Characterization of
Mono-Energetic Charged-Particle Radiography for
High Energy Density Physics Experiments
by
Mario John-Errol Manuel
B.S., Astronomy, University of Washington (2006)
B.S., Aero/Astro Engineering, University of Washington (2006)
B.S., Physics, University of Washington (2006)
Master of Science in Aeronautics and Astronautics
at the
Massachusetts Institute of Technology
June 2008
@2008 Massachusetts Institute of Technology
All rights reserved
/7
Signature of Author: .............................
Department of Aeronautics and Astronautics
May 23, 2008
Certified by: ............ ........
Dr. Richaird D. Petrasso
Senior Research Scientist, Plasma Science and Fusion Center
Thesis Advisor
'
nA
Certified by: ............. ..........................................................
- ..........................
...........................
Professor Manue Martinez-Sanchez
Professor of Aeftnautics and Astronautics
Thesis Advisor
Accepted by: .....................................
Professor David L.Darmofal
MASSACH~•Ei
TS
tNS
Associate Department Head
OF TEOHNOLOGY
Chair, Committee on Graduate Students
AUG 0 12008VE8
LIBRARIES
Characterization of
Mono-Energetic Charged-Particle Radiography for
High Energy Density Physics Experiments
by
Mario John-Errol Manuel
Submitted to the Department of Aeronautics and Astronautics
on May 23, 2008 in partial fulfillment of the requirements for the degree of
Master of Science
Abstract
Charged-particle radiography, specifically protons and alphas, has recently been used to
image various High-Energy-Density Physics objects of interest, including Inertial Confinement
Fusion capsules during their implosions, Laser-Plasma Interactions, and Rayleigh-Taylorinstability growth. An imploded D23 He-filled glass capsule - the backlighter - provides monoenergetic 15-MeV and 3-MeV protons and 3.6-MeV alphas for radiographing these various
phenomena. Because the backlighter emits mono-energetic particles, information about areal
density and electromagnetic fields in imaged systems can be obtained simultaneously. One of
the most important characteristics of the backlighter is the fusion product yield, so
understanding the experiment parameters that affect it is essential to the future of chargedparticle radiography. Empirical studies of backlighter performance under a variety of conditions
are presented, along with proton yield parameterizations based on backlighter and laser
parameters. In order to investigate the limits and capabilities of this diagnostic, the Geant4
Transport Toolkit is introduced as the supplementary simulation tool to accompany this novel
diagnostic; benchmark simulations with experimental data are presented.
Thesis Advisor:
Manuel Martinez-Sanchez
Professor in the Department of Aeronautics and Astronautics
Thesis Advisor:
Richard D. Petrasso
Senior Research Scientist at the Plasma Science and Fusion Center
This work was performed in part at the LLE National Laser Users Facility (NLUF) supported in
part by the LLE subcontract 6917101, Defense Program subcontract 6899251, Fusion Science
Center subcontract 6897008, and NLUF subcontract 6915158.
-2-
Acknowledgements
My arrival into the field of High Energy Density Physics emerged through a series of
serendipitous events, concluding with a random stop at a physics poster session at MIT. At this
poster session I met James Ryan Rigg, who introduced me to the HEDP group at MIT, led by Rich
Petrasso. I would like to sincerely thank Ryan for the introduction to this field of research and
for all of the invaluable conversations and help in accustoming myself to a new and exciting
field of research. I would also like to thank Rich Petrasso for the 'extreme' encouragement
given to me regularly, and the late conversations of what to do next. Without the help of
Fredrick Seguin, I would never have acquired the understanding of programming and numerical
computation that I have now. I am very pleased to continue working with Fredrick in the
capacity of programming and simulation, as well as the understanding of CR39 analysis
procedures and characteristics. I am grateful to Johan Frenje and Chikang Li for their in depth
knowledge of the field, theoretically and experimentally, and hope to continue learning from
their experience and familiarity in the field. Special thanks also go to Jocelyn Schaeffer and
Irina Cashen for all of their help in the etching and scanning of the CR39, and imbuing some of
that knowledge to me to lighten the load. I would also like to thank Sean McDuffee for his help
and side conversations regarding CR39 characteristics as well as programming techniques.
Having the opportunity to run new and exciting experiments only comes with access to a great
facility. None of this research would have been possible without the elaborate help from the
OMEGA operations crew, but specifically Sam Roberts and Michelle McCluskey for all of their
assistance and support in the setup and execution required to perform these experiments.
However great the experiment, or amazing the senior scientists, the fact is that it must
be an enjoyable experience, and that means good officemates. I would like to sincerely thank
Dan Casey for always being there to impart his knowledge here and there, but most
importantly, the numerous discussions of physics, computer simulations, and life in general that
take place, in the office and out. I would also like to thank my new officemate, Nareg Sinenian,
for his help in programming and electronics, which will prove invaluable in the future; also now
that there are three of us it makes the discussions, and arguments, in the office that much
more interesting.
Throughout the endeavors of my education here at MIT, I have required continual
support. I thank my girlfriend, Eleonora Ottoboni, for her constant reinforcement through this
adventure, and hope she can bare it for another few years. Naturally, I wouldn't be where I am
today without the love and support of my parents, Paul Manuel and Rebecca Purdy, and I thank
them for everything they have given me, and for their continued encouragement for what I am
doing. And last, but certainly not least, I sincerely thank Bryan Henderson for his help with the
editing process of this document.
-3-
Table of Contents
List of Figures ....................................................................................................................
6
List of Tables..........................................................................................................................
10
1
2
1.1
High Energy Density Physics ............................................................................................ 11
1.2
Inertial Confinem ent Fusion ............................................................................................ 13
1.3
Outline .............................................................................................................................
2.1
Geom etric Setup..............................................................................................................
17
2.2
Backlighter ..................................................
18
5
............................................... 18
2.2.1
Backlighter Param eters........................................
2.2.2
Fusion Produced Charged Particles ..................................... ..................
2.2.3
Directly Driven Exploding Pusher M odel ........................................
CR39 Plastic Track Detector........................................
19
.......... 20
............................................... 22
W hat is M ECPR sensitive to? ...........................................................................................
24
3.1
The Im portance of pR in IFE.............................................................................................
24
3.2
Electrom agnetic Fields in HEDP ............................................................................
25
3.3
Charged-Particle Coulom b-Scattering .....................................
....................26
3.3.1
Physics of Coulom b Scattering........................................................................
3.3.2
Param eterization of M CS in Cold M atter............................... .....
3.4
4
14
Radiography Overview ............................................ ................................................... 16
2.3
3
11
Introduction .................................................
Measurem ents Using MECPR ............................................................
26
............ 28
........................ 30
3.4.1
Areal Density ............................................................................................................. 30
3.4.2
Electrom agnetic Fields .............................................................................................. 31
3.4.3
Resolution Lim its..............................................
................................................... 34
Backlighter Perform ance .................................................................................................
.................................................. 36
4.1
Em pirical Data Analysis............................................
4.2
The Im portance of Particle Statistics ................................
4.3
Sam ple Radiographs ...............................................
...............
.............
........... 39
................................................... 40
Geant4 Transport Toolkit ................................................................................................
~4~
36
43
6
........................... 43
5.1
Geant4 Physics Packages ................................................................
5.2
Current Status of Benchmark Simulations .....................................
...........
45
5.2.1
Unimploded Capsule ...............................................................................................
46
5.2.2
Unim ploded Cylinder ..............................................................
............................ 48
Conclusions and Future Work ..........................................................................................
Appendix A: Coulomb Collision Derivation .....................................
50
..............
51
A.1
Solution to the 2-particle Problem ...........................................
A.2
Energy Loss ..................................................................................................................
53
A.3
Rutherford Cross Section.............................................................................................
54
............... 51
Appendix B: Scattering Parameterization Data and Plots......................................
.
57
Appendix C: Backlighter Parameterization Data and Plots ..................................................... 60
Appendix D: Geant4 Benchmark Experimental Data ..........................
o..........
D.1
Experimental Data for OMEGA shot 46531 ........................................
D.2
Experimental Data for OMEGA shot 45953 .........................................
..............
71
................ 72
.......... 73
Appendix E: Acronyms ...........................................
74
Works Cited ......................................................
75
-5-
List of Figures
Figure 1-1: Physical phenomena which exist in the High Energy Density Physics regime. This
figure does not include dynamic processes which make up a large portion of HEDP experiments
such as shock waves, material ablation, radiative cooling, etc. (2). Regions accessible by the
OMEGA facility are shown, as well as what will be accessible by the National Ignition Facility
(NIF) (28) currently under construction .................................... ............................................. 12
Figure 2-1: Schematic diagram of a general MECPR setup, including the three major elements:
17
backlighter, subject, and detector pack ..........................................................
Figure 2-2: (a) Charged particle spectra taken from OMEGA shot 20297. The capsule used for
this shot was larger and had more energy on target than typical backlighters, but the yield
proportionality is the same for similar backlighter parameters. (b) Typical temporal emission
spectra (arbitrary units on right axis) with overlain laser pulse power (TW/beam on left axis),
this particular case shows a burn duration with a FWHM of "130-ps ...................................... 20
Figure 2-3: (left) Track Diameter vs. Proton Energy curves at three different etch times in 80*C
6.0 molar NaOH. The estimated energy and yield of the particle of interest dictates the etch
time required for a given piece. Etching is also used to bring the real track signal 'up above', in
contrast, the intrinsic noise on the piece, however care must be taken not to etch too far, or
tracks will be etched away for shorter range particles such as the DD-protons and D3 He-alphas.
(right) Actual microscope frame of DD-proton tracks on CR39. The image is 410 x 310 Itm (18).
........................................... 2 2
.........................................................................
Figure 3-1: Equation 3.9 plotted against exit angle 6 for a 10-MeV proton into Tantalum (Z=73).
The Rutherford Cross Section obviously shows that Coulomb scattering will be dominated by
small angle deflections. The cross sections at very low exit angles are many orders of
magnitude higher than at higher angles. For this particular case, at 6 = rt/100 the slope begins
27
. . .....
to flatten out...... ...................................................................................................
Figure 3-2: Schematic of a simple scattering simulation. Average energy loss, energy straggle,
and exit angle 6, were parameterized to incoming energy, atomic number of incident particle
and scattering substrate, areal density, and scattering substrate atomic mass ....................... 28
Figure 3-3: This diagram shows a region of constant field, E- or B- (blue), and the effective
direction of force (red) acting on the charged particle, which enters with a velocity vi, and
leaves at an angle 6 with velocity vf. Because these particles are moving extremely fast, the
change in speed is negligible. a) A constant E-field forces the particle into a parabolic trajectory
across the field region accelerating the particle parallel to the field. b) A constant B-field
directed out of the page directs the particle in a circular path across the field region ............ 31
Figure 3-4: A generic schematic used to derive a relationship between the exit angle from the
subject area and the measurements made on the detector. The length of the interaction region
-6-
in the subject is much smaller than the dimensions of the imaging system, so that demagnifying
the displacement using M will not distort the measurement at the subject appreciably.......... 33
Figure 3-5: This schematic emphasizes the three main sources of image blurring in MECPR:
finite source size, scattering in the subject, and broadening in the detector. Each mechanism
can be characterized by the convolution of the image with a Gaussian parameterized by a 1/e
radius; Rsrc, Rsub, and Rdet for the source, subject, and detector respectively .......................... 34
Figure 4-1: (left) OMEGA shot 46528 with 15-MeV protons incident at the subject at 1.58-ns
with a total yield of 0.45*108. (right) OMEGA shot 46529 with 15-MeV protons incident at the
subject at 1.56-ns with a total yield of 3.56*108 (individual image width is "2.8-mm at the
subject plane). In the fluence radiographs darker indicates higher fluence, while lighter colors
indicate less fluence. These images illustrate very well what a factor of ~8 difference in particle
yield can do to an image. For our typical MECPR setup, the detector is"25-30-cm away from
the source, we hope for a minimum yield on the order of ~108; this was achieved for shot
46529, but not 46528. It is essential for the success of MECPR that the particle yields attain this
order of magnitude. Without proper statistics useful information will be lost in the noise ..... 39
Figure 4-2: (left) OMEGA shot 46531, a 15-MeV proton fluence radiograph of an unimploded
Fast-Ignition style target. The outside diameter of the capsule is "430-pm in the subject plane.
The gold cone clearly scatters out all of the protons and even the small cone inside the.capsule
can be seen. (right) OMEGA shot 46529, a 15-MeV proton fluence radiograph 1.56-ns after the
onset of the laser pulse of a cone-in-shell target capsule. The central fluence peak is attributed
to an inwardly directed electric field and the outer striated structures are theorized to be
established by complex magnetic field structures frozen into the plasma blow off; the scales are
equal the sam e in both im ages ..................................................................................................... 40
Figure 4-3: The above series of radiographs were taken on different shot days at the OMEGA
facility (shot numbers above radiographs), but used identical laser and plastic foil parameters.
The line plot on the bottom of the figure shows the typical 1-ns square pulse with arrows
indicating the arrival time of the imaging protons and their corresponding fluence radiographs.
During the laser pulse, it can be seen that the bubble structure stays fairly coherent and
symmetric, growing in time. Then, after the laser pulse the bubble decays away in a somewhat
chaotic and asym metric fashion...........................................................................................
. 41
Figure 5-1: (left) This plot displays the azimuthally averaged line outs of an unimploded
capsule, with similar dimensions to that of shot 46531, using three different physics packages
on Geant4. The measured outer diameter of the capsule, 429.1-pm is also shown, and seems
to coincide with the inflection points of the curves. (right) From top to bottom, simulated
fluence radiographs using the LHEP_BERT, PRSimPhys-Old, and PRSimPhys-New physics
packages. The simulations were done using a total proton yield of 2.31*108 with a sourcesubject distance of 1-cm and a source-detector distance of 25-cm .................................... 44
~7~
Figure 5-2: A schematic of the standard MECPR setup, made using the visualization software
WIRED (24) supplied to users of Geant4 from the Geant4 website. As stated earlier, the
simulation is setup to have the user modify the backlighter and detector parameters, as well as
change the subject to be imaged. The two benchmark simulations that will be presented are
those of a spherical shell (left) and a hollow cylinder (right), however other standard subjects
include meshes, waved foils, and capped cylinders, to name a few. Of course the code is a
work-in-progress so other subjects will be added later .......................................
........ 46
Figure 5-3: Azimuthally averaged radial lineouts for experimental data (OMEGA shot 46531),
simulation with experimentally measured yield, and simulation with a factor 10 higher yield;
the capsule edge isalso shown in this plot. When taking radial lineouts, the statistics get worse
at smaller radii because there are less particles at a given radius and for this radiograph there
was also some noise on the CR39 piece near the center of the capsule; for these reasons the
inner radii are less important in matching experiment with simulation............................ 47
Lineouts for experimental data (OMEGA shot 45953), simulation with
Figure 5-4:
experimentally measured yield, and simulation with a factor 10 higher yield. The cylinder edge
is also shown in this plot. The experimental particle statistics for this shot were quite poor, but
comparisons between the data and simulations can still be made, and some insight gained.... 48
Figure A-1: Schematic diagram of a Coulomb collision with important quantities labeled. To
analyze the collision, the coordinate system isput into the rest frame of the field particle, which
therefore, is stationary (infinite mass) and the test particle will have the relative velocity
(reduced mass). The particles have atomic numbers Zt and Zf with mass mt and mf for testparticle and field-particles, respectively. The schematic is drawn for two like-charged particles,
but the analysis is the same for oppositely charged particles; the trajectory of the test particle
............. 51
would just be flipped about the horizontal axis .........................................
Figure A-2: Schematic used in deriving the Rutherford Cross Section. Particles which come
through the impact parameter ring on the left, must come out in the scattered ring on the right.
The RCS defines the probability for a particle to end up at a given solid angle. To calculate a
total cross section the RCS must be integrated over all 4Tr Steradians (sr); also note that e is
55
now the exit angle, the subscript 'final' has been dropped ...........................................
Figure B-1: The three preceding graphs are simply the simulated data on the x-axis, and using
the same independent variables, the parameterized calculation of the dependent variables on
the y-axis: average energy out, energy straggle, and scattering exit angle. The one-to-one line,
where the parameterized fit value equals the simulated data exactly, is also shown on each
plot. ............................................................................................................................................. 59
Figure C-1: The twelve preceding graphs show the comparison between the parameterizations
and the data for both the proton and neutron yields (proton yield comparisons on the left and
neutron comparisons on the right). The one-to-one line is displayed in each plot as well, and
represents a perfect fit to the data. Error bars on the parameterized quantities were derived
-8-
from the average percent error of the fit, proton yield measurement errors are ~50%, and
neutron yield measurement errors are ~10%. Overall, most of the parameterizations fit the
data well, but more work and data will be needed for a more rigorous analysis, and will be
pursued during m y Doctoral work ................................................................................................ 64
Figure D-1: (top) Contrast vs. Diameter diagram in logarithmic contour form. There are two
distinct peaks, one high in contrast, the other low; the low contrast peak is the signal, and can
be generally encompassed by the contrast limits of 0 - 40% and diameter limits of 2.5 - 20-pm.
