Mono-energetic proton radiography is a vital diagnostic for numerous high-energy-density-physics, inertial-confinement-fusion, and laboratory-astrophysics experiments at OMEGA. With a large number of campaigns executing hundreds of shots, general trends in D3He backlighter performance are statistically observed. Each experimental configuration uses a different number of beams and drive symmetry, causing the backlighter to perform differently. Here, we analyze the impact of these variables on the overall performance of the D3He backlighter for proton-radiography studies. This study finds that increasing laser drive asymmetry can degrade the performance of the D3He backlighter. The results of this study can be used to help experimental designs that use proton radiography.

Mono-energetic proton radiography is an essential diagnostic for a number of impactful studies in the area of high-energy-density-physics. Proton radiography1 enables the study of electromagnetic fields2 and warm-dense-matter stopping power3 in laser produced plasmas at OMEGA and on the National Ignition Facility (NIF). It has allowed researchers to explore the kinking behavior of the Crab Nebula jet,4 visualize the fields inside and outside an inertial-confinement-fusion (ICF) implosion,5 see the fields inside indirect drive hohlraums,6 and detect collisionless shocks driven by fast plasma flows.7 Numerical methods have recently been applied to proton radiography, enabling the reconstruction of path integrated electromagnetic fields present in the plasma.8 

Proton radiography implodes a capsule (also called a backlighter) filled with deuterium and helium-3 fuel to produce protons at two specific energies through the nuclear reactions shown in the following:

D+DT (1.01 MeV)+p (3.02 MeV),
(1)
D+He3α(3.6 MeV)+p (14.7 MeV).
(2)

Note that the energies of the protons are not exactly the same as their birth energies. The protons are born while the laser is still causing the proton energies to be upshifted.1 These protons will travel through a subject plasma where they are deflected by electromagnetic fields and Coulomb collisions.9 The protons are collected using a CR39 nuclear track detector.10 Etching in NaOH reveals the particle tracks and brings forth the radiograph.

Over the past four years, we have supported over 300 deuterium helium-3 (D3He) backlighter shots at OMEGA from more than 40 experimental shot days. This paper analyzes these shots to find how experimental parameters affect the performance of the D3He backlighter.

The finding of this work is that laser drive asymmetry on the D3He backlighter can affect performance. For a given laser energy, increasing the asymmetry of the laser drive degrades the DD and D3He proton yields. Low laser energy and large asymmetry could compromise the quality of the proton radiographs.

This paper is organized as follows: Section II discusses the experimental parameters in the analysis dataset. The subject of laser drive asymmetry will be discussed in some detail. Section III shows power-law fits of experimental parameters to DD and D3He proton yields. A subset of the shots chosen to isolate capsule conditions shows that yields are affected by asymmetry. Section IV summarizes the study and offers experimental design suggestions for proton radiography experiments.

The performance of the D3He backlighter can be quantified by measuring the DD and D3He proton yields. For the purpose of the present work, the DD proton yield is inferred from the DD neutron yield measured by the neutron time of flight detectors (nTOFs) at OMEGA.11 The D3He proton yield is inferred from reactivity scaling12 using the ion temperature measured by the nTOFs. Yields that are too low can cause very few proton tracks on the CR39, resulting in low quality radiographs. The exact lower bound on the acceptable proton yield will depend on factors such as magnification. For this study, we take the boundary between acceptable and unacceptable proton yields to be 1 × 108. Figure 1 shows histograms of the DD and D3He proton yields. Note that a few of the D3He proton yields for the dataset are below the threshold for good radiography data. For some experiments with strong fields and/or high density, the D3He proton radiograph can provide cleaner and higher quality data than the DD proton radiographs. This is because the D3He proton has higher energy and is therefore stiffer than the lower energy DD proton. The DD proton radiograph is more likely to be washed out if the fields are strong enough to cause particle trajectories to cross. Hence, some shots that have low D3He proton yields can compromise the success of an experiment.

FIG. 1.

Summary of the proton yields from the dataset. (a) Histogram of the DD proton yields. (b) Histogram of the inferred D3He proton yields. The black dashed line shows the 108 yield boundary under which the radiograph quality can be questionable. Note that some of the shots have D3He proton yields below this boundary.

FIG. 1.

Summary of the proton yields from the dataset. (a) Histogram of the DD proton yields. (b) Histogram of the inferred D3He proton yields. The black dashed line shows the 108 yield boundary under which the radiograph quality can be questionable. Note that some of the shots have D3He proton yields below this boundary.

