ABSTRACT
The fundamental assumptions of the adiabatic theory do not apply in the presence of sharp field gradients or in the presence of well-developed magnetohydrodynamic turbulence. For this reason, in such conditions the magnetic moment µ is no longer expected to be constant. This can influence particle acceleration and have considerable implications in many astrophysical problems. Starting with the resonant interaction between ions and a single parallel propagating electromagnetic wave, we derive expressions for the magnetic moment trapping width Δµ (defined as the half peak-to-peak difference in the particle magnetic moments) and the bounce frequency ω(b). We perform test-particle simulations to investigate magnetic moment behavior when resonance overlapping occurs and during the interaction of a ring-beam particle distribution with a broadband slab spectrum. We find that the changes of magnetic moment and changes of pitch angle are related when the level of magnetic fluctuations is low, δB/B(0) = (10(-3),10(-2)), where B(0) is the constant and uniform background magnetic field. Stochasticity arises for intermediate fluctuation values and its effect on pitch angle is the isotropization of the distribution function f(α). This is a transient regime during which magnetic moment distribution f(µ) exhibits a characteristic one-sided long tail and starts to be influenced by the onset of spatial parallel diffusion, i.e., the variance <(Δz)(2)> grows linearly in time as in normal diffusion. With strong fluctuations f(α) becomes completely isotropic, spatial diffusion sets in, and the f(µ) behavior is closely related to the sampling of the varying magnetic field associated with that spatial diffusion.
