Abstract
In a laser wakefield accelerator (LWFA), two dimensional particle-in-cell simulations were performed to demonstrate the fluctuation of the maximum beam energy while varying the plasma density under the transition from mildly relativistic regime to relativistic regime. The fluctuation of the beam energy is induced by the unstable accelerating structure, which length is dynamically oscillating between the plasma wavelength and the relativistic plasma wavelength. The simulation results also reveal the existence of the parameter space for the stable operation of a LWFA.An empirical formulation was derived by the calculated radius of curvature of the returning electrons along the boundary of the plasma bubble in a stably operated LWFA. The comparisons between the energy scaling law derived from the empirical formulation, the two-dimensional and three-dimensional PIC simulation and previous experimental results with self-guided laser pulses show good agreement. The scaling law derived in the study can provide a correct estimation of the maximum beam energy for a newly designed LWFA experiment with an optimal configuration of the laser pulse.In addition, in order to study the space charge effect of the charge number for the injected electrons in LWFA, the simplified simulation model equivalent to first plasma bubble in LWFA considering full electromagnetic field, relativistic field, and parabolic potential profile was constructed. The space-charge-limited current was studied by the equivalent model and compared with the electron charge in the 2D LWFA simulation.