  This paper makes use of a one-dimensional kinetic model to investigate the
nonlinear longitudinal dynamics of electron beams generated in the plasma under
the influence of a self-generated electric field. It is expressed as where is a
wave potential, , and charge particle distribution functions satisfy the Vlasov
equation. It is proved that its correct solution is characterized by sudden
change in the resonant part of the distribution function. Hence, in particular,
the incorrectness of the established in the literature point of view follows
that the fast, with velocities over V, and slow, with velocities under V,
trapped particles are described by the same distribution function. Also for the
first time it is shown that the self-generated strong electric field always
produces antitropic electron beams with the velocities much larger than the
value V, including the cold plasma limit. The possibility of implementing a new
class of self-consistent wave structures with a nonzero average potential is
shown. Maximum possible amplitude of a self-generated electric field in a
stationary collisionless plasma is determined.