The upper limit in contrast is chosen by the minimum between the two peaks (where the signal
begins to be overtaken by the intrinsic noise). (bottom left) Final fluence radiograph for OMEGA
shot 46531, darker color implies higher fluence. The black spots down the image are intrinsic
noise that I couldn't remove without losing some signal, so I left them, but they have no
physical significance. The image has also been cone-smoothed with a radius of three to
eliminate high frequency statistical noise. (bottom right) The same final radiograph with the
shaded portion covering azimuthal angles from -40 - 210", the region used to find the
azimuthally average radial lineout for benchmarking with Geant4 ..................................... 72
Figure D-2: (top) Contrast vs. Diameter diagram for OMEGA shot 45953 in logarithmic contour
form. Again, the contour peak at lower contrast is the signal. For this image, the contrast limits
chosen were 0 - 35% with a diameter range of 2 - 18-pm. (bottom left) Final product
radiograph using the limits determined from the Contrast vs. Diameter plot. A cone-smoothing
of radius three was applied to the image. The high fluence band, in line with the stock holding
the cylinder, is a product of some kind of electromagnetic field present, it is not yet well
understood, but does affect that portion of the radiograph. (bottom right) The swath used to
construct the lineout is shown on the final radiograph. It is averaged across the width and
plotted as a function of length along the swath. I attempted to avoid the high fluence area or
the stock in order to only account for scattering through the cylinder shell........................... 73
~9-.-
List of Tables
Table 2-1: The two fusion reactions used to create source particles for MECPR. The reactants
are assumed to be at thermal energies, and that the exothermic reactions supply kinetic energy
to the products in accordance with conservation of energy and momentum ......................... 19
Table 3-1: This table shows relevant data pertaining to the scattering and straggling
parameterizations mentioned above. The residual and percent errors are ideally zero, and the
R-squared value is ideally 1 for a perfect fit to all of the data. Plots of the SRIM simulated data
and fit data are show n in Appendix B........................................................... ......................... 29
Table 4-1: This table gives the form of the equations used in the parameterization of the
proton yield for MECPR. The nominal values of the independent variables are tshell = 2.0 Plm,
2, and PD2/P3He = 0.5. However,
Dout = 400 plm, EonTarg = 10 kJ, Eflux = 0.02 J/lm
these values are
never exact, and the implications of these deviations from the nominal can drastically change
the proton yield. Furthermore, the number of lasers and the energy per laser beam is not
always the same. For example, Fit 5 has the lasers incident on the capsule from the top and
bottom (Pole Driven), and this greatly changes the implosion dynamics ................................. 37
Table B-i: The table below gives the 50 data points used in the power regression fit for the
scattering parameters: <Eout>, GEout, and <0>. The Monte Carlo program SRIM was used with
the independent variables shown on the right of the black bar with 10,000 particles for each
simulation. The four dependent variables, on the right of the black bar, were calculated for
each simulation. Matlab was used to fit power law functions to each of the dependent
variables. Only protons and alpha particles were used as incident beams, and the areal density
was used in the fitting process instead of the actual density of the target, because areal density
is referred to more often than density, since the actual density of a subject may not be known
57
during a dynam ic process............................................... ...............................................
Table C-1: This table gives a complete list of parameterization coefficients for proton and
neutron yields from MECPR backlighters. Fits for similar laser parameters are displayed one on
top of the other for a direct comparison of fits between proton and neutron yields ............. 61
Table C-2: This table gives a complete list of all thin glass D23He-filled backlighter capsules since
2005. Some data were not gathered before the shot, and hence will never be measured; these
data are represented by a -1. Not all of these data were used in the parameterization of the
proton and neutron yields, but the most pertinent laser configurations were parameterized.. 65
- 10~
1
Introduction
In grade school everyone istaught about the three states of matter: solid, liquid, and gas;
each evolving from the previous, respectively, by adding more energy. As we continue to add
energy to a gas, the electrons in orbit about the nucleus gain enough energy to be stripped
from their bound states in neutral atoms. Through this process of separation of positive nuclei
(ions) and negative electrons, known as ionization, a new state of matter called plasma is
realized.
Because of the high ionization potentials of neutral atoms, plasmas are intrinsically hot
substances. For example, the ionization potential of hydrogen is 13.6-eV ("160,000 K or
particle thermal energy of ~2*10 -18 J)i. These extreme temperatures, ranging from hundreds of
thousands to hundreds of millions of degrees Kelvin, coupled with extremely high particle
densities, ~1024 - 1026 particles/cm3 (compare with air at STP ~1019 molecules/cm 3 ) leads to a
physical regime where plasmas exist at extremely high energy densities. This physical regime is
known as High Energy Density Physics (HEDP).
In Section 1.1 HEDP will be defined quantitatively and described in more detail.
Examples of relevant phenomena in the HEDP regime are discussed briefly as well as a short
history of the hardware needed for experimentalists to explore this new realm of physics.
Section 1.2 gives a brief overview of Inertial Confinement Fusion (ICF) (1) basics and how it is
strongly coupled to Mono-Energetic Charged Particle Radiography (MECPR). This chapter
finishes with an outline of this thesis in its entirety.
1.1
High Energy Density Physics
HEDP is defined as a physical system whose energy density is greater than 105 J/cm 3 or
1011 Pa (1 Mbar)(2). Physical phenomena in this regime exist naturally in the universe in solar
and gas-giant cores, supernovae, neutron stars, black hole accretion disks, etc. or man-made
systems such as Inertial Fusion Energy (IFE) plasmas and high-intensity-laser induced plasmas.
Figure 1-1 was adapted from a figure in the NRC Report Frontiers in High Energy Density
Physics: The X-Games of Contemporary Science which was published in 2003 and shows
relevant areas of study which exist in the HEDP regime (3). However, Figure 1-1 does not show
dynamic processes, but still gives a good overview of current research areas of interest in HEDP.
The electron volt (eV) is used throughout this thesis when referring to temperatures (thermal energies) as
well as kinetic energies; the following conversions may be useful:
1-eV= 11,605 Kelvin; 1-eV= 1.6*10-19-Joules
-
11
-
20
25
log n(H) [m-]
30
35
0X
0
-2
-10
-5
0
log p [g/cm3]
5
10
Figure 1-1: Physical phenomena which exist in the High Energy Density Physics regime. This
figure does not include dynamic processes which make up a large portion of HEDP
experiments such as shock waves, material ablation, radiative cooling, etc. (2).
Regions accessible by the OMEGA facility are shown, as well as what will be
accessible by the National Ignition Facility (NIF) (28) currently under construction.
Energy densities of this magnitude were not available to investigate by experiment until
the early 1900s. The advent of the particle accelerator in the 1930s gave physicists the
hardware needed to energize and collimate particle beams. By focusing high energy particle
beams onto stationary targets, the HEDP regime could be experimentally investigated. This led
to the concept of beam fusion, which was found to be an extremely inefficient means to
achieving fusion energy because of the large particle losses and minimal fusion reactions.
Subsequently in 1960 the first Light Amplification by Stimulated Emission of Radiation (laser)
was demonstrated by Theodore Maiman at Hughes Research Laboratories and paved the way
towards higher power laser systems (4).
Laser technology has since developed to the point of achieving relatively high intensities
("kJ/mm 2 = 109 J/m2 on the OMEGA Laser (5)) and ultra short pulse durations ("fs = 10-15 s). In
-
12-
today's laser systems, one talks in Terawatts (1012 W) or Petawatts (1015 W) of power because
of the high energies delivered in such short timescales. These high power lasers are used to
create environments in which HEDP phenomena can be studied, create spectra of X-rays or
protons for radiography, and compress ICF fuel capsules to high densities and temperatures
whereby fusion reactions occur and release copious energy.
1.2
Inertial Confinement Fusion
In 1972 John Nuckolls sparked the idea to pursue fusion energy and ignition through
laser compression of a fuel capsule to thousands of times liquid density (1). The Inertial
Confinement Fusion approach to fusion energy is conceived by the compression of a spherical
target capsule through laser irradiation at the surface which results in a spherical rocket
implosion of the fuel capsule. The term 'ignition' refers to a capsule whose DT-alphas are used
to heat the remainder of the fuel in an outward propagating alpha-wave burn without the need
for further outside power input. Nuckolls' initial estimate of the energy needed to achieve
ignition was insufficient due to the presence and prominence of instabilities, both of a
hydrodynamic (Rayleigh-Taylor, Richtmyer-Meshokov, etc.) and Laser-Plasma-Interaction (LPI)
(2-w, 3-w, etc.) nature during the compression of the capsule (6). Most research in Inertial
Fusion Energy (IFE) since conception in 1972 has been focused on the understanding and
mitigation of these instabilities in search of a functioning fusion reactor design. There are
currently three main concepts on how to efficiently compress and ignite the fuel: direct drive,
indirect drive, and fast ignition.
All three concepts for IFE involve energy deposition by high powered pulsed laser
systems. However, the method in which the energy is deposited to the fuel varies. Direct drive
implosions involve the irradiation of the spherical target surface by direct illumination of the
laser pulse on target. This causes ablation at the surface outwards which, by Newton's Third
Law, forces the rest of the shell and fuel inwards, creating a spherical rocket, heating the
central hot spot and compressing the fuel around it. Indirect drive involves the lasers being
incident upon the inside of a high-Z (high atomic number), cylindrical object called a hohlraum.
The irradiation of the inner hohlraum wall converts the laser energy to black body emission Xrays which ablates the spherical target surface and leads to the hot spot in the center in a
similar fashion as direct drive. By using the black body X-rays, the irradiation on the target
surface is more uniform than direct illumination. Fast Ignition (FI) capsules are designed with a
high-Z material cone partially inside a spherical capsule with the flattened cone tip near the
center of the capsule. FI is similar to direct drive in that the lasers are incident directly on the
capsule, however the high-Z cone is used to shield a path for an ultra-short high intensity laser
~ 13
pulse which irradiates the inside of the cone and forces relativistic electrons into the central hot
spot igniting the fuel. For purposes of this thesis all three IFE concepts are introduced because
MECPR has been, or will be used, to examine dynamic processes relating to each.
1.3
Outline
Mono-Energetic Charged Particle Radiography (MECPR) has proven to be an unmatched
diagnostic in characterizing HED plasmas and resulting electric and magnetic field structures(7).
An understanding and characterization of the backlighter performance as a source of monoenergetic charged particles is essential in the continued success of MECPR. This thesis covers
two avenues of investigation into the backlighter: empirical analysis of backlighter
performance based on D-3 He yield and simulation of backlighter parameter impact on
radiographs. It is expected that a better understanding of backlighter performance will improve
radiograph quality and reproducibility.
Chapter 1 gives a brief overview of HEDP as a scientific field and what experimental
hardware made probing this regime of physics possible. There is a brief introduction to IFE and
the three main concepts for achieving ignition, as well as this outline.
Chapter 2 includes a general overview of MECPR; how a typical geometry looks and how
all the pieces work together. A detailed description of the backlighter parameters and typical
spectra are discussed, as well as a brief description of the CR39 plastic track detectors.
Chapter 3 contains brief descriptions of the physical phenomena that we observe using
MECPR and how we can calculate quantitative measures from the radiographs. The crucial ICF
parameter pR is described and how it is measured using MECPR, as well as how quantitative
measures of electromagnetic fields can be made.
Chapter 4 provides an empirical analysis of backlighter performance based, primarily, on
D-3 He proton yield. Which backlighter parameters most impact the proton yield are discussed,
as well as a description and presentation of a regression model fit for proton yield. This chapter
finishes with a brief display of some experimental MECPR images.
Chapter 5 discusses the workings of Geant4 as a simulation tool for MECPR. A
discussion of the different physics packages are given, and their impact on the use of Geant4.
Current benchmark simulations are compared with experiments and discussed.
-~14~-
Chapter 6 ends the thesis with the conclusions drawn from these studies and the
impacts on future MECPR experiments. The future direction of this line of study is also stated,
as I will continue in this line of research for my Doctoral Thesis.
Appendices are included after Chapter 6 and contain reference material, experimental
data used in this thesis, as well as a list of acronyms that are used throughout. All works cited
within are presented at the very end of this document.
-~15~-
2
Radiography Overview
Radiography, by definition, is the process of imaging with radiation other than visible
light. X-ray radiography, is probably the most familiar and widely used. X-rays are attenuated
by high density materials, such as bone, but pass through lower density materials, soft tissue,
unaffected, and the resultant image is a shadowgraph of the subject being imaged-an X-ray
one might see at the doctor's office. Charged particle radiography functions in a similar
manner, except that charged particles lose energy, to first order, as a function of areal density,
which is defined as the path integrated density along the particle's trajectory through the
subject. With regard to physics applications, charged particles have an advantage over
photons, sensitivity to electromagnetic fields; however charged particles are also scattered
more in materials than photons. Therefore, charged particles have simultaneous sensitivity to
electromagnetic fields and density fluctuations with some sacrifice of spatial resolution,
whereas radiography using electromagnetic radiation is sensitive only to density perturbations.
Charged particle radiography began by using protons created by an intense short laser
pulse incident onto a thin foil target (8), (9), (10), (11). When incident on a foil, the laser
produces a plasma bubble, as well as accelerates fast electrons from the front foil surface
through the material. Protons are also excited on the front surface, but are 'pulled' by the fast
electrons and both exit the foil on the opposite side; the magnetic field generated by the fast
electron population serves to focus the electron beam while the proton beam is slightly
scattered upon exiting of the foil. Protons emitted in this fashion have a continuous
exponential spectrum with an endpoint-energy dependent on the incident laser intensity, but
can reach above 50-MeV. When using charged particle radiography with a spectral source, the
image receptors are either stacks of radiochromic film or CR39 (a plastic track detector) with
intermittent filtering between layers. This method was the first approach to charged particle
radiography, and was the only method until the High Energy Density Physics division of the
Plasma Science and Fusion Center at MIT developed a technique for producing a monoenergetic proton source -a backlighter- for radiography (the reader isencouraged to reference
(8), (9), (10), (11) for further information regarding spectral proton radiography).
The backlighter source, discussed more in Section 2.2, used in mono-energetic charged
particle radiography emits particles, not exponentially, but Gaussian with a deviation from the
mean of only a few percent (12), (13). It consists of a thin glass spherical shell filled with D2,
molecular deuterium, and 3 He, the light isotope of helium, typically "400-jim in outer diameter
with a shell thickness of ~2-im SiO 2 (glass). This small capsule is compressed in the direct drive
fashion, similar to an IFE capsule, by "20 laser beams at the OMEGA laser facility in Rochester,
NY at the Laboratory for Laser Energetics (LLE). The laser shock-compresses the fuel, deuterium
-16
-
and helium-3, to a high enough temperature and density for fusion to occur, and the fusion
products are the particles used to radiograph the subject. Since we know the birth energy of
these particles, and can measure the energy at the detector, information about the areal
density in the subject can be inferred. Furthermore, this allows for the measurement of
electromagnetic fields, which deflect the particles near the subject, through deflectometry
techniques. More information concerning how measurements are made using MECPR is
discussed in Section 3.4.
2.1
Geometric Setup
The general geometric setup for all MECPR experiments is the same, see Figure 2-1; it
consists of three components: backlighter, imaged subject, and detector pack. This setup
creates an imaging system with a magnification defined by the parameters of the specific
experiment
CR39 for
15-MeV
protons
D
18
9for
eV protons
and
3.5-MeV alphas
Figure 2-1: Schematic diagram of a general MECPR setup, including the three major elements: backlighter,
subject, and detector pack.
The magnification, M, from a point source is defined by the system parameters: Ldet [cm], the
distance from the subject plane to the detector pack, and Lsub [cm], the distance from the
source to the subject plane through the relationship:
M =
Ldet
Lsub+Ldet
- 17 -
(2.1)
The experimentalist has a certain freedom in choosing the magnification of the experiment
based on physical limitations in the chamber and an expected particle yield of the backlighter
which falls off as "~r2; the quality of the radiograph increases with particle yield up to the
saturation point of the detector.
2.2
Backlighter
The source of charged particles used in MECPR is emitted from an imploded thin-glass
spherical-shell target filled with D23 He gas. This backlighter is imploded using "20 beams' on
the OMEGA Laser at LLE in Rochester, NY which deposits "500-J/beam of energy on the target
surface. The fuel inside is heated by the inward driven shock, and compressed by the shell
mass that was not ablated away by the laser. The two most crucial parameters in
characterizing the backlighter implosion are the D-3He 15-MeV proton yield (YD3He-p) and the ion
temperature (Ti). Both of these values depend on many other factors, and are themselves
related through the D-D neutron yield (YDD-n).
2.2.1
Backlighter Parameters
The quality of backlighter performance for a specific shot strongly depends on the
physical characteristics of the backlighter capsule in addition to the interaction with the
OMEGA laser. The physical features of the backlighter which are to some extent controllable
are fill pressure of D2 and 3He, glass-shell thickness, and capsule diameter. The independent
laser parameters are pulse shape, number of beams on target, energy per beam, and laser
focus where all four contribute to the total on-target-energy. With all of this in mind, the
characterizing parameters of the backlighter as a source are YD3He-p, YDD-n, and the ion
temperature; of which only two are dependent. The third parameter can be calculated by the
ratio of the volumetric reaction rate relationships:
RD3He-P
= nDn3He(OrV)DHe.P
RDD-n='
(O-V)DD.n
L1s
[
]
(2.2)
(2.3)
Backlighters have been imploded with as little as 6 beams, however typically the number of beams incident on
the backlighter is between 17 - 21
-18 -
where no and n3He [1/cm 3] are the number density of deuterium and helium-3 respectively, and
3
(oV)D3Heand (ov)DDare the reactivities [cm /s], averaged over a Maxwellian distribution in
velocity for the D-3He-proton and DD-neutron reactions respectively.
