Self-Modulation and Self-Focusing of Electromagnetic Waves in Plasmas

The nonlinear frequency shift of a strong electromagnetic wave in a plasma, due to weak relativistic effects and the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}$ force, can cause modulation and self-focusing instabilities. These processes are explored, and their relation to self-focusing driven by the ponderomotive force is described.