds in laser-produced plasmas. Physical Review Letters, 108(25):255006, June 2012. doi: 10.1103/PhysRevLett.108.255006. URL http://link.aps.org/doi/10.1103/PhysRevLett.108.255006.

[93] P. W. McKenty, T. C. Sangster, M. Alexander, R. Betti, R. S. Craxton, J. A. Delettrez, L. Elasky, R. Epstein, A. Frank, V. Yu Glebov, V. N. Goncharov, D. R. Harding, S. Jin, J. P. Knauer, R. L. Keck, S. J. Loucks, L. D. Lund, R. L. McCrory, F. J. Marshall, D. D. Meyerhofer, S. P. Regan, P. B. Radha, S. Roberts, W. Seka, S. Skupsky, V. A. Smalyuk, J. M. Soures, K. A. Thorp, M. Wozniak, J. A. Frenje, C. K. Li, R. D. Petrasso, F. H. S´eguin,K. A. Fletcher, S. Padalino, C. Freeman, N. Izumi, J. A. Koch, R. A. Lerche, M. J. Moran, T. W. Phillips, G. J. Schmid, and C. Sorce. Direct-drive cryogenic target implosion performance on OMEGA. Physics

162 of Plasmas (1994-present), 11(5):2790–2797, May 2004. ISSN 1070-664X, 1089-7674. doi: 10.1063/1.1692106. URL http: //scitation.aip.org/content/aip/journal/pop/11/5/10.1063/1.1692106.

[94] Labratory For Laser Energetics. OMEGA System Operations Manual Volume I–System Description. 2003.

[95] E. Kirk Miller. Mach-zehnder ﬁber-optic links for inertial conﬁnement fusion diagnostics. Stockpile Stewardship Quarterly, 2(3):5–6, November 2012.

[96] E. Kirk Miller, H. W. Herrmann, W. Stoeffl, and C. J. Horsfield. Mach-zehnder fiber-optic links for reaction history measurements at the national ignition facility. Journal of Physics: Conference Series, 244(3):032055, August 2010. ISSN 1742-6596. doi: 10.1088/1742-6596/244/3/032055. URL http://iopscience.iop.org/1742-6596/244/3/032055.

[97] Le Nguyen Binh and Itzhak Shraga. An optical ﬁber dispersion measurement technique and system. Technical report, Monash University, 2005.

[98] E.L. Wooten, K.M. Kissa, A. Yi-Yan, E.J. Murphy, D.A. Lafaw, P.F. Hallemeier, D. Maack, D.V. Attanasio, D.J. Fritz, G.J. McBrien, and D.E. Bossi. A review of lithium niobate modulators for ﬁber-optic communications systems. IEEE Journal of Selected Topics in Quantum Electronics, 6(1):69–82, January 2000. ISSN 1077-260X. doi: 10.1109/2944.826874.

[99] B. Beeman, A. G. MacPhee, J. R. Kimbrough, G. A. Lacaille, M. A. Barrios, J. Emig, J. R. Hunter, E. K. Miller, and W. R. Donaldson. Mach-zehnder modulator performance using the comet laser facility and implications for use on NIF. page 850507, October 2012. doi: 10.1117/12.931436. URL http://spie.org/Publications/Proceedings/Paper/10.1117/12.931436.

[100] Govind P. Agrawal. Fiber-Optic Communication Systems. Wiley, 4 edition edition, November 2012.

[101] Kumar Appaiah, Sriram Vishwanath, and Seth R. Bank. Impact of ﬁber core diameter on dispersion and multiplexing in multimode-ﬁber links. Optics Express, 22 (14):17158, July 2014. ISSN 1094-4087. doi: 10.1364/OE.22.017158. URL http: //www.opticsinfobase.org/oe/fulltext.cfm?uri=oe-22-14-17158&id=295843.

[102] Chandrasekhar Roychoudhuri and Society of Photo-optical Instrumentation Engineers. Fundamentals of photonics. SPIE, [Bellingham, Wash.], 2008. ISBN

163 9780819471284 0819471283. URL http://www.spiedigitallibrary.org/ebooks/spie/tutorial_texts/tt79.

[103] Keiji Isamoto, K. Kato, A. Morosawa, Changho Chong, H. Fujita, and H. Toshiyoshi. A 5-v operated MEMS variable optical attenuator by SOI bulk micromachining. IEEE Journal of Selected Topics in Quantum Electronics, 10(3):570–578, May 2004. ISSN 1077-260X. doi: 10.1109/JSTQE.2004.828475.

