The report is devoted to the theoretical study and numerical simulation of the excitation of wake-fields in plasma and their application for charged particle acceleration. It is shown that at a given relationship between the parameters of the "plasma bunch - magnetic field" system in the magnetoactive plasma owing to the hybrid space-surface character of wake-field waves excited by a relativistic electron bunch (REB), the accelerated bunch energy εmax can appear essentially higher than the exciting bunch energy even if the longitudinal REB charge density profiling is not used. With the help of 2.5 D numerical simulation of wake-fields excited by a single REB or a REB sequence it has been established the following: the ion channel is formed owing to transverse ion motion in self- consistent electromagnetic fields, this channel stabilizes REB propagation and thus serves to increase the REB excited fields; the self-modulation of a long pulsed REB is a very promising way both to obtain high rates of charged particle acceleration and to modulate the bunch and plasma densities (this gives evidence that the linear approach cannot be used to describe the plasma even in the low beam density case). These results make it possible to clarify the prospects and to evaluate the possibility of creating new-type charged particle accelerators which will have acceleration rates much higher than the conventional resonant accelerator has.
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