A MODEL CYLINDRICAL MAGNETRON VLASOV DISTRIBUTION FUNCTION

The analysis of the planar magnetron Vlasov distribution function [Phy s. Fluids 31, 2362 (1988)] is extended to the cylindrical case. In mom entum space, the model distribution function is f(w,p(theta)) = Ne(-be taww)e-(OMEGAbetatheta/4p0)(ptheta-p0)2 where w(p(theta)) is the singl e particle energy (angular momentum), beta(w)(beta(theta)) is the inve rse of the thermal energy associated with variations in w(p(theta)), p 0 is the angular momentum at the cathode, and OMEGA is the electron cy clotron 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 sig nificantly more complex than the one used in the planar case, to solve the resulting nonlinear ordinary differential equation for the spatia l dependence of the distribution function, density, electrostatic pote ntial, and drift velocity.