Theory and simulation of cyclotron heating in a linear octupole

A simple conductivity model is used to calculate the cyclotron heating rate (electron or ion) in an arbitrary non-uniform magnetic field. The result is applied to an ideal linear octupole field, which, because of its complexity, offers a severe test of the theory. The theory is compared with the results of a numerical simulation in which the trajectories and average energy of a collection of non-interacting particles are calculated as a function of time. The theory and simulation are in surprisingly good agreement over a wide range of heating frequency, plasma temperature, electric field strength, and wave number.