164 APPENDIX A - DERIVATION OF LAWSON CRITERION

In a steady state reactor the energy generated by a reactor remains constant. Therefore the change of work (dW ) provided over a period of time (dt) is:

dW = 0 (1.1) dt

In order for this system to remain in equilibrium the power provide from both internal sources (Pinternal) and external source (Pexternal) must be equal to the total energy lost by the system (Ploss):

Pinternal + Pexternal − Ploss = 0 (1.2)

In the case of an ICF fusion reactor all the Pinternal is derived from the two products of the

D-T fusion reaction (Pfusion). For any fuel Pfusion is:

Pfusion = nAnBσ(A,B)v(A,B)E(A,B) (1.3)

Where:

• n is the density of particles.

• σ is the fusion nuclear cross section.

• v is the average velocity of atoms.

• E(A,B) is the energy released from the fusion reaction.

In the case of a 50-50 D-T fusion reaction

Pfusion = nDnT σDT vDT EDT (1.4)

165 By taking the average of σDT and vDT over the Maxwellian velocity distribution at a plasma temperature (T ) the previous equation becomes:

1 P = n2hσ v i E (1.5) fusion 4 DT DT T DT

Now that the energy produce by the system has been determined, we now need to deter-

mine how long we need to confine the plasma. The confinement time (τE) of the system is defined by the rate at which the reactor loses energy to its environment. It can be written in terms of the total energy density of the system per unit volume (W ) divided by the power

loss per unit density (Ploss): W τE = (1.6) Ploss

For a 50-50 DT plasma W is equal too:

W = 3nkBT (1.7)

Where:

• n is the density of particles.

• kB is the Boltzmann constant.

• T is the temperature of the plasma.

In order to have a working fusion reactor, the energy gained from fusion reaction must be greater than or equal to the total energy lost. This results in the following inequality:

Pfusion ≥ Ploss (1.8)

Replacing Pfusion for the value found in Equation 1.5:

1 n2hσ v i E ≥ P (1.9) 4 DT DT T DT loss

166 Inserting Equation 1.9 and Equation 1.7 into Equation 1.6:

3nk T τ ≤ B (1.10) E 1 2 4 n hσDT vDT iT EDT

Rearranging Equation 1.10 in order to isolate n and τE:

12 kBT nτE ≥ (1.11) EDT hσDT vDT iT

Taking Equation 1.11 and multiplying both sides by T we get the Lawson Criterion:

2 12 kBT nT τE ≥ (1.12) EDT hσDT vDT iT

167 APPENDIX B - KINDLE GRH GEOMETRY DEFINITION

Below list the Kindle code which deﬁnes the geometry of the Gamma Reaction History detector. GRH.world 1 # GRH.world

2 # ======

3 # Defines geometry for Gamma Reaction Histroy (GRH) detector (kindle).

4 # Author: Elliot Grafil

5 #

6 version 4

8 #---- detector ------

10 detector

11 name cathode

12 suppressZeroDeposit 0

13 report

14 detectorCode

15 primaryIndex

16 positionX

17 positionY

18 positionZ

19 process

20 processCode

21 particleCode

22 particleName

23 deposit

24 KE

25 Wavelength

26 timeend

27 timestart

28 end

30 compress

31 trackID

32 end

33 end

35 # Pressure Chamber Dome Cover

168 36 # ------

37 domeCover

38 name Domey

39 radius 63.5000 mm

40 bump 22.2250 mm

41 thickness 3.1750 mm

42 material AluminumMetal

43 interfacemat CerenkovGas

44 position 0.0000 0.0000 0.0000 mm

45 rotate 0.00 0.00 0.00 deg

46 color 0.50 0.50 0.50

47 parent World

48 end

51 ### ------

52 ### 312743a, Cover,tube,pressure chamber

53 ### ------

55 # GasA: pressurized gas inside Pressure Chamber flange surrounding converters

56 # ------

57 cylinder

58 name ConverterGasA

59 radius 63.5000 mm

60 innerRadius 63.1190 mm

61 length 13.9916 mm

62 material CerenkovGas

63 position 0.0000 0.0000 -6.9958 mm

64 color 0.50 0.50 0.00

65 parent World

66 end

68 # GasB: pressurized gas inside Pressure Chamber flange filling the rest

69 # ------

70 cylinder

71 name ConverterGasB

72 radius 63.5000 mm

73 innerRadius 0.0000 mm

74 length 11.0084 mm

75 material CerenkovGas

76 position 0.0000 0.0000 -19.4958 mm

169 77 color 0.50 0.50 0.00

78 parent World

79 end

81 # ConverterShield: Tungsten target

82 # ------

83 cylinder

84 name ConverterShield

85 radius 63.1190 mm

86 innerRadius 0.0000 mm

87 length 5.0000 mm

88 material ConverterMetal

89 position 0.0000 0.0000 -2.5000 mm

90 color 0.50 0.00 0.00

91 parent World

92 end

94 # Converter: Aluminum target

95 # ------

96 cylinder

97 name Converter

98 radius 63.1190 mm

99 innerRadius 0.0000 mm

100 length 8.9916 mm

101 material ConverterMetal

102 position 0.0000 0.0000 -9.4958 mm

103 color 0.50 0.00 0.50

104 parent World

105 end

106

107 # ConverterFlange:

