Stochastic heating of protons by fast hydromagnetic wave

The stochastic heating of protons by a random magnetosonic wave propagating normal to the magnetic field is suggested as an explanation of the observation that the protons are hotter than the electrons in the plasma sheet of the magnetotail. A perturbation analysis is used to find the proton trajectories under the influence of the electric and magnetic fields of the driving wave. The gradients of the field quantities across a proton orbit are included by using the first term in a Taylor series expansion. The inclusion of the field gradients and particle drifts gives the result that the heating depends not only on the energy in the wave spectrum at the gyrofrequency but also on that at the first harmonic of the gyrofrequency, and suggests, furthermore, that the faster protons are heated more strongly with the result that their distribution function can be broadened, consistent with observation. A nonlinear mechanism that can decouple the particles from the wave is suggested, and it is shown to yield proton energy gains of the correct order of magnitude for the plasma sheet.