Improving accuracy of field work calculations for the analysis of the electron acceleration mechanisms in near-critical density plasma

It is demonstrated that the inherent structure of Boris pusher may result in the accumulation of errors in numerical integration when estimating the works of electric fields on particles. This, in turn, leads to an incorrect estimations of particle acceleration mechanisms. A method of error correction, reducing error to the acceptable levels of $<10\%$, is implemented. Numerical integration error in question is most pronounced in scenarios where substantial number of electrons are injected into the accelerating structure through wave breaking of plasma waves i.e. in near-critical density plasma.