Self-consistent solution for a collisionless plasma slab in motion across a magnetic field

Echim, Marius M.; Lemaire, Joseph F.; Roth, Michel
July 2005
Physics of Plasmas;Jul2005, Vol. 12 Issue 7, p072904
Academic Journal
The problem of the dynamics of a plasma slab moving across a magnetic field is treated in the framework of the kinetic theory. A velocity distribution function (VDF) is found for each plasma species, electrons and protons, in terms of the constants of motion defined by the geometry of the problem. The zero- and first-order moments of the VDF are introduced into the right-hand side term of Maxwell’s equations to compute the electric and magnetic vector potentials and corresponding fields. The solutions are found numerically. We obtain a region of plasma convection—the slab proper—where the plasma moves with a uniform velocity, Vx=V0=(E×B/B2)x. At the core margins two plasma “wings” are formed, each being the result of a pair of interpenetrated boundary layers with different transition lengths. Inside these wings, the plasma velocity is not uniform, Vx≠(E×B/B2)x. It decreases from the maximum value obtained in the core to a minimum value in the central region of the wings where a flow reversal is found with the plasma convecting in the opposite direction to the core motion. There is also an asymmetry of the velocity gradient at the borders of the core, which results in a corresponding asymmetry in the thickness of the wings. Furthermore, it is found that the reversed plasma flow in the thinner wing is larger than that in the broader wing. For a fixed direction of the magnetic field the two plasma wings interchange position with respect to the center of the slab when the plasma bulk velocity reverses sign.


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