Stability Analysis of Relativistic and Charge-Displacement Self-Channeling of Intense Laser Pulses

Abstract

Theoretical modeling of the stability of relativistic and charge displacement self-channeling of high power laser pulses in plasmas leads to the establishment of stability maps for self-channeling propagation of laser pulses. The problem of stability of relativistic and charge displacement self-channeling of intense ultrashort laser pulses in cold undercritical plasmas against small azimuthal perturbations is analyzed. The problem is studied for both an initially uniform plasma and for a preformed plasma column. In the plane of dimensionless parameters ρo = roωp,o/c and η = Po/Pcr, which depends on the initial values of the focal spot radius, power of the laser beam and the unperturbed density of the plasma, the boundary separating the regimeis of the stable self-channeling and of the strong filamentation is defined. It is found that for ρ o ≈ ρeig,o (ρeig,o being the dimensionless radius of the zeroth eigenmode of the studied problem) the relativistic and charge-displacement self-channeling is stable for any value of initial power Po > Pcr. It is also shown that in the case where η ≈ 10, the relativistic and charge-displacement self-channeling is stable for practically any value of ρo. It is found that the location of the boundary separating the two regimes of propagation is essentially independent of the initial curvature of the phase front of the beam. The dependence of the location of the stable region on the parameters governing the amplitude of the azimuthal perturbation is also weak. The results emphasize the extreme importance of the stabilizing role of charge-displacement in these plasma interactions. A procedure for optimization of laser beam and plasma parameters for experimental realization of the relativistic and charge-displacement self-channeling is developed. The proposed method of investigation of the stability and the optimization of the self-channeling of laser pulses can be applied generally to various cases involving nondissapative media with saturating nonlinearities.