Self similar solution of superradiant amplification of ultrashort laser pulses in plasma

Abstract

Based on the self-similar method, superradiant amplification of ultrashort laser pulses by the counterpropagating pump in a plasma is investigated. Here, we present a governing system of partial differential equations for the signal pulse and the motion of the electrons. These equations are transformed to ordinary differential equations by the self-similar method and numerically solved. It is found that the increase of the signal intensity is proportional to the square of the propagation distance and the signal frequency has a red shift. Also, depending on the pulse width, the signal breaks up into a train of short pulses or its duration decreases with the inverse square root of the distance. Moreover, we identified two distinct categories of the electrons by the phase space analysis. In the beginning, one of them is trapped in the ponderomotive potential well and oscillates while the other is untrapped. Over time, electrons of the second kind also join to the trapped electrons. In the potential well, the electrons are bunched to form an electron density grating which reflects the pump pulse into the signal pulse. It is shown that the backscattered intensity is enhanced with the increase of the electron bunching parameter which leads to the enhanced efficiency of superradiant amplification.