The effects of shock dynamics on compressibility of indirect-drive ignition-scale surrogate implosions, CH shells filled with D3He gas, have been studied using charged-particle spectroscopy. Spectral measurements of D3He protons produced at the shock-bang time probe the shock dynamics and in-flight characteristics of an implosion. The proton shock yield is found to vary by over an order of magnitude. A simple model relates the observed yield to incipient hot-spot adiabat, suggesting that implosions with rapid radiation-power increase during the main drive pulse may have a 2× higher hot-spot adiabat, potentially reducing compressibility. A self-consistent 1-D implosion model was used to infer the areal density (ρR) and the shell center-of-mass radius (Rcm) from the downshift of the shock-produced D3He protons. The observed ρR at shock-bang time is substantially higher for implosions, where the laser drive is on until near the compression bang time (“short-coast”), while longer-coasting implosions have lower ρR. This corresponds to a much larger temporal difference between the shock- and compression-bang time in the long-coast implosions (∼800 ps) than in the short-coast (∼400 ps); this will be verified with a future direct bang-time diagnostic. This model-inferred differential bang time contradicts radiation-hydrodynamic simulations, which predict constant 700–800 ps differential independent of coasting time; this result is potentially explained by uncertainties in modeling late-time ablation drive on the capsule. In an ignition experiment, an earlier shock-bang time resulting in an earlier onset of shell deceleration, potentially reducing compression and, thus, fuel ρR.

In the inertial confinement approach to laboratory fusion,1,2 substantial compression of the fuel is required in MJ-scale implosions such as those at the National Ignition Facility (NIF).3 A spherical convergence ratio (ratio of initial to final radius) of ∼35 is necessary to achieve the conditions required for ignition and energy gain.2 

While ignition experiments at the NIF use targets with cryogenic layers of DT fuel, numerous surrogate implosions have been conducted, where the layer of DT ice is replaced with a surrogate mass of ablator material (CH). The hydrodynamics before deceleration are nearly identical for the cryogenic layered and surrogate implosions,4 enabling complementary studies and diagnostics of implosion dynamics, such as symmetry5,6 and velocity.7,8 One of the main objectives of using these surrogate implosions is to characterize the implosion at various stages to benchmark radiation-hydrodynamics simulations.4,9–11

In an implosion, a series of spherically converging shocks are launched with increasing strength. These shocks eventually coalesce at the capsule's inner edge and then converge at the center of the implosion. The final shock “rebounds” and briefly creates high-ion-temperature conditions at the center of the implosion. In the case of surrogate implosions at NIF with a D3He gas fill, this ion temperature is high enough to produce energetic protons via the fusion reaction

D + 3 He α ( 3.67 MeV ) + p ( 14.7 MeV ) .
(1)

For surrogate implosions at the NIF, this “shock burn” occurs several hundred ps before the main compression burn, and is approximately concurrent with peak shell implosion velocity. This is shown for a typical surrogate implosion in Fig. 1 using the radiation-hydrodynamics code HYDRA,11 where the simulated shock trajectories for the four launched shocks and final merged shock are shown in Fig. 2(a) as contours of the normalized pressure gradient | ( 1 / P ) d P / d r |. The laser pulse is shown in Fig. 2(b), a detailed view of the shock dynamics around the shock-bang time and compression-bang time is shown in Fig. 2, and the capsule dimensions are shown in Fig. 3.

FIG. 1.

NIF surrogate shot N120408-001-999 (CH shell with D3He gas, see Fig. 3). (a) Simulated shock trajectory, visualized as the pressure gradient | ( 1 / P ) d P / d r |, where black indicates a higher value. The shock plot shows the four shocks launched into the shell, which merge to form the final shock that travels to the center, where it rebounds, increasing the temperature and density, creating the shock burn at 22.03 ns. The compression bang time is at 22.83 ns. Simulated shock (s) and compression (c) bang times are indicated by the arrows. (b) Laser pulse (foot before 10 ns not shown). In the drive, the pickets at ∼13 and ∼16 ns launch the 2nd and 3rd shocks, respectively, with the 4th launched by the rise to peak power.

FIG. 1.

NIF surrogate shot N120408-001-999 (CH shell with D3He gas, see Fig. 3). (a) Simulated shock trajectory, visualized as the pressure gradient | ( 1 / P ) d P / d r |, where black indicates a higher value. The shock plot shows the four shocks launched into the shell, which merge to form the final shock that travels to the center, where it rebounds, increasing the temperature and density, creating the shock burn at 22.03 ns. The compression bang time is at 22.83 ns. Simulated shock (s) and compression (c) bang times are indicated by the arrows. (b) Laser pulse (foot before 10 ns not shown). In the drive, the pickets at ∼13 and ∼16 ns launch the 2nd and 3rd shocks, respectively, with the 4th launched by the rise to peak power.

Close modal
FIG. 2.

Shock trajectory through rebound, shock burn, and compression phases, for the same simulation as in Fig. 1(a).

FIG. 2.

Shock trajectory through rebound, shock burn, and compression phases, for the same simulation as in Fig. 1(a).

Close modal
FIG. 3.

Typical NIF surrogate capsule (see Table II for more information). The plastic shell (ρ = 1.08 g/cm3) is filled with 30:70 atomic D and 3He fuel.

FIG. 3.

Typical NIF surrogate capsule (see Table II for more information). The plastic shell (ρ = 1.08 g/cm3) is filled with 30:70 atomic D and 3He fuel.

Close modal

After the final merged shock rebounds at ∼22 ns, the shock burn occurs over ∼100 ps, producing energetic D3He protons (Eq. (1)). These escaping protons are used to probe the in-flight characteristics of the shell at a radius of ∼250 μm.

D3He proton spectroscopy is a well-developed technique for diagnosing inertial fusion implosions12–16 at the OMEGA laser facility17 and, now, at the NIF.18,19 A typical measured D3He proton spectrum is shown in Fig. 4. The protons have been energy downshifted to ∼11.5 MeV from the birth energy of 14.7 MeV. The downshift is caused by Coulomb collisions with the imploding plasma electrons,20 and the observed downshift can be related to the implosion areal density (ρR) using a charged-particle stopping theory.21 The shock yield observed (8.7 × 107) is related to the final merged shock strength.16,22 The center-of-mass radius (Rcm) of the imploding shell is inferred in addition to ρR using 1-D modeling discussed in Sec. II.

FIG. 4.

Sample D3He proton spectrum from NIF shot N101004-002-999, measured on the equator (DIM 90-78 WRF #1) after hohlraum correction. The D3He average birth energy of 14.7 MeV is shown by the vertical dashed line. The red dashed line is a Gaussian fit to the spectrum. Surplus protons at low energy, ∼8–9 MeV, are due to the onset of compression burn. More details are given in Appendix  A.

FIG. 4.

Sample D3He proton spectrum from NIF shot N101004-002-999, measured on the equator (DIM 90-78 WRF #1) after hohlraum correction. The D3He average birth energy of 14.7 MeV is shown by the vertical dashed line. The red dashed line is a Gaussian fit to the spectrum. Surplus protons at low energy, ∼8–9 MeV, are due to the onset of compression burn. More details are given in Appendix  A.

Close modal

As a probe of the implosion shock dynamics, this technique is unique in that it probes the strength of the final merged shock when it hits and rebounds from the center of the implosion. This measurement is complementary to the shock-timing measurements of the shock velocity that uses an interferometry technique,23 which has been highly successful at understanding the shock dynamics in the shell for radii larger than 600–700 μm.24–27 At smaller radii, the interferometry measurements “blank.” As a result, the interferometry measurement would not see any additional shocks launched later in the implosion after the blanking, and does not probe the shock dynamics in the gas, when spherical convergence effects are significant; as the shock strength increases with convergence,22 non-hydrodynamic behavior may become important.28,29

The paper is organized as follows: an implosion model for interpreting the spectral results is presented in Sec. II. Section III gives an overview of the experiments, Sec. IV discusses a down-selection of the available shots, which are analyzed in Sec. V to study the shock dynamics, Sec. VI interprets the results and their relevance to implosion compressibility, and the paper is concluded in Sec. VII.

The D3He protons slow down monotonically as they traverse any material between the source and spectrometer. The measured proton downshift is directly related to the implosion ρR at the time of shock burn. This is illustrated in Fig. 5, which shows the birth spectrum plus modeled spectra for several values of the shell center-of-mass radius (Rcm) and ρR using the model described in this section. These values span the typical range at shock-bang time in NIF implosions.

FIG. 5.

For illustration, modeled D3He proton spectra at birth (black) downshifted through 64 (red), 83 (green), and 118 (blue) mg/cm2 of ρR are shown. The downshifts are calculated with a 1-D self-consistent model. Values of the shell Rcm associated with each spectrum are also shown.

FIG. 5.

For illustration, modeled D3He proton spectra at birth (black) downshifted through 64 (red), 83 (green), and 118 (blue) mg/cm2 of ρR are shown. The downshifts are calculated with a 1-D self-consistent model. Values of the shell Rcm associated with each spectrum are also shown.

Close modal

To relate the measured D3He proton spectrum to the implosion conditions, a model involving charged-particle stopping theory21 is required. The simplest 0-D model is to take a single characteristic plasma composition, density, and electron temperature from a simulation or an estimate, and then use a stopping power theory to calculate dE/dr. This works well for OMEGA implosions, where the dense shell dominates slowing,15 but for ignition-scale surrogate implosions being conducted at the NIF, a significant fraction of proton slowing during the shock burn occurs in the fuel and ablated material. These plasmas have much lower density and higher temperature than the dense shell, so a single choice of plasma conditions cannot accurately describe the entire system.

This necessitates a 1-D self-consistent model, which is constructed using initial target conditions and assumptions about in-flight plasma conditions to specify the density and temperature profiles of the implosion. As the shell converges, the ρR increases and the energy of emitted protons decreases. The shell center-of-mass radius Rcm is taken as a free parameter and, thus, is varied to obtain ρR(Rcm) with ρ R 0 ρ ( r ) d r. Similarly, the energy of protons escaping the implosion is calculated as a function of Rcm by

E p ( R c m ) = E 0 0 d E d r ( r , R c m ) d r ,
(2)

where E0 is the average birth energy of the protons. The charged-particle stopping power dE/dr depends on plasma conditions specified by the model and, thus, on both r and Rcm. The Li-Petrasso theory21 is used in this work.

The initial capsule conditions are used as a model input: the shell material, inner and outer radii, and gas fill (composition and initial pressure). Fig. 3 illustrates the typical capsule dimensions and gas fill. The model makes assumptions about the in-flight characteristics of the implosion, informed by data when available or 1-D HYDRA11 simulations: temperature in the fuel, shell, and ablated mass, the thickness30 and mass remaining of the shell, and an ablated mass profile.

With the initial conditions and in-flight assumptions, the gas density and ρR scale with Rcm as

ρ gas = ρ 0 , gas ( R i R c m Δ R s / 2 ) 3 ,
(3)
ρ R gas = ρ gas ( R c m Δ R s / 2 ) ,
(4)

where ρ0,gas is the initial gas density, Ri is the initial inner shell radius, and ΔRs is the in-flight shell thickness. Similarly, the shell conditions are given by

ρ shell = M r e m ρ 0 , shell ( R o 3 R i 3 ) ( R c m + Δ R s / 2 ) 3 ( R c m Δ R s / 2 ) 3 ,
(5)
ρ R shell = ρ shell Δ R s ,
(6)

where ρ0,shell is the initial shell density, Mrem is the remaining mass fraction, and Ro and Ri are, respectively, the initial outer and inner radii of the shell.

The ablated mass profile is specified by

ρ ( r ) = { ρ max × e ( r r 0 ) / λ if r 0 r r 1 ρ min if r 1 r r 2 ,
(7)

where r0 = Rcm + ΔRs/2 is the outer radius of the imploding shell, ρmax and ρmin are the maximum and minimum densities of ablated material, and λ is a characteristic scale length in the ablation region. The radius r1 is determined by requiring continuity of the ablated mass density profile as described by Eq. (7), and r2 is determined by conservation of total mass. The values of ρmax, ρmin, and λ are model assumptions. The areal density of ablated material is

ρ R abl = r 0 r 2 ρ ( r ) d r = ρ max λ [ 1 e ( r 1 r 0 ) / λ ] + ( r 2 r 1 ) ρ min .
(8)

An example of the modeled density profile is shown for Rcm = 250 μm in Fig. 6. The components of ρR, e.g., Eqs. (4), (6), and (8) are calculated as functions of Rcm both in absolute values of mg/cm2 and also as fractions of the total ρR (Fig. 7). The gas and shell ρR depend strongly on convergence (Eqs. (4) and (6)), while the ablated material ρR only increases modestly as Rcm decreases. Thus, for Rcm ∼ 200–300 μm, the shell ρR will dominate with 60%–70% of the total ρR.

