Nonlinear interaction of electromagnetic pulses with an electron–positron plasma––a coupled NLS equation

Nonlinear interaction of strong electromagnetic pulse with an electron–positron plasma is analysed. A dispersion relation is deduced which can be used to analyse the parametric instabilities due to nonlinear coupling between high frequency and low frequency motions. It is shown that the electromagnetic wave envelope is governed by a coupled nonlinear Schrödinger equation which also possesses solitary wave like solutions. The dispersion relation turns out to be nonlinear being dependent on the incoming electromagnetic wave amplitude . The growth or decay calculated as a function of this amplitude shows a saturation type behaviour for fixed temperature, whereas it goes to zero with temperature for a fixed value of the amplitude . The amplitude of the nonlinear wave also exhibits a saturating behaviour with respect to . So the nonlinear mode of propagation and interaction in an electron–positron plasma shows a remarkable feature quite distinct from the linear mode.