Abbreviated Journal Title
NEUTRAL ELECTRON FLOW; PLANAR DIODE; STABILITY PROPERTIES; FIELD; INSTABILITY; Physics, Fluids & Plasmas
The analysis of the planar magnetron Vlasov distribution function [Phys. Fluids 31, 2362 (1988)] is extended to the cylindrical case. In momentum space, the model distribution function is f(w,p(theta)) = Ne(-betaww)e-(OMEGAbetatheta/4p0)(ptheta-p0)2 where w(p(theta)) is the single particle energy (angular momentum), beta(w)(beta(theta)) is the inverse of the thermal energy associated with variations in w(p(theta)), p0 is the angular momentum at the cathode, and OMEGA is the electron cyclotron frequency (= eB0/mc). The problem is shown to be too ''stiff '' numerically to permit a pure numerical solution even using very high accuracy and state-of-the-art numerical schemes. It is shown that one may use a global singular perturbation expansion, similar to, but significantly more complex than the one used in the planar case, to solve the resulting nonlinear ordinary differential equation for the spatial dependence of the distribution function, density, electrostatic potential, and drift velocity.
Physics of Plasmas
Kaup, D. J. and Choudhury, S. Roy, "A Model Cylindrical Magnetron Vlasov Distribution Function" (1994). Faculty Bibliography 1990s. 1086.