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The generalized heat flux in plasmas is analytically calculated using the linear relativistic Fokker–Planck equation. The thermal conductivity and the convective heat flux coefficients are calculated for arbitrary collisionality and plasma temperature. The role of relativistic effects coupled with nonlocal effects on the transport is studied. It was found that the thermal conductivity coefficient decreases with increasing Knudsen number and increasing relativistic effects. In addition, the convective heat flux coefficient is significant in the collisionless range and for the weakly relativistic regime. In particular, in laser-created plasmas, the damping of the plasma eigenmodes should increase with increasing relativistic effects and decrease with increasing nonlocal effects. Consequently, the growth rates of parametric instabilities in plasmas created in the context of inertial confined fusion are expected to be reduced by relativistic effects. [ABSTRACT FROM AUTHOR]

On the basis of kinetic theory, the stability of an electron beam interacting with inhomogeneous plasma is investigated at Knudsen numbers of the order of 1. The theory has been tested on the example of a low-voltage beam discharge in a rear gas. It is shown that in the case of an inhomogeneous plasma even if the attenuation of a beam is neglected, several perturbations can propagate simultaneously at the same frequency, but with different phase and group velocities and increments. The case of a linear dependence of the plasma density on the coordinate is investigated in detail. In this case, there are two solutions: n- and p-waves, only the n-wave having a physical meaning. It is found that an increase in the plasma density gradient leads to a decrease in the increment and an increase in the phase and group velocities of propagation of perturbations with a frequency of the order of plasma frequency. A system with a growing plasma density along the beam direction is more stable than that with a constant density. For a significant change in the growth rate of the disturbance, the relative gradient of plasma density by an amount of about 10% at the wavelength is sufficient. All the observed features of the perturbation parameters depending on the plasma density gradient are physically interpreted. The calculations are confirmed by experimental data. [ABSTRACT FROM AUTHOR]

In laser plasmas, the electron distribution function is not Maxwellian but super-Gaussian due to the inverse bremsstrahlung heating, and the electron heat transport is generally nonlocal because of the large Knudsen number. Starting from the Fokker–Planck equation, we develop a nonlocal electron heat transport model based on the non-Maxwellian distribution function. In our study, we follow the method in Schurtz et al. [Phys. Plasmas 7, 4238 (2000)] and derive a differential equation for calculating the nonlocal electron heat flux based on the non-Maxwellian distribution function. The numerical results show that the non-Maxwellian distribution function would reduce the nonlocal heat flux in the laser heated region. The preheat effect due to nonlocal electron heat transport in the conduction region is also reduced by the non-Maxwellian distribution function. This nonlocal electron heat transport model can be easily implemented in two-dimensional and three-dimensional hydrodynamics codes. [ABSTRACT FROM AUTHOR]

Simultaneously measured DD, DT, and D3He reaction histories are used to probe the impacts of multi-ion physics during the shock phase of inertial confinement fusion implosions. In these relatively hydrodynamiclike (burn-averaged Knudsen number ⟨ N K ⟩ ∼0.3) shock-driven implosions, average-ion hydrodynamic DUED simulations are able to reasonably match burnwidths, nuclear yields, and ion temperatures. However, kinetic-ion FPION simulations are able to better simulate the timing differences and time-resolved reaction rate ratios between DD, DT, and D3He reactions. FPION simulations suggest that the D3He/DT reaction rate ratio is most directly impacted by ion species separation between the 3He and T ions, whereas the D3He/DD reaction rate ratio is affected by both ion species separation and ion temperature decoupling effects. [ABSTRACT FROM AUTHOR]

