Diffusion of Electrons in Mutually Perpendicular Electric and Magnetic Fields

Abstract

The collective behavior of electrons in mutually perpendicular static electric and magnetic fields is considered. A known instability, first described by Buneman, of laminar electron flow in mutually perpendicular electric and magnetic fields is shown to necessitate a statistical description of the motion of the electrons. The motion of the electrons is described as diffusion; the diffusion tensor transverse to the magnetic field is obtained. Buneman's instability of laminar flow is shown to cause the conversion of E × B drift energy into energy of gyration about the magnetic field. The transverse diffusion tensor is obtained from the rate at which the conversion of energy takes place; this rate is taken to be equal to the growth rate of the instability obtained by Buneman. The transverse‐diffusion coefficients are found to be proportional to the square of the static electric field and inversely proportional to the cube of the static magnetic field. It is shown how the results may be generalized to the case of diffusion of electrons across a magnetic field in ionized gases, by replacing the square of the velocity E/B by the mean‐square thermal velocity of the electrons in the ionized gas. The results are in agreement with experimental results.