Charge Separation Effects in the Chapman-Ferraro-Rosenbluth Cold Plasma Sheath Model

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Abstract
The boundary layer between a cold streaming plasma and a perpendicular magnetic field is treated for the case where significant charge separation effects occur and the electrons but not the ions are relativistic. This case is characterized by 1 ≲ γ ≪ M/2m, where γ = Mu2/2mc2 is the ratio of the initial ion streaming energy to the electron rest energy. Only the over-all charge neutral boundary layer in which the electrons turn in the magnetic field before the ions is considered. It is found that the length scale of the magnetic field before the electron turning point is the plasma skin depth c/ωpe as in the boundary layer with γ ≪ 1, but that the electron number density diverges near the turning point with a length scale at least u/c smaller. For large γ the fraction of the ion streaming energy gained by the electrons as kinetic energy is approximately (2/γ2)1/2, and the ions are found to penetrate a distance somewhat less than (2/3)(u/ωpi) beyond the electrons.