Close modal

A number of experimental parameters contribute to the performance of the D3He backlighter for proton radiography. Capsule conditions such as capsule outer diameter, capsule shell thickness, capsule shell roughness, capsule D2 pressure, and capsule 3He pressure are determined for each shot. Laser conditions such as laser energy, laser focusing, and laser drive asymmetry are also determined for each shot. The dataset for this study includes all these parameters.

The capsules are normally 420 μm in outer diameter. This capsule size was found to result in a small source size needed for radiography to resolve small scale structures.1 Because these capsules are not the main experimental subject of the experiment, the quality of the capsules is not a priority during target manufacturing. Capsules, therefore, will tend to have variations in capsule outer diameter, shell thickness, and shell roughness. Similarly, the laser conditions on the backlighter are not of the highest quality. Typically, no phase plates or smoothing by spectral dispersion13 (SSD) is used to illuminate the backlighter. Both laser and capsule conditions contribute to relatively large shot-to-shot yield variations from the D3He backlighter.

Experimental constraints can result in anisotropic illumination of the D3He backlighter. Beams are often blocked by targets or other objects in the target chamber. The laser beams used to illuminate the backlighter are typically the leftover beams. Beams that illuminate other targets are chosen first. Changes in the experimental configuration during the shot day further add to beam constraints because repointing beams to the backlighter costs time and could delay shots. All these factors combine to make the laser illumination of the D3He backlighter typically asymmetric.

Laser drive asymmetry needs to be quantified in order to observe its impact on DD and D3He proton yields. For a given laser configuration, VISRAD14 is used to generate a laser illumination map. This describes the laser intensity on the backlighter as a function of polar and azimuthal angle. Let this illumination map be f(θ, ϕ). A spherical harmonic decomposition gives a set of expansion coefficients for this function,

fm=02πdϕ0πdθsin(θ)f(θ,ϕ)Ym(θ,ϕ).
(3)

Summing these expansion coefficients normalized to the average laser power on the target gives the asymmetry measure A,

A2==1maxm=fmf002.
(4)

For each , there are 2 + 1 expansion coefficients. The expansion grows as 2, making high mode expansions expensive. This study used an max of 10.

Figure 2 shows a comparison between a 60 beam backlighter illumination map and a 39 beam backlighter illumination map. No phase plates are used in either configuration, and the laser focus is the same. Mounting stalks cause the blank region at 180 polar degrees for the 60 beam configuration and the blank region at 0 polar degrees for the 39 beam configuration. Note that there are regions of the 39 beam illumination map that receive no laser light. One would expect that the asymmetry measure would be larger for the 39 beam configuration than that for the 60 beam configuration. Applying the method described above, the asymmetry measure of the 60 beam configuration is found to be 0.06, and the asymmetry measure for the 39 beam configuration is found to be 0.44.

FIG. 2.

Laser illumination maps generated from VISRAD. (a) 60 beam configuration at OMEGA. (b) 39 beam configuration. The laser focus conditions are the same for both images. The asymmetry measure for (a) was 0.06, and the asymmetry measure for (b) was 0.44.

FIG. 2.

Laser illumination maps generated from VISRAD. (a) 60 beam configuration at OMEGA. (b) 39 beam configuration. The laser focus conditions are the same for both images. The asymmetry measure for (a) was 0.06, and the asymmetry measure for (b) was 0.44.

Close modal

Trends can be extracted from the dataset of many capsule and laser conditions. A good method for exposing trends in the data is to use a simple power-law model. A least-squares15,16 method was used to fit the model,

YDDp=a×(OD)b×(ΔR)c×(E)d×(F)e×(A)f×(ptot)g×(Rp)h×(Cr)i,
(5)
YD3Hep=a×(OD)b×(ΔR)c×(E)d×(F)e×(A)f×(ptot)g×(Rp)h×(Cr)i
(6)

to the DD and D3He proton yields, respectively. Here, OD is the capsule outer diameter; ΔR is the capsule shell thickness; E is the laser energy on the capsule; F is the focus offset of the laser; A is the asymmetry measure of the laser illumination; ptot is the total capsule pressure; Rp is the pressure ratio between 3He and D2; and Cr is the capsule roughness. The power-laws are fit to all known parameters.

