Electron acceleration by an intense laser pulse inside a density profile induced by non-linear pulse evolution

By sophisticated application of particle-in-cell simulations, we demonstrate the ultimate role of non-linear pulse evolutions in accelerating electrons during the entrance of an intense laser pulse into a preformed density profile. As a key point in our discussions, the non-linear pulse evolutions are found to be very fast even at very low plasma densities, provided that the pulse length exceeds the local plasma wavelength. Therefore, these evolutions are sufficiently developed during the propagation of typical short density scale lengths occurred at high contrast ratios of the pulse, and lead to plasma heating via stochastic acceleration in multi-waves. Further analysis of simulation data at different physical parameters indicates that the rate of evolutions increases with the plasma density leading to higher plasma heating and overgrown energetic electrons. In the same way, shortening the density scale length results into increase in the evolution rate and, simultaneously, decrease in the interaction time. This behavior can describe the observed optimum value of pre-plasma scale length for the maximum electron heating.