Study Of Modulation Instability For The Intense Laser Beam In Unmagnetized Plasma

In laser-plasma interaction, the ponderomotive force originated from the laser radiation arouses low-frequency ion-acoustic waves, then they interplay with the high frequency electromagnetic wave in reverse so that the amplitude of the laser field becomes modulated, and the modulation instability occurs. The development of modulation instability would induce a variety of nonlinear processed such as filamentation, field collapse, envelope solution and so on, which is widely used in laser fusion, fast ignition. Thus the investigation of modulation instability in laser-plasma is significantly important. In this paper, we adopt a very simple method to study the three-dimensional modulation instability of various polarized intense laser beam propagating in unmagnetized plasmas comprised of different kind of charged particles.For the linearly polarized intense laser, based on the existed nonlinear dispersive relations of linearly polarized laser in low density region and near the critical surface associated with the unmagnetized plasmas, the three-dimensional nonlinear governing equations for the envelope of electric field are obtained via Karpman equation and the modulation instabilities are analyzed, in which the first-and second-order nonlinear effects induced by the weak relativistic electron mass variations have considered. The result shows that, the second-order nonlinear effect induced by the weak relativistic electron mass variations has little influence on the modulation instability.For the elliptically and circularly polarized laser, we have derived the nonlinear dispersive relations of elliptically polarized laser in unmagnetized electron-ion plasmas and circularly polarized laser in electron-positron-ion plasmas by the Lorentz technique, respectively. Then, the three-dimensional nonlinear governing equation for the envelope of electric field is obtained via the generalized Karpman equation. Based on the nonlinear governing equation, the modulation instability is analyzed. The conditions for instability and the temporal growth rate as a function of perturbed wave number are obtained. In particular, the modulation instability is discussed in detail for the case that the amplitude of initial laser field is coplanar with amplitude of all the perturbations. During the discussion, the magnitudes of instability temporal growth rate in different plasma regions and for various laser pump intensities have been compared. One can find that, in the weakly relativistic regime, the growth rate increases with the increasing laser pump intensity, and grows significantly when laser approaches to the critical surface. When the circularly polarized laser propagates in an electron-positron-ion plasma, the effect of charged particles on the modulated temporal growth rate has been taken into account. It is found that, the increase in positron-to-electron density ratio shifts the instability region towards higher vertical wave numbers but does not cause displacement along the parallel wave number direction, and the growth rate increases as the positron-to-electron density ratio increases, that means that the presence of the positron stimulates the occurrence of modulation instability but suppressed with increasing ion concentration.