The backlighters are designed to have equal numbers of deuterium and helium-3 nuclei
to optimize the yield. Because the yield is proportional to the reaction rate, and both gases
occupy the same volume, YDD-n and YD3He-p have the following relation:
YDD-n = YD3He-p
(O'V)DD-n
1l
(2.4)
The reaction rate is a strong function of ion temperature only, and therefore this equation
relates the three parameters used to characterize the backlighter as a source. Because of the
compression of the fuel, the fusion reactions take place in a much smaller volume than the
unimploded fuel occupies; theoretically, the source takes the form of a 3D-Gaussian in space
with a typical 1/e radius of -30 pm (14), (15).
2.2.2
Fusion Produced Charged Particles
The three particles of interest in MECPR come from the D-D and D-3 He reaction, see
Table 2-1. These particles are created in the burn region of the backlighter and serve to image
the HEDP subject of interest. Since each particle has a different energy-to-mass ratio, they
arrive at the subject at slightly different times. This allows data to be accumulated at different
instances, which is vital for the study of dynamic processes.
Table 2-1: The two fusion reactions used to create source particles for MECPR. The reactants are assumed to be
at thermal energies, and that the exothermic reactions supply kinetic energy to the products in
accordance with conservation of energy and momentum.
Reaction
D+ D
-- T (1.01 MeV)+ p (3.02 MeV)
D + 3He -
a (3.6 MeV) + p (14.7 MeV)
Label
Q (MeV)
D-D
4.03
D-3He
18.3
The actual birth energies of these particles deviate by a small amount from their nominal
values; Doppler broadening occurs in the source and isdependent on the ion temperature (15)
by:
o2
Ti = - [keV]
~ 19-
(2.5)
where C [keV] is 5880 for D-3 He reactions and 1510 for D-D reactions, and a [keV] is the
Doppler-broadened width. For example, if the source ion temperature is 10-keV, this gives a
Doppler broadening of 1.6%, 6.7%, and 4.1% for D3He-protons, D3He-alphas, and DD-protons,
respectively; therefore the source is considered to be monoenergetic. This method, however,
cannot be used to find an absolute ion temperature, only an upper limit, because the spectrum
is also vulnerable to other causes of line broadening including different pathlengths through the
shell, time-varying acceleration, and pR evolution on the timescale of the burn duration (16).
The source emits, temporally, as a pulse lasting ~150-ps, meaning that we can only probe
phenomena in a regime where the dynamic timescale is greater than this pulse duration. This
provides a lower limit on the temporal resolution of MECPR. An actual birth spectrum from a
thin glass capsule with similar parameters to a nominal backlighter is given in Figure 2-2 along
with a particle burn history with overlain laser pulse.
In
no
a)
n-n
Proton
E
0u.
0.5
0.4
'-I
*5
o
U
D-3He
Proton
D-'He
0
Alpha
a-- I-i?
,
0
"'
.
nl""I"'
i
5
10
0
15
n
20
-500
0
0
500
1000
1500
Time (ps)
Energy (MeV)
Figure 2-2: (a) Charged particle spectra taken from OMEGA shot 20297. The capsule used for this shot was
larger and had more energy on target than typical backlighters, but the yield proportionality is
the same for similar backlighter parameters. (b) Typical temporal emission spectra (arbitrary
units on right axis) with overlain laser pulse power (TW/beam on left axis), this particular case
shows a burn duration with a FWHM of ~130-ps.
2.2.3
Directly Driven Exploding Pusher Model
Exploding pusher targets were widely used in early direct drive IFE experiments. The
attractive features of exploding pusher targets included the insensitivity to instabilities of
present, typical IFE capsules such as the Rayleigh-Taylor (RT) and electron preheat instabilities
(17). However, because of its intrinsically different dynamic structure, the exploding pusher
- 20 -
could also never be used to reach ignition conditions because the density of the compressed
fuel will never become great enough to sustain the propagation of an alpha-heating-wave.
In 1979, M. D. Rosen and J. H. Nuckolls derived a theoretical model to calculate the
neutron yield of a DT exploding pusher (17). That form has been re-derived for a thin glass
equamolar D-3He filled exploding pusher backlighter, and takes the form:
YD3He-p
= 5.6925 * 1017 R1 rl• (O')D3Hn-p
(2.6)
where Ro [Vlm] is the unimploded radius of the fuel volume, n = pf/po is the compression ratio,
(or)D3He-p [cm 3/s] is the Maxwellian-averaged reactivity of the D-3 He reaction, and Ti [keV] is
the ion temperature during charged particle emission. Because the reactivity is only a function
of Ti and Ro is known, the only two parameters that must be pinned down are n and Ti (the
reader is encouraged to reference (17) for a deeper background of these derivations). The
compression ratio r is related to the density of the glass shell Pshell [g/cm3 ], the average
unimploded density of the fuel po [g/cm3], the shell thickness AR [Vlm], and Ro [lim] by:
_
4 A..R)
(1 + ~
(2.7)
This formula is based on conservation of mass, with half of the shell mass ablated away, as a
first approximation, and was iterated upon using 1-D simulations to come to its final form. To
find a theoretical expression for Ti, knowledge of the energy absorbed by the capsule is needed.
In reference (17) the laser pulse was assumed to be Gaussian and a method was devised to
estimate the ion temperature based on that pulse shape. However, for the backlighters used in
MECPR, the laser pulse is not Gaussian.
A 1-ns 'square' laser pulse is typically used to implode the backlighter capsule, and the
pulse has the shape seen in Figure 2-2. However, the model Rosen and Knuckolls derived in
order to calculate the ion temperature was based solely on a Gaussian pulse, and will therefore
not function properly for this application. A new method for finding the ion temperature must
be introduced, which entails a theoretical model for laser-energy absorption in the shell and
how that energy isconverted into P-V work during the compression of the fuel. This is currently
in progress, and will be an ongoing project as part of my Doctoral work.
~21~
-
CR39 Plastic Track Detector
2.3
The detector pack shown on the right side of Figure 2-1 consists of, from right to left, a
front filter (Fl), a CR39 track detector (Bert), another filter (F2), and a final CR39 track detector
(Ernie). A full description of CR39 as a charged particle track detector can be found in reference
(16), a brief yet necessary overview will be given in this thesis as it is vital to MECPR. As
charged particles travel through CR39, they break the bonds of the plastic and create
destructive holes in the substrate. These holes are extremely small and the diameter and
eccentricity are dependent on the particle charge, type, and incident angle. To make the holes
visible under a microscope the CR39 is etched in NaOH, wherein the plastic inside the holes is
eroded away faster than the nominal surface of the piece. After etching, the piece is scanned
using a laser-auto-focused microscope, and the position, diameter, eccentricity, and contrast of
each particle track is retained. The CR39 has been calibrated using our accelerator for protons
and alphas at specified energies in order to create a curve to convert diameter to energy, see
Figure 2-3.
2u
15
E
W
E
10
0::
I-
:;:::-D
5
::::
.;
:::.::
d6
i,,
:·
-- ;;: "';~~""-3-ss -F~~~3;-:~i··
;·-: alF
0
2
-:"~~_·L.-·)
"~Sua '--;~·-'--~--ea:.
i ___
s'~~":sesi:··G~P
K.
'a
10
8
6
4
Proton Energy (MeV)
Figure 2-3: (left) Track Diameter vs. Proton Energy curves at three different etch times in 80*C 6.0 molar
NaOH. The estimated energy and yield of the particle of interest dictates the etch time required
for a given piece. Etching isalso used to bring the real track signal 'up above', in contrast, the
intrinsic noise on the piece, however care must be taken not to etch too far, or tracks will be
etched away for shorter range particles such as the DD-protons and D3He-alphas. (right) Actual
microscope frame of DD-proton tracks on CR39. The image is410 x 310 pm (18).
As seen in Figure 2-3, higher energies give a very shallow slope, increasing the
uncertainty in which one can convert a measured track diameter to incident energy. For this
reason, filtering is used before the CR39 to range down particles into the steeper slope region.
The purpose of having both the Bert and Ernie pieces of CR39 is to gain information from both
-
22
-
the lower energy particles (DD-protons and D3He-alphas-using F1 and Bert) and the higher
energy particles (D3He-protons-using F2 and Ernie). In this way the filtering for Bert and Ernie
can be optimized separately such that a typical particle will end in the proper energy range for
efficient detection and energy conversion. The filtering design is based on what particles are of
interest for that particular experiment and what assumed pL (path integrated areal density) the
particles will traverse in the subject.
-~23 -
3
What is MECPR sensitive to?
A mono-energetic particle source and an energy sensitive detector system lead to an
efficient and novel way to calculate the path integrated areal density (pL). Another advantage
of this imaging system is that the magnification can be changed simply by shifting the detector
array closer to or farther away from the subject. This is especially interesting when looking at
electromagnetic fields because of their focusing (or defocusing) effects on charged particles.
MECPR sets itself apart from electromagnetic radiation (X-Ray) radiography in that besides
being sensitive to mass by way of energy loss, charged particles are also affected by
electromagnetic fields through deflections. Nevertheless, charged particles are more prone to
scattering in matter than photons, and must be accounted for in the processing of radiographs.
The sensitivity to mass and electromagnetic fields provides a niche for MECPR in diagnosing
previously unobservable phenomena in HEDP plasmas.
3.1
The Importance of pR in IFE
One of the most important parameters in IFE is the capsule areal density, pR. This
parameter appears in many IFE relevant calculations, two of which will be briefly presented
here: the Lawson Criterion (netE) and Burn Efficiency (f). The Lawson Criterion isthe product of
energy confinement time (TE) and electron number density (ne) of the burning plasma. This
product tells us how long to confine plasma with a specific electron number density. It gives a
lower limit for fusion plasmas to ignite and can be written in terms of the compressed fuel
density pf [g/cm3], the compressed fuel radius Rf [cm], the mass of the compressed fuel mf [g],
and the sound speed c, [cm/s] :
neT•E
m
p,=
2i 1014
[*
(3.1)
The sound speed is written in terms of the Boltzmann constant kB, the ion temperature Ti [keV],
and the average mass of a fuel ion mion [g] with the familiar form:
S=
2kBT
-
mion
3.2*10-12Ti
mion
[]
(3.2)
E
The other IFE relevant parameter that will be discussed here is the Burn Efficiency (c). It is
defined as the ratio of the number of fusion reactions to the total number of fuel pairs; in the
case for DT, it is the number of DT reactions over the number of DT fuel pairs. This measure
- 24-
tells us how much of the fuel was actually burned to give positive energy out and can be written
in the following form:
0
(3.3)
pfRf
HB+pfRf
where pf [g/cm3 ] is the compressed fuel density, Rf [cm] is the compressed fuel radius, and He
[g/cm 2] is the burn parameter, which has the form:
H s,=m
HB=
(or)
[g
[cm2]
(3.4)
where c, [cm/s] isthe sound speed in the compressed fuel, mf [g] isthe compressed fuel mass,
and (av) [cm 3/s] isthe Maxwellian averaged reactivity. The Burn Efficiency has the limits of # =
1 for high-burn efficiency (pfRf >> HB) and =- pfRf/HB for low-burn efficiency (pfRf/HB << 1) (6).
These two calculations have been shown to be deeply dependent on the compressed pR of the
fuel. Furthermore, this parameter has become one of the most important in IFE, and hence the
ability to accurately measure pR is invaluable.
3.2
Electromagnetic Fields in HEDP
Matter exists as plasma when in the HEDP regime, implying the existence of moving
charges and therefore electromagnetic fields. Maxwell's Equations are paramount in the
theoretical understanding of plasmas, hence the measurements of electromagnetic field
structures involved in various plasmas is vital to experimental comprehension. Laboratory
HEDP phenomena such as Laser-Plasma-Interactions, Rayleigh-Taylor growth in plasmas, and
IFE, to name a few, involve moving charged particles and dynamic complex electromagnetic
fields. Charged particles are affected by electromagnetic fields by the Lorentz force:
FL=qE+qVxB [N]
(3.5)
where q [C] isthe charge on the particle, E [V/m] is the background electric field, V [m/s] is the
velocity of the particle, and B [T] is the background magnetic field. By using charged particles
to probe HEDP phenomena, we have access to information about electromagnetic fields in the
plasma through direct measurement of the displacement of the backlighter particles.
- 25~
3.3
3.3.1
Charged-Particle Coulomb-Scattering
Physics of Coulomb Scattering
The dominant energy loss and scattering mechanism for charged particles in both
plasma and solid matter is Coulomb Collisions. Elastic and inelastic nuclear collisions and
Brehmsstrahlung radiation play very minor roles. The scattering of charged particles through
Coulomb interactions is inherently a 2-body problem; it consists of the field particle and the
test particle, wherein the test particle is incident onto a group of field particles. A careful
derivation of the equations in this section is provided in Appendix A. The 2-body problem is
solved in the relative frame of the particles, such that the field particle is held stationary, and
the test particle is deflected, through the Coulomb force:
2
ZtZ f
Fco
47reor
[N]
(3.6)
where Zt and Zf are the atomic numbers of the test particle and field particle respectively, ec (C)
is the elementary charge, E0 [F/m] is the permittivity of free space, r [m] is the relative distance
between the test particle and field particle, and r is the unit vector pointing from the fieldparticle to the test-particle. Using conservation of energy and momentum, and converting from
the rest frame of the field particle to the lab reference frame, the energy loss per unit length
along the trajectory of the test particle can be written as:
dE
dt
-nf-7b24
" in
1-b 1+ ( minN2
) Er
p
[
_b9-0 ) J
m9mf
I
(3.7)
where dEP and Ep [J] is the change in test particle energy and the particle energy at any point
along the trajectory respectively, dl [m] is the distance along the trajectory in which the particle
loses dEp, m, [kg] isthe reduced mass of the system, mt [kg] is the mass of the test particle, mf
[kg] is the mass of the field particle, b90 [m] is the impact parameter that would give a 90"
deflection angle of the test particle, and bmax [m] and bmin [m] are the maximum and minimum
impact parameters of interest for a given physics problem, respectively. The impact parameter
limits must be given for this equation to have meaning, but must be defined by the physics of
the situation.
The next important parameter to come from the Coulomb Collision analysis is that of
the Rutherford Cross Section (RCS). This cross section is derived through the conservation of
particles and supplies the probability of a test particle to scatter into a solid angle dO in terms
- 26
-
of the scattering angle relative to the incoming trajectory e [rad] and the impact parameter for
a 90" deflection angle b9o:
(da
dn)
-
b
o
bafrns
1028l
(3.8)
sr I
4 sin'(0/2)
or since the cross section iscylindrically symmetric:
(0)
= 7rb 22
1028
barns
(3.9)
rad I
106
10 4
102
100
10-2
nr/4
n/2
3nr/4
Exit Angle 0 [rad]
Figure 3-1: Equation 3.9 plotted against exit angle 0 for a 10-MeV proton into Tantalum (Z=73). The
Rutherford Cross Section obviously shows that Coulomb scattering will be dominated by small
angle deflections. The cross sections at very low exit angles are many orders of magnitude
higher than at higher angles. For this particular case, at 0 = n/100 the slope begins to flatten
out.
Figure 3-1 shows an example of how the Rutherford Cross Section varies in exit angle for a 10MeV proton incident into Tantalum; (3.9) cannot be arbitrarily integrated over e from 0 to R
because the integrand is singular at 0, other bounds would have to be defined by some physics
constraints. Nonetheless, insight can be obtained by noting the form of (3.9) in Figure 3-1. It is
extremely high at low angles, implying that an individual Coulomb Collision is most likely to
- 27~-
result in a small angle deflection. For this reason, Coulomb scattering in matter is typically
referred to as Multiple Coulomb Scattering (MCS) because as a particle traverses a medium, the
net result may be that it is deflected by a substantial angle, but physically this is a result of
many individual small angle deflections.
3.3.2
Parameterization of MCS in Cold Matter
Since Coulomb scattering is really based on many single interactions, it is useful to have
a general idea of how much physical scatter and energy straggle will occur for a specific particle
incident onto a specific amount of material. It is not possible to say what the exact position or
I
Mono-Energetic
Beam with zero
radius
---- ---1,
Incident on a
uniform, flat
scattering foil
Figure 3-2: Schematic of a simple scattering simulation. Average
energy loss, energy straggle, and exit angle 0, were
parameterized to incoming energy, atomic number of
incident particle and scattering substrate, areal density,
and scattering substrate atomic mass.
energy of any particle will be after exiting the material, but we can estimate a distribution using
Monte Carlo algorithms and parameterize their outputs for an estimate of energy loss and
scatter. Using the Monte Carlo program SRIM (19), a database was formed for different
thicknesses of various materials with incident protons and alpha particles of assorted energies.
