In the standard numerical approach, the numerical correction in the speed of the laser pulse either requires infinitely small spatial grid resolution (which needs large computation platform) or force to compromise with the numerical accuracy. A numerical error of the order of 10 − 4 − 10 − 3 in the calculation of the speed of the driving laser pulse results in a significant error in the total injected charge, energy gain and other critical parameters of the accelerated electron bunches. The numerical dispersion, which is specific for the PIC modeling, affects not only the dephasing lengths in LWFA but also the total amount of the self-injected electrons. Particle-in-cell (PIC) simulation is an efficient numerical tool that can provide such evaluations unless the effect of numerical dispersion is not diminished. Total charge and energy evaluations for the electron beams generated in the laser wakefield acceleration (LWFA) is the primary step in the determination of the required laser and target parameters.
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