Exploration of the Transition from the Hydrodynamiclike to the Strongly Kinetic Regime in Shock-Driven Implosions

Abstract

Clear evidence of the transition from hydrodynamiclike to strongly kinetic shock-driven implosions is, for the first time, revealed and quantitatively assessed. Implosions with a range of initial equimolar D 3 He gas densities show that as the density is decreased, hydrodynamic simulations strongly diverge from and increasingly overpredict the observed nuclear yields, from a factor of ∼2 at 3.1 mg=cm 3 to a factor of 100 at 0.14 mg=cm 3 . (The corresponding Knudsen number, the ratio of ion mean-free path to minimum shell radius, varied from 0.3 to 9; similarly, the ratio of fusion burn duration to ion diffusion time, another figure of merit of kinetic effects, varied from 0.3 to 14.) This result is shown to be unrelated to the effects of hydrodynamic mix. As a first step to garner insight into this transition, a reduced ion kinetic (RIK) model that includes gradient-diffusion and loss-term approximations to several transport processes was implemented within the framework of a one-dimensional radiation-transport code. After empirical calibration, the RIK simulations reproduce the observed yield trends, largely as a result of ion diffusion and the depletion of the reacting tail ions. Inertial confinement fusion implosions, whether for ignition [1] or nonignition [2,3] experiments, are nearly exclusively modeled as hydrodynamic in nature with a single average-ion fluid and fluid electrons [4,5]. However, in the early phase of virtually all inertial fusion implosions, strong shocks are launched into the capsule where they increase in strength and speed as they converge to the center and abruptly and significantly increase the ion temperature in the central plasma region. In this process, and in the rebound of the shock from the center, which initiates a burst of fusion reactions (i.e., the fusion shock burn or shock flash [6]), the mean-free path for ion-ion collisions can become, especially for lower-density fueled implosions, sufficiently long that both the shock front itself and the resulting central plasma are inadequately described by hydrodynamic modeling. This process and the transition of regimes from hydrodynamiclike to strongly kinetic are the focus of this Letter.Recent kinetic and multiple-ion-fluid simulations have begun to explore deviations from average-ion hydrodynamic models, particularly during the shock phase of implosions when such effects are potentially paramount. For example, in an effort to explain observed yield anomalies in multiple-ion fuels of D 3 He, DT, and DT 3 He [7][8][9], researchers have investigated multiple-ionfluid effects [10][11][12] as well as utilized a hybrid fluidkinetic model [13,14]. Other modeling work has included ion viscosity and nonlocal ion transport [15] in order to reduce discrepancies with shock-generated nuclear yields. Very recently, a model for Knudsen layer losses of energetic ions [16], based in part on earlier work [17], was explored for a variety of plastic capsule implosions with relatively thick walls, all largely ablatively driven (not shock driven) a...

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

“…This difference between the σv and T exp , to leading order, results from the former being governed by the ion number density within the Gamow window, whereas the latter is governed by higher moments and finer features of the distribution function. The size of the predicted effect is consistent with the discrepancy between the temperature observed in exploding pusher experiments, in which N K can be even higher than shown in Fig 4, and that predicted by simulations [3][4][5][6]. Of course, in these experiments kinetic effects can also lower the actual temperature by reducing the shock heating; however, employing standard formulae for the spectrum width would diminish the inferred temperature even further.…”

“…Recent exploding pusher experiments [1][2][3][4][5][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].…”

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