The average energy upon exit (with standard deviation) and average output scattering angle
were thereby computed. Ten thousand particles were run for each simulation in SRIM, and the
database, seen in Appendix B, was created using the output files. Then, using the regression
tools from Matlab, power law fits were obtained for the three output parameters: average
energy, energy straggle, and average scattering angle. Figure 3-2 shows a schematic of the
simulated setup, mono-energetic beam, scattering material, and exit angle. All three
dependent parameters were fit to the same general form, only different powers were found for
each:
- 28 ~
(Eout) = 0.2095 *
=
1174.4 *
(\1
M
-0.237
Ein
0.628127
N-0.195
- )Eo,
0.628
g•
/
=11M g
Ein•.313-, pimu
(0)= 2.152 .•,u-"
Msub -2.10 (Z, 245
am
-0.783 [MeV] (3.10)
(Zsub)0.0261(Zp52
(3
[keV] (3.11)
-
,o
0.617
1sa
-0
(Zsub)0.313(Z
36
[rad]
(3.12)
where (Eout) [MeV] is the average energy at the exit, aEut [keV] is the standard deviation of
the exit energy, (0) [rad] is the average exit angle with respect to the incoming particle
trajectory, Ein is the energy of the incoming particle, pRsub is the areal density through the
scattering substrate of a straight trajectory, Msub is the atomic mass of the substrate, Zsub is
the effective atomic number of the scattering substrate, and Zp is the atomic number of the
incident particle beam. Table 3-1 shows the values of the average residual, average percent
error, and the R-squared value for an analysis of the goodness-of-fit.
Table 3-1: This table shows relevant data pertaining to the scattering and
straggling parameterizations mentioned above. The residual and
percent errors are ideally zero, and the R-squared value is ideally 1
for a perfect fit to all of the data. Plots of the SRIM simulated data
and fit data are shown in Appendix B.
<Eout> [MeV]
OEout [keV]
0 [rad]
Average Residual
-2.73E-02
2.00E+00
4.62E-04
Average %Error
16.40%
10.30%
10.30%
R-squared Value
0.902
0.959
0.965
Although I currently do not have a direct physical interpretation of the parameterized
formulas, some simple inference checks can be made for each equation. The exit energy goes
up with increasing incident particle energy and is inversely related to the areal density, mass of
the scattering substrate, and incident particle atomic number. Conversely, it increases with
increased substrate atomic number, which does not make physical sense; if Coulomb collisions
are the dominant scattering mechanism, then the exit energy should be inversely related to
both the particle and substrate charge. The deviation in the exit energy decreases with
increased energy while it increases with areal density and particle charge. However, the
inverse relationship to the substrate atomic mass and extremely low dependence on the
substrate charge cannot be interpreted. In the exit scattering angle formulation, all the
~ 29-
dependences make good physical sense, except for the inverse relationship with the substrate
atomic mass, but this is an extremely weak dependence. Overall, the three equations above fit
the simulated data very well, and with a little physical intuition, most of the dependences make
sense. These parameterizations are useful for quick calculations of approximate energy loss,
energy straggling, and physical scatter through a subject, and can be helpful in designing an
MECPR experiment and filtering for efficient track detection in CR39; further investigation will
be performed throughout my Doctoral work.
3.4
3.4.1
Measurements Using MECPR
Areal Density
Charged particles will be ranged down in energy while traveling through matter: solid,
liquid, gas, or plasma. MECPR provides a means to measure the areal density present in the
subject. However the actual measurement made of areal density is not pR, but pL. Both
parameters are areal densities, in the sense of being a density multiplied by a path length inside
that density distribution. Though the two parameters are similar, they describe very different
aspects of an experiment. The areal density mentioned in Section 3.1 regarding IFE (pR) in
terms of the density as a function of radius from the capsule center p(r) [g/cm 2] and the outer
radius of the capsule R[cm] is written as:
pR = f p(r) dr
2
(3.13)
This definition refers to how much areal density is seen by the particle from the birth point to
the outside of an implosion capsule, and is used accordingly in the IFE calculations mentioned in
section 3.1. Using MECPR, we can actually measure areal density in a slightly different form, pL:
pL = f0 p(l) dl
-
(3.14)
where p(l) [g/cm 3 ] is the density as a function of path length along the actual particle
trajectory, L [cm] isthe total integrated path length. This measurement provides the total areal
density encountered by the charged particle along its entire trajectory. The simplest
connection between pL and pR is that, for small scattering angles, in the center of the capsule
pL = 2*pR since L= 2*R.
-~30
The first step in diagnosing the areal density in the subject is to examine the diameters
of the tracks made on the CR39 by the mono-energetic charged particles. Next, using the
Diameter vs. Energy calibration curves shown in Figure 2-3 for the proper etch-time, we convert
the diameter of the particle to energy. This gives us the energy of the particle when it was
incident on the CR39. Using a program, written by Fredrick Seguin based on SRIM (19) ranging
tables and the knowledge of filter and CR39 thicknesses in the detector array, the particle
energy can be traced back to when it was first incident on the detector. During charged particle
radiography experiments, other diagnostics are used which provide the exact energy spectrum
delivered by the backlighter (recall that the birth spectrum is mono-energetic to within a few
percent). Now, knowing the energy of the particles before and after traversing the subject, a
total areal density, pL, can be inferred in the subject.
3.4.2
Electromagnetic Fields
While traversing through a region containing electromagnetic fields, ions are
accelerated parallel to the electric field vector and perpendicular to the plane containing the
magnetic field and velocity vectors at every location along the particle trajectory. In MECPR
these particles traverse medium containing electromagnetic fields and end up on a CR39 plastic
Figure 3-3: This diagram shows a region of constant field, E- or B- (blue), and the effective
direction of force (red) acting on the charged particle, which enters with a velocity
vi, and leaves at an angle 0 with velocity vf. Because these particles are moving
extremely fast, the change in speed is negligible, a) A constant E-field forces the
particle into a parabolic trajectory across the field region accelerating the particle
parallel to the field. b) A constant B-field directed out of the page directs the
particle in a circular path across the field region.
-
31-
track detector where the recording of individual particle positions and energies takes place.
Because the source used in MECPR is quasi-isotropic, any large deviations in fluence (number of
particles per unit area) must be due to either electromagnetic trajectory perturbations or
scattering through non-homogeneous matter-density fluctuations. These perturbations can be
observed by either a quasi-homogeneous 'sheath' of particles incident upon the subject in
which any large inhomogeneities of fluence can be measured. Otherwise, the 'sheath' can be
broken into charged particle beamlets by introducing a mesh substrate before the subject. The
mesh acts to separate particles into two groups: particles which went through the mesh-holes
(Group 1) and those that did not (Group 2). Group 2 particles will be scattered out and ranged
down while traversing through the mesh substrate.
However, Group 1 particles travel
unperturbed through the mesh-holes to create charged particle beamlets. Consequently, the
parameter of interest in both cases is the deflection of a particle, or beamlet, perpendicular to
its unperturbed motion. In other words, any acceleration in the subject parallel to the
trajectory will not result in a large enough change in energy to be measureable on the detector.
Figure 3-3 shows the simplified, limiting cases for estimating a constant electric or magnetic
field acting on a charged particle over a finite distance. The charged particles used in MECPR
are extremely energetic and are exposed to the region of intense fields for a very short period
of time, so short as not to greatly change the speed of the particle. That is, vi is approximately
equal to vf. The equations of motion for a constant electric or magnetic field perpendicular to
the particle velocity have the form:
d#
dt= q
dt
(3.15)
[N]
[N]
= qxB
(3.16)
where ' [kg*m/s] is the momentum of the particle, q [C] is the charge, E [V/m] isthe constant
electric field, i [m/s] is the velocity of the particle, and B [T] is the constant magnetic field.
Using the approximation that the speed is relatively constant and that the exit deflection angle
is small, these equations can be solved for the exit angle in terms of the particle kinetic energy
E, [J], the particle mass mp [kg], the particle speed vp [m/s], the exit angle from the field region
0 [rad], and the infinitesimal length along the particles path dl [m] which take the form:
0 [V]
fJ ldl L=
q
q
- 32 -
(3.17)
These relationships come about by the fact that the change in the velocity vector is
approximately "vi*O, while the speed is constant. In order to estimate a field magnitude, a
method to finding 0 and dl must be defined.
The deflection angle, 0, in the subject can be calculated from measurements of the
radiograph and knowledge of the geometric setup, whereas the scale length, dl, must be
estimated based on the specific experiment, or some a priori knowledge of the dynamics in the
subject. Figure 3-4 shows a schematic used to derive the relationship between 8 and the
measured displacement, M(, where M is the magnification of the system. Using purely
geometric arguments the exit angle, the 'apparent' displacement in the subject plane k [m], the
MP;;IjrPd
Subject
Plane
dsub
Figure 3-4: A generic schematic used to derive a relationship between the exit angle
from the subject area and the measurements made on the detector.
The length of the interaction region in the subject is much smaller than
the dimensions of the imaging system, so that demagnifying the
displacement using M will not distort the measurement at the subject
appreciably.
distance from the source to the detector ddet [m], and the distance from the source to the
subject plane dsub [m] are related by:
0 = tan - 1
Mfu)
[rad]
(3.19)
Because the measured displacement in the detector plane is so small when compared to the
dimensions of the system, the exit angle can also be written as simply:
0=
M
ddet-dsub
-~33
[rad]
(3.20)
Now, knowing the exit angle and the (mono-energetic) energy of the particles, a scale length
must be chosen to approximate an electric or magnetic field magnitude. This quantity is
dependent on the specific situation in the experiment. More specifically, if we are probing
filamentary field structure, then the scale length of the filament is a good approximation (7). If
we are instead looking at proton beamlets through a plasma bubble, then the radius of the
bubble is a good approximation (12). Using MECPR, each experiment must be considered
individually when finding a proper scale length to estimate field magnitudes.
3.4.3
Resolution Limits
MECPR is subject to three main sources of image blurring: finite source size, scattering
in the subject, and scattering in the detector. To analyze these sources of blurring, there must
be a way to characterize each. However such a characterization does not account at all for any
Broadening in
Finite
C
rre•
e
the Detecto
in the Subject
(Rsub)
,
.....
.......
.....
-------------
d..b1
Rndde~t
Filters <
Magnification:
M = ddet/dsub
CR39 -
Figure 3-5: This schematic emphasizes the three main sources of image blurring in MECPR: finite source
size, scattering in the subject, and broadening in the detector. Each mechanism can be
characterized by the convolution of the image with a Gaussian parameterized by a 1/e radius;
Rsrc, Rsub, and Rdet for the source, subject, and detector respectively.
electromagnetic fields that might be present near the source, or in the subject. Luckily, all
three mechanisms have the similar effect of convoluting the image with a Gaussian of a
characteristic rl/e (one-over-e-radius):
r
~e
2
rile
(3.21)
Using this formulation, we have made the assumptions that the source has a fusion burn profile
of a spherical Gaussian in space and that the scattering in the subject and the detector is
- 34 -
Gaussian in nature. The scattering is roughly Gaussian for energies above ~1-MeV, which, in
MECPR, we are always above. The blurring radii that we are interested in are projected onto
the detector and then demagnified to the subject plane (since the real data is the projection of
the subject onto the detector plane). Figure 3-5 shows a schematic of the generic MECPR
setup, with proper definitions of important parameters, and where the different methods of
image blurring occur. If the source has a l/e radius of rsrc, the particles have a l/e scattering
angle exiting the subject of Osub and a 1/e broadening in the detector of rdet, then the
demagnified projections of each of these mechanisms can be written as:
Rrc
=
M-1
(3.22)
---Trc
Rsub
ddet-dsub
Rdet
det
ub
(3.23)
1
(3.24)
The three blurring methods act together multiplicatively so that the total blurring of the image
isthe convolution of a Gaussian with the form:
r2
~e R~ot
Rtot = Rc +R +Ret
(3.25)
(3.26)
In MECPR the glass capsules used as the mono-energetic charged particle source are typically
400-pm in diameter, nominally. Using the Proton Core Imaging System (PCIS) it was found that
typical backlighters have a nominal l/e radius of rrc = 30-pm (14). The magnification of the
system is typically ~10 - 30 so that Rsrc = rsrc. The broadening in the detector is dependent on
the filtering chosen for the system and the amount of energy loss in the subject. This
broadening is characteristically ~15-jim - 45-pm without demagnification. Therefore in the
subject plane it is only a few microns and is typically ignored. The last contributor to image
blurring is that due to scattering in the subject, which is entirely dependent on the experiment.
Such scattering can completely blur out the image, or have little to no effect at all. Hence, for
an experiment with little scattering in the subject, the resolution limit is defined by the size of
the source. Otherwise, the square root of the quadrature sum of source size blurring and
scattering in the subject sets the resolution limit for a given experiment.
-~35 ~-
4
Backlighter Performance
The first 400- pm D23He-filled thin glass capsules shot by the HEDP division at MIT were
performed in late 2005. Since then many other capsules have been shot by this group, and
other collaborators at LLE. Each capsule has input parameters specific to a given shot (as briefly
discussed in Section 2.2.1) and many experiments have included this type of backlighter since
2005, thereby providing a database to study the performance of the backlighters themselves.
The input parameters are never exactly the same, and therefore the outputs of these
backlighters vary. Even for similar capsules and laser settings, small variations make a
difference in the capsule yield. The exploding pusher model discussed in Section 2.2.3 gives an
estimate on what to expect for a proton yield, but is still only an approximate theoretical
model. In Section 4.1 an empirical analysis of all data since 2005 is presented, along with
power fit models for different input parameters. In Section 4.2 a display of some resultant
images from MECPR experiments is given, while in Section 4.3 a brief description of the
importance of particle statistics is presented.
4.1
Empirical Data Analysis
As discussed in Section 2.2.1, the relevant input parameters for the backlighter are fill
pressure of D2 and 3 He, glass-shell thickness, capsule diameter, pulse shape, number of beams
on target, energy per beam, and laser focus. As many of these values as possible have been
recorded for each shot involving a backlighter. Some measurements of the capsules were
never made, and since they are destroyed after the shot, they never will be made. Appendix C
gives a complete list of all backlighter data to date for reference, with a -1 referring to data that
was not obtained. The proton yield is the primary output parameter to characterize since that
is the most important for MECPR. Using Matlab's regression fitting tools, empirical power law
fits of multiple independent variables were made for various sets of data. These data sets were
chosen based on pulse shape, laser drive, and laser focus (5).
Six different data sets were chosen to parameterize for the neutron and proton yields,
however only the proton yield parameterization will be presented in this chapter as it is more
of a concern than the neutron yield for MECPR. In this analysis, the hope isthat some insight of
how backlighter parameters affect the proton yield will be gained. The two statistical tools that
were used in analyzing the goodness-of-fit was the average percent error between the
predicted values using the fit and the values from the database, as well as the R-squared
statistic given by (20):
-
36-
R2
(4.1)
5 2
)
(DiD-)(pp-=(Dj-D2Z(P-P-)2
where Di is a single value from the database, D is the average of the data values, Pi is a single
predicted value, and P is the average of the predicted values. The closer R-squared is to 1, the
better the linear correlation between the two data sets. However this says nothing of statistical
relevance. Fits 2 and 3 were done with less than 10 data points only because there were no
Table 4-1 gives the coefficient values for the proton yield
more data available.
parameterization for six different data sets.
Table 4-1: This table gives the form of the equations used in the parameterization of the proton yield for
=
MECPR. The nominal values of the independent variables are tshell = 2.0 Jim, Dut = 400 pm, EonTafr
Z
the
and
exact,
never
are
values
these
However,
=
0.5.
PD2/P3He
and
,
10 kJ, Efux = 0.02 J/pm
implications of these deviations from the nominal can drastically change the proton yield.
Furthermore, the number of lasers and the energy per laser beam is not always the same. For
example, Fit 5 has the lasers incident on the capsule from the top and bottom (Pole Driven), and
this greatly changes the implosion dynamics.
Y. = Const*(th.,I)a*(Efl..)b*(PD2P
3He)C
1
SSD:SG1018
(9RI
4.99E+09
-7.2793
3.5235
-0.37522
0.871
18.1
3
Leg(Z.):51Ult
5.91E-03
-6.7032
-2.2216
-2.5249
0.919
13.9
5
SSD:SG1018
(300um-:'Pole Driven')
2.42E+03
-3.8479
1.2797
0.78286
0.415
46.9
0.0656
48.1
(9R)
Yp = Const*(tshe.)a*(Dout)b*(EonTarj)C*PD2/P3He)
6
SSD:SG1017
(9R)
8.40E+63
-2.0459
-0.71143
-15.579
d
-0.9744
Here, I will only present the values of the coefficients and describe their meaning with
respect to the proton yield, while neutron yield parameterization coefficients will be shown in
Appendix C. The parameterizations in Table 4-1 are good for calculating a simple estimate of
the proton yield for a set of laser and backlighter conditions. Currently there are no exact
physical interpretations of these formulae. However some simple inferences can be made. The
proton yield has a strong inverse relationship to the shell thickness. This makes physical sense,
since a thicker shell would indicate less compression of the fuel, and hence, less yield. The
~37
-
dependence on shell thickness varies across all of the formulae, but all seem to have a strong
inverse dependence. Fits 1, 4, and 5 show an increase in proton yield with increased energy
flux, which is simply the total on target energy spread uniformly over the shell surface. This
also makes physical sense, because more energy on target would suggest more compression.
The other three equations show an inverse relationship between the energy on target and the
proton yield. However, Fits 2 and 3 have a low number of data points, and are therefore not as
relevant, and Fit 6 has an extremely low R-squared value implying that the fit does not
represent the data very well. Fit 6 is presented for completeness and the chosen
parameterization formula gave a better fit than the formula used for the other five, but another
parameterization equation is still needed for these data. The dependence on the pressure
ratio, and hence the number density ratio, is not obvious, and more work will be needed to
further understand what affect it has on the proton yield. With this said, the pressure ratio
dependences listed above do help the predicted values match the data.
