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The quality of the electron or positron beam, accelerated in plasma accelerators, is still insufficient for applications. Accurate control over the properties of the electron or positron beam is a key issue for wakefield plasma accelerators. The effect of the presence of a witness-beam (the effect of the spatial charge distribution of the witness beam) (see [*, **]) to compensate the energy spread of the positron beam in plasma wakefield accelerators has been studied. This paper presents the results of a numerical simulation on the optimization of the parameters of the driver-bunch and witness-bunch for the formation of a self-consistent longitudinal distribution of the accelerating plateau-type field, which leads to the same values of the wakefield for the whole bunch of accelerated particles and minimizing bunch degradation during acceleration by means of an ion-driver-bunch with external injection into the plasma wake accelerator. The dependence of the longitudinal distribution of the accelerating wakefield on the density and shape of the accelerated bunch in the blowout regime was investigated. Plateau formation and energy spread compensation were observed.
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Ovsiannikov et al. (2021) studied this question.