Nonlinear space charge dynamics and modulational instability in the interaction of intense laser pulses with electron-positron plasmas

Nonlinear space charge dynamics and modulational instability in the interaction between ultrashort, intense laser pulses and electron-positron pair plasmas are investigated taking into account the relativistic ponderomotive force and the relativistic mass of electrons and positrons. By coupling Maxwell's equations and hydrodynamic model, the electron and positron density distributions and the dispersion relation for the modulational instability are obtained. Moreover, two coupled nonlinear equations for the scalar and vector potentials are derived and numerically solved. The results show that the growth rate of instability increases with the decrease in the electron and positron temperatures. Moreover, it is shown that when the temperatures of electrons and positrons are not equal to each other, the profiles of scalar potential are similar to bright-like or dark-like solitons.