The parameterizations given above provide a simple way to estimate the proton yield
for specified laser and backlighter parameters. Fits 1 and 4 are probably the most important
because Fit 1 corresponds to typical laser parameters used in current MECPR experiments, and
Fit 4 gives an overall picture of the SG1018 laser pulse for three different drivers and foci. More
energy on target and a thinner shell will increase the proton yield within the parameter space
probed by these parameterizations. More work, and data, will be needed for a better
Another factor that would help in the
understanding of backlighter performance.
parameterization of the proton yield is an algorithm which would use the uncertainties in the
measurements of the independent variables. Currently the values in the database are
considered perfect when used in the fitting algorithm for the coefficients, but we might
produce better results when the uncertainties are included in addition to some intuitive
physical limits on coefficient values. These parameterizations will be reanalyzed and refitted as
more data is accumulated over the next few years, and a more complete explanation will be
formed during my Doctoral work. For more information regarding the parameterization
analysis, the reader is encouraged to see Appendix C.
-~38 ~-
4.2
The Importance of Particle Statistics
As stated in Section 4.1, the proton yield is one of the most important characterizing
good
parameters for the backlighter in MECPR. It takes a large number of particles to make a
useless.
radiograph
image, and if there are too few particles, it can render the resultant
is dependent on
Naturally, the actual number of particles necessary to radiograph accurately
the distance
the experiment being run; specifically the distance between source and subject,
a total yield
Figure 4-1: (left) OMEGA shot 46528 with 15-MeV protons incident at the subject at 1.58-ns with
1.56-ns with
at
subject
the
at
incident
protons
15-MeV
with
of 0.45*108. (right) OMEGA shot 46529
the fluence
In
plane).
subject
the
at
~2.8-mm
is
width
a total yield of 3.56*108 (individual image
images
These
fluence.
less
indicate
colors
lighter
while
radiographs darker indicates higher fluence,
our
For
image.
an
to
do
can
yield
particle
in
difference
-8
of
illustrate very well what a factor
minimum
a
for
hope
we
source,
the
from
away
typical MECPR setup, the detector is ~25-30-cm
the
yield on the order of ~108; this was achieved for shot 46529, but not 46528. It isessential for
statistics
proper
Without
magnitude.
of
order
this
attain
success of MECPR that the particle yields
useful information will be lost in the noise.
between subject and detector, and the amount of deflection expected in the subject. What
really matters is the particle flux at the detector and, therefore, the solid angle that the
detector subtends with respect to the source. Obviously there exists a saturation point for the
detector, but typical particle yields for MECPR are never near this value. Figure 4-1 shows two
different images of a dynamic process where the charged imaging particles arrived at the
subject at same time, but during different shots. It is obvious that the difference in radiograph
quality is substantially decreased with decreasing particle yield. For this reason, it is extremely
important to understand which laser and backlighter parameters affect the particle yield.
- 39 ~
4.3
Sample Radiographs
This section is dedicated to the exhibition of some of the resultant images we have
obtained using MECPR. The most recent publication of MECPR images at the writing of this
thesis was an article in the journal Science, February 29, 2008 issue, wherein the results of
Figure 4-2: (left) OMEGA shot 46531, a 15-MeV proton fluence radiograph of an unimploded Fast-Ignition style
target. The outside diameter of the capsule is~430-pm in the subject plane. The gold cone clearly
scatters out all of the protons and even the small cone inside the capsule can be seen. (right)
OMEGA shot 46529, a 15-MeV proton fluence radiograph 1.56-ns after the onset of the laser pulse
of a cone-in-shell target capsule. The central fluence peak is attributed to an inwardly directed
electric field and the outer striated structures are theorized to be established by complex magnetic
field structures frozen into the plasma blow off; the scales are equal the same in both images.
recent Fusion Science Center (FSC) supported OMEGA shots were released.
The subjects
imaged in this series, were the Fast-Ignition capsules (recall the brief description given in
Section 1.2 of the high-Z cone imbedded into a plastic spherical capsule). Figure 4-2 shows the
two radiographs shown in the Science article (7). The left image is a fluence radiograph of the
unimploded cone-in-shell subject made by 15-MeV protons from the D-3 He fusion reactions in
the backlighter. It is clearly seen that the protons are completely scattered out by the gold
cone, and are scattered through the capsule shell resulting in a lower fluence (lighter color)
where the shell sits and a slightly higher fluence (darker color) outside the shell. The
radiograph on the right was taken such that the 15-MeV protons from the backlighter would
arrive at the FI capsule at 1.56-ns after the onset of the laser pulse. The resultant image
contains information which is extracted by the deflectometry techniques described in Section
3.4.2 and the measured distances between fluence fluctuations. Using this formalism, it was
found that an inwardly directed electric field of ~1.5-GV/m would be necessary to deflect the
-~40 ~-
protons to the degree seen in the radiograph. Also, it was discovered, using the related
equations for magnetic fields, that a magnetic field of order ~60-T would be needed to cause
the striation separation measured in the radiograph. The radiograph on the right of Figure 4-2
is very impressive because it is the first direct measurement of field structures outside of an IFE
capsule, and may have large impacts on IFE research. However, it should also be noted that the
large fluence fluctuations observed are a 2-D projection of 3-D phenomena. More theoretical
and simulation work will be needed to complete the understanding of the sources of these field
structures. Some physical interpretations have been made for the cause for these fields, but
the reader is encouraged to seek the reference material listed at the end of this thesis for
further information.
The next set of images that will be shown here are some of the first experiments done
using the MECPR technique, of which some images were presented in Physical Review Letters
(PRL) in 2006 (12). Figure 4-3 shows a series of images obtained using the MECPR technique of
the evolution of a laser-induced plasma bubble. When the laser is incident upon a plastic foil,
42767
42768
44423
0
44432
44424
44433
44425
1.8 ns
2.3 ns
3.0 ns
2
2.5
!
L
?
0.3 ns
44422
0.6 ns
OS9 ns
0.5
1.2 ns
1.5 ns
1.5
Time (ns)
3
Figure 4-3: The above series of radiographs were taken on different shot days at the
OMEGA facility (shot
numbers above radiographs), but used identical laser and plastic foil parameters. The line
plot on
the bottom of the figure shows the typical 1-ns square pulse with arrows indicating the
arrival time
of the imaging protons and their corresponding fluence radiographs. During the laser pulse,
it can
be seen that the bubble structure stays fairly coherent and symmetric, growing in time.
Then, after
the laser pulse the bubble decays away in a somewhat chaotic and asymmetric fashion.
the HEDP regime of Laser-Plasma Interaction (LPI) isachieved and can then be probed.
In these
experiments one laser beam was incident onto a plastic foil and, over a series of
shots at the
OMEGA facility, 15-MeV protons arrived at the foil interface at different discrete
times. In
doing so they went through a nickel mesh which creates the proton beamlets seen
in the figure
-41~-
and a time evolution of the resultant plasma bubble from the LPI can be generated. During the
laser pulse, the bubble is symmetric and it is apparent that the beamlets traversing the center
of the bubble are deflected less than those farther away, which pile up near the bubble edge.
This can be interpreted as the bubble having the strongest magnetic field near the bubble edge
and decaying in magnitude as one looks radially inward. Using the same deflectometry
techniques, as previously discussed, the maximum magnetic field was found to be ~0.5-MG at
the bubble edge.
-~42 -
5
Geant4 TransportToolkit
For every good experiment, there must be a supplementary simulation. Geant4
(GEometry ANd Tracking) is an open source three dimensional transportation toolkit written in
C++ (21), (22), (23). This toolkit is used to write individual simulations for specific experiments.
Geant4 is simply a library of functions of which the programmer has complete access. The
open-endedness of this code has its pros and cons; the programmer can manipulate anything
that he/she wants, but within that freedom falls the responsibility on the programmer to
account for relevant physics and benchmark individual simulations against experimental data.
Even though there is a skeletal structure that must be followed in every simulation, all of the
details, including the geometry, physics, step sizes, and tracking methods, are defined by the
programmer. This means that for a given simulation the user must define the physics to be
accounted for as he/she chooses, as well as has the freedom to create and simulate new
physics. Geant4 is not run self consistently, meaning that when simulating a large number of
particles, those particles do not affect one another; they are only affected by the environment
defined by the programmer. This includes physical objects made of any arbitrary material in a
number of typical geometric shapes, as well as electromagnetic fields defined by the user. It
does not have a self-consistent electromagnetic package to solve Maxwell's equations, but will
accept defined field structures in analytical or table form and propagate charged particles
accordingly. Geant4 is an internationally recognized and benchmarked code used in many
astronomical, medical, and particle physics applications. However, given the open-endedness
of the code, every simulation (with included physics packages, step sizes, and tracking methods)
must be separately benchmarked in order to provide confidence in the simulations to the user.
5.1
Geant4 Physics Packages
Because of the object-oriented nature of C++, the physics in Geant4 is split up into many
small modules. If the programmer has the proper understanding of the implementation
techniques used in Geant4, these modules can be applied individually. Alternatively, one can
use classes already written by the Geant4 support group which can include a large number of
physics modules, some of which the programmer might not intend to use. The fact that the
programmer has complete control over how the physics is simulated in Geant4, he/she also
takes on the responsibility to include any and all relevant physics to a specific experiment. For
this reason, it is important to test different physics and tracking methods in order to find the
format which will best simulate one's experiments.
A simulation has been written using the Geant4 toolkit to simulate MECPR experiments.
It implements finite source size, Doppler broadening in the birth energy spectrum, as well as
~ 43 -
the entire filtering and CR39 detector arrangement. This simulation also includes a number of
options to choose from for the imaged subject: shell capsule, simple cylinder, cylinder with
caps, meshes of various frequencies, simple scattering foils, and electromagnetic field
structures. Because MECPR is used to image so many different types of subjects and the source
and detectors can change from experiment to experiment, it was necessary to build in an easy
0.25
E 0.2
=L
0
. 0.15
0
200
400
Radius (prm)
600
800
____________
Figure 5-1: (left) This plot displays the azimuthally averaged line outs of an unimploded capsule, with
similar dimensions to that of shot 46531, using three different physics packages on
Geant4. The measured outer diameter of the capsule, 429.1-pm is also shown, and seems
to coincide with the inflection points of the curves. (right) From top to bottom, simulated
fluence radiographs using the LHEP BERT, PRSimPhys-Old, and PRSimPhys-New physics
packages. The simulations were done using a total proton yield of 2.31*108 with a sourcesubject distance of 1-cm and a source-detector distance of 25-cm
way to switch the source size, ion temperature, subject, and/or detector pack between
simulations. This has all been done, such that the user can quickly implement any geometry
fitting the standard geometry of an MECPR experiment, and simulate the radiograph. However,
the difficult component in writing this simulation isfinding a physics package that will work well
for the data we are trying to simulate, and eventually predict.
-~44
To illustrate the differences between physics package implementation and its
implication to simulated radiographs, simulations of a plastic spherical shell were done using
three different physics package. The three packages were: a simple physics package derived
from an example simulation which implements Coulomb scattering and ionization for ion
species, and some radiation physics for electrons, gammas, and sub-atomic particles
(PRSimPhys-Old); an extension of the first package which include some elastic and inelastic
hadron physics with a different ionization model for protons and ions (PRSimPhys-New); and a
completely built package from the Geant4 team which includes a number of hadron physics
processes, standard E&M, as well as other processes which I do not fully understand
(LHEP_BERT). Figure 5-1 displays three radiographs of an unimploded spherical capsule for a
qualitative analysis, and an azimuthally averaged radial plot for a more quantitative study.
It is clearly seen in Figure 5-1 that the LHEP_BERT radiograph is characteristically
different than those of PRSimPhys-Old and -New, with the two latter being very much alike.
The major differences between the PRSimPhys- lists is that the -New list contains some elastic
and inelastic nuclear collision physics, and the -Old list does not. With that said, the
PRSimPhys- simulated radiographs look very much alike, implying that nuclear collisions do not
contribute much to the transportation physics of protons with these energies (which is a
reasonable deduction to make) However, the purpose of Figure 5-1, isto illustrate the variation
of simulation outputs when using different physics lists in Geant4. For this reason, it is the
obligation of the simulation programmer to be sure that the physics lists, step sizes, etc. are
accurate for the types of physics experiments that are to be simulated. Benchmarks with
experimental data are essential to the success of the simulation tool.
5.2
Current Status of Benchmark Simulations
Currently, the physics package being used in my Geant4 simulations is the LHEP BERT
package mentioned in the previous section. This package was chosen because, at this time, it
best represents the experimental data and will be presented in the following sections.
However, there is more work to be done in the understanding and parameter tweaking of the
physics packages. Experimental images and other plots used in the analysis will be shown, and
briefly discussed in Appendix D. The following benchmark experiments consist of a typical
MECPR geometric setup consisting of backlighter, subject, and detector, with different subjects
for each benchmark. Because of the quasi-isotropy of the source and non-uniformities in the
CR39, any discrepancies between the background yield of the simulation and the experiment
were remedied by a scale factor. The two subjects that will be exhibited here are an
unimploded spherical plastic capsule, and an unimploded plastic cylinder, see Figure 5-2 below.
~ 45 ~-
l.,
.LI:,
L,,l..
·L
.-
.. a.
Figure 5-2: A schematic of the standard MECPR setup, made using the visualization software WIRED (24)
supplied to users of Geant4 from the Geant4 website. As stated earlier, the simulation is setup to
have the user modify the backlighter and detector parameters, as well as change the subject to be
imaged. The two benchmark simulations that will be presented are those of a spherical shell (left)
and a hollow cylinder (right), however other standard subjects include meshes, waved foils, and
capped cylinders, to name a few. Of course the code is a work-in-progress so other subjects will be
added later.
5.2.1
Unimploded Capsule
Experimental data for an unimploded capsule was obtained for OMEGA shot 46531.
The capsule used in this experiment was of the Fast Ignition variety, consequently there was a
gold cone imbedded in the shell. The cone was not simulated, and the azimuthally averaged
radial lineout was only taken though azimuthal angles which did not contain the cone. More
detail on the analysis of this shot is given in Appendix D. For this shot a yield of 2.31*108 15MeV protons was measured and was subsequently used for the simulation as well.
Nevertheless, the measured background yield for the experimental radiograph was slightly less
than this, and a scale factor of 1.27 was applied to the experimental fluence radiograph lineout.
Figure 5-3 shows the azimuthally averaged radial lineouts for the experimental and the
simulated radiographs, as well as another simulation using a factor 10 higher yield for
comparison of the statistics. There is an overall agreement between the simulation and the
experiment; but there are some slight inconsistencies. Inside the capsule at small radii,
the
simulations seem to deviate from the experimental data. However, when
taking radial lineouts,
the statistics get worse at smaller radii because the number of particles at a given
radius
decreases with the circumference. Also, the large enhancement at "60-lim in the data
is not
-
46
reflected in the simulations. This enhancement comes from a spot of intrinsic noise on the
CR39 near the center of the capsule. This, obviously, is not simulated, and can be ignored in the
comparison. The important characteristics to compare are the placement, depth, and width of
the fluence 'trough' (decrease in average fluence) in addition to the shape and height of the
'scatter bump' (increase in fluence outside of the shell) outside of the capsule shell. With
respect to the trough, the simulations are slightly shallower (~13% higher than the data) and
are almost as wide. The scatter bump in the simulations is slightly higher and quite broader
n
-~
41
S0.2
-W
o
C
0
I-
0.1
0
200
400
600
800
Radial Distance (pm)
Figure 5-3: Azimuthally averaged radial lineouts for experimental data (OMEGA shot 46531),
simulation with experimentally measured yield, and simulation with a factor 10
higher yield; the capsule edge is also shown in this plot. When taking radial
lineouts, the statistics get worse at smaller radii because there are less particles
at a given radius and for this radiograph there was also some noise on the CR39
piece near the center of the capsule; for these reasons the inner radii are less
important in matching experiment with simulation.
than the data. It should also be noted that the simulation with the higher yield is not much of a
statistical improvement than that found with the measured yield. This implies that the yield
achieved with the backlighter in this experiment was statistically good. However the average
background proton flux in the experimental radiograph was less than expected, perhaps due to
intrinsic noise in the CR39. The discrepancies mentioned regarding the depth of the trough and
shape of the scatter bump are not extreme and could be partially attributed to poor statistics in
the data. Though, a better understanding of the LHEP_BERT physics list and its constituent
numerics (i.e. step size, cutoff values, and etcetera) could also attribute to the difference
between the data and the simulation.
-~47 ~-
5.2.2
Unimploded Cylinder
Data for an unimploded cylinder was obtained for OMEGA shot 45953. The cylinder
used in this experiment also had caps on its ends, but were not simulated because the
comparison is for the scattering through the shell of the cylinder and not its caps. The yield for
this shot was measured to be 1.57*107 15-MeV protons, but the background in the
experimental radiograph implies a slightly higher yield such that a factor of 1.15 was applied to
the simulated lineouts. To compare the experimental data with the simulations, lineouts were
taken across the cylinder so that scattering through both edges could be compared.
Figure 5-4 shows lineouts across the cylinder for the data, simulation, and a simulation
with a factor of 10 higher yield. The agreement in this comparison is somewhat better than
that for the unimploded spherical capsule with respect to the trough depth, but seems slightly
worse in the trough width. Qualitatively, within the statistical errors, the depths of the troughs
--
-
0.025
E
-=
0.02
a)
CS0.015
0
0.01
-900
-600
0
-300
300
600
900
Distance from Cylinder Center (pm)
Figure 5-4: Lineouts for experimental data (OMEGA shot 45953), simulation with experimentally
measured yield, and simulation with a factor 10 higher yield. The cylinder edge is also
shown in this plot. The experimental particle statistics for this shot were quite poor, but
comparisons between the data and simulations can still be made, and some insight
gained.
