Impulsive excitation of electrostatic waves at the upper hybrid branch: A boundary value problem

Abstract

The problem of impulsive excitation of longitudinal waves at the upper hybrid branch of a bounded cold magnetized plasma is considered. The disturbing antenna is supposed to be a point source localized at the center of a plasma-filled circular cylindrical cavity with perfectly conducting walls. The boundary conditions at the edge of the cavity naturally characterize the space discrete spectral composition for the emanated electrostatic waves. We describe a formalism that allows an analytical treatment of the temporal evolution equation of the magnetized plasma response. Particular attention is paid to the statement of the initial values of the generated electrostatic eigenmodes. On the basis of the technique of solving the Volterra integral equation, an algebraic expression of the solution is inferred.