Self-focusing of Gaussian laser beam in warm collisional plasma with ramp-up density

Abstract

In this work, the propagation characters of an intense Gaussian laser beam through warm collisional plasma are investigated by considering the ponderomotive force nonlinearity, upward electron density and complex eikonal function. The ponderomotive force (PF) on the plasma electrons causes periodic self-focusing of the Gaussian laser beam. The PF mechanism changes the dielectric permittivity of plasma (refractive index) by expelling the electrons from the high intensity region (axial region) when the laser intensity is strong enough1. In our previous work2, we studied the thermal self-focusing of a laser beam in homogeneous warm collisional plasma. In the present work, propagation characters of Gaussian laser beam in warm collisional plasma under density ramp have been studied. By introducing the dielectric permittivity of warm unmagnetized plasma according to the Boltzmann equation3, the coupled differential equations defining the variations of laser beam parameters are obtained and solved numerically. The variation of beam width parameter with respect to dimensionless distance of propagation is investigated for different values of initial laser intensity, electron temperature and collision frequency. The results show that, there is a temperature interval in which the self-focusing can occur, while the beam diverges outside of this region. In addition, the results represent the existence of a “turning point temperature” in the mentioned interval in which the self-focusing has the strongest strength. And it is shown that, the collision frequency strongly affects the beam width parameter due to the energy attenuation. Moreover, the effect of the upward plasma density profile on the beam width parameter is studied. Results also show that, using the plasma density ramp-up, the self-focusing temperature range expands and its strength increases.