Relativistic theory of frequency blue-shift of an intense ionizing laser beam in a plasma

Frequency up-conversion of a laser beam causing gas ionization in a cavity is considered in a fully relativistic fashion. A simple ionization model, based on one-photon and multiphoton processes is used. A Vlasov fully nonlinear and ionization-model independent description is used in calculating the current which drives the wave equation for the electric field. The evolution of the wave frequency and its upshift are contrasted with those obtained in the nonrelativistic limit. It is found that the nonrelativistic treatment overestimates the frequency upshift by a factor more than two. Purely relativistic effects, such as a significant frequency modulation and a respective temporal pulse compression, are observed in the exact case.