Propagation of an ultrashort, intense laser pulse in a relativistic plasma

A Maxwell-relativistic fluid model is developed for the propagation of an ultrashort, intense laser pulse through an underdense plasma. The separability of plasma and optical frequencies (omega(p) and omega, respectively) for small omega(p)/omega is not assumed; thus the validity of multiple-scales theory (MST) can be tested. The theory is valid when omega(p)/omega is of order unity or for cases in which omega(p)/omega much less than 1 but strongly relativistic motion causes higher-order plasma harmonics to be generated which overlap the region of the first-order laser harmonic, such that MST would not be expected to be valid, although its principal validity criterion omega(p)/omega much less than 1 holds.