Analytical solutions of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles

A two-stream Maxwellian distribution function with two unknown parameters corresponding to the mean velocity and the shear stress is used to obtained an approximate analytic solution of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles. For small magnetic field, solutions are presented for the four moments equations and the Maxwell's equations. The dynamical behaviour of the electron and ion gas is examined.