Wave-trapped particle interaction in a weak transverse magnetic field

Damping of an electrostatic plasma wave loaded with a small density bunches of trapped electrons and propagating across a weak magnetic field is studied. To describe the time evolution of the wave, simple algebraic equations are derived under some restrictions on the parameters of the physical system. It is shown that the nonlinear frequency shift of the wave due to the presence of the trapped particles plays an important role and must be taken into account in the self-consistent treatment of the wave–particle interaction.