Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma. I. Paraxial approximation

Abstract

The propagation of a high-irradiance laser beam in a plasma whose optical index depends nonlinearly on the light intensity is investigated through both theoretical and numerical analyses. The nonlinear effects examined herein are the relativistic decrease of the plasma frequency and the ponderomotive expelling of the electrons. This paper is devoted to focusing and defocusing effects of a beam assumed to remain cylindrical and for a plasma supposed homogeneous along the propagation direction but radially inhomogeneous with a parabolic density profile. A two-parameter perturbation expansion is used; these two parameters, assumed small with respect to unity, are the ratio of the laser wavelength to the radial electric-field gradient length and the ratio of the plasma frequency to the laser frequency. The laser field is described in the context of a time envelope and spatial paraxial approximations. An analytical expression is provided for the critical beam power beyond which self-focusing appears; it depends strongly on the plasma inhomogeneity and suggests the plasma density tailoring in order to lower this critical power. The beam energy radius evolution is obtained as a function of the propagation distance by numerically solving the paraxial equation given by the two-parameter expansion. The relativistic mass variation is shown to dominate the ponderomotive effect. For strong laser fields, self-focusing saturates due to corrections of fourth order in the electric field involved by both contributions.

Focusing of Dark Hollow Gaussian Electromagnetic Beams in a Plasma With Relativistic-Ponderomotive Regime

“…In such a case the nonlinearity in the dielectric function occurs is caused by the electron mass variation due to large laser irradiance and the change in electron density as a consequence of the ponderomotive force. Very few studies on self focusing [35,36] and cross focusing [37] of the laser beams have been made, incorporating the combined effect of relativistic and ponderomotive nonlinearities. Further the effect of an ultra intense laser pulse on the propagation of an electron plasma wave has been analyzed by Kumar et al [38] in the relativistic-ponderomotive regime.…”

Soliton solutions for quasilinear Schrödinger equations, I

“…Quasilinear equations of form (1) appear more naturally in mathematical physics and have been derived as models of several physical phenomena corresponding to various types of h, the superfluid film equation in plasma physics by Kurihara in [13] (cf. [14]) for h(s) = s. In the case h(s) = (1 + s) 1/2 , (1) models the self-channeling of a high-power ultra short laser in matter; see [4], [6], [8], [23] and the references in [5]. Equation (1) also appears in plasma physics and fluid mechanics [13], [14], [17], [19], [21], in the theory of Heisenberg ferromagnets and magnons [2], [12], [15], [22], [25], in dissipative quantum mechanics [10] and in condensed matter theory [18].…”

Multifocal terahertz radiation by intense lasers in rippled plasma

“…The relativistic ponderomotive force in the presence of an intense electromagnetic beam can be represented [17,18] as…”