On the charged particles surfatron acceleration in space plasmas

It is considered the highly relativistic acceleration of charged particles by finite amplitude electromagnetic wave in space plasmas (so-called the surfatron mechanism of charges acceleration). Using relativistic equations for accelerated charge the integral motion is obtained. Then the problem considered is reduced to the analysis of second order nonstationary, nonlinear equation for the wave phase at the particle trajectory which is solved numerically. The purpose of this paper is to study the influence of other wave mode with different phase velocity on charge capture and its following acceleration. It is shown that such influence may be negligible if some conditions on incoming wave parameters are fulfilled. So the strong particle acceleration by electromagnetic wave will occur if the wave modes with comparable amplitudes have the phase velocity difference large enough.