Electron plasma interactions in crossed fields

In this paper the interactions of a non-neutral electron plasma in the presence of non-uniform cross fields within a slow wave structure is investigated. A variational approach is applied to calculate modifications to both RF wave and plasma parameters. The RF wave is modeled with a modal solution of the boundary value problem, while a cold-fluid approximation is taken for the plasma. The specific case is non-relativistic ans assumes propagation of a single. The results of the analysis show frequency shifts obtained by taking appropriate variations of plasma parameters