Self-Similar Structure and Experimental Signatures of Suprathermal Ion Distribution in Inertial Confinement Fusion Implosions

Abstract

The distribution function of suprathermal ions is found to be self-similar under conditions relevant to inertial confinement fusion hot spots. By utilizing this feature, interference between the hydrodynamic instabilities and kinetic effects is for the first time assessed quantitatively to find that the instabilities substantially aggravate the fusion reactivity reduction. The ion tail depletion is also shown to lower the experimentally inferred ion temperature, a novel kinetic effect that may explain the discrepancy between the exploding pusher experiments and rad-hydro simulations and contribute to the observation that temperature inferred from DD reaction products is lower than from DT at the National Ignition Facility. Recent exploding pusher experiments [1-6] reveal substantial kinetic effects on the implosion performance. Specific mechanisms potentially responsible for these observations include the inter-ion-species diffusion [7][8][9][10] and reactivity reduction due to ion tail depletion [11][12][13][14][15][16][17][18]. Theoretical evaluation of these phenomena is challenging, however, and while fully kinetic simulations allow study of a certain stage of implosion in specific configurations [19,20], such calculations are computationally prohibitive for the modeling of a realistic inertial confinement fusion (ICF) experiment. A substantial simplification results from treating thermal and suprathermal ions separately [21]. For the former, the mean free path λ ð0Þ is often much smaller than the characteristic scale of the system L, making fluid equations (including interspecies diffusion) a valid model. The latter constitute only a small fraction of the ion density, momentum, and energy and do not appear explicitly in the fluid equations. However, it is the suprathermal ions that are most likely to undergo fusion reactions, so they do affect the fluid equations implicitly as an energy source. For these ions, the mean free path is much larger than λ ð0Þ and can be comparable to L even if λ ð0Þ ≪ L. Hence, self-consistent modeling of ICF implosions would appear to require a kinetic treatment of suprathermal ions capable of predicting the fusion reactivity at each time step of the fluid equations' evolution.While suprathermal ions can be described by a reduced linear (as opposite a to fully nonlinear) kinetic equation [22], this task is still nontrivial. All prior studies rely on either a direct numerical solution [15][16][17][18] or phenomenological assumptions that affect the structure of the kinetic equation [13,14]. Until now, no simple solution to the firstprinciples kinetic equation for the suprathermal ions has been found even in the one-dimensional (1D) planar case. The issue becomes particularly pressing in light of hydroinstabilities at the fuel-pusher interface [23][24][25][26][27][28][29][30]. It is near this interface that the suprathermal ion distribution is modified most, so one should expect substantial interference between the instabilities and the fusion reactivity. However, applying direct...

Indications of flow near maximum compression in layered deuterium-tritium implosions at the National Ignition Facility

“…This narrows the width of the neutron energy distribution, reducing inferred apparent T ion . At a Knudsen number of 0.05 and thermal T ion of 5 keV, the expected T ion ratio due to this effect alone would be 0.95 [37]. However, nominal Knudsen numbers calculated for the neutron-producing compression phase of these implosions are too small for the depletion to be significant at (1-3) × 10 −3 .…”

“…A number of possible mechanisms have been proposed that would give rise to a DT T ion greater than the DD T ion in these implosions. These include flows [23], species separation [35], and Knudsen tail depletion [36,37]. However, before any such effects are invoked to describe the data, it is important to consider that a difference in measured apparent DT and DD T ion is also expected based on the spatial and temporal burn weighting of the neutron emission because of the different temperature dependence of the DD and DT reactivities [38].…”

“…However, nominal Knudsen numbers calculated for the neutron-producing compression phase of these implosions are too small for the depletion to be significant at (1-3) × 10 −3 . Local Knudsen numbers might increase due to turbulence and mix, elevating the impact of this effect [37], but such smallscale turbulence is expected to be reduced by viscosity [51]. PHYSICAL Three-dimensional dynamics seeded by laser drive asymmetry, engineering features, ice-layer nonuniformity, etc., are believed to play a substantial role in these implosions [52][53][54][55].…”

Kinetic studies of ICF implosions

“…Finally, we have demonstrated that the inferred ion burn temperature, as evaluated from the standard Brysk prescription [33], is lower than the actual one due to the same ion tail depletion effect. This mechanism has a stronger impact on the DD reaction than on DT, thereby making the apparent DD temperature lower than DT [32]. Such a trend is often observed at NIF [34] and explanations available to date include the bulk fluid motion [35,36], neutron scattering and burn weighting due to reactivity dependence on temperature [34].…”

“…Indeed, we have found that the reactivity reduction can be substantially aggravated by these instabilities [32]. This analysis utilized the self-similarity feature of the suprathermal ion distribution, which has been verified in the 1D planar and spherical cases with the newly developed code solving the reduced kinetic equation.…”