FIG. 6.

Density profile used in the 1-D model at Rcm = 250 μm. This center-of-mass shell radius is typical for NIF shots at shock-bang time. The gas material is shown in red (8 mg/cm2), the shell is shown in blue (53 mg/cm2), and the ablated mass is in green (23 mg/cm2).

FIG. 6.

Density profile used in the 1-D model at Rcm = 250 μm. This center-of-mass shell radius is typical for NIF shots at shock-bang time. The gas material is shown in red (8 mg/cm2), the shell is shown in blue (53 mg/cm2), and the ablated mass is in green (23 mg/cm2).

Close modal
FIG. 7.

ρR components (gas, shell, and ablated material) as a function of Rcm for typical model parameters. The results are plotted as absolute ρR (a) and normalized to the total (b).

FIG. 7.

ρR components (gas, shell, and ablated material) as a function of Rcm for typical model parameters. The results are plotted as absolute ρR (a) and normalized to the total (b).

Close modal

The final result of the model is the relationships between the three quantities: Rcm, ρR, and emitted proton energy (Ep). For the typical parameters, the model produces the curves shown in Fig. 8. For completeness, we show the ρR vs Rcm, Ep vs Rcm, and, finally, the ρR vs Ep curves. Thus, the measured quantity (Ep) can be converted directly into ρR and Rcm using these relationships.

FIG. 8.

(a) Modeled ρR vs Rcm, (b) average energy of emitted protons vs Rcm, and (c) average energy of emitted protons vs ρR. The dashed curves indicate the uncertainties in the modeling. The instrumental lower cutoffs are shown in (c) by dotted lines at 5 MeV (pole), and 7–8 MeV for the equator, increased due to the energy loss in the hohlraum wall (see Fig. 10).

FIG. 8.

(a) Modeled ρR vs Rcm, (b) average energy of emitted protons vs Rcm, and (c) average energy of emitted protons vs ρR. The dashed curves indicate the uncertainties in the modeling. The instrumental lower cutoffs are shown in (c) by dotted lines at 5 MeV (pole), and 7–8 MeV for the equator, increased due to the energy loss in the hohlraum wall (see Fig. 10).

Close modal

Each quantity used in the model has an associated error bar, which is used to calculate the uncertainty in the inferred quantities. This is done by an in-line sensitivity analysis to variations in the input quantities. For details of the model inputs and uncertainties, see Appendix  C. As the model uncertainties are assumed to be uncorrelated, they are added in quadrature. Any uncertainties in the proton measurement are propagated in quadrature with the model uncertainties. Uncertainties are shown in Fig. 8 by the dashed curves.

This model can be validated against radiation-hydrodynamic simulations using HYDRA. In the simulation, full profiles of hydrodynamic variables (density and temperature) are output at several times. The emitted D3He proton energy is then calculated using the full profiles. The calculated energy is then analyzed with the model, and the model-inferred values for ρR and Rcm can be compared to known values directly extracted from the simulation. This is shown in Fig. 9 for two different simulations of shot N120408, where six snapshots are used from each simulation corresponding to varying ρR and Rcm. The blue points correspond to a nominal simulation, while the red points are a simulation with significant preheat (changing the implosion trajectory and plasma conditions in the shell). Typical model error bars are shown. The chosen times span the typical range of shock ρR and Rcm observed. The model's agreement with both simulations of shot N120408, with significantly different plasma conditions between the simulations, shows that the uncertainties used in the model cover the range of expected variation in plasma conditions. This comparison shows excellent agreement between the simulation and model, demonstrating the model's fidelity as an analysis tool.

FIG. 9.

Comparison between model-inferred ρR (top) and Rcm (bottom) using synthetic emitted proton energies from HYDRA simulations, compared to values directly extracted from the simulation. Six time snapshots are used from two simulations: nominal (blue) and high preheat (red).

FIG. 9.

Comparison between model-inferred ρR (top) and Rcm (bottom) using synthetic emitted proton energies from HYDRA simulations, compared to values directly extracted from the simulation. Six time snapshots are used from two simulations: nominal (blue) and high preheat (red).

Close modal

The compact Wedge Range Filter (WRF) proton spectrometers18,31,32 have been used at the NIF since 2009. Between 1 and 4 spectrometers are fielded on the polar (0–0) and equatorial (90–78) diagnostic manipulators (DIMs).33 Each WRF provides a complete spectral measurement of the D3He protons, from which yield, ρR, and Rcm are inferred.

WRF proton spectrometers have been used on a total of 85 surrogate D3He gas-filled indirect-drive implosions on the NIF, forming the basis of this work. For these experiments, the total laser energy varied in the range 0.9–1.9 MJ, and the peak laser power was between 243–522 TW. Gas-filled Au or depleted U (DU) hohlraums were used in these experiments. The hohlraum width was 5.44 mm (“544” geometry) or 5.75 mm (“575” geometry) with varying lengths in the range of 9–10 mm. Details of the experimental geometry are conceptually shown in Fig. 10. Spectra measured on the equator must be corrected for energy loss in the hohlraum wall, see Appendix  B.

FIG. 10.

WRF setup on the NIF. Compact WRF proton spectrometers are placed at ±13.6° to the DIM axis on both the pole [DIM (0, 0)] and equator [DIM (90, 78)].

FIG. 10.

WRF setup on the NIF. Compact WRF proton spectrometers are placed at ±13.6° to the DIM axis on both the pole [DIM (0, 0)] and equator [DIM (90, 78)].

Close modal

The capsules were primarily CH with an outer radius varying from 1087 to 1169 μm and thickness from 188 to 231 μm. Si and Ge dopants are used within the shell. The gas fill was typically a 30:70 atomic mixture of D and 3He at an initial gas density of 6.3 mg/cm3. Each of these parameters is used in the ρR modeling described in Sec. II (also see Fig. 3).

The complete dataset is shown in Fig. 11. Within a DIM, multiple WRFs are averaged when available to reduce random and statistical errors; the weighted mean and resulting uncertainty are shown. The measured ρR is shown in Fig. 11(a). The random/statistical errors associated with the ρR values are dominated by the larger systematic and model uncertainties (see Sec. II and Appendix  C). Many of the shots have asymmetries between the pole and equator: these asymmetries are discussed in a separate publication.19 Overall the ρR typically varies between 70–110 mg/cm2. The most notable set of outliers are the implosions with ρR in the range of 160–170 mg/cm2 measured on DIM 90–78. The distinguishing feature for these implosions is that they were conducted as part of a series of low-power short-coast implosions.

FIG. 11.

WRF data for all surrogate implosions. (a) Shock ρR data. When available both polar (DIM 0-0) and equatorial data (DIM 90-78) are shown. (b) Shock proton yield measured by WRFs on DIM 90-78. (c) Center-of-mass shell radius (Rcm) plotted as average values for both pole (DIM 0-0) and equator (DIM 90-78).

FIG. 11.

WRF data for all surrogate implosions. (a) Shock ρR data. When available both polar (DIM 0-0) and equatorial data (DIM 90-78) are shown. (b) Shock proton yield measured by WRFs on DIM 90-78. (c) Center-of-mass shell radius (Rcm) plotted as average values for both pole (DIM 0-0) and equator (DIM 90-78).

Close modal

The proton shock-yield data for the entire dataset are shown in Fig. 11(b). Only data from the equator (DIM 90–78) are shown. This is because the polar yield data are affected by transverse electromagnetic field structures at the LEH, which can cause deflections and, thus, a reduction in the apparent yield observed by the WRFs on the pole.34–36 A significant shot-to-shot yield variation is observed, i.e., (1–35) × 107. Fundamentally, the large variability is due to the extreme temperature sensitivity of the D3He reaction, which makes the shock-proton yield very sensitive to the final shock strength.16,22

Finally, the inferred shell center-of-mass radius (Rcm) is shown in Fig. 11(c). According to this analysis, the shell is typically at a radius of 250–300 μm at the shock-bang time. In the high ρR cases, the inferred Rcm is as low as ∼190 μm. However, the error bars are large, typically ±25–30 μm, caused by the model uncertainties (described in Sec. II).

Due to the large shot-to-shot parameter variations during the NIF campaigns, it is necessary to select a subset of implosions with similar overall conditions for detailed analysis. We perform this down-selection using the following criteria:

  1. Standard capsules (CH with D3He fill, see Fig. 3).

  2. 5.75 mm diameter hohlraums.

  3. WRF data available on both pole and equator.

  4. Low-adiabat (“4-shock”) pulse shapes.

This reduces the number of shots to 30. Criterion #3 is required to allow for modeling of the observed ρR asymmetries (see Fig. 11(a) and Ref. 19) and determining of average values for ρR and Rcm. Shots selected via these criteria are used in subsequent analysis and are denoted in Fig. 11 by square markers.

The shock dynamics of the down-selected set of 30 implosions can now be explored. The observations indicate that the shock dynamics are most sensitive to the peak power of the laser drive, the coasting time of the implosion, and the rise time of the main laser pulse, see Fig. 12.

FIG. 12.

Relevant variables of the laser pulse: rise time, peak power, and coast time. In this case, the rise time is 2 ns, the peak incident power is 300TW, and the coasting time is 0.9 ns (short-coast, while long-coast is ∼2 ns). The bang time is indicated by the red line.

FIG. 12.

Relevant variables of the laser pulse: rise time, peak power, and coast time. In this case, the rise time is 2 ns, the peak incident power is 300TW, and the coasting time is 0.9 ns (short-coast, while long-coast is ∼2 ns). The bang time is indicated by the red line.

Close modal

Since the effective drive experienced by the capsule depends on the absorption of the incident laser light and the effectiveness of conversion to x rays, we add 25TW to the actual laser power for DU hohlraums to account for the latter and, then, multiply by the observed absorption fraction to account for the former. The 25TW effective increase in power is based upon measured enhancements in radiation temperature when using DU hohlraums.37 This gives an “effective peak power,” which is used in this work. The coasting time of an implosion is defined as the difference between the end of the laser drive and the measured compression bang time. The rise times used in these experiments are discrete, with design values of 1, 2, or 3 ns.

With these definitions, the main observables (average ρR and shock yield) are plotted versus the effective peak power, coasting time, and rise time. The data are shown in Fig. 14. To eliminate the effect of low-mode asymmetries observed in these implosions, this analysis uses an average ρR obtained from a fit to the polar and equatorial ρR data (see Appendix  D and Ref. 19). The different rise times used are differentiated by marker color. Furthermore, the hohlraum material is specified by marker shape: square markers for DU and circular markers for Au hohlraums.

FIG. 14.

Shock ρR and yield data [ρR (a-c) and Yp (d-f)] versus effective peak power (a) and (d), coast time (b) and (e), and rise time (c) and (f). For the rise time, points are artificially displaced for clarity around the values 1, 2, or 3 ns (see c.f.). Rise time is further specified by point color: 1 ns (blue), 2 ns (green), and 3 ns (red) to improve clarity in the power and coast time plots. Additionally, Au-wall hohlraums are denoted by circular markers and DU-wall hohlraums by square markers.

FIG. 14.

Shock ρR and yield data [ρR (a-c) and Yp (d-f)] versus effective peak power (a) and (d), coast time (b) and (e), and rise time (c) and (f). For the rise time, points are artificially displaced for clarity around the values 1, 2, or 3 ns (see c.f.). Rise time is further specified by point color: 1 ns (blue), 2 ns (green), and 3 ns (red) to improve clarity in the power and coast time plots. Additionally, Au-wall hohlraums are denoted by circular markers and DU-wall hohlraums by square markers.

Close modal

The distribution of implosion parameters used (peak power, coast time, and rise time) is illustrated by Fig. 13. With a few exceptions, the experiments fall into two groups

  1. Low-power (∼275–325 TW), short-coast (∼1–1.5 ns), and slow-rise (3 ns).

  2. High-power (∼325–375 TW), long-coast (∼2–2.5 ns), and fast-rise (1 or 2 ns).

FIG. 13.

Coast time and peak power of down-selected experiments. With a few exceptions, implosions have been conducted at low-power, short-coast (∼300 TW and ∼1 ns) conditions or high-power, long-coast (∼350 TW and ∼2 ns) conditions.

FIG. 13.

Coast time and peak power of down-selected experiments. With a few exceptions, implosions have been conducted at low-power, short-coast (∼300 TW and ∼1 ns) conditions or high-power, long-coast (∼350 TW and ∼2 ns) conditions.