A multi-species plasma ion transport model has been added to the adaptive mesh refinement radiation hydrodynamics code, xRage, to include kinetic transport effects when the particle distributions are near Maxwellian, with deviations proportional to a Knudsen number smaller than one. The model is first verified against self-similar solutions reported previously for the pressure equilibrium case, and next shown to be relatively insensitive to the choice of equation of state for the ions. Simulations are then used to examine Inertial Confinement Fusion dynamics in a 1D spherical geometry characteristic of an Omega implosion with a plastic (CH) shell containing a deuterium-tritium (DT) fuel, and with an added heavy ion impurity, argon. Even in this simplified 1D geometry, several interesting results are apparent. Ion stratification occurs similarly to that reported previously in purely kinetic simulations. The hydrogen in the plastic shell is transported radially inward, carried with the main drive shock, and thus migrates away from the C ions. The fuel D and T ions show the expected stratification with an increase in the lighter species concentration during the shock implosion and a reversal, with heavier species concentrations enhanced after shock expansion from the center. This stratification during burn yields different burn weighted ion temperatures, Ti, for the reactions, Ti[DD] < Ti[DT] < Ti[TT], consistent in their ordering with experiments. The mix widths per ion, measured where concentrations fall to 10% of their interfacial value, are evaluated as a function of time, and these are seen to be significant (of order 10 μm) even at early times, well before the main shock converges and before the shell deceleration. The 1D geometry may be a reasonable approximation for this early time mix and implies that this transport may play a role in reducing or modifying the instabilities driven by initial perturbations, ablation, and Rayleigh-Taylor unstable deceleration. An apparent depletion of the heavier ions seen at the incoming ion shock front warrants further investigation. [ABSTRACT FROM AUTHOR]

The hydrodynamic mix of fusion fuel and inert pusher can simultaneously generate smaller fuel pockets and finer pusher layers that separate them. Smaller fuel pockets have greater local Knudsen numbers, which tend to exacerbate the Knudsen layer reactivity reduction. A thinner pusher layer separating the neighboring fuel pockets, on the other hand, can enable the diffusive tunneling of Gamow fuel ions through the pusher layer and hence alleviate the Knudsen layer reactivity degradation. Here, the diffusive tunneling phenomenon describes a random walk process by which the Gamow fuel ions from one fuel pocket can traverse the inert pusher layer to join a neighboring fuel pocket without losing much of their energy. This is made possible by the much slower collisional slowing down rate compared with the pitch angle scattering rate of light fuel ions with heavier pusher ions. In an isobaric target mixture where fuel and pusher segments can have distinct temperatures, due to their different compressibilities, the temperature effect on the critical pusher layer areal density below which diffusive tunneling can occur, which is a property of the hydrodynamic mix, is understood by computing the ion charge state distribution using a collisional radiative model. This information is fed into the collisionality evaluation, enabling a parametric scan of the diffusive tunneling physics in terms of the target pressure, fuel, and pusher temperatures. It is found that when the gold pusher layer has a temperature above 1 keV, the variation of the pusher temperature has little effect on the critical areal mass density below which diffusive tunneling can occur. If the pusher layer is 1 keV or below, the critical areal mass density rises sharply, indicating that for a stronger fuel-pusher temperature disparity, the onset of diffusive tunneling will be at an earlier stage of the hydrodynamic mix when the fuel-pusher mixing structures are of less reduced size. [ABSTRACT FROM AUTHOR]

Fast ion transport and the resulting fusion yield reduction are computed at a gas-metal interface. The extent of fusion yield reduction is observed to depend sensitively on the charge state of the surrounding pusher material and the width of the atomically mixed region. These sensitivities suggest that idealized boundary conditions often implemented at the gas-pusher interface for the purpose of estimating fast ion loss will likely overestimate fusion reactivity reduction in several important limits. In addition, the impact of a spatially complex material interface is investigated by considering a collection of droplets of the pusher material immersed in a DT plasma. It is found that for small Knudsen numbers, the extent of fusion yield reduction scales with the surface area of the material interface. As the Knudsen number is increased, however, the simple surface area scaling is broken, suggesting that hydrodynamic mix has a nontrivial impact on the extent of fast ion losses. [ABSTRACT FROM AUTHOR]

