Anomalous Group velocity and Plasma Dispersion in the Laser Wakefield Accelerator through a new Relativistic Theory

Abstract

A new cold relativistic theory is proposed to describe the Laser WakeField Accelerator (LWFA) in the presence of pulse evolutions, capable of being utilized to study the group velocity and the plasma dispersion. This new capability is mainly due to exploiting the concept of the real Lorentz-boost Pulse Co-Moving (LPCM) frame, in spite of previous studies. The theory is reduced to the well-known Quasi-Static Approximation (QSA) in the absence of the pulse evolutions, and shows excellent agreement with Particle-In-Cell (PIC) simulations in terms of its new results. The obtained results show the extremely extra-ordinary nature of the fully nonlinear plasma physics of LWFA. It is turned out that the local group and phase velocities of the light are approximately equal. The obtained group-velocity evolves in time according to ( and are parameters depending on wake amplitude and initial group velocity) at early stages, showing non-explicit density dependency and remaining above the linear value over a long period of the propagation. The obtained equations for the carrier-mode, on the other hand, consistently suggest the emergence of a new dispersion branch with the linear relation ( is the light speed). Regarding these remarks, we expend on the plasma dispersion in details with the aid of simulations, confirming the observed anomalies and the emergence of the new branch. In addition, a detailed description of the spectral evolutions in the dispersion plan is provided and it is shown that the dispersion anomalies tend to cease at long pulse lengths.