Close modal

Since these two groups are diametrically opposed in all three parameters disentangling their effects require using a few select implosions that do not fall into these groups. For the rise time, a set of three implosions was conducted, where only the rise time was varied, significantly aiding this interpretation.

First, the interpretation of the shock-yield data can be aided by a set of three shots conducted in which only the rise time was varied. These data are shown in Fig. 15(a). The faster rise pulse shapes clearly create higher shock yields. This is consistent with the data in Fig. 14(f).

FIG. 15.

Shock yield (a) and ρR (b) versus rise time for a set of three shots, where only the rise time was varied.

FIG. 15.

Shock yield (a) and ρR (b) versus rise time for a set of three shots, where only the rise time was varied.

Close modal

Conversely, the coast time (Fig. 14(e)) has no clear effect on the shock yield, since short- and long- coast times have data with both high- and low- shock yield.

For the peak power, the data in Fig. 14(d) suggest a trend, where lower peak power creates a weaker shock. This is intuitive and consistent with the fact that all low power (≲ 300 TW) shots have low yield, but at higher power, the shock yield displays significant variation.

We conclude that the faster-rise pulses create shock yields 2–3× higher (Figs. 14(f) and 15) with other variables constant, and that increasing the peak power may increase the shock yield. We note that the shock yield varies by approximately 15× over the dataset, indicating substantial variation in shock strength.

Two shots that do not fit into the overall implosion parameter grouping are essential to understanding the data: N120409, which was a high-power short-coast shot and N130213, which was a low-power long-coast shot. These two are specifically annotated in Figs. 13, 14(a), and 14(b).

Fig. 14(a) plots the shock ρR versus effective peak power. Neglecting the results from shots N120409 to N130213, the data show an anti-correlated trend between ρR and peak power. However, shots N120409 and N130213 clearly suggest that this trend is due to the preponderance of high-power long-coast and low-power short-coast implosions. For the coasting, a clear trend is observed in Fig. 14(b), including both N120409 and N130213, where large coast times generate significantly lower shock ρR than short-coast implosions.

In Fig. 15, the set of three shots with a controlled rise time shows no change in shock ρR as the rise time is varied. This demonstrates that the rise time has no effect on the shock ρR; the apparent trend in Fig. 14(c) is due to the low coasting times in the 3 ns rise implosions.

The dependence between shock ρR and coast time can be further investigated. Fundamentally, the ρR is mainly determined by the shell Rcm at the shock-bang time (see Sec. II).

On many of these shots, simultaneous x-ray radiographs of the implosion trajectory were obtained,7,8,38 and from the x-ray radiographs, Rcm(t) is determined near the shock-bang time. Presently, the shock-bang time is not directly measured, but the combination of the trajectory measurement and WRF-inferred Rcm from shock-produced protons can be used to estimate the shock-bang time. This technique is shown in Fig. 16.

FIG. 16.

Rcm versus time before compression-bang time for shot N120408-001-999. As the shell trajectory (black) and Rcm (blue) are determined from x-ray radiography and WRF proton spectroscopy, respectively, the shock-bang time (red) can be estimated. Error bars are shown by dashed lines. For this shot, ΔBT = 0.34 ± 0.13 ns.

FIG. 16.

Rcm versus time before compression-bang time for shot N120408-001-999. As the shell trajectory (black) and Rcm (blue) are determined from x-ray radiography and WRF proton spectroscopy, respectively, the shock-bang time (red) can be estimated. Error bars are shown by dashed lines. For this shot, ΔBT = 0.34 ± 0.13 ns.

Close modal

From the x-ray data, we know the shell velocity at Rcm = 200 or 300 μm. The absolute timing uncertainty of the x-ray measurement relative to compression bang time is ±50 ps. We know that the compression-bang time uncertainty is typically ±50 ps or better. From this information, combined with the x-ray and proton data, a shock-bang time can be determined relative to compression-bang time: ΔBT ≡ tshocktcomp, to remove any variation in absolute implosion timing. The uncertainty in Rcm from this analysis is used to determine the uncertainty in the shock-bang time in addition to the uncertainty in timing of the x-ray measurement and shell velocity.

The shock-bang time is estimated for a set of 14 experiments (a subset of Fig. 14), where x-ray radiography is available, and shown in Fig. 17. The estimated bang time difference ranges from ∼0.4–0.8 ns. The displayed error bars represent random (shot-to-shot) uncertainties, while the larger systematic uncertainty is ±0.11 ns.

FIG. 17.

(a) Estimated difference in time between shock and compression bang, contrasted to simulations, for 2DConA (square) and ConA (round) implosions, which were also probed with in-flight x-ray radiography. The two points at coasting time ∼2.5 ns show good agreement between the two experimental platforms. Uncertainties are random, with an additional ±0.11 ns systematic uncertainty. (b) ρR data for the same shots versus coast time. Higher ρR corresponds to higher convergence and, thus, smaller ΔBT.

FIG. 17.

(a) Estimated difference in time between shock and compression bang, contrasted to simulations, for 2DConA (square) and ConA (round) implosions, which were also probed with in-flight x-ray radiography. The two points at coasting time ∼2.5 ns show good agreement between the two experimental platforms. Uncertainties are random, with an additional ±0.11 ns systematic uncertainty. (b) ρR data for the same shots versus coast time. Higher ρR corresponds to higher convergence and, thus, smaller ΔBT.

Close modal

For this data, a clear trend is shown, where the long-coast implosions have substantially larger differential bang time (more negative ΔBT) than the short-coast shots.

Simulations of ΔBT exist for five of these shots (one of which, N120408-001-999, was simulated and presented earlier in Figs. 1 and 2); these simulations are also shown in Fig. 17. The simulations predict a nearly constant ΔBT of ∼−(0.7–0.8)ns, while the data show a clear trend, where long-coast implosions have a larger differential bang time.

The data indicate that the shock-bang time occurs earlier relative to the main compression burn in long-coast implosions than in short-coast implosions. The interpretation of this observation is that the imploding shell is at a larger radius (Rcm) during the shock bang for the long-coast implosions. This means that the final rebounding shock, which creates the shock bang, is either faster relative to the implosion velocity or launched earlier for the long-coast pulses.

The shock transit time in the gas (after break-out from the shell) is ∼4 ns according to HYDRA simulations (see Fig. 2(a)). This can also be estimated using simple models. For example, using the Hugoniot conditions, a shock launched by 100 MBar of pressure at the ablation front propagates through the pre-compressed shell in approximately 450 ps. This shock propagates through the density discontinuity at the inner surface of the shell39 and spherically converges as a Guderley shock22 through the initial gas, which takes an additional ∼4.1 ns. However, at the time when the shock is launched into the gas, the sound speed in the shell c = γ P / ρ is quite low. For an ideal gas at 100 MBar pressure and density of ρ = 20 g/cc, the speed of sound is only ∼30 μm/ns (in the frame of the imploding shell). But since the inward shell fluid velocity at shock breakout is ∼60 μm/ns and the shock velocity in the lab frame is ∼150 μm/ns, the shock is already effectively decoupled from the driving piston of the ablation front. The coasting dynamics happen later in time and, thus, cannot directly affect the shock strength in this scenario.

The late-time drive will affect the implosion (shell) trajectory. If the implosion comes in late relative to the shock, the bang-time differential will increase. This could occur, for instance, due to in-flight decompression and deceleration of the shell if the ablation pressure decreases, while the shell is still at a large radius. Since the data and simulations are discrepant for the short-coast implosions, this suggests that the late-time drive (during the last ns) is not well modeled in the simulation. This could be related to the drive degradation multipliers40 not accurately reflecting the late-time drive, an uncertainty in radiation transport through the ablated shell material or an uncertainty in the compressed ablator equation of state. Another possibility is that severe mix in the coasting implosions may truncate the compression burn, moving the apparent compression bang time earlier and decreasing ΔBT.

One potential significance of an earlier shock-bang time is its implications for the deceleration phase of the implosion. Deceleration begins when the rebounding shock (as a heat wave) encounters the incoming shell. The rebound phase can also be calculated using Guderley's solution.22 For a constant shock strength, an earlier shock-bang time means that the rebounding shock will hit the incoming shell at an earlier time (larger radius) and, thus, deceleration will begin earlier. This could reduce the compression and final ρR of the implosion. Interestingly, data in cryogenic implosions show 25%–50% higher ρR and higher inferred stagnation pressure for short-coast implosions.37,41 This is consistent with this work's interpretation of the short-coast implosions, where the shock dynamics is more amenable to high compression, i.e., later shock-bang time relative to compression.

The significance of large variation in shock proton yield can be interpreted in the context of the shock dynamics and hot-spot adiabat. The initial heating of the low-density material at the center of the implosion is from the imploding and rebounding shock, which sets the incipient hot-spot adiabat prior to the onset of deceleration and subsequent PdV heating of the hot spot. The hot-spot adiabat can be roughly characterized as the ratio of its pressure to the Fermi pressure

α P P f = n e k B T e + n i k B T i ( 3 π 2 ) 2 / 3 2 5 m e n e 5 / 3 .
(9)

The shock preferentially heats ions over electrons16 and, in this Guderley model, they are assumed to be uncoupled (τei long compared to dynamical timescales).42 

We can interpret the shock proton yield via a simple model based on the Gudelery spherically imploding shock solution.16,22 The Guderley model gives hydrodynamic profiles in a self-similar solution as a function of a single shock strength parameter, ξ. For a single choice of ξ, the D3He yield (Y) is calculated from

Y = f D f 3 H e n i 2 σ v d 3 r d t ,
(10)

where fD and f3He are the fuel ion fractions and σ v is the temperature-dependent fusion reactivity. A mass-weighted hot-spot adiabat is also calculated via Eq. (9), evaluated when the rebounding shock encounters the incoming shell material. The shock strength ξ is then varied to map out a relationship between the proton shock yield and hot-spot adiabat, and this relationship is well described by a power law

α = 2.10 Y 0.247 + 16.4 ,
(11)

where the coefficients are from a fit to the model results. This relation is shown in Fig. 18.

FIG. 18.

Inferred hot-spot adiabat (α) versus proton shock yield using a Guderley model. Points are at values of ξ from 250–350 (at intervals of 5) μm/ns0.688. The solid curve is a power-law fit (see Eq. (10)).

FIG. 18.

Inferred hot-spot adiabat (α) versus proton shock yield using a Guderley model. Points are at values of ξ from 250–350 (at intervals of 5) μm/ns0.688. The solid curve is a power-law fit (see Eq. (10)).

Close modal

Using this model, the adiabat can be determined from the yield and, thus, rise time (see Fig. 19). The hot-spot adiabat increases for faster rise times due to a stronger launched shock. This empirical result can be compared qualitatively to modeled hot-spot adiabats43 for cryogenic implosions,37,44,54 in which a very similar trend is seen, where α increases from ∼100 to ∼160 as the rise time decreases from 3 to 1 ns. The absolute values of α inferred for these surrogate implosions are expected to be higher than cryogenic implosions, since ablation of low-adiabat ice material in the latter decreases the hot-spot adiabat. Further, modeling is required to directly relate surrogate hot-spot adiabat to cryogenic hot-spot adiabat, but this is motivated by the lack of any other direct measurement of the hot-spot adiabat. Additionally, 3-D effects are expected to alter the inferred hot-spot adiabat in cryogenic experiments, so a better understanding of the incipient adiabat and hot-spot formation process may increase our understanding of these 3-D effects.

FIG. 19.

(a) Modeled adiabat versus rise time for the same dataset as shown in Fig. 15. (b) Modeled hot-spot adiabat in cryogenic implosions.

FIG. 19.

(a) Modeled adiabat versus rise time for the same dataset as shown in Fig. 15. (b) Modeled hot-spot adiabat in cryogenic implosions.

Close modal

Inferred values of α as a function of measured radiation-temperature rise rate are shown for the 30 downselected shots used in Fig. 20, analogous to Fig. 59 of Ref. 37. The factor of 10× variation in shock proton yield corresponds to ∼75% variation in α, as seen from the power 0.247 in Eq. (10). For the entire dataset (Fig. 11), a 35× min-max variation in shock yield is observed, corresponding to a ∼2.4× variation in α.

FIG. 20.

Modeled adiabat versus rise rate for the same dataset as Figs. 14(d)–14(f).

FIG. 20.

Modeled adiabat versus rise rate for the same dataset as Figs. 14(d)–14(f).

