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In some laboratory and most astrophysical situations plasma wake-fieldacceleration of electrons is one dimensional, i.e. variation transverse to thebeam's motion can be ignored. Thus, one dimensional (1D), particle-in-cell(PIC), fully electromagnetic simulations of electron plasma wake fieldacceleration are conducted in order to study the differences in electron plasmawake field acceleration in MeV versus GeV and linear versus blowout regimes.First, we show that caution needs to be taken when using fluid simulations, asPIC simulations prove that an approximation for an electron bunch not to evolvein time for few hundred plasma periods only applies when it is sufficientlyrelativistic. This conclusion is true irrespective of the plasma temperature.We find that in the linear regime and GeV energies, the accelerating electricfield generated by the plasma wake is similar to the linear and MeV regime.However, because GeV energy driving bunch stays intact for much longer time,the final acceleration energies are much larger in the GeV energies case. Inthe GeV energy range and blowout regime the wake's accelerating electric fieldis much larger in amplitude compared to the linear case and also plasma wakegeometrical size is much larger. Thus, the correct positioning of the trailingbunch is needed to achieve the efficient acceleration. For the considered case,optimally there should be approximately $(90-100) c/\omega_{pe}$ distancebetween trailing and driving electron bunches in the GeV blowout regime.

Differences in 1D electron plasma wake field acceleration in MeV versus GeV and linear versus blowout regimes