On cyclotron damping of longitudinal wave

Average equations of motion of relativistic charged particles in the field of HF (high frequency) wave packets are obtained in the range of cyclotron resonance in the case of strong LF (low frequency) electric field. Strong electric field means that the characteristic velocity of the particle comparable with the electric drift velocity ((v sim v_E)). It is shown that with taking into account the electric drift velocity, new mechanisms of damping of longitudinal waves become possible. The effect of a strong electrostatic field on the resonant interaction of relativistic particles with high-frequency waves, as well as the relativistic effect, on cyclotron resonance for a longitudinal wave, is analyzed. The analytical solution of the averaged system of equations in the quasi-relativistic approximation is analyzed, as well as a numerical experiment for the Langmuir wave under the condition of cyclotron resonance in the case of a strong electric field.