Classical transport equations for burning gas-metal plasmas

Abstract

Thermonuclear inertial confinement fusion plasmas confined by a heavy metal shell may be subject to the mixing of metal into the gas with a resulting degradation of fusion yield. Classical plasma diffusion driven by a number of gradients can provide a physical mechanism to produce atomic mix, possibly in concert with complex hydrodynamic structures and/or turbulence. This paper gives a derivation of the complete dissipative plasma hydrodynamics equations from kinetic theory, for a binary ionic mixture plasma consisting of electrons, e, a light (hydrogenic gas) ion species, i, and a heavy, high ZI plasma metal species, I. A single mean ionization state for the heavy metal, ZI, is assumed to be provided by some independent thermodynamic model of the heavy metal ZI=ZI(ni,nI,Te). The kinetic equations are solved by a generalized Chapman-Enskog expansion that assumes small Knudsen numbers for all species: NKe≡λe/L≪1,NKi≡λi/L≪1. The small electron to ion mass ratio, me/mi≪1, is utilized to account for electron-ion temperature separation, Te≠Ti, and to decouple the electron and ion transport coefficient calculations. This produces a well ordered perturbation theory for the electrons, resulting in the well known “Spitzer” problem of Spitzer and collaborators and solved independently by Braginskii. The formulation in this paper makes clear the inherent symmetry of the transport and gives an analytic solution for all values of the effective charge Zeff, including Zeff<1. The electron problem also determines the ambipolar electric field and the “thermal forces” on both ion species that are needed for the ion kinetic solution. The ion transport problem makes use of the small mass ratio between ion species, mi/mI≪1, to identify an “ion Spitzer problem” that is mathematically identical to that for the electrons but with different thermodynamic forces. The ionic scattering parameter, ΔI≡nIZI2/ni, replaces the Zeff of the electron problem, but has an extended domain, 0≤ΔI<∞, to cover all mixture fractions from the pure gas to the pure metal plasma. The extension of the Spitzer problem to include this extended domain is given in this work. The resulting transport equations for the binary gas-metal plasma mixture are complete and accurate through second order. All transport coefficients are provided in analytic form.

A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation

“…In strongly collisional regimes, AP methods (as defined in the references) guarantee that the penalized FPL solution is a Maxwellian, f M , to O( ) [27] , with a measure of the collisional time scale normalized to the characteristic time scale of interest ( 1 in strongly collisional regimes). However, accurate transport computations in collisional regimes require computing f to O( 2 ) [29,30,31] and to our knowledge, there are no variants of AP schemes which satisfy this.…”

Localization and Screening Enhancement in Asymmetric Binary Ionic Mixtures

“…We apply several models to estimate the diffusivity of hydrogen in the high-Z lattice. One set of models provides the interdiffusion coefficient based on plasma kinetic theory and is most accurate for high temperatures, where the coupling between all species is weak [43][44][45][46][47]. To examine the low temperature behavior, we also employ the high temperature limit of a model for tracer diffusivity of hydrogen in a solid metal [48,49].…”

Transport properties of an asymmetric mixture in the dense plasma regime

“…Understanding this behavior is crucial, so much so that experiments are designed to monitor and control mixing of the ablator into the fuel. Further motivation comes from the mixing of a gas/metal interface [5][6][7]. In such cases, interfaces lead to strong concentration gradients and mixing.…”