TITLE Enhanced acceleration of charged particles by crossing electromagnetic waves in a magnetized plasma, Resonant Moments Method AUTHOR Maxim PONOMARJOV ABSTRACT A mechanism for enhanced acceleration of charged particles in crossing electromagnetic waves propagating at different angles with respect to an external magnetic field is investigated. This mechanism consists in introducing a lower amplitude secondary wave in order to improve the parallel momentum transfer from the higher amplitude primary wave to charged particles. The theoretical analysis of the acceleration mechanism is based on the Resonance Moments Method (RMM) in which the velocity distribution and its moments are approximated by using an average over the resonant layers (RL) only instead of a complete phase-space average. The quantities obtained using this approach, referred to as Resonant Moments (RM), suggest the existence of optimal angles of propagation for the primary and secondary waves as long as the maximization of the parallel flux of charged particles is considered. The secondary wave tends to maintain a pseudo-equilibrium velocity distribution by continuously re-filling the RL. Our suggestions are confirmed by direct numerical simulations of particle trajectories based on a Hamiltonian dynamics, the parameters for these simulations are relevant to magnetic plasma fusion experiments in electron cyclotron resonance heating and electron acceleration in planetary magnetospheres. Although measures of the distributions clearly show a departure from a thermal equilibrium, the stochastization effect of the secondary wave yields a clear increase (up to one order of magnitude) of the average parallel velocity of the particles. It is a quite promising result since the amplitude of the secondary wave is ten times lower the one of the first wave.