Self-focusing and channel-coupling effects on short laser pulses propagating in a plasma channel

Nonparaxial, nonlinear propagation of a relativistic laser pulse in a preformed plasma channel having a parabolic density profile is analyzed. Nonlinearity arises due to relativistic motion of plasma electrons and their coupling with plasma channel. The effect of nonlinearities on betatron oscillations is analyzed and the nonlinear critical channel depth required for propagation of a matched laser pulse is evaluated. Mismatch due to nonlinear effects and additional condition for matched pulse propagation are obtained. Amplitude of the matched, as well as mismatched, beam is derived and finite pulse effects are studied.