Comparison of ablators for the polar direct drive exploding pusher platform
Heather D. Whitley, G. Elijah Kemp, Charles Yeamans, Zachary Walters, Brent E. Blue, Warren Garbett, Marilyn Schneider, R. Stephen Craxton, Emma M. Garcia, Patrick W. McKenty, Maria Gatu-Johnson, Kyle Caspersen, John I. Castor, Markus Däne, C. Leland Ellison, James Gaffney, Frank R. Graziani, John Klepeis, Natalie Kostinski, Andrea Kritcher, Brandon Lahmann, Amy E. Lazicki, Hai P. Le, Richard A. London, Brian Maddox, Michelle Marshall, Madison E. Martin, Burkhard Militzer, Abbas Nikroo, Joseph Nilsen, Tadashi Ogitsu, John Pask, Jesse E. Pino, Michael Rubery, Ronnie Shepherd, Philip A. Sterne, Damian C. Swift, Lin Yang, Shuai Zhang
CComparison of ablators for the polar direct driveexploding pusher platform
Heather D. Whitley a,1 , G. Elijah Kemp a , Charles Yeamans a , ZacharyWalters a , Brent E. Blue a , Warren Garbett b , Marilyn Schneider a , R. StephenCraxton c , Emma M. Garcia c , Patrick W. McKenty c , Maria Gatu-Johnson d ,Kyle Caspersen a , John I. Castor a , Markus D¨ane a , C. Leland Ellison a , JamesGaffney a , Frank R. Graziani a , John Klepeis a , Natalie Kostinski a , AndreaKritcher a , Brandon Lahmann d , Amy E. Lazicki a , Hai P. Le a , Richard A.London a , Brian Maddox a , Michelle Marshall a , Madison E. Martin a , BurkhardMilitzer e , Abbas Nikroo a , Joseph Nilsen a , Tadashi Ogitsu a , John Pask a , JesseE. Pino a , Michael Rubery b , Ronnie Shepherd a , Philip A. Sterne a , Damiani C.Swift a , Lin Yang a , Shuai Zhang c a Lawrence Livermore National Laboratory, Livermore, California 94550, USA b AWE plc, Aldermaston, Reading RG7 4PR, United Kingdom c Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623,USA d Massachusetts Institute of Technology, Plasma Science and Fusion Center, Cambridge,Massachusetts 02139, USA e University of California, Berkeley, California 94720, USA
Abstract
We examine the performance of pure boron, boron carbide, high density carbon,and boron nitride ablators in the polar direct drive exploding pusher (PDXP)platform. The platform uses the polar direct drive configuration at the Na-tional Ignition Facility to drive high ion temperatures in a room temperaturecapsule and has potential applications for plasma physics studies and as a neu-tron source. The higher tensile strength of these materials compared to plasticenables a thinner ablator to support higher gas pressures, which could help opti-mize its performance for plasma physics experiments, while ablators containingboron enable the possiblity of collecting addtional data to constrain models ofthe platform. Applying recently developed and experimentally validated equa- (cid:73)
Manuscript prepared for the proceedings of IFSA2019.
