Modulation instability of intense laser beam in an electron–positron plasma

Modulation instability of an intense right-hand elliptically polarized laser beam propagating through an electron–positron plasma is investigated by a new method. The nonlinear dispersion relation, in which the relativistic and ponderomotive nonlinearities are taken into account, is obtained for the laser radiation in electron–positron plasma by the Lorentz transformation. The Karpman equation is generalized to the case of three dimensions with three field components. When the nonlinear frequency shift of the electromagnetic field in plasma is involved, the nonlinear evolution equation for the slowly varying envelope of the laser field is obtained. Thus, modulation instability of the intense laser beam in electron–positron plasma is studied and the temporal growth rate of the instability is derived. The analysis shows that the growth rate of modulation instability is increased significantly near the critical surface in a laser-plasma.