S48
seem to agree very well, whereas the widths of the troughs in the data are somewhat larger
than in either simulation. The discrepancy on the inner wall of the cylinder is similar to that
seen in the comparison of the unimploded spherical capsule, except somewhat larger; this
could be due to poor particle statistics. The scatter bump on both edges is hard to compare
with the data because of the statistics, but it should be noted that the simulation with a ten
times higher yield levels out a lot of the noise seen in the simulations using the actual particle
yield. This again shows the importance of the particle yield when using MECPR. Within the
statistical errors of the experimental radiograph, the simulations do match well and with a little
more work and understanding of the physics capabilities available in Geant4, it will prove to be
an invaluable simulation tool to complement an invaluable HEDP diagnostic.
~ 49 ~-
6
Conclusions and Future Work
Mono-Energetic Charged Particle Radiography is a new novel diagnostic used to probe
plasma in the High Energy Density Physics regime. MECPR has opened up doors to explore new
phenomena in the HEDP regime that was previously impossible to investigate. Measurements
of electromagnetic fields in various experiments can now be made and new physics explored,
while areal density maps can be made of Inertial Confinement Fusion capsules to aid in fusion
energy research. This diagnostic uses fusion product charged particles to image various
subjects of interest, and is simultaneously sensitive to density perturbations as well as
electromagnetic fields. Each of these facets is measureable because the detector array used is
sensitive to the exact position and energy of every charged particle incident upon it. The
quality of experimental data obtained from MECPR is highly dependent on the charged particle
yield from the backlighter source and is therefore an important parameter to understand and
have the ability to predict.
To pursue the problem of characterizing the backlighter yield with respect to other
experimental parameters, empirical data has been collected for over 100 experiments involving
typical MECPR backlighters. These data cover a wide range in the laser and backlighter
parameter space, where different laser conditions define different spaces to work with the
backlighter parameters. Laser conditions have a strong affect on implosion dynamics, and
hence, in some cases should be treated separately. Parameterization fits for proton yield as a
function of energy flux on target, shell thickness, and fill pressure ratio were presented for
various laser configurations. The general trends between different parameterizations were
made, and it was shown that the proton yield has a very strong inverse relationship with the
shell thickness. The exact magnitude of this relationship will be determined with more data
and better fitting algorithms.
The other avenue chosen for analyzing MECPR as a diagnostic for HEDP is that of a good
simulation tool, Geant4. Because Geant4 is a completely open source transportation code, the
opportunities available to simulate MECPR experiments are invaluable. It is a well known code,
benchmarked in many areas of physics, and now must be benchmarked for use in simulating
the MECPR imaging system. More specifically, Geant4 will simulate the scattering in matter of
various geometries, and perhaps in the future, even scattering in plasmas relevant to MECPR.
Two benchmark simulations were presented with the current physics implementation and tend
to match the experimental data well. However, more work needs to be done in the
understanding of the physics packages and involved numerics. I am continuing this line of
research for my PhD and plan to have some of the questions presented in this thesis answered,
and the problems presented, analyzed and remedied.
-so50 -
Appendix A: Coulomb Collision Derivation
A.1
Solution to the 2-particle Problem
The dominant scattering mechanism for charged particle scattering, in plasma and solid
matter, is Coulomb Collisions (also known as Coulomb Scattering). As a non-relativistic charged
particle (test particle) traverses through a medium (field particles), electrons and nuclei will
interact by the non-relativistic Coulomb force:
Fcou=-
ZtzfeC
o
[N]
(A.1)
/
//
test
Vrel
Si
\ rmin
ib
'
,'
Vt -------------------------------
-
-
mf, Zf
field
Figure A-1: Schematic diagram of a Coulomb collision with important quantities labeled. To analyze
the
collision, the coordinate system is put into the rest frame of the field particle, which
therefore, is stationary (infinite mass) and the test particle will have the
relative velocity
(reduced mass). The particles have atomic numbers Zt and Ze with mass mt and mf for testparticle and field-particles, respectively. The schematic is drawn for two like-charged
particles, but the analysis is the same for oppositely charged particles; the trajectory of the
test particle would just be flipped about the horizontal axis.
where Zt and Zf are the atomic numbers of the test particle and
field particle respectively, ec (C)
is the elementary charge, E0 [F/m] is the permittivity of free space, r
[m] is the relative distance
between the test particle and field particle, and P is the unit vector
pointing from the field- to
the test-particle. A schematic drawing of the Coulomb interaction is
shown in Figure A-1.
The analysis begins in the rest frame of the field particle, which is fixed in space with
charge ecZf. The test particle has charge ecZt and has a mass equal to the reduced mass of the
system which is related to the rest mass of the test particle mt [g] and the rest mass of the field
particle mf [g] by:
mt = m
mf
mt+mf
[g]
(A.2)
By approaching the problem in this manner, the initial analysis is simpler. The problem is now
confined to the plane which contains both r' and V, and is axially symmetric. Furthermore, the
angular momentum and energy of the reduced mass particle is conserved. Through the use of
these conservation laws and some trigonometry, the expression for 8 final becomes:
8final =
7
- 2bfo0
r"min
Eu = ztz7eo
dr
b2
2bE
2
r
U
EK
(A.3)
(A.4)
[J]
EK = 2mve
[rad]
(A.5)
[I]
where b [m] is the impact parameter, r [m] is the distance from the test- to field-particle, rmin
[m] is the distance at closest approach, Eu is the Coulomb potential energy of the test (reduced
mass) particle, and EK is the kinetic energy of the test particle. If the effective energy potential
was not the Coulomb potential, A.3 could still be used by exchanging Eu for the proper
potential. After performing the integral in A.3 one obtains an equation for efinal in terms of the
impact parameter b and the 90* impact parameter b90 which causes a 90" deflection of the test
particle:
Ofinal = 2 cot -
, bb
90
b90 = ztzfec
1
bo =Z4reo
mrvrel
[rad]
(A.6)
[mn]
(A.7)
This result gives the exit angle for a given impact parameter and covers the range 0 < efinal < nt
for impact parameters 0 < b < o.
S52
-
The solution found in A.6 is in the rest frame of the field particles, we must transform
back into the lab frame. This is easily done using the fact that the Center-of-Mass velocity is
constant during the interaction. This leads to the formulae for exit velocity:
r
ffbnaa
+ [sin Ofina
mf m, + cos Ofinal
mt+mf 1mZ
Vtfinal
=
me
U1 - cos Ofinat&
- [sin Ofina]9)
me+mf
Vrei
Ofinal,lab = tan-
m
I
(A.8)
(A.9)
(A.10)
inc Ofinal
With A.8 and A.9, the solutions can be transformed from the rest frame of the field particle to
an outside observer's frame, the lab frame.
A,2
Energy Loss
Using the formalisms from section A.1 and the conservation of energy, it is
straightforward to show that the energy lost by the test particle with initial energy Eo to the
field particle is:
Elost
Eo
=
4m
memf
sinM
n2 ( Ofinal -2
4m
(A.11)
mtmf 1+(b/b o9
The amount of energy lost by a particle traveling a distance dl through the medium can be
found by multiplying the number of collisions it has along dl by the energy lost:
dElost = nfElostdV = nfElostbdbdld(p []]
(A.12)
where nf [cm -3 ] is the number density of the field particles, dV [cm 3 ] is the elemental volume,
and Elost [J] is the energy lost as a function of impact parameter b. To find the energy lost of a
particle with energy Ep as a function of length along the trajectory dl, one must only integrate
over the impact parameter range of interest to obtain the differential equation:
(A.13)
-sE
=
2
E
+ma
-nf irb9 24mn)2
0
I1
-~53~-
]
(A.13)
where dEp and Ep [J] isthe change in energy of the particle and the particle energy at any point
along the trajectory respectively, and dl [m] is the distance along the trajectory in which the
particle loses dEp. The limits bmax and bmin must be defined by the physics of the problem in
question. Typically in plasma bmax isthe Debye Length (AD), and bmin is 0, which results in:
dE
-nf2b
In 1+
o
S=
ore
b29
E, [L]
[mt]
(A.14)
(A.15)
neec
where E0 [F/m] is the permittivity of free space, Te [eV] is the electron temperature in the
plasma, ne [m-3 ] is the electron number density, and ec [C] is the elementary charge. The
differential equation in A.13 or A.14 is not trivial to solve since b90 also holds information on the
energy of the particle. The natural log term in A.14 is called the Coulomb Logarithm, and is
typically notated as In[A], or just A, and for a large range of typical plasma parameters it is
approximately constant, ~10-20. Even with the simplification of assuming the Coulomb
Logarithm to be constant, there is still no analytic solution to A.13 or A.14 and therefore it is
evaluated numerically. The next piece of information from A.6 that can be deduced is that of
the exit angle of the test particle.
A.3
Rutherford Cross Section
For scattering purposes we are interested in the Rutherford Cross Section (RCS) for
Coulomb collisions. If the test particle is much smaller than the field particle, then Blab e
Ofinal =
e. The RCS gives the probability of a test particle with impact parameter between b and b+db,
to scatter into a solid angle dO. It can be geometrically defined (see Figure A-2 for a schematic)
by setting the initial small area on the impact parameter ring equal to the scattering area
(probability) per Steradian (the RCS) multiplied by an infinitesimal solid angle:
bdbdo= U
sin 0 dOdp
(A.16)
d(P
b+ db
_ ----------------b
Figure A-2: Schematic used in deriving the Rutherford Cross Section. Particles which come through the
impact parameter ring on the left, must come out in the scattered ring on the right. The RCS
defines the probability for a particle to end up at a given solid angle. To calculate a total cross
section the RCS must be integrated over all 4n Steradians (sr); also note that e is now the exit
angle, the subscript 'final' has been dropped..
where bdbd# [barns] isthe small area with impact parameters between b and b+db, sineded4
[sr] is the small solid angle to which the particles will be scattered into, and
) [barns/sr] is
the Rutherford Cross Section. This equation can be solved for the RCS as a function of b [m]
90
(as defined by A.7) and 8 [radians] (the scattering angle with respect to the original trajectory in
the rest-mass frame of the field particle):
(d=
bI
I[barns
(A.17)
Using A.6 with A.17 one obtains the RCS for Coulomb Collisions:
(dor
dO!
or
(d)
b2 0
barns
1028
4 sin (0/2)
2
kdO)=69
(A18)
S
)
1028
tan(0/2)sin2(/
)2
rad]
[rad
(A.19)
A.19 diverges as 8 approaches 0, implying that at smaller exit angles there are larger
cross
sections. This means that Coulomb scattering is dominated by small
angle deviations. Yet,
large deviations would occur due to multiple Coulomb scattering events over some distance in
the medium. The total scattering of the particles through the entire medium is what gives a
resolution limit in MECPR. Also, this result blows up as e -4 0, but the value e=0 is not physical,
since that would mean that the test particle went through the field particle. Therefore, physical
limits, which depend on the application, must be put on the exit angle 0 to calculate total cross
sections.
-56-
Appendix B: Scattering Parameterization Data and Plots
Table B-1: The table below gives the 50 data points used in the power regression fit for the scattering
parameters: <Eut>, OEout, and <1>. The Monte Carlo program SRIM was used with the independent
variables shown on the right of the black bar with 10,000 particles for each simulation. The four
dependent variables, on the right of the black bar, were calculated for each simulation. Matlab
was used to fit power law functions to each of the dependent variables. Only protons and alpha
particles were used as incident beams, and the areal density was used in the fitting process instead
of the actual density of the target, because areal density is referred to more often than density,
since the actual density of a subject may not be known during a dynamic process..
Tarxet
Incident
Particle
Energv
(MeV)
16
Areal
Density
(g/cmA2)
3.696E-03
15
10
5.96
5.96
Target
Tareet
Density
fe/cmA3)
Thickness
(um)
1.848
1.848
20
40
1.848
Test
Particle
Atomic
Radial
Scatter
StdDev
Exit
Tarmet
Tar•et
Mass
(amul
Atomic
4
1
0.027
7.392E-03
9.01
9.01
Ave
(MeV)
15.905
4
1
0.060
13
1.848E-03
9.01
4
1
15
10
8.940E-03
50.94
23
5
8
2.980E-03
50.94
5.96
10
4
5.960E-03
50.94
2.702
50
3
1.351E-02
2.702
200
6.6
2.702
150
2.702
(um)
Enermy
Exit
Enermyv
StdDev
(keV)
Exit Angle
Average
(rad)
15.886
4.263E-03
14.799
23.029
5.508E-03
0.008
12.944
10.837
2.724E-03
1
0.114
9.740
25.234
2.287E-02
23
1
0.036
7.898
14.220
1.932E-02
23
1
0.158
3.657
21.479
3.990E-02
26.98
13
1
1.331
1.655
42.008
8.263E-02
5.404E-02
26.98
13
1
6.305
3.527
107.706
8.134E-02
11.8
4.053E-02
26.98
13
1
1.745
10.540
59.007
3.023E-02
20
14.7
5.404E-03
26.98
13
1
0.075
14.563
20.251
1.083E-02
16.601
5
11.3
8.301E-03
180.95
73
1
0.038
11.157
22.984
2.422E-02
16.601
10
9.7
1.660E-02
180.95
73
1
0.277
9.381
33.749
4.827E-02
16.601
15
12
2.490E-02
180.95
73
1
0.233
11.585
39.788
4.438E-02
16.601
20
14.5
3.320E-02
180.95
73
1
0.353
14.013
47.036
4.217E-02
16.601
2
3
3.320E-03
180.95
73
1
0.224
2.870
28.269
6.955E-02
1.03
1500
14
1.545E-01
6.51
3.5
1
22.258
7.261
175.417
4.505E-02
1.03
20
10
2.060E-03
6.51
3.5
1
0.028
9.905
13.934
5.019E-03
1.03
5
2.8
5.150E-04
6.51
3.5
1
0.013
2.735
6.898
9.031E-03
1.03
100
15.3
1.030E-02
6.51
3.5
1
0.248
14.964
32.003
6.942E-03
1.03
1000
13.7
1.030E-01
6.51
3.5
1
14.955
9.526
127.772
3.609E-02
19.311
10
12.8
1.931E-02
196.97
79
1
0.212
12.502
35.156
4.086E-02
19.311
5
8.2
9.656E-03
196.97
79
1
0.098
8.001
24.757
4.487E-02
19.311
2
3.3
3.862E-03
196.97
79
1
0.043
3.162
15.628
6.392E-02
19.311
25
11.2
4.828E-02
196.97
79
1
0.810
10.373
58.510
7.998E-02
8.8955
5
3.2
4.448E-03
58.69
28
1
0.086
2.912
18.881
4.794E-02
8.8955
25
6.3
2.224E-02
5.368
49.393
6.406E-02
8.5
1.156E-02
28
28
0.774
13
58.69
58.69
1
8.8955
1
0.145
8.124
29.728
2.988E-02
8.8955
50
12.7
4.448E-02
58.69
28
1
0.933
11.602
61.559
8.8955
75
14.9
6.672E-02
58.69
28
1
1.736
13.427
78.260
4.240E-02
5.100E-02
- 57 -
1.3
1500
14.5
1.950E-01
7.41
3.946
1
1.3
1025
12.3
1.333E-01
7.41
3.946
1.3
500
7.5
6.500E-02
7.41
3.946
1.3
100
3.1
1.300E-02
7.41
16.601
5
5
8.301E-03
16.601
3
3.5
16.601
10
16.601
26.776
5.962
213.859
5.752E-02
1
17.776
5.899
156.435
4.993E-02
1
10.911
2.430
149.651
6.735E-02
3.946
1
2.039
1.176
54.891
6.621E-02
180.95
73
2
0.284
2.700
71.095
1.573E-01
4.980E-03
180.95
73
2
0.188
1.928
61.749
1.675E-01
10
1.660E-02
180.95
73
2
0.454
6.854
109.498
1.096E-01
7.5
15
1.245E-02
180.95
73
2
0.194
13.220
67.198
5.437E-02
2.702
35
12
9.457E-03
26.98
13
2
0.495
8.441
73.298
3.490E-02
2.702
25
9
6.755E-03
26.98
13
2
0.443
5.819
100.646
4.610E-02
2.702
10
4.5
2.702E-03
26.98
13
2
0.165
2.501
36.578
4.899E-02
2.702
7.5
3.5
2.027E-03
26.98
13
2
0.153
1.754
33.422
5.814E-02
19.311
2
5
3.862E-03
196.97
79
2
0.094
4.046
57.468
8.869E-02
19.311
1.5
2.5
2.897E-03
196.97
79
2
0.104
1.513
43.388
1.688E-01
19.311
5
10
9.656E-03
196.97
79
2
0.159
8.313
58.026
7.779E-02
1.848
10
3
1.848E-03
9.01
4
2
0.125
0.580
33.469
5.365E-02
1.848
20
4.5
3.696E-03
9.01
4
2
0.261
0.303
55.052
7.707E-02
1.848
50
8.5
9.240E-03
9.01
4
2
0.524
1.690
110.060
4.371E-02
1.848
25
5.5
4.620E-03
9.01
4
2
0.273
1.048
67.091
4.512E-02
8.8955
15
9
1.334E-02
58.69
28
2
0.444
3.730
99.252
8.909E-02
8.8955
5
4
4.448E-03
58.69
28
2
0.195
1.204
55.898
1.266E-01
,,
LU
> 200
15
N
M C
E
10
a
a, 150
(.