Close modal

The overall shock dynamics may be significantly affected by kinetic effects. For example, recent OMEGA experiments have shown experimental evidence for long ion-ion mean-free-path effects,28 enhanced diffusive mix,29 and temperature anomalies in shock-heated plasmas.45 Relative to the OMEGA experiments of Refs. 28, 29, and 45, in these experiments, the initial gas density is ∼2× higher and the shock is weaker; at similar initial density to this work, an indirect-drive exploding pusher on NIF showed excellent agreement with simulation, suggesting a lack of kinetic effects.46 Further experiments and computational studies are needed to assess whether kinetic effects could be playing a role in these observed anomalies in the NIF low-adiabat implosion shock dynamics.

The shock dynamics of surrogate implosions at the NIF have been studied. From proton spectroscopy, the shock ρR, proton yield, and shell radius at shock-bang time are determined using a simple self-consistent 1-D implosion model. The shock ρR data show dependence on the coasting time of the implosion, with short-coast implosions having higher shock ρR. The proton shock yield data show a clear dependence on the laser-pulse rise time, and possibly peak power. Using the inferred center-of-mass radius and in-flight x-ray radiography, a shock-bang time is estimated. The short-coast implosions are observed to have significantly smaller differences between the shock- and compression-bang times than the long-coast implosions. This could be due to uncertainties in modeling the late-time drive on the capsule, which is the primary difference between short- and long-coast experiments. An earlier shock-bang time in long-coast implosions could reduce compressibility due to an earlier onset of deceleration; in cryogenic implosions, lower compression ρR is measured in long-coast implosions. Further, the large variation in shock yield indicates a variation in post-shock temperature and, thus, adiabat of the incipient hot-spot material. A model is introduced to relate the proton shock yield to adiabat; this analysis suggests an increase in hot-spot adiabat of up to 2× in fast-rise implosions, potentially reducing compressibility.

Future campaigns could be conducted to more systematically study the effect of coasting time, rise time, and peak power on shock dynamics, or to study the effect of hohlraum material (not addressed in this work). Implementation of a diagnostic for direct measurements of the shock-bang time, which is in progress,47 will be a direct and higher-precision diagnostic of the differential bang time. This new diagnostic will be used to further investigate the discrepancy observed in this work between the model-inferred differential bang time and radiation-hydrodynamics simulations (Fig. 17). The potential impact of kinetic effects on these observations should be studied with dedicated experiments (e.g., varying the gas fill density) and kinetic simulations. Accurate modeling of the shock phase in ignition experiments essentially sets the initial conditions for hot-spot formation. The observed inaccuracies in standard hydrodynamic models for the surrogate implosions strongly suggest that the ignition experiments are not being accurately modeled.

We thank the operations crews and engineering staff at NIF for supporting these experiments, and M. McKernan, M. Cairel, and M. Valadez for their work processing the CR-39. This work is part of the first author's Ph.D. thesis, and was supported in part by the U.S. DoE (Grant Nos. DE-NA0001857 and DE-FC52-08NA28752), LLNL (No. B597367), LLE (No. 415935- G), the Fusion Science Center at the University of Rochester (No. 524431), and the National Laser Users Facility (No. DE-NA0002035). This material was based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 1122374.

For the sample spectrum shown in Fig. 4, the results of the spectral analysis and subsequent ρR modeling are shown in Table I.

TABLE I.

Results from the analysis of the D3He proton spectrum for N101004-002-999 on DIM 90-78.

Quantity Value ± ± ±
Random Systematica Model
Energy (MeV)  11.34  0.10  0.10   
σ (MeV)  0.43  0.10  n/a   
Yield  8.71 × 107  0.94 × 107  n/a   
ρR (mg/cm2 96.0  3.1  6.1  5.3 
Rcm (μm)  242  35  34 
Quantity Value ± ± ±
Random Systematica Model
Energy (MeV)  11.34  0.10  0.10   
σ (MeV)  0.43  0.10  n/a   
Yield  8.71 × 107  0.94 × 107  n/a   
ρR (mg/cm2 96.0  3.1  6.1  5.3 
Rcm (μm)  242  35  34 
a

Includes model uncertainty.

Error bars are 1σ. For the proton energy, the systematic uncertainty primarily comes from the energy calibration of the WRFs,48 and random uncertainty comes from a combination of factors such as the hohlraum, variation in CR-39 properties, and statistical uncertainty. For the yield and line width, there are no systematic uncertainties, and the random uncertainties are primarily variation in CR-39 and statistics.

The energy uncertainties propagate to the modeled quantities ρR and Rcm. The systematic uncertainties for these quantities also include, and are dominated by, the modeling uncertainty. The model uncertainty is also listed separately in Table I.

WRFs fielded on the equator always look through the hohlraum wall in indirect-drive experiments at the NIF. The large patches that would be required to give a clear line of sight for the 4 WRFs that are fielded on DIM 90-78 would unacceptably impact the implosion performance.

In addition to the high-Z hohlraum wall, which is made of Au or DU, there is a Thermo-Mechanical Package (TMP) made of thin aluminum. For most experiments, the hohlraum wall profile is defined by engineering drawings, and the energy correction due to the hohlraum wall is done by calculating the average thickness intercepted by the WRF line-of-sight. The uncertainties in hohlraum thickness (±1 μm for the hohlraum wall and ±3 μm for the TMP) are standard tolerances, and these uncertainties are propagated through the analysis. In this case, the hohlraum uncertainty contributes ±56 keV of uncertainty to the final determined energy.

The actual energy correction is applied to the entire spectrum, as shown in Fig. 21 by shifting each energy using cold-matter stopping powers.49 The use of cold-matter stopping power in the hohlraum wall is a good approximation and has been checked against fully integrated radiation-hydrodynamics hohlraum calculations. Because of the non-linearity in stopping power with proton energy, lower proton energies experience more downshift than higher energy protons, which has an “accordion” effect on the spectrum, though a Gaussian shape is maintained for the energies in this work (≳5 MeV).

FIG. 21.

Sample D3He proton spectrum from NIF shot N101004-002-999, measured on the equator (DIM 90-78) before (red) and after (blue) hohlraum correction. In this case, the hohlraum thickness was 24.2 ± 1 μm of Au and 74.1 ± 3 μm of Al.

FIG. 21.

Sample D3He proton spectrum from NIF shot N101004-002-999, measured on the equator (DIM 90-78) before (red) and after (blue) hohlraum correction. In this case, the hohlraum thickness was 24.2 ± 1 μm of Au and 74.1 ± 3 μm of Al.

Close modal

For some hohlraum designs, a “bump” feature is present in the WRF line of sight. During the laser pulse, a shock passes through the wall, and in the bump material flows laterally out of the line of sight. This situation is calculated with 2-D radiation-hydrodynamic simulations, and the wall thickness is corrected based on these simulations.

Typical parameters and assumptions in the 1-D implosion model are shown in Table II with uncertainties. The first six (shell material, inner and outer radius, fuel pressure, and fuel fill) are determined from a database of shot setup parameters. The values shown in the table are typical numbers. For the shell material, the ablator dopant (Ge or Si) is included, though the dopant level (∼1%) has negligible effect on the inferred quantities. The following 10 parameters are treated as assumptions in the model and characterize the in-flight properties of the implosion. The ablated mass density profile (defined by ρmax, ρmin, and λ) is given in Eq. (7).

TABLE II.

Typical values used in the model.

N101004 ± ρR
Parameter Value ± mg/cm2
Initial conditions 
Shell materiala  CH  n/a  n/a 
Inner radius (μm)  900  0.05 
Outer radius (μm)  1100  0.0 
Fuel fill (mg/cm3 6.3  0.1  0.06 
Fuel D fraction  0.3  0.0 
Fuel 3He fraction  0.7  0.0 
In-flight assumptions 
Gas T (keV)  4.43 
Mix T (keV)  0.5  0.2  0.23 
Shell T (keV)  0.2  0.1  0.23 
Ablated mass T (keV)  0.3  0.1  0.01 
ρmax (g/cc)  1.5  0.5  1.02 
ρmin (g/cc)  0.1  0.05  1.25 
λ (μm)  70  30  1.25 
Mix fractionb  0.5%  0.5%  0.16 
Shell thicknessc  40  10  1.65 
Mass remainingd  17.5%  5%  1.10 
N101004 ± ρR
Parameter Value ± mg/cm2
Initial conditions 
Shell materiala  CH  n/a  n/a 
Inner radius (μm)  900  0.05 
Outer radius (μm)  1100  0.0 
Fuel fill (mg/cm3 6.3  0.1  0.06 
Fuel D fraction  0.3  0.0 
Fuel 3He fraction  0.7  0.0 
In-flight assumptions 
Gas T (keV)  4.43 
Mix T (keV)  0.5  0.2  0.23 
Shell T (keV)  0.2  0.1  0.23 
Ablated mass T (keV)  0.3  0.1  0.01 
ρmax (g/cc)  1.5  0.5  1.02 
ρmin (g/cc)  0.1  0.05  1.25 
λ (μm)  70  30  1.25 
Mix fractionb  0.5%  0.5%  0.16 
Shell thicknessc  40  10  1.65 
Mass remainingd  17.5%  5%  1.10 
a

Dopant type and level included; typically 1.084 g/cc, 57.2% H, 42.3% C, and 0.5% O atomic plus mid-Z dopant (Ge or Si).

b

Percentage of the initial shell mass.

c

Full width of the in-flight shell (μm).

d

For surrogate implosions, the quoted mass remaining includes the surrogate mass of CH.

For the assumed in-flight conditions, experimental data are used in the choice of value whenever possible. The shell thickness and mass remaining are measured with x-ray radiography8 and typical values from that data are used here. The temperature profile and ablated mass density profile are unmeasured and, thus, typical values are taken from HYDRA calculations, where the implosion trajectory (i.e., bang time) is well matched. Since the simulation may not accurately represent the experimental conditions, large uncertainties are assigned to these values (see Table II).

In the table, we also give the resulting uncertainties in ρR for shot N101004 (see also Fig. 4 and Appendix  A) resulting directly from the uncertainties in the model parameters. The dominant sources are the uncertainty in fuel temperature, ablated mass density profile (collectively from ρmax, ρmin, and λ), in-flight shell thickness, and mass remaining. The other sources of uncertainty are negligible (≪ 1 mg/cm2). The shell thickness has a smaller effect than might be expected; the reason for this is that it only affects the inferred ρR through the stopping power Coulomb logarithm.

A mix model was added to this framework to evaluate the potential impact of mix on the proton dE/dx, primarily in the fuel, where the electron temperature can be high. The modeled mix is a uniform CH mix into the fuel specified by the amount of the initial shell mass, which is mixed. Even assuming an implausibly large variation in mix (0%–1% of the initial shell) causes only a 0.3 mg/cm2 difference in inferred ρR; since 1% mix corresponds to a mix mass of 25 μg, about ∼10× higher than the worst observed,50 we conclude that mix in unimportant for shock proton spectroscopy.

The primary effect of the changing density and temperature in the three regions is variation in the stopping power, which is shown in Fig. 22. The higher temperature in the fuel leads to a much higher energy Bragg peak. At high energy, the stopping power in the shell is lower than in the fuel or the ablated mass due to the higher density in the shell (leading to a smaller log Λ).

FIG. 22.

Stopping power for the three components of the implosion model: fuel, shell, and ablated mass.

FIG. 22.

Stopping power for the three components of the implosion model: fuel, shell, and ablated mass.

Close modal

A stated choice in this work, which affects the reported ρR values, is the model used to calculate the charged-particle stopping power. In these dense plasma regimes, no experimental data exists to differentiate between models. In this work, the Li-Petrasso theory21 has been used. However, this choice represents a potential quasi-systematic uncertainty in the inferred values. The magnitude of this effect is investigated by evaluating the implosion model at equivalent nominal conditions but with various choices of stopping model. In particular, we choose Zimmerman's parameterization of the Maynard-Deutsch model51,52 and the Brown-Preston-Singleton (BPS) model.53 

A comparison of the stopping power for the three models is shown in Fig. 23. The magnitude of the BPS and Zimmerman stopping are quite close. In the gas, these other two models have a smaller magnitude of dE/dx than Li-Petrasso, while they are higher in the shell and ablated material. A direct comparison of inferred ρR values using the implosion model and varying only the stopping model is shown in Fig. 24. For a wide range of relevant ρR, the Zimmerman and BPS stopping power would lead to an inferred ρR that is lower by ∼10% or ∼12%, respectively.

FIG. 23.

Stopping power for the three models [Li-Petrasso (LP), Brown-Preston-Singleton (BPS), and Zimmerman (Z)] for each region of the implosion model: gas, shell, and ablated material.

FIG. 23.

Stopping power for the three models [Li-Petrasso (LP), Brown-Preston-Singleton (BPS), and Zimmerman (Z)] for each region of the implosion model: gas, shell, and ablated material.

Close modal
FIG. 24.

