Generalized linear wave equation for bi-Maxwellian electron beams in crossed fields

Abstract

A general wave equation is kinetically derived for a bi-Maxwellian electron beam to describe the linear electrostatic perturbations propagating in the arbitrary direction with respect to all applied magnetic field ill crossed-field devices such as magnetrons in which the operating electric field and the electron density are inhomogeneous. The first-order Vlasov and Poisson equations are introduced and the necessary velocity and time integrations are carried out to get the desired wave equation. By taking appropriate limits, we obtain various types of waves such as perpendicular and parallel waves which agree well with the previous results. The massless guiding center and the cold electron limits are also derived.