The loss of fuel ions in the Gamow peak and other kinetic effects related to the a particles during ignition, run-away burn, and disassembly stages of an inertial confinement fusion D-T capsule are investigated with a quasi-1D hybrid volume ignition model that includes kinetic ions, fluid electrons, Planckian radiation photons, and a metallic pusher. The fuel ion loss due to the Knudsen effect at the fuel-pusher interface is accounted for by a local-loss model by Molvig et al. [Phys. Rev. Lett. 109, 095001 (2012)] with an albedo model for ions returning from the pusher wall. The tail refilling and relaxation of the fuel ion distribution are captured with a nonlinear Fokker-Planck solver. Alpha heating of the fuel ions is modeled kinetically while simple models for finite alpha range and electron heating are used. This dynamical model is benchmarked with a 3 T hydrodynamic burn model employing similar assumptions. For an energetic pusher (~40 kJ) that compresses the fuel to an areal density of ~1.07g/cm² at ignition, the simulation shows that the Knudsen effect can substantially limit ion temperature rise in runaway burn. While the final yield decreases modestly from kinetic effects of the a particles, large reduction of the fuel reactivity during ignition and runaway burn may require a higher Knudsen loss rate compared to the rise time of the temperatures above ~25 keV when the broad D-T Gamow peak merges into the bulk Maxwellian distribution. [ABSTRACT FROM AUTHOR]

A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. - JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to close the fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produce two systems of linear equations (for "vector" and "tensor" portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The general formulation is employed in Paper II [A. N. Simakov and K. Molvig, Phys. Plasmas 23, 032116 (2016)] to evaluate the individual ion drift velocities and the total ion heat flux and viscosity for specific cases of two and three ion species plasmas. [ABSTRACT FROM AUTHOR]

Experiments designed to investigate the transition to non-collisional behavior in D³He-gas inertial confinement fusion target implosions display increasingly large discrepancies with respect to simulations by standard hydrodynamics codes as the expected ion mean-free-paths λc increase with respect to the target radius R (i.e., when the Knudsen number NK = λc/R grows). To take properly into account large NK's, multi-ion-species Vlasov-Fokker-Planck computations of the inner gas in the capsules have been performed, for two different values of NK, one moderate and one large. The results, including nuclear yield, reactivity-weighted ion temperatures, nuclear emissivities, and surface brightness, have been compared with the experimental data and with the results of hydrodynamical simulations, some of which include an ad hoc modeling of kinetic effects. The experimental results are quite accurately rendered by the kinetic calculations in the smaller-NK case, much better than by the hydrodynamical calculations. The kinetic effects at play in this case are thus correctly understood. However, in the higher-NK case, the agreement is much worse. The remaining discrepancies are shown to arise from kinetic phenomena (e.g., inter-species diffusion) occurring at the gas-pusher interface, which should be investigated in the future work. [ABSTRACT FROM AUTHOR]

The significance and nature of ion kinetic effects in D3He-filled, shock-driven inertial confinement fusion implosions are assessed through measurements of fusion burn profiles. Over this series of experiments, the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, NK) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al., Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatially resolved measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantities to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows that models including ion transport effects are able to better match the experimental results. In implosions characterized by large Knudsen numbers (NK~3), the fusion burn profiles predicted by hydrodynamics simulations that exclude ion mean free path effects are peaked far from the origin, in stark disagreement with the experimentally observed profiles, which are centrally peaked. In contrast, a hydrodynamics simulation that includes a model of ion diffusion is able to qualitatively match the measured profile shapes. Therefore, ion diffusion or diffusion-like processes are identified as a plausible explanation of the observed trends, though further refinement of the models is needed for a more complete and quantitative understanding of ion kinetic effects. [ABSTRACT FROM AUTHOR]

