Particle trajectories and potentials in a plane sheath moving in a magnetoplasma

A plane sheath moving in the direction of its normal across the magnetic field through a magnetoplasma is analyzed. The self consistent analytic solution for solution for electric field and trajectories of univelocity attracted particles as a function of sheath edge entry angle is derived. For simplicity, the sheath edge is assumed to be sharp. The solution is similar to that for a planar magnetron found much earlier. A quantity q, the square of the ratio of plasma frequency to gyrofrequency, is found to be critical in the behavior of the attracted species. If it is more than a limiting (cutoff) value, am, that depends only on entry angle and Mach number, M, the particles penetrate the whole sheath, some or all of the particles return to the sheath edge. In the frame of the object plane, for M<<1, q sub m is 1.2(2M) at vertical and infinity at grazing incidence; for M=1, q sub m = 1; for M>>1, q sub m is 1.2. So the effect of magnetic field can increase greatly for drift velocity much less than thermal speed. The range of entry angles is derived. For typical low earth orbit conditions, electrons enter between grazing incidence and 45 deg, and have a value of q less than a third of q sub m, whereas 0+ ions enter within 7 deg of vertical incidence and have a value of q over 10 to the 5th power times larger than q sub m. So the magnetic field effects the electrons greatly but the ions only very slightly.