Modulational instability of ultra-intense linearly polarized laser pulse in electron-positron plasmas

Based on the wave equation of ultra-intense linearly polarized laser pulse propagating in electron-positron plasmas, the modulational instability is investigated. The nonlinear dispersion relation and the growth rate of instability are derived. The effects of plasmas number density, temperature, and laser intensity on the growth rate are analyzed. Results show that in an electron-positron plasma with certain background density, the intensity of the modulation instability is mainly determined by the competition between the nonlinearity in the interaction and the relativistic light ponderomotive driven density responses.