The result of the power-law fits for both DD and D3He proton yields is shown in Fig. 3. The power-law fit for the DD proton yield does a good job for most of the shots. Most shots have a predicted yield within a factor of two of the measured proton yield. The fit to the D3He proton yield data is not as good as the DD proton yield fit but is good enough to capture the trends in the data. Most shots are within a factor of three of the inferred D3He proton yield. Recall that these implosions do not use the highest quality capsule or laser conditions. Spread in the proton yields is, therefore, expected. The best fit power-laws are shown as follows:

YDDp=9.77×104×(OD)2.54×(ΔR)0.59×(E)0.64×(F)0.40×(A)0.68×(ptot)2.10×(Rp)1.37×(Cr)0.06,
(7)
YD3Hep=1.17×102×(OD)2.21×(ΔR)0.70×(E)1.46×(F)1.44×(A)1.22×(ptot)1.60×(Rp)1.80×(Cr)0.09.
(8)
FIG. 3.

Least squares power-law fits of the DD and D3He proton yields compared to observed yields. The dashed line shows when the power-law yield is the same as the observed yield. (a) shows this for the DD protons, and (b) shows this for the D3He protons.

FIG. 3.

Least squares power-law fits of the DD and D3He proton yields compared to observed yields. The dashed line shows when the power-law yield is the same as the observed yield. (a) shows this for the DD protons, and (b) shows this for the D3He protons.

Close modal

Note that these power-law equations should not be extrapolated outside the range of experimental parameters present in the dataset. It would be incorrect to assume that, for example, moving the focus offset as close as possible to the capsule would result in a very large yield. Therefore, the power-law equations are only good approximations within the range of the experimental parameters present in the dataset. The power-law coefficients need to be considered in the context of the range of parameters (see Table I for the magnitude of the scaling for each parameter). Also note that these power-law fits are not meant to allow one to predict the yield of the D3He backlighter. The goal of the fits is instead to observe trends present in the data.

TABLE I.

Range of parameters and their significance for the DDp and D3Hep power-law fit. The magnitude of the scaling is the ratio of the maximum and minimum values of a parameter raised to the absolute value of the power-law coefficient for that variable.

Power-law valueMagnitude
ParameterMin valueMax valueDDpD3HepDDpD3Hep
OD (μm) 387.6 440.1 2.54 2.21 1.38 1.32 
ΔR (μm) 1.7 2.4 0.59 0.70 1.23 1.27 
E (kJ) 4.38 19.1 0.64 1.46 2.57 8.60 
F (μm) 1.6 1.89 0.40 −1.44 1.07 1.27 
A 0.151 0.957 −0.68 −1.22 3.51 9.51 
ptot (atm) 17.5 21.3 2.19 −1.22 1.51 1.37 
Rp 1.875 2.344 1.37 1.80 1.36 1.49 
Cr (μm) 0.05 0.85 0.06 0.09 1.19 1.29 
Power-law valueMagnitude
ParameterMin valueMax valueDDpD3HepDDpD3Hep
OD (μm) 387.6 440.1 2.54 2.21 1.38 1.32 
ΔR (μm) 1.7 2.4 0.59 0.70 1.23 1.27 
E (kJ) 4.38 19.1 0.64 1.46 2.57 8.60 
F (μm) 1.6 1.89 0.40 −1.44 1.07 1.27 
A 0.151 0.957 −0.68 −1.22 3.51 9.51 
ptot (atm) 17.5 21.3 2.19 −1.22 1.51 1.37 
Rp 1.875 2.344 1.37 1.80 1.36 1.49 
Cr (μm) 0.05 0.85 0.06 0.09 1.19 1.29 

The power-law fits suggest two important trends. More asymmetry in the laser drive leads to a lower predicted yield. More laser energy leads to a higher predicted yield. To more closely examine the impact of asymmetry, a subset of shots with similar capsule conditions is studied.

Figure 4(a) shows the DD proton yield as a function of asymmetry. The shots shown here were selected to have similar capsule outer diameters and capsule shell thicknesses, as well as a moderate number of beams. This figure shows a clear decrease in yield with increasing asymmetry. Controlling the other experimental parameters lets us conclude that laser drive asymmetry degrades backlighter performance. Figure 5 shows the same but for the D3He proton yield. The same trends are clear here: asymmetry degrades the yield while laser energy improves the yield. Note that a few of the higher asymmetry D3He proton yields are below the threshold for good radiography data. This shows that asymmetry can cause a shot to produce a radiograph of questionable quality.

