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Total charge and energy evaluations for the electron beams generated in thelaser wakefield acceleration (LWFA) is the primary step in the determination ofthe required target and laser parameters. Particle-in-cell (PIC) simulations isan efficient numerical tool that can provide such evaluations unless the effectof numerical dispersion is not diminished. The numerical dispersion, which isspecific for the PIC modeling, affects not only the dephasing lengths in LWFAbut also the total amount of the self-injected electrons. A numerical error ofthe order of $10^{-4}-10^{-3}$ in the calculation of the speed of light resultsin a significant error in the total injected charge and energy gain of theaccelerated electron bunches. In the standard numerical approach, the numericalcorrection of the speed of light either requires infinitely small spatial gridresolution (which needs large computation platform) or force to compromise withthe numerical accuracy. A simple and easy to implement numerical scheme isshown to suppress the numerical dispersion of the electromagnetic pulse in PICsimulations even with a modest spatial resolution, and without any specialtreatments to the core structure of the numerical algorithm. Evaluated chargesof the self-injected electron bunches become essentially lower owing to thebetter calculations of the wake phase velocity.

Amendment of the numerical dispersion in particle-in-cell methods for  evaluation of charges of self-injected electron bunches in the laser  wakefield acceleration