Session UO4: ICF Kinetic Effects and Codes

On the Potential Role of Species Separation in DT Fuels on Implosion Performance

The measurement of strong, self-generated electric fields (1-10 GVolts/m) in imploding capsules [1], their attribution to polarized (plasma) shock fronts [2], and the identification of plasma-enhanced binary species diffusion from barodiffusion and electrodiffusion [3] have led to a growing interest in the potential role of species separation in inertial-confinement-fusion (ICF) thermonuclear fuels. The potential for anomalous heating from transient frictional or resistive drag between D and T across a finite thickness shock front will be assessed and applied towards ignition thresholds and understanding some outstanding anomalies in the Omega implosion database.\\[4pt] [1] J.R. Rygg \textit{et al}., Science 319, 1223 (2008); C.K. Li \textit{et al}., Phys. Rev. Lett. 100, 225001 (2008).\\[0pt] [2] P.A. Amendt, J.L. Milovich, S.C. Wilks, C.K. Li, R.D. Petrasso and F.H. S\'{e}guin, Plasma Phys. Control. Fusion 51, 124048 (2009).\\[0pt] [3] P. Amendt, C. Bellei and S.C. Wilks, Phys. Rev. Lett. (to appear).   

Separation of d and t ions in exploding pusher simulations

It is shown by means of hybrid particle-in-cell simulations that convergence of the spherical shock wave that propagates through the inner gas of an exploding pusher experiment is accompanied by separation of d and t ions across the shock front. Deuterons run ahead of the tritons and reach the center $\sim $100 ps before the tritons. The rising edge of the DD and TT fusion rate is also temporally separated by the same amount, which should be a measurable observable in experiments and would be a direct proof of the ``stratification conjecture'' [1,2]. Moreover, decoupling of the d and t ions, in terms of both density and temperature, leads to a degradation of the DT fusion yield around shock flash. This suggests the necessity of including multiple-species effects in ICF simulations. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and supported by LDRD 11-ERD-075. \\[4pt] [1] P. Amendt et al, Phys. Plasmas 18, 056308 (2011).\\[0pt] [2] D. T. Casey, et al., PRL 108, 075002 (2012)   

Kinetic Effects in Plasmas Relevant to Hot Spot Ignition

The use of radiation hydrodynamics codes to study laser-based Inertial Confinement Fusion and High Energy Density Physics is ubiquitous. In general, a single species fluid approximation is adequate during most of the interaction. However, there are critical times where electric fields, magnetic fields, or kinetic effects are potentially non-negligible. A number of examples where these effects are observed with the hybrid simulation code LSP will be presented. In particular, the effects of the tail of the electron and ion energy distributions on the fuel assembly and burn phases of hot spot ignition have been investigated in detail. The influence of electric and magnetic fields in 2-D will also be discussed.   

Estimation of Species Diffusivities in Dense Plasma Mixtures Modeled with the Yukawa Interionic Potential

We employ classical molecular dynamics (MD) to investigate species diffusivity in binary Yukawa mixtures. The Yukawa potential is used to describe the screened Coulomb interaction between the ions, providing the basis for models of dense stellar materials, inertial confined plasmas, and colloidal particles in electrolytes. We use Green-Kubo techniques to calculate self-diffusivities and the Maxwell-Stefan diffusivities, and evaluate the validity of the Darken relation over a range of thermodynamic conditions of the mixture. The inter-diffusivity (or mutual diffusivity) can then be related to the Maxwell-Stefan diffusivities through the thermodynamic factor. The latter requires knowledge of the equation of state of the mixture. To test these Green-Kubo approaches and to estimate the activity contribution we have also employed large-scale non-equilibrium MD. In these simulations we can extract the inter-diffusivity value by calculating the rate of broadening of the interface in a diffusion couple. We also explore thermodynamic conditions for possible non-Fickian diffusivity. The main motivation in this work is to build a model that describes the transport coefficients in binary Yukawa mixtures over a broad range of thermodynamic conditions up to 1keV.   