Email address: [email protected] (Heather D. Whitley) Presenting and corresponding author
Preprint submitted to High Energy Density Physics June 30, 2020 a r X i v : . [ phy s i c s . c o m p - ph ] J un ion of state models for the boron materials, we examine the performance ofthese materials as ablators in 2D simulations, with particular focus on changesto the ablator and gas areal density, as well as the predicted symmetry of theinherently 2D implosion. Keywords: direct drive, exploding pusher, ablators, inertial confinementfusion
1. Introduction
The Polar Direct Drive Exploding Pusher (PDXP) platform was proposedand developed as a platform for studying electron-ion temperature equilibrationand thermal conduction in the high energy density regime that is relevant to in-ertial confinement fusion at the National Ignition Facility (NIF)[1, 2] It has sincebeen applied in both nucleosynthesis experiments[3] and as a neutron source.[4]Our initial PDXP proposal for NIF called for a thin ablator, enabling full ab-lation of the capsule shell, which we believed would lead to better uniformityof the plasma during the proposed time-resolved spectroscopic measurements ofthe plasma temperature. Early design studies indicated that the performancefor heat flow measurements was optimized with a gas fill pressure of 8-10 atmbased on 500 kJ of laser energy incident on a 3 mm outer diameter capsule.Because the proposed measurements of plasma temperature rely on using Ar asa spectroscopic dopant, the platform required that the signal from the Ar spec-tral lines must be significantly higher than the emission from the backgroundplasma, and the Ar mass in the target must be well known. We had initiallyconsidered SiO or Be ablators for these measurements due to the ability tofabricate thin capsules of either material. The SiO design was ruled out dueto calculations that showed high background emission, and thus low Ar signal,during the proposed measurement, and Be was ruled out because the sputteringprocess used to make Be ablators generally results in significant Ar remainingin the shell. For these reasons, and the lack of capabilities to build high den-sity carbon (HDC) capsules of the desired size at the time, we based our point2esign on glow discharge polymer (GDP) ablators, which necessitated capsulesof ∼ µ m thickness for the desired fill pressure.[5] The initial shots were thusfielded using 3 mm diameter GDP capsules with thicknesses of 18-20 µ m and ∼ ∼ × cm − ),regardless of laser drive or capsule geometry. Although these capsules are drivenby relatively short laser pulses, 2D simulations show that the laser beams tendto continually imprint a specific pattern on the imploding shell, and this imprintappears to contribute to the observed capsule asymmetry at bang time basedon comparison of the self-emission images from N170212-003 and N170212-004to 2D simulations.[3]One possible route for mitigating the asymmetry, which would presumablyallow for the generation of more uniform plasma conditions, would be to designcapsules that have a thinner ablator with better coupling to the laser. Suchan ablator could potentially enable the use of a shorter pulse, and the higherthermal conductivity of a higher density material could help to mitigate the3onuniformity of the laser energy deposition. Due to the linear relation be-tween tensile strength and capsule burst pressure,[5] materials such as boron(B), high density carbon (HDC), boron carbide (B C), and boron nitride (BN),which have tensile strength 5-10 times higher than that of GDP, could presum-ably support the 8-10 atm fill pressures of the nominal PDXP point design atsubstantially reduced thickness relative to GDP. While HDC is now a commoncapsule material, our interest in boron-containing materials is motivated by thepossibility of collecting data to help constrain simulation models of the PDXPplatform. In PDXP capsules with a DT gas fill, high yields can be achieved, andthus comparing gamma reaction history (GRH) measurements[8, 9] from implo-sions using an ablator containing natural boron to measurements using a GDPcapsule could potentially provide constraining data for the gas areal densityduring burn due to the impact of knock-on deuterons on the B(d,n γ . ) Creaction on the GRH.[10] In addition, our best fitting simulations of previousshots invoke a diffusive mix model for ablator-fuel mix.[1] The B( α ,p γ ) Creaction, which produces γ signals around 3.5 MeV, could provide data to helpdistinguish between diffusive mix and hydrodynamic instabilities, potentiallyvalidating the use of this diffusive mix model.[11] We note that our interest inthe pure B and BN ablators is specifically motivated by the absence of carbon inthese ablators, which eliminates potential cross talk from other reactions withC.[12] These same reactions with C are useful for constraining shell areal den-sity based on GRH data[13], but would complicate the diagnostics we proposehere for examining the gas density and distinguishing between diffusive mix andhydrodynamic instabilities.Over the past several years, advances in additive manufacturing and tar-get fabrication techniques have made the possibility of fielding shots with B Cablators more tangible.[14] Novel techniques have also been applied to maketargets for planar equation of state experiments on BN at the NIF.