Laser Wakefield Electron Acceleration in a Periodically Modulated Plasma Density Profile

We investigate laser wakefield electron acceleration in a periodic plasma density profile using 2D PIC simulations with the EPOCH code. The profile of the electron density has the form n(x)=n01+δsin2πx/x0, where n0 is the steady electron density, x0=100m is the spatial periodicity in the laser propagation direction and δ, taking the values 0, 0.1, 0.3, 0.5 and 0.7, is the modulation parameter. The bubble size varies with the modulated plasma density, thereby influencing the electron acceleration, which occurs within a continuously changing bubble structure. We propose an analytical model to estimate the energies of the accelerated electrons, and evaluate the maximum electron energies at 500 fs intervals for the five modulated density profiles. We then calculate the dephasing and depletion lengths for these modulated plasma profiles and examine their dependence on δ. The results show a growth in both lengths with δ, with depletion being the main limitation in these cases. Additionally, we compute and compare the transverse emittance of the self-injected electron bunches corresponding to the various density profiles at the same simulation time, and other characteristics, like the center energy and energy spread. Emittance is observed to experience a decrease with the increase in the modulation parameter.