Measurements of yield, ion temperature, areal density (ρR), shell convergence, and bang time have been obtained in shock-driven, D2 and D³He gas-filled "exploding-pusher" inertial confinement fusion (ICF) implosions at the National Ignition Facility to assess the impact of ion kinetic effects. These measurements probed the shock convergence phase of ICF implosions, a critical stage in hot-spot ignition experiments. The data complement previous studies of kinetic effects in shock-driven implosions. Ion temperature and fuel ρR inferred from fusion-product spectroscopy are used to estimate the ion-ion mean free path in the gas. A trend of decreasing yields relative to the predictions of 2D draco hydrodynamics simulations with increasing Knudsen number (the ratio of ion-ion mean free path to minimum shell radius) suggests that ion kinetic effects are increasingly impacting the hot fuel region, in general agreement with previous results. The long mean free path conditions giving rise to ion kinetic effects in the gas are often prevalent during the shock phase of both exploding pushers and ablatively driven implosions, including ignition-relevant implosions. [ABSTRACT FROM AUTHOR]

In inertial confinement fusion, the loss of fast ions from the edge of the fusing hot-spot region reduces the reactivity below its Maxwellian value. The loss of fast ions may be pronounced because of the long mean free paths of fast ions, compared with those of thermal ions. We introduce a fusion utility function to demonstrate essential features of this Knudsen layer effect, in both magnetized and unmagnetized cases. The fusion utility concept is also used to evaluate the restoring reactivity in the Knudsen layer by manipulating fast ions in phase space using waves. [ABSTRACT FROM AUTHOR]

Inertial confinement fusion requires an imploded target in which a central hot spot is surrounded by a cold and dense pusher. The hot spot/pusher interface can take complicated shape in three dimensions due to hydrodynamic mix. It is also a transition region where the Knudsen and inverse Knudsen layer effect can significantly modify the fusion reactivity in comparison with the commonly used value evaluated with background Maxwellians. Here, we describe a hybrid model that couples the kinetic correction of fusion reactivity to global hydrodynamic implosion simulations. The key ingredient is a non-perturbative treatment of the tail ions in the interface region where the Gamow ion Knudsen number approaches or surpasses order unity. The accuracy of the coupling scheme is controlled by the precise criteria for matching the non-perturbative kinetic model to perturbative solutions in both configuration space and velocity space. [ABSTRACT FROM AUTHOR]

Recent work by Molvig et al. [Phys. Rev. Lett. 109, 095001 (2012)] examined how fusion reactivity may be reduced from losses of fast ions in finite assemblies of fuel. In this paper, this problem is revisited with the addition of an asymptotic boundary-layer treatment of ion kinetic losses. This boundary solution, reminiscent of the classical Milne problem from linear transport theory, obtains a free-streaming limit of fast ion losses near the boundary, where the diffusion approximation is invalid. Thermonuclear reaction rates have been obtained for the ion distribution functions predicted by this improved model. It is found that while Molvig's 'Knudsen distribution function' bounds from above the magnitude of the reactivity reduction, this more accurate treatment leads to less dramatic losses of tail ions and associated reduction of thermonuclear reaction rates for finite fuel volumes. [ABSTRACT FROM AUTHOR]

Knudsen layer losses of tail fuel ions could reduce significantly the fusion reactivity of highly compressed cylindrical and spherical targets in inertial confinement fusion (ICF). With the class of magnetized ICF targets in mind, the effect of embedded magnetic fields on Knudsen layer formation is investigated for the first time. The modified energy scaling of ion diffusivity in magnetized hot spots is found to suppress the preferential losses of tail-ions perpendicular to the magnetic field lines to a degree that the tail distribution can be at least partially, if not fully, restored. Two simple threshold conditions are identified leading to the restoration of fusion reactivity in magnetized hot spots. A kinetic equation for tail-ion transport in the presence of a magnetic field is derived, and solutions to the equation are obtained numerically in simulations. Numerical results confirm the validity of the threshold conditions for restored reactivity and identify two different asymptotic regimes of the fusion fuel. While Knudsen layer formation is shown to be suppressed entirely in strongly magnetized cylindrical hot spot cavities, uniformly magnetized spherical cavities demonstrate remnant, albeit reduced, levels of tail-ion depletion. [ABSTRACT FROM AUTHOR]