The effect of self focused hollow Gaussian laser beam (HGLB) (carrying null intensity in center) on the excitation of electron plasma wave (EPW) and second harmonic generation (SHG) has been investigated in collisionless plasma, where relativistic-ponderomotive and only relativistic nonlinearities are operative. The relativistic change of electron mass and the modification of the background electron density due to ponderomotive nonlinearity lead to self-focusing of HGLB in plasma. Paraxial ray theory has been used to derive coupled equations for the self focusing of HGLB in plasma, generation of EPW, and second harmonic. These coupled equations are solved analytically and numerically to study the laser intensity in the plasma, electric field associated with the excited EPW, and the power of SHG. Second harmonic emission is generated due to nonlinear coupling between incident HGLB and EPW satisfying the proper phase matching conditions. The results show that the effect of including the ponderomotive nonlinearity is significant on the generation of EPW and second harmonic. The electric field associated with EPW and the power of SHG are found to be highly sensitive to the order of the hollow Gaussian beam.

In the present investigation, the excitation of an upper hybrid wave (UHW) in a hot collisionless magneto-plasma by a relativistic laser beam propagating perpendicular to the static magnetic field and having its electric vector polarized along the direction of the static magnetic field (ordinary mode) is presented. Due to nonuniform intensity distribution of pump laser, the background electron concentration is modified. The amplitude of the UHW, which depends on the background electron concentration, is thus nonlinearly coupled with the laser beam. The effect of nonlinear coupling between the pump laser and UHW is studied. The effect of the relativistic electron mass nonlinearity and the relativistic self-focusing of the pump laser on the excitation of the UHW have been incorporated. The dynamics of the excitation of the UHW in different power domains of the laser beam is accordingly modified. It has been seen that the effect of changing the strength of the static magnetic field on the nonlinear coupling and the dynamics of the excitation of the UHW is significant. The focusing behavior of the UHW may find its relevance in the heating of plasmas near the upper hybrid resonance.

This paper presents the effects of a laser spike (superimposed on an intense laser beam) and a static magnetic field on the excitation of the upper hybrid wave (UHW) in a hot collisionless magnetoplasma, taking into account the relativistic nonlinearity. The laser beam is propagating perpendicular to the static magnetic field and has its electric vector polarized along the direction of the static magnetic field (ordinary mode). Analytical expressions for the growth rate of the ripple, the beam width of the rippled laser beam, and the UHW have been obtained. It is found that the coupling among the main laser beam, ripple, and UHW is strong. The ripple gets focused when the initial power of the laser beam is greater than the critical power for focusing. It has been shown that the presence of a laser spike affects significantly the growth rate and the dynamics of the UHW. In addition, it has been seen that the effect of changing the strength of the static magnetic field on the nonlinear coupling and on the dynamics of the excitation of the UHW is significant. The results are presented for typical laser plasma parameters.

This paper presents an effect of relativistic mutual interaction of two laser beams of different frequencies on the growth of a laser ripple in laser produced plasmas. The nonlinearity due to relativistic mass variation depends not only on the intensity of one laser but also on the second laser. Therefore, one laser beam affects the dynamics of the second beam and hence a mutual nonlinear interaction~cross-focusing! takes place. The dynamical equations governing the laser intensity of two laser beams and the perturbation present on one laser beam~ripple! have been set up and a numerical solution has been presented for typical laser plasma parameters. It is found that a change in the intensity of the second laser beam can affect the growth of the laser ripple significantly. This study is important in plasma beat wave excitation and collective laser particle accelerators.

This paper explores the self-focusing of hollow Gaussian laser beam (HGLB) in collisionless magnetized plasma and its effect on the generation of THz radiation in the presence of relativistic-ponderomotive nonlinearity. The relativistic change of electron mass and electron density perturbation due to the ponderomotive force leads to self-focusing of the laser beam in plasma. Nonlinear coupling between the intense HGLB and electron plasma wave leads to generation of THz radiation in plasma. Resonant excitation of THz radiation at different frequencies of laser and electron plasma wave satisfies proper phase matching conditions. Appropriate expressions for the beam width parameter of the laser beam and the electric vector of the THz wave have been evaluated under the paraxial-ray and Wentzel-Kramers Brillouin approximations. It is found that the yield of THz amplitude depends on the focusing behaviour of laser beam, magnetic field, and background electron density. Numerical simulations have been carried out to investigate the effect of laser and plasma parameters on self-focusing of the laser beam and further its effect on the efficiency of the generated THz radiation.