Top: Inferred ρR versus final proton energy for three models [Li-Petrasso (LP), Brown-Preston-Singleton (BPS), and Zimmerman (Z)]. Bottom: Difference (%) between the Zimmerman or BPS models and Li-Petrasso.

FIG. 24.

Top: Inferred ρR versus final proton energy for three models [Li-Petrasso (LP), Brown-Preston-Singleton (BPS), and Zimmerman (Z)]. Bottom: Difference (%) between the Zimmerman or BPS models and Li-Petrasso.

Close modal

A simple extension of the implosion model to 2- and 3-D is essential for analysis of asymmetries observed between multiple detectors in these implosions, enabling the work presented in Ref. 19. An asymmetry is modeled as Legendre modes in the shape of the imploding shell

R c m ( θ , ϕ ) = R ¯ [ 1 + Δ × 2 + 1 4 π ( m ) ! ( + m ) ! e i m ϕ P m ( cos θ ) ] ,
(D1)

where θ and ϕ are the polar and azimuthal angles, respectively, R ¯ is the unperturbed shell radius, Δ is the fractional asymmetry amplitude, and P m is an associated Legendre polynomial.

From the 1-D model presented in this paper, we have ρR(Rcm). Areal density asymmetries in 2- or 3-D can, thus, be modeled as the convolution of Rcm(θ, ϕ) and ρR(Rcm) giving ρ R ( θ , ϕ , R ¯ , Δ , , m ). The data points, each with their own coordinates (θ, ϕ), are then be fit using this convolution, where Δ and R ¯ are free parameters and and m are chosen.

An example of this analysis is shown in Fig. 25 for shot N101218-002-999. In this case, a P2 mode is assumed ( = 2 and m = 0). The best fit parameters are R ¯ = 250 ± 2 μ m and Δ = −0.21 ± 0.02. The error bars are due to random/statistical errors only, excluding systematic detector calibration uncertainties and model uncertainties.

FIG. 25.

ρR asymmetry analysis ( = 2 and m = 0) for shot N101218-002-999, which had an usually large observed asymmetry. The polar (red) and equatorial (blue) data are shown with random/statistical errors only. The fit is shown as ρR(θ) and Rcm(θ) (right axis).

FIG. 25.

ρR asymmetry analysis ( = 2 and m = 0) for shot N101218-002-999, which had an usually large observed asymmetry. The polar (red) and equatorial (blue) data are shown with random/statistical errors only. The fit is shown as ρR(θ) and Rcm(θ) (right axis).

Close modal

For the ConA2D implosions (see Appendix  E) in-flight 2-D, x-ray radiography is used to measure the symmetry. Unfortunately, the radiography requires large patches on the hohlraum wall, which induce a known m = 2 azimuthal asymmetry. This asymmetry is roughly aligned with the WRF equatorial line of sight, leading to an unconstrained problem between the modes  = 2 and m = 2 plus modes such as  = 4. To address this issue, we use the radiography-measured mode amplitudes for the  = 2 and  = 4 and fit the amplitude of the m = 2 mode

R c m ( θ , ϕ ) = R ¯ [ 1 + Δ m = 2 sin θ cos ( 2 ϕ + ϕ 0 ) + Δ = 2 × 5 4 π P 2 0 ( cos θ ) + Δ = 4 × 9 4 π P 4 0 ( cos θ ) ] ,
(D2)

where Δm=2 is the free parameter and ϕ0 is taken as aligned with the equatorial line of sight (78°). The polar amplitudes Δ=2 and Δ= 4 are determined from x-ray radiography.

A summary of the data used in the shock dynamics analysis is shown in Table III.

TABLE III.

Data summary of shots used in the shock dynamics analysis.

