DOE OSTI2014
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.