Relativistic unstable periodic BGK waves (Q1290893)

The authors describe a collisionless plasma of ions and electrons by the relativistic Vlasov-Maxwell (RVM) procedure in order to avoid arbitrarily large speeds of nonrelativistic particles. To simplify the treatment, the calculations are performed in one spatial direction. The authors discuss the levels of instability in the formalism. The main result on the full nonlinear RVM system states that the solution shows exponential growth. The paper contains a detailed mathematical study of this statement.