The theory of electron acceleration in a plasma wake wave is developed, and
the dependence of the main characteristics of accelerated electron bunches
on the wakefield parameters is investigated. It is shown that using a preb
unching stage, under proper conditions, the final electron density of a com
pressed and accelerated bunch can exceed the initial electron beam density
by orders of magnitude and that longitudinal bunch compression provides qua
si-monoenergetic acceleration to high energies. It is demonstrated that, fo
r an initial electron beam radius smaller than the optimal one for efficien
t beam trapping, the energy spread of the compressed and accelerated electr
on bunch and its length can be evaluated by using the simple analytical pre
dictions of a one-dimensional (I-D) theory, The obtained analytical results
are confirmed by three-dimensional (3-D) numerical modeling.