The fundamental assumptions of the adiabatic theory do not apply in presence of sharp field gradients as well as in presence of well developed magnetohydrodynamic turbulence. For this reason in such conditions the magnetic moment $mu$ is no longer ex
pected 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 $Delta mu$ (defined as the half peak-to-peak difference in the particle magnetic moment) and the bounce frequency $omega_b$. We perform test-particle simulations to investigate magnetic moment behavior when resonances overlapping occurs and during the interaction of a ring-beam particle distribution with a broad-band slab spectrum. We find that magnetic moment dynamics is strictly related to pitch angle $alpha$ for a low level of magnetic fluctuation, $delta B/B_0 = (10^{-3}, , 10^{-2})$, 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 $f(alpha)$. This is a transient regime during which magnetic moment distribution $f(mu)$ exhibits a characteristic one-sided long tail and starts to be influenced by the onset of spatial parallel diffusion, i.e., the variance $<(Delta z)^2 >$ grows linearly in time as in normal diffusion. With strong fluctuations $f(alpha)$ isotropizes completely, spatial diffusion sets in and $f(mu)$ behavior is closely related to the sampling of the varying magnetic field associated with that spatial diffusion.
Cluster observations in the near-Earth magnetotail have shown that sometimes the current sheet is bifurcated, i.e. it is divided in two layers. The influence of magnetic turbulence on ion motion in this region is investigated by numerical simulation,
taking into account the presence of both protons and oxygen ions. The magnetotail current sheet is modeled as a magnetic field reversal with a normal magnetic field component $B_n$, plus a three-dimensional spectrum of magnetic fluctuations $delta {bf B}$, which represents the observed magnetic turbulence. The dawn-dusk electric field E$_y$ is also included. A test particle simulation is performed using different values of $delta {bf B}$, E$_y$ and injecting two different species of particles, O$^+$ ions and protons. O$^+$ ions can support the formation of a double current layer both in the absence and for large values of magnetic fluctuations ($delta B/B_0 = 0.0$ and $delta B/B_0 geq 0.4$, where B$_0$ is the constant magnetic field in the magnetospheric lobes).
