Particle acceleration by stochastic fluctuations and dawn-dusk electric field in the Earth’s magnetotail

This work is devoted to investigate the interaction between protons and stochastic time-dependent electromagnetic fields generated by oscillating clouds of finite size, randomly positioned in the x–y  -plane. The geometry of the system is two-dimensional and, beside the time-dependent electromagnetic fluctuations, a steady-state, dawn-dusk electric field, _Ey$E_y$, has been added along the y-direction. The simultaneous presence of the stochastic time-dependent fluctuations and of the constant electric field component in the same system gives rise to two types of acceleration mechanisms operating on test particles: a second order Fermi-like process and a direct acceleration. By performing a parametric study, we extensively study the contribution of the two processes to proton acceleration. The energy values reached by test particles in this simple model are in good agreement with those observed in the Earth’s magnetotail region. Possible applications to the problem of particle acceleration in the terrestrial magnetosphere are widely discussed, and guidelines for future works are drawn.