[15] It there-fore seems timely to examine these materials as potential ablators. We are notcurrently aware of a fabrication technique for making a pure B capsule, thoughwe include our results for B for future comparison purposes. We present a brief4ummary of simulations examining the performance of B, B C, HDC, and BNablators in 2D. Our 2D models are based on previously developed postshot mod-els for N160920-005, which fielded a GDP ablator and 8 atm D gas fill at roomtemperature. Due to the inherent uncertainties in modeling capsule implosions,we seek to minimize controllable sources of error in this work. As a preludeto this study, we therefore applied a variety of theoretical methods to examinethe equation of state (EOS) of pure boron, B C, and BN[16, 17, 18] since thesematerials have not yet been used in capsule experiments at the NIF. New EOSmodels were developed for B and BN based on our earlier work, and we make useof a previously developed model for B C[19] in this baseline comparison study.The EOS of HDC and GDP were also previously studied in detail.[19, 20, 21]
2. Model description and results
Our 2D direct drive simulations are carried out using the Ares radiationhydrodynamics simulation code.[22, 23] For the purpose of this study, we useN160920-005 as the baseline for tuning the initial model and we use the laserpulse as delivered in this shot for all simulations reported here. In this shot, wefielded a 2.955 mm outer diameter GDP with a 19 µ m thickness ablator, filledwith 7.941 atm of D gas with 5 × − atomic fraction of Ar as a spectroscopicdopant. The capsule was driven with a 1.8 ns square pulse, delivering 479 kJof total energy with slightly higher power in the outer beams to provide addi-tional power near the equator of the capsule.[1] The calculated power profile onthe capsule surface is shown in Figure 1. We use a laser ray trace method fordepositing the energy in the capsule, which takes into account the 3D pointinggeometry, but does not include the effects of cross-beam energy transfer or nonlo-cal electron thermal transport. Both of these effects are known to be importantfor modeling laser-matter interactions in direct drive implosions,[24, 25, 26] butwe have nonetheless found that the salient features of our shots are modeled wellusing a more approximate treatment. Our models employ multigroup diffusionfor the propagation of radiation, and we apply a flux limiter to the electron ther-5 igure 1: Computed laser power on the capsule surface for N160920-005. The black dotsindicate the pointing on the capsule surface. mal conduction in the ablator during the laser pulse. We tune the flux limiterand a multiplier on the total laser power to fit the observed x-ray bang time ofthe shot, as described in Ref. [1]. In this study, we used a flux limiter of 0.0398,and we find a good fit to the neutron bang time by assuming an energy mulit-plier of 0.875. We have also applied the multicomponent Navier-Stokes (mcNS)model for species diffusion in simulations of this shot, and we find that usingthis model enables a good match to the measured burn-averaged ion tempera-ture and the neutron yield, provided a that multipler is applied to the diffusioncoefficient.[1] However, we have no reason to expect that the multiplier that wedetermined for the GDP capsules will also apply to the ablators considered inthis study, and so we did not exercise the species diffusion model in this study.Table 1 summarizes the ablator characteristics of the 2D simulations per-formed in this study. For HDC, we considered both a thin design and a thickerdesign. For the thicker design, the ablator thickness was chosen to be 6.0 µ min order provide a mass match to the GDP ablator, whereas for the thinner6blator Thickness Capsule Mass Density EOS Models( µ m) (mg) (g/cc)GDP 19 0.54 1.046 L5400[19, 20]HDC 6 0.54 3.32 L9061[21]B 6 0.40 2.46 X52[16]B C 5.86 0.40 2.52 L2122[19]BN 6 0.37 2.25 X2152[17] and L2150HDC 4.45 0.40 3.32 L9061[21]
Table 1: Capsule parameters and EOS models used in this study. designs, we first considered an HDC capsule where the total ablator mass isreduced to 0.4 mg, corresponding to a thickness of 4.45 µ m. The thicknesses ofthe B and B C ablators were then chosen to match the total mass of the thinnerHDC design (6.0 µ m and 5.86 µ m, respectively). Similar to HDC, BN can existeither in a cubic (diamond) lattice or in a hexagonal (graphitic) lattice. In thiswork, we consider BN in the hexagonal phase, with a density of 2.25 g/cc, sothe mass of the BN ablator is just slightly lower than that of the other thincapsule designs. The BN capsule was chosen to have a thickness that matchesthe thin HDC capsule.Table 1 also lists the equation of state model used for each material in thetable. For BN, we applied both a model that was recently developed (X2152)[17]and an older model from the LEOS library that was developed by D. A. Youngand is based on a Thomas-Fermi model (L2150). These two models were com-pared in our previous report on the BN equation of state.[17] For each of thesecalculations, we assumed a D fill pressure of 7.941 atm at room temperature,which was chosen to match N160920-005. We use the L1014 model for the EOSof D , consistent with our previous 1D simulation studies.[1, 16]Table 2 lists some of the computed results for each of the capsules. Thetotal yield of the capsules predictably increases as a function of the total en-7blator/thickness ( µ m) Absorbed Neutron Convergence T ion Energy (kJ) Yield Ratio (keV)GDP/19 282 4 . × . ×
