Test particle motion in the cyclotron resonance regime

Abstract

Test particles moving in the field of an electromagnetic wave propagating in a background magnetic field can gain significant energy when the wave parameters and particle energy are such that the cyclotron resonance condition is satisfied. Central to the acceleration process and long time scale periodic behavior is the coherent accumulation over many cyclotron orbits of a small change in energy during each orbit, a result of the circularly polarized component of the wave electric field. Also important is the small change in the relative wave phase during each orbit resulting from relativistic variations of the cyclotron frequency and wave-induced streaming along the background magnetic field. The physical mechanisms underlying cyclotron resonance acceleration are explored using a set of heuristic mapping equations (the PMAP) describing changes in the particle momentum and relative wave phase. More accurate (but less transparent) descriptions of the particle motion are pursued in the context of orbit-averaged Hamiltonian theory. A discrete set of mapping equations for the slowly varying canonical action and angle are derived (the QMAP) but are found to generate inaccurate solutions in certain regions of phase space when the resonance number l is such that {↓l}↓=1 and the particles are initially cold. These difficulties are avoided by constructing a continuous time orbit-averaged Hamiltonian and solving the resultant canonical equations of motion. Assuming the momentum is small relative to mc (where m is the particle mass and c is the speed of light), details of the distribution of particle trajectories in the action-angle phase space for {↓l}↓=1 and {↓l}↓=2 are presented and criteria for the existence of orbits oscillatory in angle are derived.