Shot Type Hohlraum Laser Effective Absorption Rise Coast Average Equatorial Rcm (μm) ΔBT (ns)
energy power time time ρR shock
(MJ) (TW) (ns) (ns) (mg/cm2) yield
N110728-001-999  Symcap  Au  1.39 ± 0.03  368 ± 7  0.83 ± 0.03  1.94 ± 0.11  91 ± 13  (3.8 ± 1.3) × 107  247 ± 36   
N111007-002-999  ConvAblW  Au  1.29 ± 0.02  350 ± 7  0.84 ± 0.03  2.46 ± 0.04  80 ± 6  (7.1 ± 1.1) × 107  269 ± 40   
N111011-004-999  ConvAbl  Au  1.27 ± 0.02  346 ± 7  0.86 ± 0.03  2.55 ± 0.04  82 ± 11  (1.1 ± 0.1) × 108  265 ± 40  − 0.75 ± 0.16 
N111013-001-999  Symcap  Au  1.24 ± 0.02  367 ± 7  0.84 ± 0.03  2.52 ± 0.05  88 ± 11  (6.3 ± 1.4) × 107  252 ± 38   
N111014-001-999  Symcap  Au  1.26 ± 0.02  368 ± 7  0.84 ± 0.03  2.44 ± 0.05  87 ± 6  (1.4 ± 0.1) × 108  255 ± 40   
N111106-002-999  Symcap  Au  1.27 ± 0.02  365 ± 7  0.83 ± 0.03  2.48 ± 0.08  84 ± 12  (9.2 ± 2.6) × 107  260 ± 40   
N111109-002-999  Symcap  Au  1.26 ± 0.03  370 ± 7  0.86 ± 0.03  2.43 ± 0.08  86 ± 12  (8.1 ± 2.1) × 107  256 ± 39   
N111119-002-999  ConvAblW  Au  1.17 ± 0.02  342 ± 7  0.85 ± 0.03  2.51 ± 0.04  77 ± 10  (5.5 ± 0.9) × 107  277 ± 43   
N111120-002-999  Symcap  Au  1.50 ± 0.03  375 ± 7  0.84 ± 0.03  1.74 ± 0.08  94 ± 12  (1.6 ± 0.2) × 108  242 ± 36   
N111219-001-999  ConvAblW  Au  1.41 ± 0.02  353 ± 7  0.85 ± 0.03  1.95 ± 0.10  92 ± 12  (1.1 ± 0.2) × 108  245 ± 38   
N111220-002-999  ConvAblW  Au  1.41 ± 0.03  352 ± 7  0.84 ± 0.03  2.03 ± 0.10  89 ± 12  (1.6 ± 0.3) × 108  251 ± 38   
N120408-001-999  ConvAbl  1.52 ± 0.03  292 ± 5  0.81 ± 0.03  0.92 ± 0.05  139 ± 10  (3.0 ± 0.4) × 107  191 ± 28  − 0.34 ± 0.12 
N120409-001-999  ConvAbl  1.65 ± 0.03  350 ± 7  0.86 ± 0.02  1.01 ± 0.05  137 ± 9  (1.0 ± 0.1) × 108  193 ± 29  − 0.38 ± 0.13 
N120418-001-999  ConvAbl  1.70 ± 0.03  336 ± 6  0.82 ± 0.03  1.12 ± 0.05  152 ± 10  (2.1 ± 0.4) × 107  181 ± 29  − 0.31 ± 0.13 
N120421-006-999  ConvAbl  Au  1.63 ± 0.03  306 ± 6  0.85 ± 0.03  1.04 ± 0.06  133 ± 9  (3.4 ± 0.1) × 107  196 ± 28  − 0.46 ± 0.13 
N120629-002-999  ConvAblW  1.34 ± 0.03  297 ± 6  0.84 ± 0.02  1.61 ± 0.06  138 ± 10  (2.5 ± 0.2) × 107  191 ± 27   
N120709-003-999  ConvAblW  Au  1.57 ± 0.03  298 ± 6  0.85 ± 0.03  1.15 ± 0.06  137 ± 9  (1.8 ± 0.2) × 107  192 ± 28   
N120726-003-999  Symcap  Au  1.37 ± 0.03  345 ± 7  0.84 ± 0.02  2.31 ± 0.06  105 ± 7  (4.3 ± 0.3) × 107  226 ± 36   
N120909-001-999  Symcap  Au  1.43 ± 0.03  370 ± 7  0.86 ± 0.02  2.00 ± 0.05  81 ± 13  (1.4 ± 0.6) × 107  266 ± 42   
N120910-001-999  Symcap  Au  1.46 ± 0.03  376 ± 8  0.86 ± 0.02  2.06 ± 0.05  92 ± 6  (5.1 ± 0.7) × 107  245 ± 38   
N121008-002-999  ConvAblW  1.28 ± 0.03  290 ± 5  0.86 ± 0.02  1.68 ± 0.09  149 ± 11  (2.0 ± 0.2) × 107  183 ± 26   
N121202-001-999  ConvAbl2D  Au  1.28 ± 0.03  315 ± 7  0.86 ± 0.02  1.97 ± 0.09  110 ± 8  (2.4 ± 0.2) × 107  219 ± 31  − 0.60 ± 0.13 
N121210-001-999  ConvAbl2D  Au  1.28 ± 0.03  315 ± 7  0.86 ± 0.02  1.99 ± 0.09  110 ± 7  (2.4 ± 0.2) × 107  219 ± 31  − 0.60 ± 0.13 
N121218-004-999  ConvAbl2D  Au  1.29 ± 0.03  317 ± 7  0.87 ± 0.02  2.02 ± 0.09  107 ± 7  (2.2 ± 0.2) × 107  223 ± 32  − 0.60 ± 0.13 
N121219-001-999  ConvAbl2D  Au  1.29 ± 0.03  302 ± 7  0.87 ± 0.02  2.01 ± 0.09  119 ± 8  (3.5 ± 0.3) × 107  209 ± 31  − 0.57 ± 0.13 
N130211-003-999  ConvAbl2D  Au  1.28 ± 0.03  325 ± 6  0.91 ± 0.03  2.04 ± 0.09  110 ± 8  (5.5 ± 0.3) × 107  220 ± 32  − 0.58 ± 0.13 
N130212-001-999  ConvAbl2D  Au  1.27 ± 0.03  321 ± 6  0.90 ± 0.03  2.18 ± 0.09  100 ± 7  (6.2 ± 0.5) × 107  233 ± 33  − 0.61 ± 0.13 
N130213-002-999  ConvAbl2D  Au  0.96 ± 0.02  222 ± 4  0.91 ± 0.03  2.66 ± 0.09  105 ± 8  (8.7 ± 0.8) × 106  226 ± 32  − 0.79 ± 0.19 
N130226-002-999  ConvAbl2D  Au  1.28 ± 0.02  323 ± 5  0.90 ± 0.03  1.95 ± 0.09  100 ± 7  (5.0 ± 0.5) × 107  233 ± 34  − 0.71 ± 0.13 
N130227-002-999  ConvAbl2D  Au  1.28 ± 0.02  322 ± 4  0.89 ± 0.03  2.13 ± 0.09  98 ± 7  (6.4 ± 0.6) × 107  236 ± 33  − 0.71 ± 0.12 
Shot Type Hohlraum Laser Effective Absorption Rise Coast Average Equatorial Rcm (μm) ΔBT (ns)
energy power time time ρR shock
(MJ) (TW) (ns) (ns) (mg/cm2) yield
N110728-001-999  Symcap  Au  1.39 ± 0.03  368 ± 7  0.83 ± 0.03  1.94 ± 0.11  91 ± 13  (3.8 ± 1.3) × 107  247 ± 36   
N111007-002-999  ConvAblW  Au  1.29 ± 0.02  350 ± 7  0.84 ± 0.03  2.46 ± 0.04  80 ± 6  (7.1 ± 1.1) × 107  269 ± 40   
N111011-004-999  ConvAbl  Au  1.27 ± 0.02  346 ± 7  0.86 ± 0.03  2.55 ± 0.04  82 ± 11  (1.1 ± 0.1) × 108  265 ± 40  − 0.75 ± 0.16 
N111013-001-999  Symcap  Au  1.24 ± 0.02  367 ± 7  0.84 ± 0.03  2.52 ± 0.05  88 ± 11  (6.3 ± 1.4) × 107  252 ± 38   
N111014-001-999  Symcap  Au  1.26 ± 0.02  368 ± 7  0.84 ± 0.03  2.44 ± 0.05  87 ± 6  (1.4 ± 0.1) × 108  255 ± 40   
N111106-002-999  Symcap  Au  1.27 ± 0.02  365 ± 7  0.83 ± 0.03  2.48 ± 0.08  84 ± 12  (9.2 ± 2.6) × 107  260 ± 40   
N111109-002-999  Symcap  Au  1.26 ± 0.03  370 ± 7  0.86 ± 0.03  2.43 ± 0.08  86 ± 12  (8.1 ± 2.1) × 107  256 ± 39   
N111119-002-999  ConvAblW  Au  1.17 ± 0.02  342 ± 7  0.85 ± 0.03  2.51 ± 0.04  77 ± 10  (5.5 ± 0.9) × 107  277 ± 43   
N111120-002-999  Symcap  Au  1.50 ± 0.03  375 ± 7  0.84 ± 0.03  1.74 ± 0.08  94 ± 12  (1.6 ± 0.2) × 108  242 ± 36   
N111219-001-999  ConvAblW  Au  1.41 ± 0.02  353 ± 7  0.85 ± 0.03  1.95 ± 0.10  92 ± 12  (1.1 ± 0.2) × 108  245 ± 38   
N111220-002-999  ConvAblW  Au  1.41 ± 0.03  352 ± 7  0.84 ± 0.03  2.03 ± 0.10  89 ± 12  (1.6 ± 0.3) × 108  251 ± 38   
N120408-001-999  ConvAbl  1.52 ± 0.03  292 ± 5  0.81 ± 0.03  0.92 ± 0.05  139 ± 10  (3.0 ± 0.4) × 107  191 ± 28  − 0.34 ± 0.12 
N120409-001-999  ConvAbl  1.65 ± 0.03  350 ± 7  0.86 ± 0.02  1.01 ± 0.05  137 ± 9  (1.0 ± 0.1) × 108  193 ± 29  − 0.38 ± 0.13 
N120418-001-999  ConvAbl  1.70 ± 0.03  336 ± 6  0.82 ± 0.03  1.12 ± 0.05  152 ± 10  (2.1 ± 0.4) × 107  181 ± 29  − 0.31 ± 0.13 
N120421-006-999  ConvAbl  Au  1.63 ± 0.03  306 ± 6  0.85 ± 0.03  1.04 ± 0.06  133 ± 9  (3.4 ± 0.1) × 107  196 ± 28  − 0.46 ± 0.13 
N120629-002-999  ConvAblW  1.34 ± 0.03  297 ± 6  0.84 ± 0.02  1.61 ± 0.06  138 ± 10  (2.5 ± 0.2) × 107  191 ± 27   
N120709-003-999  ConvAblW  Au  1.57 ± 0.03  298 ± 6  0.85 ± 0.03  1.15 ± 0.06  137 ± 9  (1.8 ± 0.2) × 107  192 ± 28   
N120726-003-999  Symcap  Au  1.37 ± 0.03  345 ± 7  0.84 ± 0.02  2.31 ± 0.06  105 ± 7  (4.3 ± 0.3) × 107  226 ± 36   
N120909-001-999  Symcap  Au  1.43 ± 0.03  370 ± 7  0.86 ± 0.02  2.00 ± 0.05  81 ± 13  (1.4 ± 0.6) × 107  266 ± 42   
N120910-001-999  Symcap  Au  1.46 ± 0.03  376 ± 8  0.86 ± 0.02  2.06 ± 0.05  92 ± 6  (5.1 ± 0.7) × 107  245 ± 38   
N121008-002-999  ConvAblW  1.28 ± 0.03  290 ± 5  0.86 ± 0.02  1.68 ± 0.09  149 ± 11  (2.0 ± 0.2) × 107  183 ± 26   
N121202-001-999  ConvAbl2D  Au  1.28 ± 0.03  315 ± 7  0.86 ± 0.02  1.97 ± 0.09  110 ± 8  (2.4 ± 0.2) × 107  219 ± 31  − 0.60 ± 0.13 
N121210-001-999  ConvAbl2D  Au  1.28 ± 0.03  315 ± 7  0.86 ± 0.02  1.99 ± 0.09  110 ± 7  (2.4 ± 0.2) × 107  219 ± 31  − 0.60 ± 0.13 
N121218-004-999  ConvAbl2D  Au  1.29 ± 0.03  317 ± 7  0.87 ± 0.02  2.02 ± 0.09  107 ± 7  (2.2 ± 0.2) × 107  223 ± 32  − 0.60 ± 0.13 
N121219-001-999  ConvAbl2D  Au  1.29 ± 0.03  302 ± 7  0.87 ± 0.02  2.01 ± 0.09  119 ± 8  (3.5 ± 0.3) × 107  209 ± 31  − 0.57 ± 0.13 
N130211-003-999  ConvAbl2D  Au  1.28 ± 0.03  325 ± 6  0.91 ± 0.03  2.04 ± 0.09  110 ± 8  (5.5 ± 0.3) × 107  220 ± 32  − 0.58 ± 0.13 
N130212-001-999  ConvAbl2D  Au  1.27 ± 0.03  321 ± 6  0.90 ± 0.03  2.18 ± 0.09  100 ± 7  (6.2 ± 0.5) × 107  233 ± 33  − 0.61 ± 0.13 
N130213-002-999  ConvAbl2D  Au  0.96 ± 0.02  222 ± 4  0.91 ± 0.03  2.66 ± 0.09  105 ± 8  (8.7 ± 0.8) × 106  226 ± 32  − 0.79 ± 0.19 
N130226-002-999  ConvAbl2D  Au  1.28 ± 0.02  323 ± 5  0.90 ± 0.03  1.95 ± 0.09  100 ± 7  (5.0 ± 0.5) × 107  233 ± 34  − 0.71 ± 0.13 
N130227-002-999  ConvAbl2D  Au  1.28 ± 0.02  322 ± 4  0.89 ± 0.03  2.13 ± 0.09  98 ± 7  (6.4 ± 0.6) × 107  236 ± 33  − 0.71 ± 0.12 
1.
J.
Nuckolls
,
L.
Wood
,
A.
Thiessen
, and
G.
Zimmerman
,
Nature
239
,
139
(
1972
).
2.
J.
Lindl
,
Phys. Plasmas
2
,
3933
(
1995
).
3.
G.
Miller
,
E.
Moses
, and
C.
Wuest
,
Nucl. Fusion
44
,
S228
(
2004
).
4.
O. L.
Landen
,
T. R.
Boehly
,
D. K.
Bradley
,
D. G.
Braun
,
D. A.
Callahan
,
P. M.
Celliers
,
G. W.
Collins
,
E. L.
Dewald
,
L.
Divol
,
S. H.
Glenzer
,
A.
Hamza
,
D. G.
Hicks
,
N.
Hoffman
,
N.
Izumi
,
O. S.
Jones
,
R. K.
Kirkwood
,
G. A.
Kyrala
,
P.
Michel
,
J.
Milovich
,
D. H.
Munro
,
A.
Nikroo
,
R. E.
Olson
,
H. F.
Robey
,
B. K.
Spears
,
C. A.
Thomas
,
S. V.
Weber
,
D. C.
Wilson
,
M. M.
Marinak
,
L. J.
Suter
,
B. A.
Hammel
,
D. D.
Meyerhofer
,
J.
Atherton
,
J.
Edwards
,
S. W.
Haan
,
J. D.
Lindl
,
B. J.
MacGowan
, and
E. I.
Moses
,
Phys. Plasmas
17
,
056301
(
2010
).
5.
G. A.
Kyrala
,
S.
Dixit
,
S.
Glenzer
,
D.
Kalantar
,
D.
Bradley
,
N.
Izumi
,
N.
Meezan
,
O. L.
Landen
,
D.
Callahan
,
S. V.
Weber
,
J. P.
Holder
,
S.
Glenn
,
M. J.
Edwards
,
P.
Bell
,
J.
Kimbrough
,
J.
Koch
,
R.
Prasad
,
L.
Suter
,
J. L.
Kline
, and
J.
Kilkenny
,
Rev. Sci. Instrum.
81
,
10E316
(
2010
).
6.
G. A.
Kyrala
,
J. L.
Kline
,
S.
Dixit
,
S.
Glenzer
,
D.
Kalantar
,
D.
Bradley
,
N.
Izumi
,
N.
Meezan
,
O.
Landen
,
D.
Callahan
,
S. V.
Weber
,
J. P.
Holder
,
S.
Glenn
,
M. J.
Edwards
,
J.
Koch
,
L. J.
Suter
,
S. W.
Haan
,
R. P. J.
Town
,
P.
Michel
,
O.
Jones
,
S.
Langer
,
J. D.
Moody
,
E. L.
Dewald
,
T.
Ma
,
J.
Ralph
,
A.
Hamza
,
E.
Dzenitis
, and
J.
Kilkenny
,
Phys. Plasmas
18
,
056307
(
2011
).
7.
D.
Hicks
,
B.
Spears
,
D.
Braun
,
R.
Olson
,
C.
Sorce
,
P.
Celliers
,
G.
Collins
, and
O.
Landen
,
Phys. Plasmas
17
,
102703
(
2010
).
8.
D. G.
Hicks
,
N. B.
Meezan
,
E. L.
Dewald
,
A. J.
Mackinnon
,
R. E.
Olson
,
D. A.
Callahan
,
T.
Döppner
,
L. R.
Benedetti
,
D. K.
Bradley
,
P. M.
Celliers
,
D. S.
Clark
,
P. Di
Nicola
,
S. N.
Dixit
,
E. G.
Dzenitis
,
J. E.
Eggert
,
D. R.
Farley
,
J. A.
Frenje
,
S. M.
Glenn
,
S. H.
Glenzer
,
A. V.
Hamza
,
R. F.
Heeter
,
J. P.
Holder
,
N.
Izumi
,
D. H.
Kalantar
,
S. F.
Khan
,
J. L.
Kline
,
J. J.
Kroll
,
G. A.
Kyrala
,
T.
Ma
,
A. G.
MacPhee
,
J. M.
McNaney
,
J. D.
Moody
,
M. J.
Moran
,
B. R.
Nathan
,
A.
Nikroo
,
Y. P.
Opachich
,
R. D.
Petrasso
,
R. R.
Prasad
,
J. E.
Ralph
,
H. F.
Robey
,
H. G.
Rinderknecht
,
J. R.
Rygg
,
J. D.
Salmonson
,
M. B.
Schneider
,
N.
Simanovskaia
,
B. K.
Spears
,
R.
Tommasini
,
K.
Widmann
,
A. B.
Zylstra
,
G. W.
Collins
,
O. L.
Landen
,
J. D.
Kilkenny
,
W. W.
Hsing
,
B. J.
MacGowan
,
L. J.
Atherton
, and
M. J.
Edwards
,
Phys. Plasmas
19
,
122702
(
2012
).
9.
G.
Zimmerman
and
W.
Kruer
,
Controlled Fusion
2
,
51
(
1975
).
10.
S. W.
Haan
,
S. M.
Pollaine
,
J. D.
Lindl
,
L. J.
Suter
,
R. L.
Berger
,
L. V.
Powers
,
W. E.
Alley
,
P. A.
Amendt
,
J. A.
Futterman
,
W. K.
Levedahl
,
M. D.
Rosen
,
D. P.
Rowley
,
R. A.
Sacks
,
A. I.
Shestakov
,
G. L.
Strobel
,
M.
Tabak
,
S. V.
Weber
,
G. B.
Zimmerman
,
W. J.
Krauser
,
D. C.
Wilson
,
S. V.
Coggeshall
,
D. B.
Harris
,
N. M.
Hoffman
, and
B. H.
Wilde
,
Phys. Plasmas
2
,
2480
(
1995
).
11.
M.
Marinak
,
G.
Kerbel
,
N.
Gentile
,
O.
Jones
,
D.
Munro
,
S.
Pollaine
,
T.
Dittrich
, and
S.
Haan
,
Phys. Plasmas
8
,
2275
(
2001
).
12.
D. G.
Hicks
,
Charged-Particle Spectroscopy: A New Window on Inertial Confinement Fusion
(
Massachusetts Institute of Technology
,
1999
).
13.
R. D.
Petrasso
,
J. A.
Frenje
,
C. K.
Li
,
F. H.
Séguin
,
J. R.
Rygg
,
B. E.
Schwartz
,
S.
Kurebayashi
,
P. B.
Radha
,
C.
Stoeckl
,
J. M.
Soures
,
J.
Delettrez
,
V. Y.
Glebov
,
D. D.
Meyerhofer
, and
T. C.
Sangster
,
Phys. Rev. Lett.
90
,
095002
(
2003
).
14.
C. K.
Li
,
F. H.
Seguin
,
J. A.
Frenje
,
R. D.
Petrasso
,
R.
Rygg
,
S.
Kurebayashi
,
B.
Schwartz
,
R. L.
Keck
,
J. A.
Delettrez
,
J. M.
Soures
,
P. W.
McKenty
,
V. N.
Goncharov
,
J. P.
Knauer
,
F. J.
Marshall
,
D. D.
Meyerhofer
,
P. B.
Radha
,
S. P.
Regan
,
T. C.
Sangster
,
W.
Seka
, and
C.
Stoeckl
,
Phys. Plasmas
10
,
1919
(
2003
).
15.
J. A.
Frenje
,
C. K.
Li
,
F. H.
Seguin
,
J.
Deciantis
,
S.
Kurebayashi
,
J. R.
Rygg
,
R. D.
Petrasso
,
J.
Delettrez
,
V. Y.
Glebov
,
C.
Stoeckl
,
F. J.
Marshall
,
D. D.
Meyerhofer
,
T. C.
Sangster
,
V. A.
Smalyuk
, and
J. M.
Soures
,
Phys. Plasmas
11
,
2798
(
2004
).
16.
J. R.
Rygg
,
Shock Convergence and Mix Dynamics in Inertial Confinement Fusion
(
Massachusetts Institute of Technology
,
2006
).
17.
T.
Boehly
,
D.
Brown
,
R.
Craxton
,
R.
Keck
,
J.
Knauer
,
J.
Kelly
,
T.
Kessler
,
S.
Kumpan
,
S.
Loucks
,
S.
Letzring
,
F.
Marshall
,
R.
McCrory
,
S.
Morse
,
W.
Seka
,
J.
Soures
, and
C.
Verdon
,
Opt. Commun.
133
,
495
(
1997
).
18.
A. B.
Zylstra
,
J. A.
Frenje
,
F. H.
Séguin
,
M. J.
Rosenberg
,
H. G.
Rinderknecht
,
M. G.
Johnson
,
D. T.
Casey
,
N.
Sinenian
,
M. J.-E.
Manuel
,
C. J.
Waugh
,
H. W.
Sio
,
C. K.
Li
,
R. D.
Petrasso
,
S.
Friedrich
,
K.
Knittel
,
R.
Bionta
,
M.
McKernan
,
D.
Callahan
,
G. W.
Collins
,
E.
Dewald
,
T.
Döppner
,
M. J.
Edwards
,
S.
Glenzer
,
D. G.
Hicks
,
O. L.
Landen
,
R.
London
,
A.
Mackinnon
,
N.
Meezan
,
R. R.
Prasad
,
J.
Ralph
,
M.
Richardson
,
J. R.
Rygg
,
S.
Sepke
,
S.
Weber
,
R.
Zacharias
,
E.
Moses
,
J.
Kilkenny
,
A.
Nikroo
,
T. C.
Sangster
,
V.
Glebov
,
C.
Stoeckl
,
R.
Olson
,
R. J.
Leeper
,
J.
Kline
,
G.
Kyrala
, and
D.
Wilson
,
Rev. Sci. Instrum.
83
,
10D901
(
2012
).
19.
A. B.
Zylstra
 et al, “In-flight observations of low-mode ρR asymmetries in NIF implosions,”
Phys. Rev. E
(submitted).
20.
The proton velocity is high relative to the electron thermal velocity in these regimes, so electron stopping dominates.
21.
C.
Li
and
R.
Petrasso
,
Phys. Rev. Lett.
70
,
3059
(
1993
).
22.
G.
Guderley
,
Luftfahrtforschung
19
,
302
(
1942
).
23.
P. M.
Celliers
,
D. K.
Bradley
,
G. W.
Collins
,
D. G.
Hicks
,
T. R.
Boehly
, and
W. J.
Armstrong
,
Rev. Sci. Instrum.
75
,
4916
(
2004
).
24.
H. F.
Robey
,
P. M.
Celliers
,
J. L.
Kline
,
A. J.
Mackinnon
,
T. R.
Boehly
,
O. L.
Landen
,
J. H.
Eggert
,
D.
Hicks
,
S. Le
Pape
,
D. R.
Farley
,
M. W.
Bowers
,
K. G.
Krauter
,
D. H.
Munro
,
O. S.
Jones
,
J. L.
Milovich
,
D.
Clark
,
B. K.
Spears
,
R. P. J.
Town
,
S. W.
Haan
,
S.
Dixit
,
M. B.
Schneider
,
E. L.
Dewald
,
K.
Widmann
,
J. D.
Moody
,
T. D.
Döppner
,
H. B.
Radousky
,
A.
Nikroo
,
J. J.
Kroll
,
A. V.
Hamza
,
J. B.
Horner
,
S. D.
Bhandarkar
,
E.
Dzenitis
,
E.
Alger
,
E.
Giraldez
,
C.
Castro
,
K.
Moreno
,
C.
Haynam
,
K. N.
LaFortune
,
C.
Widmayer
,
M.
Shaw
,
K.
Jancaitis
,
T.
Parham
,
D. M.
Holunga
,
C. F.
Walters
,
B.
Haid
,
T.
Malsbury
,
D.
Trummer
,
K. R.
Coffee
,
B.
Burr
,
L. V.
Berzins
,
C.
Choate
,
S. J.
Brereton
,
S.
Azevedo
,
H.
Chandrasekaran
,
S.
Glenzer
,
J. A.
Caggiano
,
J. P.
Knauer
,
J. A.
Frenje
,
D. T.
Casey
,
M. G.
Johnson
,
F. H.
Séguin
,
B. K.
Young
,
M. J.
Edwards
,
B. M.
Van Wonterghem
,
J.
Kilkenny
,
B. J.
MacGowan
,
J.
Atherton
,
J. D.
Lindl
,
D. D.
Meyerhofer
, and
E.
Moses
,
Phys. Rev. Lett.
108
,
215004
(
2012
).
25.
H. F.
Robey
,
J. D.
Moody
,
P. M.
Celliers
,
J. S.
Ross
,
J.
Ralph
,
S. Le
Pape
,
L. B.
Hopkins
,
T.
Parham
,
J.
Sater
,
E. R.
Mapoles
,
D. M.
Holunga
,
C. F.
Walters
,
B. J.
Haid
,
B. J.
Kozioziemski
,
R. J.
Dylla-Spears
,
K. G.
Krauter
,
G.
Frieders
,
G.
Ross
,
M. W.
Bowers
,
D. J.
Strozzi
,
B. E.
Yoxall
,
A. V.
Hamza
,
B.
Dzenitis
,
S. D.
Bhandarkar
,
B.
Young
,
B. M.
Van Wonterghem
,
L. J.
Atherton
,
O. L.
Landen
,
M. J.
Edwards
, and
T. R.
Boehly
,
Phys. Rev. Lett.
111
,
065003
(
2013
).
26.
J. D.
Moody
,
D. A.
Callahan
,
D. E.
Hinkel
,
P. A.
Amendt
,
K. L.
Baker
,
D.
Bradley
,
P. M.
Celliers
,
E. L.
Dewald
,
L.
Divol
,
T.
Döppner
,
D. C.
Eder
,
M. J.
Edwards
,
O.
Jones
,
S. W.
Haan
,
D.
Ho
,
L. B.
Hopkins
,
N.
Izumi
,
D.
Kalantar
,
R. L.
Kauffman
,
J. D.
Kilkenny
,
O.
Landen
,
B.
Lasinski
,
S.
LePape
,
T.
Ma
,
B. J.
MacGowan
,
S. A.
MacLaren
,
A. J.
Mackinnon
,
D.
Meeker
,
N.
Meezan
,
P.
Michel
,
J. L.
Milovich
,
D.
Munro
,
A. E.
Pak
,
M.
Rosen
,
J.
Ralph
,
H. F.
Robey
,
J. S.
Ross
,
M. B.
Schneider
,
D.
Strozzi
,
E.
Storm
,
C.
Thomas
,
R. P. J.
Town
,
K. L.
Widmann
,
J.
Kline
,
G.
Kyrala
,
A.
Nikroo
,
T.
Boehly
,
A. S.
Moore
, and
S. H.
Glenzer
,
Phys. Plasmas
21
,
056317
(
2014
).
27.
R. P. J.
Town
,
D. K.
Bradley
,
A.
Kritcher
,
O. S.
Jones
,
J. R.
Rygg
,
R.
Tommasini
,
M.
Barrios
,
L. R.
Benedetti
,
L. F. B.
Hopkins
,
P. M.
Celliers
,
T.
Döppner
,
E. L.
Dewald
,
D. C.
Eder
,
J. E.
Field
,
S. M.
Glenn
,
N.
Izumi
,
S. W.
Haan
,
S. F.
Khan
,
J. L.
Kline
,
G. A.
Kyrala
,
T.
Ma
,
J. L.
Milovich
,
J. D.
Moody
,
S. R.
Nagel
,
A.
Pak
,
J. L.
Peterson
,
H. F.
Robey
,
J. S.
Ross
,
R. H. H.
Scott
,
B. K.
Spears
,
M. J.
Edwards
,
J. D.
Kilkenny
, and
O. L.
Landen
,
Phys. Plasmas
21
,
056313
(
2014
).
28.
M. J.
Rosenberg
,
H. G.
Rinderknecht
,
N. M.
Hoffman
,
P. A.
Amendt
,
S.
Atzeni
,
A. B.
Zylstra
,
C. K.
Li
,
F. H.
Séguin
,
H.
Sio
,
M. G.
Johnson
,
J. A.
Frenje
,
R. D.
Petrasso
,
V. Y.
Glebov
,
C.
Stoeckl
,
W.
Seka
,
F. J.
Marshall
,
J. A.
Delettrez
,
T. C.
Sangster
,
R.
Betti
,
V. N.
Goncharov
,
D. D.
Meyerhofer
,
S.
Skupsky
,
C.
Bellei
,
J.
Pino
,
S. C.
Wilks
,
G.
Kagan
,
K.
Molvig
, and
A.
Nikroo
,
Phys. Rev. Lett.
112
,
185001
(
2014
).
29.
H. G.
Rinderknecht
,
H.
Sio
,
C. K.
Li
,
A. B.
Zylstra
,
M. J.
Rosenberg
,
P.
Amendt
,
J.
Delettrez
,
C.
Bellei
,
J. A.
Frenje
,
M. G.
Johnson
,
F. H.
Séguin
,
R. D.
Petrasso
,
R.
Betti
,
V. Y.
Glebov
,
D. D.
Meyerhofer
,
T. C.
Sangster
,
C.
Stoeckl
,
O.
Landen
,
V. A.
Smalyuk
,
S.
Wilks
,
A.
Greenwood
, and
A.
Nikroo
,
Phys. Rev. Lett.
112
,
135001
(
2014
).
30.