108 # ------

109 cylinder

110 name ConverterFlange

111 radius 95.2500 mm

112 innerRadius 63.5000 mm

113 length 25.000 mm

114 material AluminumMetal

115 position 0.0000 0.0000 -12.5000 mm

116 color 0.50 0.50 0.50

117 parent World

170 118 end

119

120 ### ------

121 ### 312743a,tube,pressure chamber Everything is now 25 mm in z

122 ### ------

123

124 # PrimaryTubeFlange1:

125 # ------

126 cylinder

127 name PrimaryTubeFlange1

128 radius 95.2500 mm

129 innerRadius 63.8810 mm

130 length 25.400 mm

131 material AluminumMetal

132 position 0.0000 0.0000 -37.7000 mm

133 color 0.50 0.50 0.50

134 parent World

135 end

136

137 # PrimaryTubeFlange2:

138 # ------

139 cylinder

140 name PrimaryTubeFlange2

141 radius 95.2500 mm

142 innerRadius 63.8810 mm

143 length 25.400 mm

144 material AluminumMetal

145 position 0.0000 0.0000 -149.9680 mm

146 color 0.50 0.50 0.50

147 parent World

148 end

149

150

151 # PrimaryTubeFlange3:

152 # ------

153 cylinder

154 name PrimaryTubeFlange3

155 radius 95.2500 mm

156 innerRadius 63.8810 mm

157 length 25.400 mm

158 material AluminumMetal

171 159 position 0.0000 0.0000 -517.7854 mm

160 color 0.50 0.50 0.50

161 parent World

162 end

163

164 # PrimaryTube:

165 # ------

166 cylinder

167 name PrimaryTube

168 radius 65.4685 mm

169 innerRadius 63.8810 mm

170 length 505.4854 mm

171 material AluminumMetal

172 position 0.0000 0.0000 -277.7427 mm

173 color 0.50 0.50 0.50

174 parent World

175 end

176

177 # PrimaryTubeGasA:

178 # ------

179 cylinder

180 name PrimaryTubeGasA

181 radius 63.8810 mm

182 innerRadius 0.0000 mm

183 length 505.4854 mm

184 material CerenkovGas

185 position 0.0000 0.0000 -277.7427 mm

186 color 0.50 0.50 0.00

187 #forceSolid true

188 parent World

189 end

190

191 ### ------

192 ### 312728a,pressure chamber Everything is now 530.4854 mm in z

193 ### ------

194

195 # BaseMirrorBox: The base mirror box which gets items added too

196 # ------

197 box

198 name BaseMirrorBox

199 size 165.1000 381.5080 203.0222 mm

172 200 material AluminumMetal

201 position 0.0000 -120.9294 -631.9965 mm

202 color 0.50 0.50 0.50

203 parent World

204 end

205

206 # BaseMirrorBoxExtention1: Bottom extension to cube 1st side

207 # ------

208 box

209 name BaseMirrorBoxExtention1

210 size 165.1000 203.7080 8.0264 mm

211 material AluminumMetal

212 position 0.0000 -209.8294 -526.4722 mm

213 color 0.50 0.50 0.50

214 # forceSolid true

215 parent World

216 end

217

218 # BaseMirrorBoxExtention2: Bottom extension to cube 2nd side

219 # ------

220 box

221 name BaseMirrorBoxExtention2

222 size 165.1000 203.7080 8.0264 mm

223 material AluminumMetal

224 position 0.0000 -209.8294 -737.5208 mm

225 color 0.50 0.50 0.50

226 parent World

227 end

228

229 # BaseMirrorBoxExtention3: Bottom flange 1st side

230 # ------

231 trapezoid

232 name BaseMirrorBoxExtention3

233 xset 219.075 155.5750 mm

234 yset 25.4000 25.4000 mm

235 zoff 31.7500 mm

236 material AluminumMetal

237 position 98.4250 -298.9834 -631.9965 mm

238 color 0.50 0.50 0.50

239 rotate 0.00 -90.00 0.00 deg

240 parent World

173 241 end

242

243

244 # BaseMirrorBoxExtention4: Bottom flange 2nd side

245 # ------

246 trapezoid

247 name BaseMirrorBoxExtention4

248 xset 219.075 155.5750 mm

249 yset 25.4000 25.4000 mm

250 zoff 31.7500 mm

251 material AluminumMetal

252 position -98.4250 -298.9834 -631.9965 mm

253 color 0.50 0.50 0.50

254 rotate 0.00 90.00 0.00 deg

255 #forceSolid true

256 parent World

257 end

258

259 # BaseMirrorBoxExtention5: Top Front Left Flange

260 # ------

261 trapezoid

262 name BaseMirrorBoxExtention5

263 xset 140.2080 76.7080 mm

264 yset 23.6220 23.6220 mm

265 zoff 31.7500 mm

266 material AluminumMetal

267 position -98.4250 -0.2794 -542.2964 mm

268 color 0.50 0.50 0.50

269 rotate 0.00 90.00 90.00 deg

270 parent World

271 end

272

273 # BaseMirrorBoxExtention6: Top Back Left Flange

274 # ------

275 trapezoid

276 name BaseMirrorBoxExtention6

277 xset 140.2080 76.7080 mm

278 yset 23.6220 23.6220 mm

279 zoff 31.7500 mm

280 material AluminumMetal

281 position -98.4250 -0.2794 -721.6966 mm

174 282 color 0.50 0.50 0.50

283 rotate 0.00 90.00 90.00 deg

284 parent World

285 end

286

287 # BaseMirrorBoxGasA: zero point is in the middle of the top tube dead center

288 # ------

289 threeTubeJoin

290 name BaseMirrorBoxGasA

291 radius1 63.8810 mm

292 length1 203.0222 mm

293 radius2 68.6435 mm

294 length2 318.0080 mm

295 radius3 46.3550 mm

296 length3 203.0222 mm

297 material CerenkovGas

298 position 0.0000 120.9294 0.0000 mm

299 position2 0.0000 -152.6794 0.0000 mm

300 rotate2 90.00 0.00 0.00 deg

301 position3 0.0000 -200.4314 0.0000 mm

302 color 0.50 0.50 0.00

303 parent BaseMirrorBox

304 end

305

306 # BaseMirrorBoxGasB: Bottom extention to cube gas cut 1st side

307 # ------

308 cylinder

309 name BaseMirrorBoxGasD

310 radius 46.3550 mm

311 innerRadius 0.0000 mm

312 length 8.0264 mm

313 material CerenkovGas

314 position 0.0000 9.3980 0.0000 mm

315 color 0.50 0.50 0.00

316 #forceSolid true

317 parent BaseMirrorBoxExtention1

318 end

319

320 # BaseMirrorBoxGasC: Bottom extension to cube gas cut 2nd side

321 # ------

322 cylinder

175 323 name BaseMirrorBoxGasC

324 radius 46.3550 mm

325 innerRadius 0.0000 mm

326 length 8.0264 mm

327 material CerenkovGas

328 position 0.0000 9.3980 0.0000 mm

329 color 0.50 0.50 0.00

330 parent BaseMirrorBoxExtention2

331 end

332

333

334

335 ### ------

336 ### 312746a,cover,turning mirror Everything is now -530.4854 mm in z

337 ### ------

338

339 # PlateCoverBottom:

340 # ------

341 cylinder

342 name PlateCoverBottom

343 radius 109.4740 mm

344 innerRadius 0.0000 mm

345 length 25.4 mm

346 material AluminumMetal

347 position 0.0000 -324.3834 -631.9965 mm

348 color 0.50 0.50 0.50

349 rotate 90.00 0.00 0.00 deg

350 parent World

351 end

352

353

354 ### ------

355 ### 312741a,flange, pressure Everything is now -530.4854 mm in z

356 ### ------

357

358 # PlateCoverBackBottom:

359 # ------

360 cylinder

361 name PlateCoverBackBottom

362 radius 76.2000 mm

363 innerRadius 0.0000 mm

176 364 length 12.7000 mm

365 material AluminumMetal

366 position 0.0000 -200.4314 -747.8840 mm

367 color 0.50 0.50 0.50

368 parent World

369 end

370

371

372 ### ------

373 ### 312741a,flange, pressure Everything is now -530.4854 mm in z

374 ### ------

375

376 # PlateCoverBackTop:

377 # ------

378 cylinder

379 name PlateCoverBackTop

380 radius 98.4250 mm

381 innerRadius 0.0000 mm

382 length 35.5600 mm

383 material AluminumMetal

384 position 0.0000 0.0000 -751.2876 mm

385 color 0.50 0.50 0.50

386 parent World

387 end

388

389

390

391

392 ### ------

393 ### 312729a,tube, pressure window Everything is now

394 ### -522.45900 (530.4854-8.0264) mm in z and -200.4314 mm in y

395 ### ------

396

397 # PressureWindowFlange1:

