Nonlinear interaction of a modulated beam with plasma

Nonlinear evolution of h. f. instabilities excited by a premodulated electron beam in a magnetized plasma is investigated both theoretically and experimentally. Only the erenkov type of excitation (k_¦|v_b) of the upper branch of the electron plasma oscillations has been observed. The dynamics of excitation of the quasistationary fundamental wave (having the frequency of modulation) has been determined numerically. The wave absorption has been included into the theoretical model through an effective collision frequency. Numerical results agree well with the measured evolution of the amplitude and of the phase velocity of the fundamental wave along the system, as well as with the beam distribution functions. The observed bunching of beam electrons and characteristic features of plasma electrons heating are also reported. Broadening of the frequency spectrum and the occurrence of satellite waves with lower phase velocities have been observed downstream. Physical mechanism of spantaneous excitation of these satellites is suggested and their role in the process of the beam relaxation is discussed. More detailed studies of the nonlinearly excited waves have been performed by modulating the beam at two frequencies.It is a pleasure for us to thank Dr .Körbel who has kindly performed the numerical calculations.