Resonant wave-particle interaction in an explosively unstable beam-plasma system. 1

The evolution of a resonant triplet of linearly stable electrostatic waves in a beam-plasma system is considered. A set of nonlinear ordinary differential equations is derived, which allows an investigation of the explosive instability with minimum numerical expense. The model is different from the well known single wave model in taking into consideration the nonlinear susceptibilty of the plasma and in making use of the ponderomotive force description. Maximum values of the wave amplitudes are obtained numerically and it is shown that the saturation of the explosive instabilty is due to different trapping mechanisms of the beam electrons by the excited waves. (author)