10 8.8B/6 310 6 . × C/5.86 313 6 . × . × . × Table 2: Results from 2D Ares simulations. The convergence ratio is computed based onthe minimum gas volume. We note that the measured neutron yield from N160920-005 was2 . ± . × , so the clean yield computed in the 2D calculation of the GDP capsule isabout a factor of 2 larger than the experiment. ergy absorbed. Since the laser-capsule coupling is higher for the higher densityablators, the HDC and BN ablators produce the highest neutron yields. Wealso find that the two HDC capsules absorb the same amount of energy fromthe laser, but the thicker ablator produces higher yield, higher peak conver-gence ratio ( CR ) defined based on the ratio of the initial gas volume to theminimum gas volume, CR = ( V i /V min ) / , and lower burn-averaged ion tem-perature. The performance of the thicker HDC capsule appears to mimic thatof the thick GDP capsule. Results for the BN capsule are reported only forL2152 because the results from L2150 were nearly identical. As expected, thethin capsule with low ablator density near peak compression is not sensitive tothe choice of EOS model. (For the thicker capsules, variations in the EOS canimpact the computed performance, and we explore EOS variations in greaterdepth in Ref. [18].)In Figures 2-4 we plot several characteristic properties of the gas from sim-ulations of the thicker GDP and HDC capsules (Figures 2 and 3), as well as thethinner B C capsule (Figure 4) as a function of time. In each of these plots, the8urn rate is scaled by its peak value and the average ion temperature in the gasis scaled by the burn-averaged ion temperature listed in Table 2. We also plotthe average radius of the gas scaled by the initial radius, which is equivalentto the convergence ratio as defined above and listed in Table 2. These plotsdemonstrate that the two thick capsule designs behave similarly, with most ofthe neutrons being produced after the peak in the average gas temperature,while the gas is still being compressed by the remaining ablator. In contrast,the thin capsule design produces its yield at the same time as the ion tempera-ture peaks. The average ion temperature in the thin capsule design also exceedsthe burn-averaged ion temperature, in contrast to the thick capsule designs. Inthe thick designs, the burn is occuring primarily after shock convergence. Thisis consistent with what we found in our 1D study, as shown in Figures 2 and 7of Ref. [1], though in 2D the shock structure is more complicated and the burnis diminished mostly due to capsule break up, as opposed to capsule expansion,near peak compression. The break up of the capsule occurs due to lower densityregions that are generated at the points where the inner laser beams impact thecapsule.Comparing Figures 2 and 3 provides some insight into why the HDC capsuleproduced a factor of 2 higher neutron yield than the GDP capsule. First, theincrease in absorbed laser power for HDC relative to GDP leads to a strongershock, and hence higher ion temperatures. Second, the higher density ablatorprovides more remaining mass during stagnation, hence the capsule break upthat leads to the demise of burn in the GDP calculation is less severe for HDC.Third, the HDC implosion is slightly more symmetric than the GDP implosion.The better symmetry and decreased breakup are evident in the scaled radiusvs. time plot for HDC (Fig 3), which shows a more obvious minimum at peakcompression than the GDP capsule.Analogous to the similarity in the HDC and GDP thick capsules, we findthat all of the thin capsule designs behave in a similar fashion, regardless of theidentity of the ablator, producing similar yield, extremely high burn-averagedion temperatures (15-16 keV) and about a factor of 2 lower convergence ratio9
Time, ns S ca l e d Q u a n tit y GDP (thick), Scaled burn rateGDP (thick), R(t)/R(0)GDP (thick), T i /
Figure 5: Computed density profiles near peak compression for the HDC (left) and GDP(right) thicker capsule designs. The thinner B C (center) design shows significantly loweroverall density than the other two capsules. The color map is the same in all three images.For the thinner B C design, the peak density of 0.36 g/cc occurs within the center of the gasand is surrounded by a region of lower density gas that extends out to about 400 µ m in eachdirection. The thicker ablators exhibit peak densities of > . than the thicker capsule designs. Figure 5 shows the density profile at peakcompression for the B C thinner capsule design along with the computed densitynear peak compression for both the HDC and GDP thicker capsules. The blackcontour in each plot is the boundary between the ablator and the gas. In thethinner capsules, the ablator has burned away, and the overall gas density isconsequently lower than it is for the thicker capsules, consistent with the lowerconvergence shown in Fig. 4. As discussed above, Figure 5 also shows that theHDC capsule produces a more uniform compression of the gas than the GDPablator. All of the computed geometries at peak stagnation show significantasymmetry due to the polar direct drive configuration. This indicates that theproposed heat flow experiments would still require significant design advances inorder to realize a more uniform plasma, even with the use of a thinner ablator.
