Nonlinear electromagnetic waves in a relativistic plasma
Abstract
A method is given for the construction of all solutions to the relativistic Vlasov equation that depend on one Cartesian coordinate z and time t in a certain combination involving superluminal phase velocity. These solutions represent nonlinear 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. An exact analogy to the motion of a threedimensional mechanical nonlinear oscillator enables qualitative discussion of all properties of the nonlinear waves within this picture. For a quantitative discussion attention is restricted to small wave amplitudes that allow the application of a perturbation method and to a class of isotropic distribution functions. Explicit expressions are 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 of streaming velocity. The relevance of elliptically polarized transverse waves of this type to the description of pulsar waves is discussed.
 Publication:

Plasma Physics
 Pub Date:
 March 1977
 DOI:
 10.1088/00321028/19/3/002
 Bibcode:
 1977PlPh...19..209J
 Keywords:

 Electromagnetic Radiation;
 Nonlinear Equations;
 PlasmaElectromagnetic Interaction;
 Pulsars;
 Relativistic Plasmas;
 Mechanical Oscillators;
 Perturbation Theory;
 Vlasov Equations;
 Plasma Physics