Weakly relativistic nonlinear orbit dynamics for intense ordinary-mode propagation near electron cyclotron resonance

The nonlinear orbit equations are investigated analytically and numerically for a constant-amplitude electromagnetic wave (ωs, ks) with ordinary-mode polarization propagating perpendicular to a uniform magnetic field BOe-circumflexz. Relativistic electron dynamics are essential in determining the maximum orbit excursion when the incident wave frequency ωs is near the nth harmonic of the electron cyclotron frequency Ωc. Coupled nonlinear equations are obtained for the slow evolution of the amplitude Α(τ) and phase φ(t) of the perpendicular orbit when ωs∼nΩc. The dynamical equations are reduced to quadrature and simplified analytically. Physically, relativistic effects produce a nonlinear frequency shift that dynamically 'detunes' the particle motion from exact cyclotron resonance, thereby limiting amplitude growth. (author)