Eg 100
5
0-
0
a
0
5
10
15
20
50
0
0
TRIM Simulated
Average Exit Energy [MeV]
50
100
150
200
TRIM Simulated
Deviation of Exit Energy [keV}
- 58 ~
0.2
0.15
to
0.1
E
,
0.05
0
0.05
0.1
0.15
0.2
TRIM Simulated
Scattering Angle [rad]
Figure B-1: The three preceding graphs are simply the simulated data on the x-axis, and using
the same
independent variables, the parameterized calculation of the dependent variables on the
yaxis: average energy out, energy straggle, and scattering exit angle. The one-to-one
line,
where the parameterized fit value equals the simulated data exactly, is also shown
on each
plot.
-~59 ~-
Appendix C: Backlighter Parameterization Data and Plots
Because the parameterized equations for proton and neutron yield have multiple
independent variables, the easiest way to visually inspect the fit is by plotting the predicted
versus the actual yield values such that if it were a perfect fit, all the points would lie on the y=x
line. This was done for the six data sets mentioned in Section 4.1, and have been printed on
the following pages with proton yield comparisons on the left and neutron yield comparisons
on the right. Table C-1 gives all of the coefficient values and R-squared statistics for all of the
proton and neutron yield parameterizations. Overall, the parameterization coefficients of the
equation on the top of Table C-1 give fairly good agreement with the data, with the exception
of Fit 4-Yn. Fit 4-* covers three different laser drivers and 3 different laser foci, so exact
agreement was not expected. It was calculated as a general parameterization for the SG1018
laser pulse. Fit 6-* was the only parameterization which used a different fitting equation, Y2.
This formula was chosen because the agreement with equation Y1 was even worse. The reason
for not using Y2 to fit the first five formulae was that the dependence directly on the outer
diameter never made much physical sense. Therefore the energy flux was used instead of the
outer diameter and on-target-energy separately.
To fit the parameterization equations given in Table C-1, the Matlab function 'robustfit'
was used. It is an iterative weighted least squares algorithm, meaning that as it iterates to
converge on coefficient values it reweights the outlier data points less than those who are not
outliers. However, the coefficients that are calculated do not always make physical sense, and
it would be helpful for my future Doctoral work to write an algorithm which accounts for
uncertainties in the measurements as well as some intuitive limits on the values of the
coefficients. Currently in the plots below, the error bars are based on the average percent error
in the fit values, a 50% error in the proton yield measurement, and a 10% error in the neutron
measurement. The measurement errors are good estimates for the real error. A more rigorous
analysis of the measurement errors will come with further analyzation of the data.
~ 60 ~-
Table C-1: This table gives a complete list of parameterization coefficients for proton and neutron yields from
MECPR backlighters. Fits for similar laser parameters are displayed one on top of the other for a
direct comparison of fits between proton and neutron yields.
Y1 = Const*(tshella*(Eu.)b*(PD2/P
R2
3.5235
1.381
-0.3752
-0.642
0.871
0.5
% Error
18.1
18.7
-11.776
-6.2885
-1.0754
-1.1202
20.955
6.9618
0.728
0.707
25.8
14.2
5.91E-03
1.07E-02
-6.7032
-4.1309
-2.2216
-1.3759
-2.5249
-4.5991
0.919
0.854
13.9
9.63
5.61E+10
-5.1294
3.4986
5.5089
0.367
71
2.39E+02
-2.2514
0.24281
0.85702
0.0887
40.6
2.42E+03
-3.8479
1.2797
0.78286
0.415
46.9
2.06E-01
-0.6539
-4.3892
0.26645
0.188
62.2
% Error
48.1
22.6
Driver:Pulse (focus)
SSD:SG1018 (9R)
SSD:SG1018 (9R)
Const
4.99E+09
1.93E+05
a
b
-7.2793
-5.5934
2-Yp
2-Yn
SSD:SG1018 (8R)
SSD:SG1018 (8R)
2.13E+09
1.82E+03
3-Yp
3-Yn
Leg(2):SG1018 (9R)
Leg(2):SG1018 (9R)
SSD/Main/Leg(2):SG1018
(8R/9R/12R)
SSD/Main/Leg(2):SG1018
(8R/9R/12R)
5-Yn
SSD:SG1018
(300um-:Pole Driven)
SSD:SG1018
(300um-:Pole Driven)
3He)c
c
Fit
1-Yp
1-Yn
Y2 = Const*(tshe.)a*(Dout)b*l(EonTar)*(PDoPP3He )d
6-Yp
6-Yn
Driver:Pulse (focus)
SSD:SG1017 (9R)
SSD:SG1017 (9R)
Const
8.40E+63
3.14E-04
-2.0459
-1.9222
-0.7114
4.1938
c
d
2
R_
-15.579
-1.501
-0.974
0.8971
0.0656
0.3012
Fit 1: SSD:SG1018 (9R)
Fit 1: SSD:SG1018 (9R)
16
uU -
O
I-
0
i
12
c
E
E
12 0
0
r
S80
o4
-0 S8 4
4
z
0
0
4
8
12
16
0
Proton Yield from DATA (108)
I
I
4
8
I
I
12
16
20
Neutron Yield from DATA (108)
Fit 2: SSD:SG1018 (8R)
Fit 2: SSD:SG1018 (8R)
12
12 -
O*
0-
W-
,
E
0
S10
I.
8
E
26-
0
-W
0
.,
I
0
z
04
0
I
I
4
8
4
I
212
Proton Yield from DATA (108)
SI
2
I
I
4
6
I
I
8
I
I
I
10
Neutron Yield from DATA (108)
-~62 -
I
I
12
Fit 3: Leg(2):SG1018 (9R)
Fit 3: Leg(2):SG1018 (9R)
U
45
I-
I-
a: 4
Ur.
E
E
0
t.-
0
I..
I.-
"
2
C
0o
0
0
I4'
a'
a0
z
0-
I
'
I
4
0
Neutron Yield from DATA (108)
Fit 4: *:SG1018 (8R/9R/12R)
I1
0
'-*I
S10
E
0
cc
0 &
C
0
*I
0.1
I
i
I
I
*
I I
i
6
Proton Yield from DATA (108)
0.1
I
II
1
Proton Yield from DATA (108)
-~63
-
Fit 5: SSD:SG1018 (300um-)
Fit 5: SSD:SG1018 (300um-)
1
10
ou
O
e-I
0
o'-I
I-
u-
E
0
'0-
E
0
0.1
4.J
c-
O
0
0
81
z
0.01
0.1
0.01
0.1
1
0.1
Proton Yield from DATA (108)
10
Neutron Yield from DATA (108)
Fit 6: Leg(2):SG1017 (9R)
Fit 6: Leg(2):SG1017 (9R)
i
12t
VA
'6-
ES8
uL
I
E
o
"o
4
,!
CL
o
4
2-
a.
U-I
0
1
zm
I
4
0~
12
0
I
I
I
2
4
6
8
Proton Yield from DATA (108)
Neutron Yield from DATA (108)
Figure C-1: The twelve preceding graphs show the comparison between the parameterizations and the data for
both the proton and neutron yields (proton yield comparisons on the left and neutron comparisons
on the right). The one-to-one line is displayed in each plot as well, and represents a perfect fit to the
data. Error bars on the parameterized quantities were derived from the average percent error of the
fit, proton yield measurement errors are ~50%, and neutron yield measurement errors are "10%.
Overall, most of the parameterizations fit the data well, but more work and data will be needed for a
more rigorous analysis, and will be pursued during my Doctoral work.
S64-
Table C-2: This table gives a complete list of all thin glass D2 3He-filled backlighter capsules since 2005. Some data were not gathered before the shot, and
hence will never be measured; these data are represented by a -1. Not all of these data were used in the parameterization of the proton and
neutron yields, but the most pertinent laser configurations were parameterized.
Initial Da
Pressure
Initial 3He
Pressure
shot #
Target ID
Shot Date
PI
(atm )
(atm)
50539
50538
50537
50536
50535
50507
50334
49704
49703
49702
49701
49699
49694
49693
49137
49126
49125
49124
49122
49120
49119
49118
49117
49114
49113
49112
49111
49109
48357
47705
47703
IDC-LLNL 08-2-B1
IDC-LLNL 08-2-F1
IDC-LLNL 08-2-E1
IDC-LLNL 08-2-D1
IDC-LLNL 08-2-Cl
LLEC 05-26-38
LLEC 05-26-91
ISE-4Q07-07-507
ISE-4Q07-07-517
ISE-4Q07-07-09
ISE-4Q07-07-518
ISE-4Q07-07-07
ISE-4Q07-07-21
ISE-4Q07-07-503
CMF-3Q07-01-56
DDC-07-LLE 039-30
DDC-07-LLE 039-29
DDC-07-LLE 039-05
DDC-07-LLE 039-10
DDC-07-LLE 039-08
DDC-07-LLE 039-07
DDC-07-LLE 039-13
DDC-07-LLE 039-15
DDC-07-LLE 039-17
3/5/2008
3/5/2008
3/5/2008
3/5/2008
3/5/2008
3/4/2008
2/12/2008
12/5/2007
12/5/2007
12/5/2007
12/5/2007
12/5/2007
Tommasini
Tommasini
6.66
1.1
3.33
8.9
Tommasini
Tommasini
Tommasini
Sangster
Sangster
Knauer
Knauer
Knauer
Knauer
Knauer
Knauer
Knauer
Knauer
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Knauer
Li
Li
4.3
8.2
6.66
6.4
6.4
6.3
6.3
6.3
6.3
6.3
6.3
6.3
6.2
20.4
20.4
6.2
6.2
6.2
6.2
6.2
6.2
6.2
6.2
6.2
6.2
6.2
6.2
5.9
5.9
5.7
1.8
DDC-07-LLE 039-14
DDC-07-LLE 039-09
DDC-07-LLE 039-03
DDC-07-LLE 039-04
CMF-3Q07-01-35
NLUF-1Q07-02-A8
NLUF-1Q07-02-A6
12/5/2007
12/5/2007
10/16/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
10/11/2007
8/3/2007
5/30/2007
5/30/2007
3.33
18
18
13.5
13.5
14
13.5
14
14
13.5
21
46
46
15
15
15
15
15
15
15
15
15
15
15
21
15
15
~ 65
Measured D,
Pressure
(atm)
-1
-1
Measured 3He
Pressure
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
6.298
6.298
6.298
6.298
6.896
6.298
6.297
5.896
19.797
19.797
6.099
6.099
6.099
6.099
6.099
6.099
6.099
6.099
6.099
6.099
6.099
4.672
5.898
5.899
(atm)
-1
-1
11.947
11.428
11.462
11.27
8.89
11.273
11.207
11.05
41.208
41.738
12.172
11.558
12.252
11.971
12.796
11.724
12.903
12.967
12.626
12.569
12.138
15.494
12.87
13.176
D,/ 3He Fill
Pressure
Ratio
-1
-1
-1
-1
-1
-1
-1
0.5272
0.5511
0.5495
0.5588
0.7757
0.5587
0.5619
0.5336
0.4804
0.4743
0.5011
0.5277
0.4978
0.5095
0.4766
0.5202
0.4727
0.4703
0.4831
0.4852
0.5025
0.3015
0.4583
0.4477
SiO, Shell
Thickness
4
4
4
4
4
2
2
2.5
2.4
2.4
2.3
2.3
2.3
2.2
2.8
2.4
2.2
2.3
2.5
2.5
2.4
2.4
2.3
Outer
Diameter
(um)
894.6
894.4
878.8
878.8
878
890
862
436
423.8
419.8
424.6
427.6
432.6
436.4
435.6
413.8
444.4
437.6
437
447
425.8
2.5
2.2
417.8
419.6
401.4
408
428.4
2.5
423
2
417
445.4
445.8
441
2.2
2.7
2.4
2.5
shot #
Target ID
Shot Date
Pi
47702
47700
47698
47697
47696
46939
46936
46935
46934
46933
46932
46537
46536
46535
46534
46532
46531
46529
46528
46101
46100
45954
45953
45948
45943
45941
45782
45431
45430
45426
45425
45422
45421
44433
NLUF-1Q07-02-A15
NLUF-1Q07-02-A14
NLUF-1Q07-02-A13
NLUF-1Q07-02-B2
NLUF-1Q07-02-A11
FIG-1Q07-02-31
NLUF-1Q07-01-01
NLUF-1Q07-01-10
NLUF-1Q07-01-17
FIG-1Q07-02-26
NLUF-1Q07-01-14
FIG-1Q07-02-29
FIG-1Q07-02-12
FIG-1Q07-02-23
FIG-1Q07-02-22
FIG-1Q07-02-33
FIG-1Q07-02-06
FIG-1Q07-02-32
FIG-1Q07-02-14
ISE-4Q06-05-48
ISE-4Q06-05-02
ISE-1Q07-01-47
ISE-1Q07-01-46
ISE-1Q07-01-50
ISE-1Q07-01-49
ISE-1Q07-01-48
ISE-3Q06-05-29
ISE-4Q06-06-20
ISE-4Q06-06-16
ISE-4Q06-06-12
ISE-4Q06-06-08
ISE-4Q06-06-06
ISE-4Q06-06-04
NLUF-4Q06-01-05
5/30/2007
5/30/2007
5/30/2007
5/30/2007
5/30/2007
3/21/2007
3/21/2007
3/21/2007
3/21/2007
3/21/2007
3/21/2007
2/14/2007
2/14/2007
2/14/2007
2/14/2007
2/14/2007
2/14/2007
2/14/2007
2/14/2007
1/11/2007
1/11/2007
12/21/2006
12/21/2006
12/21/2006
12/21/2006
12/21/2006
12/7/2006
11/8/2006
11/8/2006
11/8/2006
11/8/2006
11/8/2006
11/8/2006
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Rygg
Rygg
Rygg
Rygg
Rygg
Rygg
Rygg
Rygg
Marshall
Marshall
Knauer
Knauer
Knauer
Knauer
Knauer
Li
Knauer
Knauer
Knauer
Knauer
Knauer
Knauer
Li
8/8/2006
Initial D;
Pressure
Initial 3He
Pressure
fatm)
(atm)
5.9
5.9
5.9
5.9
5.9
5.9
6
6
6
5.9
6
6.1
6.1
6.1
6.1
6.1
6.1
6.1
6.1
6.2
6.2
6.2
6.2
6.2
6.2
6.2
5.7
6.2
6.2
6.2
6.2
6.2
6.2
5.7
15.5
16
16.5
16.5
16
15
16
16
16
18
16
18
18
16
18
16
15
16
18
12
12
15
15
15
14
14
13
14
13
15
15
14
15
13
- 66 -
Measured D,
Pressure
.atm)
5.897
5.898
5.898
5.899
5.897
5.898
6.298
6.298
6.298
5.897
6.297
6.097
6.096
6.099
6.095
6.098
6.099
6.098
6.097
-1
-1
-1
5.8
5.2
5.2
5.2
-1
-1
-1
-1
-1
6.2
-1
5.699
Measured He
Pressure
(atm)
11.496
12.784
12.761
13.679
10.891
12.941
13.974
14.064
13.774
13.283
13.386
13.283
11.808
13.276
10.601
12.273
12.69
13.082
13.169
-1
-1
-1
11.7
11
10.6
10.6
-1
-1
-1
-1
-1
12.1
-1
12.146
D,/3He Fill
Pressure
Ratio
0.5130
0.4614
0.4622
0.4312
0.5415
0.4558
0.4507
0.4478
0.4572
0.4440
0.4704
0.4590
0.5163
0.4594
0.5749
0.4969
0.4806
0.4661
0.4630
0.5
0.5
0.5
0.4957
0.4727
0.4906
0.4906
0.5
0.5
0.5
0.5
0.5
0.5124
0.5
0.4692
SiO, Shell
Thickness
2.5
2.5
2.5
2.5
2.6
2.2
2.4
2.5
2.5
2.5
2.6
2.1
2.7
2.4
2.3
2.3
2.3
2.3
2.2
2.9
2.4
2.6
2.6
2.8
2.8
2.2
2.2
2.9
2.8
2.7
2.6
2.2
2.7
2.8
2.9
Outer
Diameter
Lum)
404
420
430
440.2
435.4
407.8
413
420
440
426.2
439.2
431.4
425.8
412.6
418.6
422.6
425.6
430.4
402.8
441.8
403.2
431.2
403.6
403.6
423.4
423.4
424.6
421.6
434.4
431.2
430.4
436.4
403.6
430.2
shot #
Target ID
Shot Date
44432
NLUF-4Q06-01-03
NLUF-4Q06-01-22
NLUF-4Q06-01-19
NLUF-4Q06-01-18
NLUF-4Q06-01-13
NLUF-4Q06-01-09
NLUF-4Q06-01-08
NLUF-4Q06-01-07
NLUF-4Q06-01-04
NLUF-4Q06-01-02
NLUF-4Q06-01-01
NLUF-1Q06-01-91
NLUF-1Q06-01-16
NLUF-1Q06-01-43
NLUF-1Q06-01-84
NLUF-1Q06-01-20
NLUF-1Q06-01-19
NLUF-1Q06-01-02
NLUF4Q05-04-20
NLUF4Q05-04-54
NLUF4Q05-04-05
NLUF4Q05-04-18
NLUF4Q05-04-45
NLUF4Q05-04-06
NLUF4Q05-04-09
NLUF4Q05-04-21
NLUF4Q05-04-41
NLUF4Q05-04-31
NLUF4Q05-03-28
NLUF4Q05-04-55
8/8/2006
8/8/2006
8/8/2006
8/8/2006
8/8/2006
8/8/2006
8/8/2006
8/8/2006
8/8/2006
8/8/2006
8/8/2006
2/28/2006
2/28/2006
2/28/2006
2/28/2006
2/28/2006
2/28/2006
2/28/2006
7/26/2005
7/26/2005
7/26/2005
7/26/2005
7/26/2005
7/26/2005
7/26/2005
7/26/2005
7/26/2005
7/26/2005
7/26/2005
7/26/2005
44431
44430
44429
44428
44427
44426
44425
44424
44423
44422
42774
42773
42772
42771
42768
42767
42765
40516
40515
40514
40513
40512
40511
40510
40509
40508
40507
40506
40505
PI
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
(leaky)
(leaky)
(leaky)
(leaky)
(leaky)
(leaky)
(leaky)
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Li
Initial Da
Pressure
(atm)
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
Initial 3He
Pressure
(atm)
13
14
14
14
13
14
13
13
13
14
13
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
-
67
Measured D,
Pressure
Measured 3He
Pressure
(atm)
(atm)
5.699
5.699
5.699
5.699
5.699
5.699
5.699
5.699
5.699
5.696
5.698
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
11.924
11.763
12.601
12.298
11.802
12.037
11.942
12.14
12.13
8.709
11.296
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
D? He Fill
Pressure
Ratio
0.4779
0.4845
0.4523
0.4634
0.4829
0.4735
0.4772
0.4694
0.4698
0.6540
0.5044
-1
-1
-1
-1
-1
-1
-1
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
Si 02Shell
Thickness
Outer
Diameter
2.2
2.6
2.8
2.3
2.5
2.4
2.6
2.9
2.8
2.8
2.8
2.5
2.5
2.5
2.5
2.5
2
2
2.2
2.6
2.3
2.1
2.3
2.2
2.1
2.6
2
2.3
2.7
2
413.4
423.2
434.6
433.6
428
412.8
408.2
405.8
439.6
418.6
422.6
410
420.2
429.6
424.6
440
423
433
430.4
464.2
427.6
428.2
445.6
427.4
455.2
427.2
436
463.6
854.4
437
(um)
Normalized
shot #
50539
50538
50537
50536
50535
50507
50334
49704
49703
49702
49701
49699
49694
49693
49137
49126
49125
49124
49122
49120
49119
49118
49117
49114
49113
49112
49111
49109
48357
47705
47703
47702
Pulse Shape
SSD:SG0801
SSD:SG0801
SSD:SG0801
SSD:SG0801
SSD:SG0801
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
Leg(2):SG1018
Leg(2):SG1018
Leg(2):SG1018
Leg(2):SG1018
Leg(2):SG1018
Leg(2):SG1018
Leg(2):SG1018
SSD:SG1018
Leg(2):SG1017
Leg(2):SG1017
Leg(2):SG1017
SSD
Modulation
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
OFF
ON
ON
OFF
ON
ON
ON
ON
ON
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
# Beams
60
60
60
60
60
60
60
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
EnerEv On
"'" E
-
Target J)
Flux
(J/um 2)
Enerev
(TJ/e)
0.00mm
0.00mm
0.00mm
0.00mm
0.00mm
0.00mm
0.00mm
300um300um300um300um300um300um300um300um8R
8R
8R
8R
8R
8R
9R
9R
9R
9R
9R
9R
9R
300um9R
9R
9R
17659.6
17505
17446.1
17482.3
16857.4
23077.3
23559.3
7808.6
7558.6
7957.7
7937.6
8025.9
7600.1
8023.6
7904.1
7580.3
7713.3
7708.9
7667.2
7777
7812.6
8619.9
8631.6
8512.6
8467.4
8585.3
8528.6
8720.2
7533.4
8874.6
8903.5
8974.4
7.024E-03
6.965E-03
7.191E-03
7.206E-03
6.961E-03
9.274E-03
1.009E-02
1.308E-02
1.340E-02
1.437E-02
1.401E-02
1.397E-02
1.293E-02
1.341E-02
1.326E-02
1.409E-02
1.243E-02
1.281E-02
1.278E-02
1.239E-02
1.372E-02
1.572E-02
1.561E-02
1.682E-02
1.619E-02
1.489E-02
1.517E-02
1.596E-02
1.209E-02
1.421E-02
1.457E-02
1.750E-02
1.6566
1.6428
1.6959
1.6994
1.6417
4.3744
4.7606
4.9341
5.2657
5.6498
5.7484
5.7311
5.3023
5.7507
4.4675
5.5391
5.3311
5.2560
4.8226
4.6752
5.3916
6.1787
6.4008
7.2116
6.1099
6.3853
5.7253
7.5295
4.2235
5.5873
5.4991
6.6046
Focus
n
ol
E
~ 68 ~
YProt
(keV)
83.2
33.5
56.1
42.2
44.6
150
240
0.168
0.119
0.473
0.322
0.503
0.424
0.395
0.026
1.55
3.89
6.17
7.61
3.54
6.96
1.31
1.11
1.34
0.912
1.97
0.803
3.81
0.141
0.752
1.04
1.04
Temp
....
