AMPLIFICATION OF A REGULAR WAVE BY AN ELECTRON-BEAM AT THE NONLINEAR PHASE RESONANCE IN A PLASMA

The possibility of the nonlinear phase resonance between an electron b eam and a plasma wave excited by this beam is demonstrated. The resona nce involves the modulation of the beam, which can cause the separatio n of the beam into individual bunches, and a synchronous decrease in t he beam velocity and the phase velocity of the excited plasma wave. Wh en the bunches are trapped by the wave, i.e., in the nonlinear stage o f the instability associated with the Cherenkov resonance, the wave am plitude is larger than in the case of a linear plasma response. For a preliminary modulated beam, if the depth of the spatial modulation is large and the dimensions (in the phase space) of individual electron b unches in the modulated beam are small, all plasma electrons are trapp ed by the wave, and the amplification of the plasma wave in a plasma-b eam system increases by more than an order of magnitude.