FIG. 4.

DD proton yield trends with (a) asymmetry measure and (b) laser energy.

FIG. 4.

DD proton yield trends with (a) asymmetry measure and (b) laser energy.

Close modal
FIG. 5.

D3He proton yield trends with (a) asymmetry measure and (b) laser energy.

FIG. 5.

D3He proton yield trends with (a) asymmetry measure and (b) laser energy.

Close modal

Collecting experimental parameters from over 300 D3He backlighter shots has enabled a unique opportunity to observe the performance of the backlighter for proton radiography at OMEGA. Parameters such as capsule outer diameter, capsule shell thickness, capsule shell roughness, capsule pressure, number of beams on the backlighter, laser energy, laser focusing, and laser drive asymmetry were collected for each shot. Fitting a power-law model to a subset of these parameters revealed trends in the data. The most important predictors of backlighter performance were found to be total laser energy on the capsule and the asymmetry of the laser drive. Down selecting shots to control capsule conditions confirms both these trends.

With these findings in mind, we are now in a place to suggest design guidelines for mono-energetic proton radiography experiments at OMEGA. The parameters studied in more detail were chosen in part because the experimental designer has control over them. In general, experimentalists do not have much control over capsule conditions. This leaves only laser conditions that can be optimized for experimental applications. The scope of the design guidelines involves only optimizing proton yields from the backlighter. Other aspects such as source size cannot be improved, given the constraints of the sizes of targets and the energy of the lasers at OMEGA.

With the finding that laser asymmetry degrades performance and laser energy increases performance, experimentalists should try to use as many beams as possible (more laser energy) while keeping track of the asymmetry of the laser drive. Many experiments utilize as few beams as possible on the backlighter. If such a configuration is asymmetric enough, the D3He backlighter could fail to produce enough yield for quality radiography.

Putting these guidelines to specific quantities for both number of beams and asymmetry is difficult and not entirely useful because of natural spread in the DD and D3He proton yields. With this caveat, we will still suggest a few bounds for consideration. Laser configurations with fewer than 18 beams should be avoided when the asymmetry measure is above 0.6. The combination of few beams and high asymmetry should be avoided whenever possible.

This work was supported, in part, by the U.S. Department of Energy NNSA MIT Center-of-Excellence under Contract No. DE-NA0003868 and by the National Laser Users Facility under Contract No. DE-NA0003938. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Raw data were generated at OMEGA. Derived data supporting the findings of this study are available from the corresponding author upon reasonable request.

1.
C. K.
Li
 et al,
Rev. Sci. Instrum.
77
,
10E725
(
2006
).
2.
C. K.
Li
 et al,
Phys. Rev. Lett.
97
,
135003
(
2006
).
3.
A. B.
Zylstra
 et al,
Phys. Rev. Lett.
114
,
215002
(
2015
).
4.
C. K.
Li
 et al,
Nat. Commun.
7
,
13081
(
2016
).
5.
J. R.
Rygg
 et al,
Science
319
,
1223
(
2008
).
6.
7.
C. K.
Li
 et al,
Phys. Rev. Lett.
123
,
055002
(
2019
).
8.
A. F. A.
Bott
 et al,
J. Plasma Phys.
83
,
905830614
(
2017
).
9.
N. L.
Kugland
,
D. D.
Ryutov
,
C.
Plechaty
,
J. S.
Ross
, and
H.-S.
Park
,
Rev. Sci. Instrum.
83
,
101301
(
2012
).
10.
F. H.
Séguin
 et al,
Rev. Sci. Instrum.
74
,
975
(
2003
).
11.
V. Y.
Glebov
 et al,
Rev. Sci. Instrum.
75
,
3559
(
2004
).
12.
H.-S.
Bosch
and
G. M.
Hale
,
Nucl. Fusion
32
,
611
(
1992
).
13.
S.
Skupsky
 et al,
J. Appl. Phys.
66
,
3456
(
1989
).
14.
J. J.
MacFarlane
,
J. Quant. Spectrosc. Radiat. Transfer
81
,
287
(
2003
).
15.
SciPy 1.0 Contributors
 et al,
Nat. Methods
17
,
261
(
2020
).
16.
K.
Levenberg
,
Q. Appl. Math.
2
,
164
(
1944
).