Non-linear electromagnetic waves in a relativistic plasma

Abstract

A method is given for the construction of all solutions of the relativistic Vlasov equation that depend on one cartesian coordinate z and time t in the combination z-Vpt only with Vp>c. These solutions represent non-linear electromagnetic waves in a relativistic plasma without static fields, which reduce for sufficiently small amplitudes to the longitudinal and transverse waves in a uniform plasma known from linear theory. Explicit expressions will be given for the influence of wave amplitude and plasma temperature on the coupling of longitudinal and transverse wave components, the dispersion relations of longitudinal and transverse waves and the modulation of plasma density and streaming velocity. The relevance of elliptically polarized transverse waves of this type to the description of pulsar waves is discussed.