The thicknesses of the in-flight shell can change depending on the laser drive. In “short-coast” implosions, the laser drive is on for a longer time, whereas “long-coast” implosions can have shell decompression due to time-truncated drive. However, the modeling reveals that this effect is not significant for interpreting this data, since the shell decompression does not significantly affect the ρR, while the shell is at Rcm ∼ 250 μm.

31.
F. H.
Séguin
,
J. A.
Frenje
,
C. K.
Li
,
D. G.
Hicks
,
S.
Kurebayashi
,
J. R.
Rygg
,
B.-E.
Schwartz
,
R. D.
Petrasso
,
S.
Roberts
,
J. M.
Soures
,
D. D.
Meyerhofer
,
T. C.
Sangster
,
J. P.
Knauer
,
C.
Sorce
,
V. Y.
Glebov
,
C.
Stoeckl
,
T. W.
Phillips
,
R. J.
Leeper
,
K.
Fletcher
, and
S.
Padalino
,
Rev. Sci. Instrum.
74
,
975
(
2003
).
32.
F. H.
Séguin
,
N.
Sinenian
,
M.
Rosenberg
,
A.
Zylstra
,
M. J.-E.
Manuel
,
H.
Sio
,
C.
Waugh
,
H. G.
Rinderknecht
,
M. G.
Johnson
,
J.
Frenje
,
C. K.
Li
,
R.
Petrasso
,
T. C.
Sangster
, and
S.
Roberts
,
Rev. Sci. Instrum.
83
,
10D908
(
2012
).
33.
W. J.
Hibbard
,
M. D.
Landon
,
M. D.
Vergino
,
F. D.
Lee
, and
J. A.
Chael
,
Rev. Sci. Instrum.
72
,
530
(
2001
).
34.
C. K.
Li
,
F. H.
Séguin
,
J. A.
Frenje
,
R. D.
Petrasso
,
P. A.
Amendt
,
R. P. J.
Town
,
O. L.
Landen
,
J. R.
Rygg
,
R.
Betti
,
J. P.
Knauer
,
D. D.
Meyerhofer
,
J. M.
Soures
,
C. A.
Back
,
J. D.
Kilkenny
, and
A.
Nikroo
,
Phys. Rev. Lett.
102
,
205001
(
2009
).
35.
C. K.
Li
,
F. H.
Séguin
,
J. A.
Frenje
,
M.
Rosenberg
,
R. D.
Petrasso
,
P. A.
Amendt
,
J. A.
Koch
,
O. L.
Landen
,
H. S.
Park
,
H. F.
Robey
,
R. P. J.
Town
,
A.
Casner
,
F.
Philippe
,
R.
Betti
,
J. P.
Knauer
,
D. D.
Meyerhofer
,
C. A.
Back
,
J. D.
Kilkenny
, and
A.
Nikroo
,
Science
327
,
1231
(
2010
).
36.
C. K.
Li
,
A. B.
Zylstra
,
J. A.
Frenje
,
F. H.
Séguin
,
N.
Sinenian
,
R. D.
Petrasso
,
P. A.
Amendt
,
R.
Bionta
,
S.
Friedrich
,
G. W.
Collins
,
E.
Dewald
,
T.
Döppner
,
S. H.
Glenzer
,
D. G.
Hicks
,
O. L.
Landen
,
J. D.
Kilkenny
,
A. J.
Mackinnon
,
N.
Meezan
,
J.
Ralph
,
J. R.
Rygg
,
J.
Kline
, and
G.
Kyrala
,
New J. Phys.
15
,
025040
(
2013
).
37.
J.
Lindl
,
O.
Landen
,
J.
Edwards
,
E.
Moses
, and
N. Team
,
Phys. Plasmas
21
,
020501
(
2014
).
38.
J. R.
Rygg
,
O. S.
Jones
,
J. E.
Field
,
M. A.
Barrios
,
L. R.
Benedetti
,
G. W.
Collins
,
D. C.
Eder
,
M. J.
Edwards
,
J. L.
Kline
,
J. J.
Kroll
,
O. L.
Landen
,
T.
Ma
,
A.
Pak
,
J. L.
Peterson
,
K.
Raman
,
R. P. J.
Town
, and
D. K.
Bradley
,
Phys. Rev. Lett.
112
,
195001
(
2014
).
39.
R.
Drake
,
High-Energy-Density-Physics
(
Springer
,
2006
).
40.

