Nonlinear particle trajectories for intense ordinary-mode propagation near electron cyclotron resonance

Abstract

The nonlinear orbit equations are investigated analytically for a constant-amplitude electromagnetic wave ( ω s , k s ) with ordinary-mode polarization propagating perpendicular to a uniform magnetic field B 0 ê z . Coupled nonlinear equations are obtained for the slow evolution of the amplitude A(τ) and phase π(τ) of the perpendicular orbit when the incident wave frequency ω s, is near the nth harmonic of theelectron cyclotron frequency Ω c . The dynamical equations are reduced to quandrature and simplified analytically. Relativistic electron dynamics are essential in determining the maximum orbital excursion. As an illustrative example, for n = 1 and moderate wave amplitude, weak relativistic effects limit the maximum perpendicular kinetic energy achieved to k max = ( 2 ϵ s) 2 3 mc 2 , where ϵ s=n sΩ s(V z/c)(V q/c) ⪡ 1 , and V q is the axial quiver velocity in the applied oscillatory field.