On Nonlinear Evolutions of the Intense, Short Laser Pulse in the   Under-Dense Plasma
  Nonlinear evolutions of an ultra-intense, short laser pulse due to the wake excitation inside the plasma are studied by means of detailed Particle-In-Cell (PIC) simulations and comprehensive analyses. Pulse lengths both longer and shorter than the plasma wavelength are considered. It is turned out that the system shows adiabatic behavior as long as the plasma evolves very slowly in the Pulse Co-Moving (PCM) frame due to the ignorable radiation back-reactions. A sophisticated treatment of the adiabatic regime is presented, based on the proper application of the local conservation laws in the PCM frame in conjunction with the Lorentz transformations. In this context, equations for the overall pulse evolutions are reduced into a single equation in terms of the global pulse group-velocity. Due to the proven equality between the local phase velocities of the plasma wave and the radiation, anomalies are observed in this regime, in the global group velocity and the plasma dispersion. The group velocity shows non-explicit density dependency and of remaining above the linear value over a long period of the propagation. These results are successfully examined against PIC simulations and their consistency with the other system evolutions and the physical intuition is fully discussed. Afterward, the interaction locality is examined in terms of the plasma dispersion and the resultant spectral evolutions. And it is found that for pulse lengths larger than the plasma wavelength, the plasma-wave evolutions inside the pulse region result in the strong light phase-modulation along with the amplitude-modulation and whereby violation of the adiabatic description. The development of these phenomena is by production of the effective radiation back-reactions. 
Jam Yazdanpanah, Elnaz Yazdani, Elnaz Khalilzadeh and Amir Chakhmachi
physics.plasm-ph