For simulations of NIF, low-adiabat implosions to match the data, in particular, the shock timing, implosion trajectory (r vs t), and bang time, multipliers must be applied throughout the pulse to decrease the effective drive on the implosion by a time-varying fraction.8,54

41.
M. J.
Edwards
,
P. K.
Patel
,
J. D.
Lindl
,
L. J.
Atherton
,
S. H.
Glenzer
,
S. W.
Haan
,
J. D.
Kilkenny
,
O. L.
Landen
,
E. I.
Moses
,
A.
Nikroo
,
R.
Petrasso
,
T. C.
Sangster
,
P. T.
Springer
,
S.
Batha
,
R.
Benedetti
,
L.
Bernstein
,
R.
Betti
,
D. L.
Bleuel
,
T. R.
Boehly
,
D. K.
Bradley
,
J. A.
Caggiano
,
D. A.
Callahan
,
P. M.
Celliers
,
C. J.
Cerjan
,
K. C.
Chen
,
D. S.
Clark
,
G. W.
Collins
,
E. L.
Dewald
,
L.
Divol
,
S.
Dixit
,
T.
Doeppner
,
D. H.
Edgell
,
J. E.
Fair
,
M.
Farrell
,
R. J.
Fortner
,
J.
Frenje
,
M. G. G.
Johnson
,
E.
Giraldez
,
V. Y.
Glebov
,
G.
Grim
,
B. A.
Hammel
,
A. V.
Hamza
,
D. R.
Harding
,
S. P.
Hatchett
,
N.
Hein
,
H. W.
Herrmann
,
D.
Hicks
,
D. E.
Hinkel
,
M.
Hoppe
,
W. W.
Hsing
,
N.
Izumi
,
B.
Jacoby
,
O. S.
Jones
,
D.
Kalantar
,
R.
Kauffman
,
J. L.
Kline
,
J. P.
Knauer
,
J. A.
Koch
,
B. J.
Kozioziemski
,
G.
Kyrala
,
K. N.
LaFortune
,
S. L.
Pape
,
R. J.
Leeper
,
R.
Lerche
,
T.
Ma
,
B. J.
MacGowan
,
A. J.
MacKinnon
,
A.
Macphee
,
E. R.
Mapoles
,
M. M.
Marinak
,
M.
Mauldin
,
P. W.
McKenty
,
M.
Meezan
,
P. A.
Michel
,
J.
Milovich
,
J. D.
Moody
,
M.
Moran
,
D. H.
Munro
,
C. L.
Olson
,
K.
Opachich
,
A. E.
Pak
,
T.
Parham
,
H.-S.
Park
,
J. E.
Ralph
,
S. P.
Regan
,
B.
Remington
,
H.
Rinderknecht
,
H. F.
Robey
,
M.
Rosen
,
S.
Ross
,
J. D.
Salmonson
,
J.
Sater
,
D. H.
Schneider
,
F. H.
Sguin
,
S. M.
Sepke
,
D. A.
Shaughnessy
,
V. A.
Smalyuk
,
B. K.
Spears
,
C.
Stoeckl
,
W.
Stoeffl
,
L.
Suter
,
C. A.
Thomas
,
R.
Tommasini
,
R. P.
Town
,
S. V.
Weber
,
P. J.
Wegner
,
K.
Widman
,
M.
Wilke
,
D. C.
Wilson
,
C. B.
Yeamans
, and
A.
Zylstra
,
Phys. Plasmas
20
,
070501
(
2013
).
42.
J. R.
Rygg
,
J. A.
Frenje
,
C. K.
Li
,
F. H.
Séguin
,
R. D.
Petrasso
,
D. D.
Meyerhofer
, and
C.
Stoeckl
,
Phys. Rev. E
80
,
026403
(
2009
).
43.
C.
Cerjan
,
P. T.
Springer
, and
S. M.
Sepke
,
Phys. Plasmas
20
,
056319
(
2013
).
44.
P. T.
Springer
,
C.
Cerjan
,
R.
Betti
,
J. A.
Caggiano
,
M. J.
Edwards
,
J. A.
Frenje
,
V. Y.
Glebov
,
S. H.
Glenzer
,
S. M.
Glenn
,
N.
Izumi
,
O.
Jones
,
G.
Kyrala
,
T.
Ma
,
J.
McNaney
,
M.
Moran
,
D. H.
Munro
,
S.
Regan
,
T. C.
Sangster
,
S.
Sepke
,
H.
Scott
,
R. P. J.
Town
,
S. V.
Weber
, and
B.
Wilson
,
EPJ Web Conf.
59
,
04001
(
2013
).
45.
H.
Rinderknecht
 et al, “Ion thermal decoupling and species separation in shock-driven implosions,”
Phys. Rev. Lett.
(submitted).
46.
S. Le
Pape
,
L.
Divol
,
L. B.
Hopkins
,
A.
Mackinnon
,
N. B.
Meezan
,
D.
Casey
,
J.
Frenje
,
H.
Herrmann
,
J.
McNaney
,
T.
Ma
,
K.
Widmann
,
A.
Pak
,
G.
Grimm
,
J.
Knauer
,
R.
Petrasso
,
A.
Zylstra
,
H.
Rinderknecht
,
M.
Rosenberg
,
M.
Gatu-Johnson
, and
J. D.
Kilkenny
,
Phys. Rev. Lett.
112
,
225002
(
2014
).
47.
H. G.
Rinderknecht
,
M. G.
Johnson
,
A. B.
Zylstra
,
N.
Sinenian
,
M. J.
Rosenberg
,
J. A.
Frenje
,
C. J.
Waugh
,
C. K.
Li
,
F. H.
Sguin
,
R. D.
Petrasso
,
J. R.
Rygg
,
J. R.
Kimbrough
,
A.
MacPhee
,
G. W.
Collins
,
D.
Hicks
,
A.
Mackinnon
,
P.
Bell
,
R.
Bionta
,
T.
Clancy
,
R.
Zacharias
,
T.
Döppner
,
H. S.
Park
,
S.
LePape
,
O.
Landen
,
N.
Meezan
,
E. I.
Moses
,
V. U.
Glebov
,
C.
Stoeckl
,
T. C.
Sangster
,
R.
Olson
,
J.
Kline
, and
J.
Kilkenny
,
Rev. Sci. Instrum.
83
,
10D902
(
2012
).
48.
N.
Sinenian
,
M. J.-E.
Manuel
,
A. B.
Zylstra
,
M.
Rosenberg
,
C. J.
Waugh
,
H. G.
Rinderknecht
,
D. T.
Casey
,
H.
Sio
,
J. K.
Ruszczynski
,
L.
Zhou
,
M. G.
Johnson
,
J. A.
Frenje
,
F. H.
Séguin
,
C. K.
Li
,
R. D.
Petrasso
,
C. L.
Ruiz
, and
R. J.
Leeper
,
Rev. Sci. Instrum.
83
,
043502
(
2012
).
49.
J.
Ziegler
,
J.
Biersack
, and
U.
Littmark
,
The Stopping and Range of Ions in Matter
(
Pergamon
,
New York
,
1985
).
50.
T.
Ma
,
P. K.
Patel
,
N.
Izumi
,
P. T.
Springer
,
M. H.
Key
,
L. J.
Atherton
,
L. R.
Benedetti
,
D. K.
Bradley
,
D. A.
Callahan
,
P. M.
Celliers
,
C. J.
Cerjan
,
D. S.
Clark
,
E. L.
Dewald
,
S. N.
Dixit
,
T.
Döppner
,
D. H.
Edgell
,
R.
Epstein
,
S.
Glenn
,
G.
Grim
,
S. W.
Haan
,
B. A.
Hammel
,
D.
Hicks
,
W. W.
Hsing
,
O. S.
Jones
,
S. F.
Khan
,
J. D.
Kilkenny
,
J. L.
Kline
,
G. A.
Kyrala
,
O. L.
Landen
,
S. Le
Pape
,
B. J.
MacGowan
,
A. J.
Mackinnon
,
A. G.
MacPhee
,
N. B.
Meezan
,
J. D.
Moody
,
A.
Pak
,
T.
Parham
,
H.-S.
Park
,
J. E.
Ralph
,
S. P.
Regan
,
B. A.
Remington
,
H. F.
Robey
,
J. S.
Ross
,
B. K.
Spears
,
V.
Smalyuk
,
L. J.
Suter
,
R.
Tommasini
,
R. P.
Town
,
S. V.
Weber
,
J. D.
Lindl
,
M. J.
Edwards
,
S. H.
Glenzer
, and
E. I.
Moses
,
Phys. Rev. Lett.
111
,
085004
(
2013
).
51.
G.
Zimmerman
,
LLNL Report No. UCRL-JC-105616
,
1990
.
52.
G.
Maynard
and
C.
Deutsch
,
Phys. Rev. A
26
,
665
(
1982
).
53.
L. S.
Brown
,
D. L.
Preston
, and
R. L.
Singleton
, Jr.
,
Phys. Rep.
410
,
237
(
2005
).
54.
O. S.
Jones
,
C. J.
Cerjan
,
M. M.
Marinak
,
J. L.
Milovich
,
H. F.
Robey
,
P. T.
Springer
,
L. R.
Benedetti
,
D. L.
Bleuel
,
E. J.
Bond
,
D. K.
Bradley
,
D. A.
Callahan
,
J. A.
Caggiano
,
P. M.
Celliers
,
D. S.
Clark
,
S. M.
Dixit
,
T.
Doppner
,
R. J.
Dylla-Spears
,
E. G.
Dzentitis
,
D. R.
Farley
,
S. M.
Glenn
,
S. H.
Glenzer
,
S. W.
Haan
,
B. J.
Haid
,
C. A.
Haynam
,
D. G.
Hicks
,
B. J.
Kozioziemski
,
K. N.
LaFortune
,
O. L.
Landen
,
E. R.
Mapoles
,
A. J.
MacKinnon
,
J. M.
McNaney
,
N. B.
Meezan
,
P. A.
Michel
,
J. D.
Moody
,
M. J.
Moran
,
D. H.
Munro
,
M. V.
Patel
,
T. G.
Parham
,
J. D.
Sater
,
S. M.
Sepke
,
B. K.
Spears
,
R. P. J.
Town
,
S. V.
Weber
,
K.
Widmann
,
C. C.
Widmayer
,
E. A.
Williams
,
L. J.
Atherton
,
M. J.
Edwards
,
J. D.
Lindl
,
B. J.
MacGowan
,
L. J.
Suter
,
R. E.
Olson
,
H. W.
Herrmann
,
J. L.
Kline
,
G. A.
Kyrala
,
D. C.
Wilson
,
J.
Frenje
,
T. R.
Boehly
,
V.
Glebov
,
J. P.
Knauer
,
A.
Nikroo
,
H.
Wilkens
, and
J. D.
Kilkenny
,
Phys. Plasmas
19
,
056315
(
2012
).