Nonlinear Pulse Evolutions in the Laser Wakefield Accelerator through a new Quasi-Static Theory

Abstract: Beginning from the set of cold-fluid plus Maxwell equations in the instantaneous, Lorentz-boosted Pulse Co-Moving Frame (PCMF), a new quasi-static theory is developed to describe the nonlinear pulse evolutions due to the wakefield excitation, and is verified through comparison with particle-in-cell (PIC) simulations. According to this theory, the plasma-motion can be treated perturbatively and produces quasi-static wakefield in the PCMF, and the pulse envelope is governed by a form of the Schrodinger equation. The pulse evolutions are characterized by local conservation laws resulted from this equation and subjected to Lorentz transformation into the laboratory frame. In this context, new formulas describing the time-behaviors of group velocity, wake amplitude and carrier frequency are derived and best confirmed by simulation data. The spectral evolutions of the radiation are described based on the properties of the Schrodinger equation, predicting the emergence of a new extra-ordinary dispersion branch with linear relation w=ck (c is the light speed) approved by simulations.