Theoretical modelling of an x-ray source based on stochastic acceleration of charged particles at electron cyclotron resonance

Abstract

The motion of charged particles in the field of H-waves of a cylindrical and a rectangular waveguide in the presence of a uniform magnetic field is investigated analytically and numerically. We obtain the equations of charged particle motion in the H-wave field under cyclotron resonance conditions, evaluate the width of nonlinear resonances, and establish the criterion for dynamical chaos emergence. The criterion is used to analyse the possibility of stochastic acceleration of charged particles by the field of H-waves of circular and rectangular waveguides in the external magnetic field for x-ray production. The stochastic acceleration of particles in two and three standing waves of a circular resonator and two counter-propagating waves of a rectangular waveguide are investigated. It is shown that, over the course of several hundreds of periods of the microwave field, the kinetic energy of the electrons reaches values of around 1.0 MeV and the average kinetic energy reaches values of the order of 0.3 MeV.