Theoretical and numerical investigation for propagation of ultrashort intense laser pulse in plasma channel

Characteristics of propagation of ultrashort intense laser pulses in a partially stripped pre-formed plasma channel, assumed to be parabolic and unperturbed, are discussed. From Maxwell equations the refractive index equation and Hamilton-Jacobi equation, which describe the evolution of the electric field, are derived including the effects of the diffraction, the third-order intensity-dependent nonlinearity, plasma defocusing, the self-focusing of the plasma channel, and the relativistic self-focusing. The envelope equation of laser propagating in the plasma channel, and the general expression relating the laser spot size with the propagation distance and the width of the plasma channel etc., are derived based on the Hamilton-Jacobi equation and the refractive index equation.