Formation and stability of polarization sheaths of a cross-field beam

Abstract

A layer of plasma (such as that comoving with the space shuttle) can travel across a magnetic field if it is flanked by ‘‘polarization sheaths’’ that create the E field necessary for E×B drift. Both the spontaneous evolution and the stability of these positive and negative sheaths can be studied by their analogy with the charge configuration in magnetron-type electron devices. That is, conservation of canonical momentum results in ‘‘Brillouin flow,’’ i.e., shear flows in a pure ion sheath on one side and a pure electron sheath on the other side of the neutral plasma beam. The equilibrium parameters of this flow were obtained and the stability of the equilibria was analyzed. Both the ion and electron sheaths were found to be one-dimensionally stable and two-dimensionally unstable in a mode variously known as ‘‘magnetron,’’ ‘‘slipping stream,’’ or ‘‘diocotron.’’ This mode connects up with the Kelvin–Helmholtz instability in neutral matter. The analytical results were confirmed both qualitatively and quantitatively by numerical simulations. The saturation of the unstable modes, observed in the simulation, allows one to estimate how the polarization sheaths eventually diffuse.