Validation of Non-Local Electron Transport Approaches, Application to Shock Ignition

For laser-plasma interactions at moderate intensities the conduction of heat cannot be captured by the classical Spitzer-H\"arm expression and an accurate treatment for non-local electron transport is necessary. A suitable method needs to discriminate between local electrons, that behave in accordance to the classical thermal conduction, and non-local electrons, that have very long mean free paths and diffuse energy all over the physical domain. Two widely known and promising schemes are examined in detail: SNB [Schurtz et al. PoP (2000)] and CMG [Manheimer et al. PoP (2008)]. Both models have been implemented in the hydrodynamic code DUED and benchmarked against the fully kinetic Vlasov-Fokker-Plank codes OSHUN and KETS. Both schemes calculate the right amount of flux in the limit of steep temperature gradients, and for the test problem of hot-spot relaxation they are both generally well-behaved at hydrodynamic time-scales ($\sim 30 \tau_{\rm ei}$). However, at kinetic time-scales (up to $\sim 30 \tau_{\rm ei}$) the SNB model better approximates the kinetic solution. 1D and 2D shock ignition simulations will be presented and the role of non-local effects in the implosion and ignition stages will be discussed.   

Knudsen Layer Reduction of Fusion Reactivity

Knudsen layer losses of tail fuel ions can significantly reduce the fusion reactivity of multi-keV DT in capsules with small fuel $\rho r$; sizeable yield reduction can result for small inertial confinement fusion (ICF) capsules. This effect is most pronounced when the distance from a burning DT gas region to a non-reacting or cold wall is comparable to the mean free path of reacting fuel ions. A simplified asymptotic theory of Knudsen layer tail depletion is presented and a non-local reduced fusion reactivity model is obtained. Application of the model in simulations of ICF capsule implosion experiments gives calculated yields and ion temperatures that are in much closer agreement with observations than are the results of \ \textquotedblleft nominal\textquotedblright\ or mixed simulations omitting the model. This work was performed under the auspices of the U.S. Dept. of Energy by the Los Alamos National Security, LLC, Los Alamos National Laboratory.   

Knudsen Reactivity Reduction: Kinetic Theory of Diffusion Process

Previous work that found significant fusion reactivity reduction due to Knudsen layer losses [1], utilized a twice simplified treatment of the loss process that first went to the diffusion limit of the transport and then replaced the spatial kinetic diffusion operator by a local loss process. The derivation of kinetic diffusion utilized a stochastic differential equation technique to show that convection in combination with pitch-angle scattering yields spatial diffusion asymptotically over long time and spatial intervals. The same technique can be extended to include the independent energy scattering stochastic process. For the linear Fokker-Planck equation that governs the tail ions this gives a very efficient (particle like) numerical technique that can solve the complete ion tail problem in the three phase space dimensions of pitch-angle, energy, and spatial coordinate. The method allows inclusion of a temperature gradient and specified ambipolar electric fields. We present simulation results of the depleted tail distributions and fusion reactivities, and compare with the predictions of the simple local loss method.\\[4pt] [1] Kim Molvig, Nelson N. Hoffman, Brian J. Albright, Eric M. Nelson, and, Robert J. Webster (\emph{submitted to Physical Review Letters, }2012)   

Optimal combination of ion-loss and turbulent mixing models in numerical simulations of ICF capsule implosions

In a diverse set of direct-drive capsule implosions at OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)], the three observable quantities DT neutron yield, average burn-rate-weighted ion temperature, and time of peak neutron production (``bang time'') can be well explained by numerical simulations that include models for two particular yield-reducing processes: (1) the preferential escape of fast ions (``Knudsen-layer reactivity'') during the hottest part of the compression around stagnation and (2) turbulent mixing [K. Molvig et al., submitted to PRL]. We report here an attempt to determine generally and quantitatively the roles of these two processes in such implosions, by seeking a global optimum in the explanatory capability of the simulations as the controlling length scales of the two processes are varied. Such a study cannot be taken as proof of the correctness of the models or of the relative importance of the processes, owing to the integrated and approximate nature of simulation codes, but can lead to improved predictive capability with reduced uncertainty.   

