Low-amplitude, wave-induced particle energy diffusion in an inhomogeneous magnetic field

The motion of a charged particle in a static, homogeneous magnetic field and a coherent electrostatic wave, whose frequency is much greater than the particle gyrofrequency, has been studied in detail by Karney. Karney found that there is a threshold in wave amplitude above which widespread diffusion of the particle energy (i.e., heating) occurs and below which the particle energy remains bounded. In this paper the effect of an inhomogeneous (or time-varying) magnetic field is examined. It is found that under general circumstances the motion of the particle can become diffusive and unbounded for values of the wave amplitude well below the threshold in the constant magnetic field case. The dependence of this diffusion on the various parameters affecting the motion is examined.