STABILITY ANALYSIS OF RELATIVISTIC AND CHARGE-DISPLACEMENT SELF-CHANNELING OF INTENSE LASER-PULSES IN UNDERDENSE PLASMAS

The stability against small azimuthal perturbations of confined modes of propagation of intense short-pulse radiation governed by relativist ic and charge-displacement nonlinearities in underdense plasmas is exa mined theoretically. In the plane of the dimensionless parameters rho( 0) = tau(0) omega(p,0)/c and eta = P-0/P-cr, defined by the critical p ower (P-cr) and the initial conditions represented by the focal radius (tau(0)) of the incident radiation, the unperturbed plasma frequency (omega(p,0)), and the peak incident power (P-0), zones corresponding t o stable (single-channel) and unstable (strong filamentation) regimes of propagation are established. The general finding is that large regi ons of stable propagation exist. The results show that for values of r ho(0) sufficiently close to the dimensionless radius of the zeroth eig enmode rho(e,0), the self-channelling is stable for all values of eta > 1, a condition of exceptional robustness. It is also found that for the region 1 < eta less than or similar to 10, the propagation is stab le for a very wide range of values of rho(0). In addition, the locatio n of the boundary separating the stable and unstable zones is largely independent of the curvature of the phase front of the incident wave a nd weakly influenced both by the magnitudes of the azimuthal perturbat ions and the detailed radial profile of the incident radiation. Since self-focusing generated solely by relativistic mechanisms tends strong ly to unstable behaviour in the eta >> 1 regime, these results demonst rate the crucial role of the ponderomotively driven charge displacemen t in stabilizing the propagation. Physically, the ponderomotive radial displacement of the electrons and the contrasting inertial confinemen t of the ions simultaneously produce the two chief characteristics of the channels. They are the refractive self-focusing of the propagating energy arising from the displaced electrons and the spatial stability of the channels produced by the immobile electrostatic spine formed b y the ions.