Neutron Output Reduction Mechanisms in NIF Implosion Targets

Using the implicit/hybrid 2D simulation code ePLAS, we explore non/local and kinetic mechanisms that may reduce neutron output in thin shell NIF target implosions. These include: 1) shock precursors, possibly driven by external hot electrons that can pre-compress the central DT fuel core and lead to its inhomogeneity, 2) the effective cooling of the central fuel from the diffusive escape of the hottest ions to cooler regions, and 3) a pre-advance [1] of the D ions ahead of the T ions, due to the attractive electric field retaining electrons in the imploding fuel shell, and leaving the central fuel richer in D ions but at too low a temperature to burn effectively. The calculations use multiple ion fluids and/or PIC particle ions with background, cold fluid electrons and fluid or PIC hot electrons. All these components are jointly collisional. \textit{E {\&} B}-fields are computed by the Implicit Moment Method for stability with economy, using a new super-hybrid method that can be run on the ion Courant time scale. Spontaneous thermoelectric $B-$fields can alter thermal conductivities and amplify inhomogeneities. We discuss possible yield optimization techniques. \\[4pt] [1] P. Amendt et al., Phys. Plasmas \textbf{18}, 056308 (2011).   

The effect of capsule convergence on ICF design approach

Recent experiment results of NIF have demonstrated the great challenges faced by the ICF community to achieve thermonuclear ignition in the current NIF design space. In this work, we examined the capsule performances compared to that of the predictions by the codes for both the previous Omega ICF as well as NIF ICF experiment shots [1]. It appears that YOC (yield over calculation) is strongly correlated to the convergence of ICF capsule. The codes (both LASNEX and HYDRA) failed to predict the capsule performance when the convergence is great than 15. Here we give a heuristic explanation of the effect of spherical convergence on the growth rate of Rayleigh-Taylor instability. Based on the experiment data and the lack of predictive capability of physics codes for high convergent capsule design, we propose to explore other design approaches in which the capsule convergence is in the range where the codes had successfully demonstrated the predicted capability. One of these candidates is the double-shell capsule with an opaque pusher using vacuum hohraums [2].\\[4pt] [1] S. W. Haan, J.D. Lindl, et al., Phys. Plasmas 18, 051002 (2011)\\[0pt] [2] P. Amendt, C. Cerjan, et al., Phys. Plasmas 14, 056312 (2007)   

Stability of Tamped Spherical Heavy Ion ICF Targets

The deeply penetrating nature of heavy ion beams makes for unique opportunities in the design of ICF targets. In this talk we describe the design of a target that takes advantage the long range and Bragg peak-like deposition profile of heavy ion beam to drive an implosion contained within a dense, high-Z tamper. The targets consist of spherical shells of DT ice, plastic, and a thin gold tamper. The design uses two different mechanisms to provide pressure to drive the implosion. Early in time, the heavy ion beams volumetrically heat the plastic layer, whose tamped expansion compresses the fuel. As the pusher blows down, the drive transitions to radiation driven ablation with the gold tamper now acting as a spherical hohlraum. This paper will discuss the stability properties of these targets. These tamped targets can be driven at large ($>$350 eV) radiation temperatures, which should provide good ablative stabilization of shell perturbations. However, the pusher phase may (since there will be no ablative stabilization) seed provide substantial RT seeds.   

Numerical simulations of late-time LMJ-like targets and comparison with LIL facility experiments

Diagnostics or optics could be damaged by unexpected shrapnel and debris coming from laser target interactions during an experiment on the Laser MegaJoule (LMJ) facility. Each LMJ target design will require a shrapnel and debris analysis based on simulations. We have then developed a numerical approach which allows us simulating LMJ experiments at late-time scale including laser holhraum target coupling, late-time plasma simulations, and fragmentation modeling. Experiments on the multikilojoule LIL system (Ligne d'Integration Laser) have been carried out to emulate fragmentation conditions that should be avoided on LMJ. A broadband soft x-ray spectrometer allows us verifying the laser hohlraum coupling and aerogel collectors are used to characterize the velocity and angular shrapnel distributions. The hohlraum expansion characteristics have been experimentally verified by measuring directions and velocities of the ejected matter.