Theory of resonance four-wave interaction of waves in a beam-plasma system

Nonlinear theory of resonance four-wave interaction of two electromagnetic modes of the wavequide with the first and second harmonics of beam charge density waves is developed. Alongside with numerical study of the nonlinear equation system qualitative analysis of the four-wave interaction dynamics is carried out. It is shown that for some characteristic time of instability development multiple energy transfer between the first and second harmonics of charge density waves takes place