Study On Modulation Instability And Collapse Of Intense Laser Beam In Magnetized Plasma

When an incident laser beam propagates through plasma, there is modulational interaction between transverse plasmons and driven ion-acoustic wave, and the long-wave-length instability, namely modulation instability, occurs. The growth rate of the modulation instability is directly proportional to the finite amplitude of the pump wave. Modulational instability is the consequence of the interplay between nonlinearity and dispersive effects. This leads to beam breakup in either space or time. The nonlinear evolution of modulation instability will lead to self-focusing of the field. The investigation of modulation instability and its nonlinear evolution is significant for the fast ignitor scheme in inertial confinement fusion.In this paper, modulation instability of an intense laser beam propagating through magnetized plasma is investigated by a new method. Firstly, the nonlinear dispersion relations, in which the relativistic and ponderomotive nonlinearities are taken into account, are obtained for the left-hand (right-hand) elliptically polarized laser radiation in magnetized electron-ion plasma and magnetized electron-positron plasma by the Lorentz transformation. 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 with three dimensions and three components in magnetized plasma is obtained using the generalized Karpman's method. Thus, modulation instabilities of the left-hand (right-hand) elliptically polarized intense laser beam in magnetized electron-ion plasma and magnetized electron-positron plasma are studied respectively. And the temporal growth rates of the instability as a function of unstable wave numbers are derived. The self-modulation instability growth rates of the laser beam with different polarization in magnetized plasma are analyzed and compared with the unmagnetized case. The temporal growth rates in different regions are studied. Lastly, on the basis of the nonlinear equations for the wave packet of the left-hand (right-hand) elliptically polarized laser electric field, the Lagrange density functions of the nonlinear equations are constructed by means of field theory. It is shown that the energy focus of the wave packet of the laser electric field possesses the characteristic of quasi-particle. The collapse dynamics of the wave packet at the later stage of modulation instability is discussed. Therefore it is shown that the left-hand (right-hand) elliptically polarized laser electric fields in magnetized electron-ion plasma and magnetized electron-positron plasma possess the collapsing behavior. The high-intensity localization structures of the laser electric field are formed. The characteristic scale of the resulting localized electric field is obtained. And it agrees with the related numerical result. On the other hand, the modulation instability of finite amplitude of the self-gravitating system in the stable modes is examined on the basis of the nonlinear governing equations.It is shown that the peak growth rate of self-modulation instability of the left-hand elliptically polarized laser electric field in magnetized plasma is reduced significantly as compared to the unmagnetized case, but the growth rate of the right-hand elliptically polarized laser beam is increased due to the presence of magnetic field. Therefore, the axial constant magnetic field enhances the self-focusing property of the right-hand elliptically polarized laser beam, but it weakens the self-focusing of the left-hand elliptically polarized laser beam. It is in agreement with the results of the related reference. It is also shown that the temporal growth rate of modulation instability is increased significantly near the critical surface in a laser-plasma.