398 # ------

399 cylinder

400 name PressureWindowFlange1

401 radius 76.2000 mm

402 innerRadius 46.0375 mm

403 length 19.0500 mm

404 material AluminumMetal

177 405 position 0.0000 -200.4314 -512.9340 mm

406 color 0.50 0.50 0.50

407 parent World

408 end

409

410 # PressureWindowFlange2:

411 # ------

412 cylinder

413 name PressureWindowFlange2

414 radius 69.8500 mm

415 innerRadius 46.0375 mm

416 length 9.6520 mm

417 material AluminumMetal

418 position 0.0000 -200.4314 -381.4128 mm

419 color 0.50 0.50 0.50

420 parent World

421 end

422

423 # PressureWindowOuterTube:

424 # ------

425 cylinder

426 name PressureWindowOuterTube

427 radius 46.0375 mm

428 innerRadius 42.9260 mm

429 length 145.8722 mm

430 material AluminumMetal

431 position 0.0000 -200.4314 -449.5229 mm

432 color 0.50 0.50 0.50

433 parent World

434 end

435

436 # PressureWindowInnerTube1: Inner tube.

437 # ------

438 cylinder

439 name PressureWindowInnerTube1

440 radius 42.9260 mm

441 innerRadius 35.0520 mm

442 length 120.0404 mm

443 material AluminumMetal

444 position 0.0000 -200.4314 -436.6070 mm

445 color 0.50 0.50 0.50

178 446 parent World

447 end

448

449 # PressureWindowInnerTube2: 2nd inner tube that holds sapphire window

450 # ------

451 cylinder

452 name PressureWindowInnerTube2

453 radius 35.0520 mm

454 innerRadius 25.4000 mm

455 length 19.4564 mm

456 material AluminumMetal

457 position 0.0000 -200.4314 -486.8990 mm

458 color 0.50 0.50 0.50

459 parent World

460 end

461

462

463 # PressureWindowInnerTube3: 1.580 tapper side inner tube

464 # ------

465 cylinder

466 name PressureWindowInnerTube3

467 radius 25.4000 mm

468 innerRadius 0.0000 mm

469 length 7.6962 mm

470 material AluminumMetal

471 position 0.0000 -200.4314 -481.0189 mm

472 color 0.50 0.50 0.50

473 parent World

474 end

475

476 # PressureWindowSapphire:

