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

TL;DR

This paper introduces a new quasi-static theory for nonlinear pulse evolution in laser wakefield accelerators, validated by simulations, revealing novel dispersion properties and detailed pulse dynamics in the plasma.

Contribution

The paper develops a novel quasi-static theoretical framework based on cold-fluid and Maxwell equations in the PCMF, providing new formulas for pulse and wakefield evolution.

Findings

The theory accurately predicts pulse group velocity and wake amplitude behaviors.

Simulation results confirm the emergence of a new dispersion branch with linear dispersion.

The pulse evolution is governed by a Schrödinger-like equation in the PCMF.

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.