Stability analysis of relativistic and charge-displacement self-channelling of intense laser pulses in underdense plasmas

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Abstract
The stability against small azimuthal perturbations of confined modes of propagation of intense short-pulse radiation governed by relativistic and charge-displacement nonlinearities in underdense plasmas is examined theoretically. In the plane of the dimensionless parameters rho 0 identical to r0 omega p,0/c and eta identical to P0/Pcr, defined by the critical power (Pcr) and the initial conditions represented by the focal radius (r0) of the incident radiation, the unperturbed plasma frequency ( omega p,0), and the peak incident power (P0), zones corresponding to stable (single-channel) and unstable (strong filamentation) regimes of propagation are established. The general finding is that large regions of stable propagation exist. The results show that for values of rho 0 sufficiently close to the dimensionless radius of the zeroth eigenmode rho c,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 >1 regime, these results demonstrate the crucial role of the ponderomotively driven charge displacement in stabilizing the propagation. Physically, the ponderomotive radial displacement of the electrons and the contrasting inertial confinement 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 by the ions.