  In this paper, a physics-oriented stochastic kinetic scheme will be developed
that includes random inputs from both flow and electromagnetic fields via a
hybridization of stochastic Galerkin and collocation methods. Based on the
BGK-type relaxation model of the multi-component Boltzmann equation, a
scale-dependent kinetic central-upwind flux function is designed in both
physical and particle velocity space, and the governing equations in the
discrete temporal-spatial-random domain are constructed. By solving Maxwell's
equations with the wave-propagation method, the evolutions of ions, electrons
and electromagnetic field are coupled throughout the simulation. We prove that
the scheme is formally asymptotic-preserving in the Vlasov,
magnetohydrodynamical, and neutral Euler regimes with the inclusion of random
variables. Therefore, it can be used for the study of multi-scale and
multi-physics plasma system under the effects of uncertainties, and provide
scale-adaptive physical solutions under different ratios among numerical cell
size, particle mean free path and gyroradius (or time step, local particle
collision time and plasma period). Numerical experiments including
one-dimensional Landau Damping, the two-stream instability and the Brio-Wu
shock tube problem with one- to three-dimensional velocity settings, and each
under stochastic initial conditions with one-dimensional uncertainty, will be
presented to validate the scheme.
