Fluid theory has been employed to investigate the magnetized plasma-wall transition properties for two ion species plasmas with a uniform background of neutral gas density in the presence of an external magnetic field. The external applied magnetic field is parallel to the surface and its magnitude varies in the direction perpendicular to the surface. The governing equations of ion and electron fluids include ionization and collision with neutral atoms. A comparative study of transition parameters for non-uniform and uniform magnetic fields is performed at equal values of the magnetic flux density at x = 0. This study shows that the sheath region shrinks for the non-uniform magnetic field case, essentially in reason of the lower value of the average magnetic field intensity in the plasma-wall transition region. We introduce a figure of merit to quantify the nonuniformity of the magnetic field , and show that for its value 0.21 it is possible to model the plasma-wall transition region considering the magnetic field as uniform and equal to its average value. Furthermore, we find that the density distribution of electrons close to the surface deviates from the Boltzmann distribution due to the influence of a strong magnetic field.
Nonlinear Magnetohydrodynamics