Nonlinear Transverse Waves in Plasmas

The propagation of nonlinear stationary transverse waves in plasmas is investigated by first solving a relativistic Vlasov equation for the electrons under the influence of a Lorentz force, due to a propagating 4-potential, rigorously and without linearization. The solution, which reduces to a given equilibrium electron velocity distribution function, is then substituted into the Maxwell equations, and a set of wave equations is obtained. While nonlinearity couples the transverse and longitudinal modes except for one special case, propagation of plane-polarized transverse waves in both cold and hot (Maxwellian) plasmas is studied in the quasineutrality approximation. The conditions for the existence of periodic solutions for the nonlinear transverse wave equations indicate that propagation is possible only when the wave velocity exceeds the velocity of light (for plasmas free from external magnetic field). Expressions for waveform and frequency in terms of elliptical integrals are derived. Unlike the case of longitudinal waves, the nonlinear effect on transverse waves is manifested primarily in the reduction of frequency rather than distortion in waveform. Several typical examples of waveform and dispersion characteristics (frequency vs phase velocity) are computed and plotted, ranging from cold to ultrarelativistically hot plasmas. The nonlinear effect is more pronounced at lower electron temperatures.