Theory of Nonlinear Waves in Plasma with a Constant Magnetic Field

Abstract

In the paper, for the first time, the analytic solution of the collisionless time-dependent Vlasov-Boltzmann kinetic equation in the presence of a constant magnetic field. By means of this new solution, the general electrodynamic equation, describing the behavior of waves, also in the nonlinear stage, is considered. The analysis is restricted to the consideration of the first nonlinear approximation, keeping the second power of the electric strength. As it is known, the plasma with a magnetic field is characterized by the abundance of different wave branches, describing which demands rather long and tedious calculations. We restrict ourselves to the consideration of perturbations propagating along the constant magnetic field. Obviously, any modification of the distribution function can lead to the essential change of wave-like behavior of plasma and the whole plasma electrodynamics. It is shown that in the nonlinear stage, the longitudinal and transversal waves cannot propagate independently – they are coupled with each other.