Technique for expansion with respect to trajectories in nonlinear electrodynamics of a non-equilibrium plasma

A novel technique for investigating nonlinear effects in a nonequilibrium plasma is presented which is based on the expansion with respect to perturbations of particle trajectories. In this approach nonlinear interaction of the waves and oscillations of the plasma particles as well as the mean field force acting on the particle are taken into account. Some concrete examples of nonlinear processes in an instable beam plasma are considered. In particular, the case of multimode excitation of waves when turbulence arises in the plasma is studied. The particle distribution function in a weakly nonlinear plasma is derived and its structure studied