Relativistic Laser-Plasma Interactions. Moving Solitary Waves in Plasma Channels and the Kinetic Dispersion Relation of Cherenkov Radiation
The propagation of an intense laser beam in a preformed plasma channel is studied. Considering a propagating Gaussian laser pulse in a relativistic plasma channel which has a parabolic density profile, the evolution equation of the laser spot size is derived analytically and solved numerically. The governing equation includes the effects of relativistic corrections to the ponderomotive self-channeling, preformed channel focusing, and self-focusing. In order to investigate the conditions for the existence of electromagnetic solitary waves, the solutions of the evolution equation for the laser spot size are discussed in terms of a relativistic effective potential. Some solitary wave solutions are illustrated numerically. The relativistic corrections to the dispersion relation of Cherenkov emission in dusty plasma is presented briefly. In the low-velocity limit, all the expressions in the present study are reduced to their associated counterparts in the nonrelativistic regime, as should be.
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