3. Summary and Conclusions
In this paper we have presented a survey of candidate ablator materials forfuture experiments on the PDXP platform. Our simulations show that thinner13apsule designs using the higher tensile strength materials should lead to morecomplete ablation of the capsule than the baseline GDP design. However, ourcalculations also show that, even in the case where a thinner ablator is used,the polar direct drive configuration is still predicted to imprint significant asym-metry on the implosion that persists through stagnation. Due to the inherentuncertaintanties in modeling direct drive implosions and the lack of experimen-tal data to validate our models for ablators other than GDP, we have not yetpursued additional optimization of either the laser pointing or the laser pulsein this study. It is possible that using a thinner ablator composed of any oneof these materials and reoptimizing the drive for the new geometry would leadto a more symmetric implosion. Ideally, such optimization of the laser pulsewould be performed using a baseline model that had been fit to experimentaldata for the actual ablator under consideration. As such, we have saved thisstudy as future work, and we hope that this work provides motivation for futureexperiments on this platform.Even with the apparent lack of symmetry, the increased coupling of the laserto the higher density materials improves the neutron yield in these implosions.One interesting finding of this study is that an HDC version of N160920-005is predicted to give about a factor of 2 higher neutron yield than the GDPablator. While the HDC capsule does give a slightly more symmetric geometryand somewhat higher gas density, the higher yield is primarily the result ofbetter laser-target coupling, which produces a stronger shock and higher iontemperatures than the GDP capsule. Because the increase in yield can belargely attributed to better laser-capsule coupling, moving to an HDC capsuleon the PDXP platform for neutron source development[4] appears to be a lowrisk change that would give higher yields than those that could be achieved inthe current GDP-based experiments.While we have observed that the 2D model gives a reasonable fit to someof the diagnostic data obtained for N160920-005, modeling these direct drivesimulations at the NIF is still relatively uncertain. In the PDXP platform inparticular, it is not clear what fraction of the yield is produced due to the strong14hock versus what fraction comes from the compression of the gas by ablator ma-terial that remains after the laser pulse. These calculations demonstrate largedifferences in the ablator areal density during the burn of the gas. Ablatorscontaining natural boron could enable us to determine whether the computedablator areal density is realistic based on GRH measurements. Demonstratingthe feasibility of those studies will require more detailed analysis of these simu-lations to determine whether there would be a measureable affect of remainingablator mass on the GRH measurement.
Acknowledgments.
This research was in part based upon work supported by theDepartment of Energy National Nuclear Security Administration under AwardNumber DE-NA0003856. Part of the work was performed under the auspicesof the U.S. Department of Energy by Lawrence Livermore National Laboratoryunder Contract No. DE-AC52-07NA27344. H. D. Whitley acknowledges thesupport of the PECASE award. LLNL-JRNL-803851This document was prepared as an account of work sponsored by an agencyof the United States government. Neither the United States government norany agency thereof, nor any of their employees, makes any warranty, expressor implied, or assumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise does not necessarily constitute orimply its endorsement, recommendation, or favoring by the U.S. Government orany agency thereof. The views and opinions of authors expressed herein do notnecessarily state or reflect those of the U.S. Government or any agency thereof,and shall not be used for advertising or product endorsement purposes.
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