  We consider a non reactive multi component gas mixture.We propose a class of
models, which can be easily generalized to multiple species. The two species
mixture is modelled by a system of kinetic BGK equations featuring two
interaction terms to account for momentum and energy transfer between the
species. We prove consistency of our model: conservation properties, positivity
of the solutions for the space homogeneous case, positivity of all
temperatures, H-theorem and convergence to a global equilibrium in the space
homogeneous case in the form of a global Maxwell distribution. Thus, we are
able to derive the usual macroscopic conservation laws. In particular, by
considering a mixture composed of ions and electrons, we derive the macroscopic
equations of ideal MHD from our model.