477 # ------

478 cylinder

479 name PressureWindowSapphire

480 radius 25.4000 mm

481 innerRadius 0.0000 mm

482 length 5.0000 mm

483 material Sapphire

484 position 0.0000 -200.4314 -487.36700 mm

485 color 0.00 0.50 0.50

486 forceSolid true

179 487 parent World

488 end

489

490 # PressureWindowInnerTube4: 1.575 tapper side inner tube

491 # ------

492 cylinder

493 name PressureWindowInnerTube4

494 radius 25.4000 mm

495 innerRadius 0.0000 mm

496 length 6.76148 mm

497 material AluminumMetal

498 position 0.0000 -200.4314 -493.24774 mm

499 color 0.50 0.50 0.50

500 parent World

501 end

502

503

504 # PressureWindowGasA: Infront of Sapphire Window

505 # ------

506 cylinder

507 name PressureWindowGasA

508 radius 42.9260 mm

509 innerRadius 0.0000 mm

510 length 25.8318 mm

511 material CerenkovGas

512 position 0.0000 -200.4314 -509.5431 mm

513 color 0.50 0.50 0.00

514 parent World

515 end

516

517 # PressureWindowGasB: Before Sapphire Window 1.575 5 degree taper

518 # ------

519 cone

520 name PressureWindowGasB

521 outerRadius1 20.5918 mm

522 innerRadius1 0.000 mm

523 outerRadius2 20.0025 mm

524 innerRadius2 0.000 mm

525 length 6.76148 mm

526 material CerenkovGas

527 position 0.000 0.000 0.000 mm

180 528 color 1.0 1.0 1.0

529 rotate 0.00 0.00 0.00 deg

530 parent PressureWindowInnerTube4

531 end

532

533 # PressureWindowGasC: After Sapphire Window 1.580 2 degree taper

534 # ------

535 cone

536 name PressureWindowGasC

537 outerRadius2 20.3346 mm

538 innerRadius2 0.000 mm

539 outerRadius1 20.0660 mm

540 innerRadius1 0.000 mm

541 length 7.6962 mm

542 material Air

543 position 0.000 0.000 0.000 mm

544 color 1.0 1.0 1.0

545 rotate 0.00 0.00 0.00 deg

546 parent PressureWindowInnerTube3

547 end

548

549

550 # PressureWindowGasD: After Sapphire Window

551 # ------

552 cylinder

553 name PressureWindowGasD

554 radius 35.0520 mm

555 innerRadius 0.0000 mm

556 length 100.5840 mm

557 material Air

558 position 0.0000 -200.4314 -426.8788 mm

559 color 0.50 0.50 0.00

560 parent World

561 end

562

563

564

565 ### ------

566 ### 312730a,cube,oap,element 2 Everything is now

567 ### -376.5868 (530.4854-8.0264-145.8722) mm in z and -200.4314 mm in y

568 ### ------

181 569

570 # CubeOAPBox: The base oap box which gets items added too

571 # ------

572 box

573 name CubeOAPBox

574 size 139.7000 152.4000 165.1000 mm

575 material AluminumMetal

576 position 0.0000 -200.4314 -294.0368 mm

577 color 0.50 0.50 0.50

578 rotate 0.00 0.00 33.00 deg

579 parent World

580 end

581

582 twoTubeJoin

583 name CubeOAPBoxGasA

584 radius1 51.8160 mm

585 innerRadius1 0.0000 mm

586 length1 82.55 mm

587 radius2 51.8160 mm

588 innerRadius2 0.0000 mm

589 length2 137.5918 mm

590 material Air

591 position 0.0000 0.0000 -41.2750 mm

592 rotate 0.00 0.00 0.00 deg

593 position2 0.0000 7.4041 41.2750 mm

594 rotate2 90.00 0.00 0.00 deg

595 color 0.50 0.50 0.00

596 parent CubeOAPBox

597 end

598

599 ### ------

600 ### 312693a,tube,oap2,oap3 Everything is now

601 ### -294.0368 (530.4854-8.0264-145.8722-165.1000/2) mm in z

602 ### -200.4314+(152.4000/2 Cos[33])=-136.525 mm in y

603 ### 152.4000/2 Sin[33]=41.5015 mm in x

604 ### ------

605

606 # TubeOAP2OAP3:

607 # ------

608 cylinder

609 name TubeOAP2OAP3

182 610 radius 41.2750 mm

611 innerRadius 38.1000 mm

612 length 184.0738 mm

613 material AluminumMetal

614 position 91.6284 -59.3364 -294.0368 mm

615 color 0.50 0.50 0.50

616 rotate 90.00 -33.00 0.00 deg

617 parent World

618 end

619

620 # TubeOAP2OAP3Flange1:

621 # ------

622 cylinder

623 name TubeOAP2OAP3Flange1

624 radius 69.8500 mm

625 innerRadius 41.2750 mm

626 length 6.3500 mm

627 material AluminumMetal

628 position 43.2307 -133.8620 -294.0368 mm

629 color 0.50 0.50 0.50

630 rotate 90.00 -33.00 0.00 deg

631 parent World

632 end

633

634 # TubeOAP2OAP3Flange2:

635 # ------

636 cylinder

637 name TubeOAP2OAP3Flange2

638 radius 60.32500 mm

639 innerRadius 41.2750 mm

640 length 6.3500 mm

641 material AluminumMetal

642 position 140.026 15.1895 -294.0368 mm

643 color 0.50 0.50 0.50

644 rotate 90.00 -33.00 0.00 deg

645 parent World

646 end

647

648 # TubeOAP2OAP3GasA:

649 # ------

650 cylinder

183 651 name TubeOAP2OAP3GasA

652 radius 38.1000 mm

653 innerRadius 0.0000 mm

654 length 184.0738 mm

655 material Air

656 position 91.6284 -59.3364 -294.0368 mm

657 color 0.50 0.50 0.00

658 rotate 90.00 -33.00 0.00 deg

659 parent World

660 end

661

662 ### ------

663 ### 312695a,cube, oap element 3 Everything is now

664 ###-294.0368 (530.4854-8.0264-145.8722-165.1000/2) mm in z

665 ### -200.4314+(152.4000/2+184.0738) Cos[30]=17.8526 mm in y

666 ### (152.4000/2+184.0738)Sin[33]=141.755 mm in x

667 ### ------

668

669 # CubeOA3PBox: The base oap3 box which gets items added too

670 # ------

671 box

672 name CubeOAP3Box

673 size 120.65 104.7750 213.36 mm

674 material AluminumMetal

675 position 167.625 63.5177 -257.2068 mm

676 color 0.50 0.50 0.50

677 rotate 0.00 0.00 33.00 deg

678 parent World

679 end

680

681 # CubeOAP3BoxGasA:

