Parametric up-conversion of an electron Bernstein mode by a relativistic electron beam in a plasma

A relativistic electron beam, propagating with velocity v0b parallel z in a magnetized plasma, parametrically up-converts a pre-existing electron Bernstein wave (ω0,k0) into electromagnetic radiation when k0·v0b<0. The Bernstein wave couples with a negative energy space-charge mode (ω,k) to produce a frequency up-converted sideband electromagnetic wave. The sideband and the Bernstein wave exert a ponderomotive force, driving space-charge mode. In the Compton regime, the growth rate of the parametric instability scales as two-third power of the pump amplitude, whereas in the Raman regime, it goes linearly