n
1440
22.7
503
2170
1430
123
229
5.81
1.11
1.82
1.66
2.3
1.89
2.45
1.33
6.48
10.4
8.57
11
6.2
8.8
3.03
2.07
2.95
2.49
3.7
1.94
4.72
9.41
4.69
4.79
3.72
!on
gang
(ratio)
TemD
(keVy)
Time
-1
-1
-1
-1
-1
12.155
11.379
3.332
4.855
6.543
5.906
6.163
6.221
5.532
2.979
6.362
7.487
9.716
9.551
8.842
10.098
7.922
8.621
8.073
7.434
8.595
7.796
10.188
2.837
5.520
6.146
6.733
8.300
9.200
7.300
7.800
7.500
10.7
10.9
-1
-1
-1
-1
-1
-1
-1
5.3
-1
7.4
-1
10.3
10.7
11.6
7.5
-1
7.8
4.9
9.6
-1
15.2
4.5
-1
-1
-1
1075
1090
1140
1144
1172
-1
644
537
526
479
495
474
498
461
-1
514
530
491
523
556
484
470
484
441
478
456
481
470
-1
-1
-1
-1
L.s
shot #
Pulse Shape
47700
47698
Leg(2):SG1017
Leg(2):SG1017
47697
Leg(2):SG1017
47696
46939
46936
46935
46934
46933
46932
46537
46536
46535
46534
46532
46531
46529
46528
46101
46100
45954
45953
45948
45943
45941
45782
45431
45430
45426
45425
45422
45421
Leg(2):SG1017
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
SSD:SG1018
44433
44432
Leg(2):SG1017
Leg(2):SG1017
SSD
Modulation
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
OFF
ON
ON
ON
ON
ON
ON
OFF
OFF
# Beams
Focus
S
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
8R
8R
300um300um300um300um300um9R
300um300um300um300um300um300um9R
9R
Enerne On
En
n
Target (J)
Enerfy
Flux
(J/um 2 )
Normalized
Energy
(TJ/R)
8996.4
9230.6
9286.1
8640.8
9463
9440.3
9488.3
9564.8
9648.7
9469.8
6892.1
6825.4
6848.6
6852.1
6846.2
6879.5
6829.1
6827.1
7670.6
7910.3
7808.1
7705.7
7814.5
7431.8
7335.5
3045.8
7975.2
7858.7
7945.9
7878.6
7969.9
7887.7
8237
8341.8
1.623E-02
1.589E-02
1.525E-02
1.451E-02
1.811E-02
1.762E-02
1.712E-02
1.573E-02
1.691E-02
1.563E-02
1.179E-02
1.198E-02
1.281E-02
1.245E-02
1.220E-02
1.209E-02
1.173E-02
1.339E-02
1.251E-02
1.549E-02
1.337E-02
1.506E-02
1.527E-02
1.320E-02
1.303E-02
5.378E-03
1.428E-02
1.326E-02
1.360E-02
1.354E-02
1.332E-02
1.541E-02
1.417E-02
1.554E-02
6.1260
5.9965
5.5348
6.2216
7.1198
6.6480
6.4609
5.9344
6.1350
7.0201
4.1188
4.7103
5.2524
5.1055
5.0050
4.9587
5.0320
4.3572
4.9171
5.6198
4.8502
5.0734
5.1450
5.6587
5.5853
1.7494
4.8120
4.6318
4.9358
5.8053
4.6544
5.1932
4.6087
6.6625
- 69 ~-
0.506
0.613
0.575
1.7
5.32
5.52
6.08
4.9
4.95
10.4
0.8
1.65
3.5
3.1
3.34
2.25
3.56
0.45
0.945
1.05
0.15
0.107
0.185
0.0603
0.0763
5.61E-03
0.094
0.115
0.267
0.327
0.185
0.0707
4.72
4.58
2.71
2.41
2.6
5.94
7.75
6.92
9.37
9.5
5.99
9.26
2.6
4.41
6.6
6.34
8.53
6.75
8.89
1.41
6.32
3.34
1.5
0.83
2.12
0.68
0.7
-1
0.8
1.29
1.19
2.1
1.42
0.39
4.69
4.34
Ion Temp
Ion
Bang
(ratio)
(keV)
TemD
(keV)
Time
5.835
6.489
6.189
6.790
9.518
10.135
9.311
8.482
10.289
11.728
6.961
7.487
8.581
8.316
7.628
7.182
7.697
7.057
5.405
7.0126605
4.752
5.149
4.529
4.557
4.878
-1
4.980
4.566
6.222
5.469
5.168
5.777
11.184
11.412
-1
-1
-1
-1
10.3
10
8.3
6.4
8
9.8
13.7
7.2
7.6
10.1
11.2
10.2
12
5.7
28.2
22
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
7.9
9.3
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
2629
2515
2225
2179
-1
-1
379
367
shot #
Pulse Shape
44431
Leg(2):SG1017
44430
44429
44428
Leg(2):SG1017
Leg(2):SG1017
Leg(2):SG1017
44427
Leg(2):SG1017
44426
Leg(2):SG1017
44425
Leg(2):SG1017
44424
44423
44422
42774
42773
42772
42771
42768
42767
42765
40516
40515
Leg(2):SG1017
Leg(2):SG1017
Leg(2):SG1017
SSD:SG0602
SSD:SG0602
SSD:SG0602
SSD:SG0602
SSD:SG1018
SSD:SG1018
SSD:SG1018
Main: SG1018
Main: SG1018
40514
40513
40512
Main: SG1018
Main: SG1018
Main: SG1018
40511
40510
Main: SG1018
Main: SG1018
40509
40508
40507
40506
40505
Main:
Main:
Main:
Main:
Main:
SG1018
SG1018
SG1018
SG1018
SG1018
SSD
Modulation
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
# Beams
Focus
Energv
On
EnergOn
Target (J)
Energy
Flux
(j/um 2 )
Normalized
Energy
(TJ/R)
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
9R
12R
12R
12R
12R
12R
12R
12R
8287.5
8300.9
8371.5
8376.8
8344.5
8356
8300.8
8303.9
8048.5
7649.6
3738.3
3473.6
2388
4821.3
9654.4
9725.1
9427.9
9477.9
9424.6
9575.8
9546.8
9428.7
9593.6
9742
9677.9
9799.4
9818.2
9918.7
9868.7
1.473E-02
1.399E-02
1.417E-02
1.456E-02
1.559E-02
1.596E-02
1.605E-02
1.368E-02
1.462E-02
1.363E-02
7.079E-03
6.262E-03
4.119E-03
8.512E-03
1.587E-02
1.730E-02
1.601E-02
1.629E-02
1.392E-02
1.667E-02
1.657E-02
1.512E-02
1.672E-02
1.497E-02
1.688E-02
1.641E-02
1.454E-02
4.325E-03
1.645E-02
5.3445
4.7134
5.8135
5.4928
6.1271
5.7919
5.2197
4.6084
4.9261
4.5937
2.6712
2.3630
1.5542
3.2122
5.9900
8.1607
S70 -
7.5501
6.9838
5.0515
6.8378
7.4454
6.1998
7.1686
6.7231
6.1248
7.7400
5.9643
1.5112
7.7591
Ion Temp
(ratio)
2.86
1.98
7.1
1.58
3.03
6.15
1.72
8.64
3.38
1.44
1.2
1.2
1.39
3.95
3.58
4.84
6.32
13
8.86
17.6
17.4
12.8
20
26.1
22.2
25.3
32.8
39.8
31.1
3.69
2.24
5.14
3.12
3.41
3.99
2.22
7.08
3.77
2.31
0.181
0.289
0.228
0.884
0.274
0.704
0.827
8.15
7.48
8.06
6.25
12.9
13.2
12.2
14
10.8
15.7
50.7
10.9
Ion
Temp
(key)
(keV)
10.007
10.579
12.844
8.426
10.604
13.484
8.7
5.2
12.2
8.6
11.2
11.6
7.2
9.4
8.2
6.5
-1
-1
-1
-1
-1
-1
-1
11.9
11.9
17.8
12.5
17.2
18.2
16.8
13.8
12.6
12.9
9.4
14.8
10.005
12.159
10.646
9.160
27.581
21.628
26.373
22.444
40.886
28.127
29.801
13.701
11.994
15.831
17.766
11.114
13.385
15.680
13.664
16.362
15.501
10.064
17.973
Bane
Time
361
301
490
259
250
277
273
-1
-1
336
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
Appendix D: Geant4 Benchmark Experimental Data
In this appendix, the experimental data used to create the final product radiographs,
which were used to benchmark the Geant4 simulations, will be shown. When analyzing the
images created by MECPR, one of the most important plots is the Contrast vs. Diameter plot.
These plots, which are very typical when analyzing CR39, have a very distinct character making
it relatively simple to extract the data from the noise when the data are good. The purpose of
etching the CR39 isto 'raise the noise' above the data in contrast. This means that after etching
the piece, the intrinsic noise in the CR39 is elevated in contrast and is typically small in
diameter. Therefore, the data tend to be lower in contrast and have diameters typically
ranging from a couple of microns to about twenty. Proper use of the Contrast vs. Diameter plot
allows the rejection of the noise, and the acceptance of the data to be represented in the final
product radiograph. The following pages contain the Contrast vs. Diameter plots, final
radiographs, and final radiographs with the swaths taken for lineout analyzation for OMEGA
shots 46531 (Figure D-1) and 45953 (Figure D-2).
D.1
Experimental Data for OMEGA shot 46531
46531_T6_3P188_Emie_Front_4hr.cpsA [from 1.5*Minimum, "2.5/Contour, Rsm=1]
0
10
Track Diameter (pm)
20
Figure D-1: (top) Contrast vs. Diameter diagram in logarithmic contour form. There
are two distinct peaks, one
high in contrast, the other low; the low contrast peak is the signal, and can be generally
encompassed by the contrast limits of 0 - 40% and diameter limits of 2.5 - 20-pm. The
upper limit
in contrast is chosen by the minimum between the two peaks (where the signal
begins to be
overtaken by the intrinsic noise). (bottom left) Final fluence radiograph for OMEGA
shot 46531,
darker color implies higher fluence. The black spots down the image are intrinsic
noise that I
couldn't remove without losing some signal, so I left them, but they have no physical
significance.
The image has also been cone-smoothed with a radius of three to eliminate
high frequency
statistical noise. (bottom right) The same final radiograph with the shaded
portion covering
azimuthal angles from -40 - 2100, the region used to find the azimuthally average
radial lineout for
benchmarking with Geant4.
- 72 -
D.2
Experimental Data for OMEGA shot 45953
45953_1P90_Emie front.cpsA [from 1.5'Minimum, '2.5lContour, Rsm=1]
0
10
Track Diameter (pm)
20
Figure D-2: (top) Contrast vs. Diameter diagram for OMEGA shot 45953
in logarithmic contour form. Again, the
contour peak at lower contrast is the signal. For this image, the
contrast limits chosen were 0 35% with a diameter range of 2 - 18-pm. (bottom left) Final product
radiograph using the limits
determined from the Contrast vs. Diameter plot. A cone-smoothing
of radius three was applied to
the image. The high fluence band, in line with the stock holding
the cylinder, is a product of some
kind of electromagnetic field present, it is not yet well understood,
but does affect that portion of
the radiograph. (bottom right) The swath used to construct the
lineout is shown on the final
radiograph. It is averaged across the width and plotted as a function
of length along the swath. I
attempted to avoid the high fluence area or the stock in order
to only account for scattering
through the cylinder shell.
-~73 ~-
Appendix E: Acronyms
Acronym
Expansion
D-3He
DT
FI
FSC
HED
HEDP
ICF
IFE
LASER
LLE
LPI
MCS
MECPR
NRC
PCIS
PRL
PSFC
RCS
RT
STP
Deuterium-Helium-3
Deuterium-Tritium
Fast Ignition
Fusion Science Center
High Energy Density
High Energy Density Physics
Inertial Confinement Fusion
Inertial Fusion Energy
Light Amplification by Stimulated Emission of Radiation
Laboratory for Laser Energetics
Laser Plasma Interaction
Multiple Coulomb Scattering
Mono-Energetic Charged Particle Radiography
Nuclear Regulatory Commission
Proton Core Imaging System
Physical Review Letters
Plasma Science and Fusion Center
Rutherford Cross Section
Rayleigh Taylor
Standard Temperature Pressure
" 74 "
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