682 # ------

683 twoTubeJoin

684 name CubeOAP3BoxGasA

685 radius1 33.2740 mm

686 innerRadius1 0.0000 mm

687 length1 69.8500 mm

688 radius2 34.0360 mm

689 innerRadius2 0.0000 mm

690 length2 96.1898 mm

691 material Air

184 692 position 3.1750 -1.5875 -1.90500 mm

693 rotate 0.00 0.00 0.00 deg

694 position2 0.0000 -2.7051 -34.9250 mm

695 rotate2 90.00 0.00 0.00 deg

696 color 0.50 0.50 0.00

697 parent CubeOAP3Box

698 end

699

700 ### ------

701 ### Detectors:

702 ### ------

703

704 # You include a macro file

705

706 ### ------

707 ### Mirrors:

708 ### ------

709

710 # MirrorA: 1st OAP mirror face is at 0 point

711 # offset+half MirrorBox= -530.4854-203.0222/2=631.9965

712 # Converter (in diagram not what we use)+optical length=607.2124+9.5250=616.7374

713 # 530.4854+203.0222/2-9.5250-607.2124 =15.2591

714 # to box length of tube converter inside face length to mirror from converter plate

715 # ------

716 oapMirror

717 name MirrorA

718 radius 63.5000 mm

719 focalLength 355.6000 mm

720 alpha 90.00 deg

721 position 0.0000 0.0000 0.0000 mm

722 rotate 0.00 0.00 270.00 deg

723 material AluminumMetal

724 color 1.00 1.00 1.00

725 parent BaseMirrorBoxGasA

726 end

727

728 # MirrorB: turning mirror same z position as Mirro A except has a 10mm offset at 45 degrees.

729 # ------

730 cylinder

731 name MirrorB

732 radius 62.4967 mm

185 733 innerRadius 0.0000 mm

734 length 5.000 mm

735 material AluminumMetal

736 position 0.0000 -195.128 -8.8388 mm

737 color 1.0 1.00 1.00

738 rotate 45.00 00.00 0.00 deg

739 forceSolid true

740 parent BaseMirrorBoxGasA

741 end

742

743 # MirrorC: 2nd OAP Mirror

744 # ------

745 oapMirror

746 name MirrorC

747 radius 50.8000 mm

748 focalLength 152.4000 mm

749 alpha 90.00 deg

750 position 0.0000 0.0000 41.2750 mm

751 rotate 90.00 0.00 90.00 deg

752 material AluminumMetal

753 color 1.00 1.00 1.00

754 parent CubeOAPBoxGasA

755 end

756

757 # MirrorD:

758 # ------

759 oapMirror

760 name MirrorD

761 radius 33.0200 mm

762 focalLength 38.1000 mm

763 alpha 90.00 deg

764 position 0.0000 0.0000 -34.9250 mm

765 rotate -90.00 0.00 90.00 deg

766 material AluminumMetal

767 color 1.00 1.00 1.00

768 parent CubeOAP3BoxGasA

769 end

770

771

772 ### ------

773 ### Mirrors Coats:

