Upper-hybrid oscillations of high current relativistic electron beam under conditions of magnetic self-insulation

Abstract

Upper-hybrid oscillations have appeared in a number of theoretical and experimental investigations of quasi-static neutral plasmas immersed in an external strong magnetic field. We theoretically demonstrate the existence of upper-hybrid oscillations (UHOs) on high current relativistic electron beam (non-neutral plasma) of Magnetically (self-)Insulated transmission Line Oscillator (MILO), which is a promising source of gigahertz-frequency, high power microwave radiation under development in a number of research laboratories. We study the non-linear autonomous system of equations governing MILO high current beam dynamics, build a first integral, which is the total relativistic energy of the non-linear perturbations of charged-particle beam in motion, and derive an explicit solution for this system in terms of elliptic integrals and Jacobi elliptic functions. The period of non-linear UHOs in a non-equilibrium relativistic plasma is derived in a closed analytical form.