The study of the wake field effects on the self-focusing and the compression of the laser pulse in plasma at the relativistic regime by Lagrangian method

The trial function in the variational-Lagrangian method is a fundamental method to explain the essential features of the laser pulse evolution in the plasma. Self-focusing behavior and compression of the laser pulse in plasma are analyzed, for both low and high intensity regimes. It is shown that the compression threshold depends on both pulse intensity and pulse length. In particular, in both regimes, the compression threshold is directly proportional to the pulse length. This is while this threshold is directly, in the linear regime, and inversely, in the nonlinear regime, proportional to pulse intensity. In the present work, the existence of oscillations is revealed, with a behavior akin to laser pulse width. Finally, the effects of pulse intensity, pulse length, and plasma density on compression are analyzed.