The nonlinear frequency shift of a strong electromagnetic wave in a plasma, due to weak relativistic effects and the $\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}}$ 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.

• Received 22 April 1974

DOI:https://doi.org/10.1103/PhysRevLett.33.209