Theory of instabilities in crossed-field discharges at low pressures

Anode layer thruster, Penning, cylindrical magnetron, and inverted-magnetron discharges all behave, at pressures below about 10-4 Torr, as crossed-field discharges. At such low pressures, a crossed-field discharge is pure electron plasma and most of the discharge voltage appears across an electron sheath so that the electric field is orthogonal to the magnetic field. The principal difficulties in the practical use of these discharges in this pressure range arise from instabilities in the discharge, which are commonly attributed to diocotron instabilities in the electron sheath. On the contrary, this paper describes a theory of the electron sheath based on the classical expression for the cross-field mobility of electrons. The theory predicts that the observed instabilities, accompanied by appearance of pulses of excess energy electrons at the cathode(s) and nonlinearity in the discharge characteristics, are simply the result of periodic travel of the electron sheath through the discharge gap.