186 774 ### ------

775

776 # MirrorSurfaceA: reflective surface of MirrorA

777 # ------

778 # 1.1300 one is added to meet up with Rindex values

779 # 5.5111 shifted to 5.194520 again see above

780 opticalSurface

781 name MirrorSurfaceA

782 volume1 BaseMirrorBoxGasA 0

783 volume2 MirrorA 0

784 type dielectric_metal

785 model unified

786 finish polished

787

788 propertyTable

789 REFLECTIVITY in eV

790 1.1300 0.903

791 1.7714 0.903

792 1.8370 0.905

793 1.9076 0.909

794 1.9840 0.913

795 2.0666 0.914

796 2.1565 0.915

797 2.2545 0.917

798 2.3619 0.920

799 2.4800 0.919

800 2.6105 0.919

801 2.7555 0.920

802 2.9176 0.921

803 3.1000 0.920

804 3.3066 0.920

805 3.5428 0.920

806 3.8153 0.921

807 4.1333 0.920

808 4.5090 0.920

809 4.9600 0.921

810 5.194520 0.927

811 end

812 end

813 end

814

187 815 # MirrorSurfaceB: reflective surface of MirrorB

816 # ------

817 opticalSurface

818 name MirrorSurfaceB

819 volume1 BaseMirrorBoxGasA 0

820 volume2 MirrorB 0

821 type dielectric_metal

822 model unified

823 finish polished

824

825 propertyTable

826 REFLECTIVITY in eV

827 1.1300 0.903

828 1.7714 0.903

829 1.8370 0.905

830 1.9076 0.909

831 1.9840 0.913

832 2.0666 0.914

833 2.1565 0.915

834 2.2545 0.917

835 2.3619 0.920

836 2.4800 0.919

837 2.6105 0.919

838 2.7555 0.920

839 2.9176 0.921

840 3.1000 0.920

841 3.3066 0.920

842 3.5428 0.920

843 3.8153 0.921

844 4.1333 0.920

845 4.5090 0.920

846 4.9600 0.921

847 5.194520 0.927

848 end

849 end

850 end

851

852 # MirrorSurfaceC: reflective surface of MirrorC

853 # ------

854 opticalSurface

855 name MirrorSurfaceC

188 856 volume1 CubeOAPBoxGasA 0

857 volume2 MirrorC 0

858 type dielectric_metal

859 model unified

860 finish polished

861

862 propertyTable

863 REFLECTIVITY in eV

864 1.1300 0.903

865 1.7714 0.903

866 1.8370 0.905

867 1.9076 0.909

868 1.9840 0.913

869 2.0666 0.914

870 2.1565 0.915

871 2.2545 0.917

872 2.3619 0.920

873 2.4800 0.919

874 2.6105 0.919

875 2.7555 0.920

876 2.9176 0.921

877 3.1000 0.920

878 3.3066 0.920

879 3.5428 0.920

880 3.8153 0.921

881 4.1333 0.920

882 4.5090 0.920

883 4.9600 0.921

884 5.194520 0.927

885 end

886 end

887 end

888

889 # MirrorSurfaceD: reflective surface of MirrorD

890 # ------

891 opticalSurface

892 name MirrorSurfaceD

893 volume1 CubeOAP3BoxGasA 0

894 volume2 MirrorD 0

895 type dielectric_metal

896 model unified

189 897 finish polished

898

899 propertyTable

900 REFLECTIVITY in eV

901 1.1300 0.903

902 1.7714 0.903

903 1.8370 0.905

904 1.9076 0.909

905 1.9840 0.913

906 2.0666 0.914

907 2.1565 0.915

908 2.2545 0.917

909 2.3619 0.920

910 2.4800 0.919

911 2.6105 0.919

912 2.7555 0.920

913 2.9176 0.921

914 3.1000 0.920

915 3.3066 0.920

916 3.5428 0.920

917 3.8153 0.921

918 4.1333 0.920

919 4.5090 0.920

920 4.9600 0.921

921 5.194520 0.927

922 end

923 end

924 end

925

926 # MirrorSurfacePrimaryTube: reflective surface of PrimaryTube

927 # ------

928 opticalSurface

929 name MirrorSurfacePrimaryTube

930 volume1 PrimaryTubeGasA 0

931 volume2 PrimaryTube 0

932 type dielectric_metal

933 model unified

934 finish polished

935

936 propertyTable

937 REFLECTIVITY in eV

190 938 1.1300 0.900

939 5.194520 0.900

940 end

941 end

942 end

943

191 APPENDIX C - KINDLE PMT GEOMETRY DEFINITION

Below list the Kindle code which deﬁnes the geometry of the PMT used in the Gamma Reaction History detector.

1 # PMT.world

2 # ======

3 # Defines geometry for a Photek A3/5244A

4 # Author: Elliot Grafil

5 #

6 version 4

8 #PMT Housing: Photek A3/5244A housing

9 # ------

10 cylinder

11 name PMTHousing

12 radius 31.95 mm

13 innerRadius 0.0000 mm

14 length 60.70 mm

15 material PMTCase

17 position 0.000 0.000 28.8750 mm

18 color 0.70 0.50 0.70

19 rotate 0.50 0.00 0.00 deg

20 parent CubeOAP3BoxGasA

21 end

23 #PMT Apature: Photek A3/5244A Apature

24 # ------

25 cone

26 name PMTApeture

27 outerRadius1 11.300 mm

28 innerRadius1 0.000 mm

29 outerRadius2 6.000 mm

30 innerRadius2 0.000 mm

31 length 5.300 mm

32 material Air

33 position 0.000 0.000 -27.7000 mm

34 color 1.0 1.0 0.00

35 rotate 0.00 0.00 0.00 deg

192 36 forceSolid true

37 parent PMTHousing

38 end

40 cylinder

41 name GlassWindow

42 radius 15.00 mm

43 innerRadius 0.0000 mm

44 length 5.600 mm

45 material Air

46 position 0.000 0.000 -22.2500 mm

47 color 0.0 0.50 0.00

48 rotate 0.00 0.00 0.00 deg

49 forceSolid true

50 parent PMTHousing

51 end

53 cylinder

54 name cathode1

55 detector cathode

56 radius 15.00 mm

57 innerRadius 0.0000 mm

58 length 0.100 mm

59 material Glass

60 position 0.000 0.000 -19.4000 mm

61 color 0.0 0.50 1.00

62 rotate 0.00 0.00 0.00 deg

63 forceSolid true

64 parent PMTHousing

65 end

193