Self-focusing of relativistic electron bunches in a dense plasma

In this paper we present results of investigations on the problem of creation ordered structures in the multiparticle unstable plasma systems. It provides an opportunity to control the collective dynamics of a plasma together with highly modulated relativistic electron beam. The foundation of this problem is the change in sign of the Coulomb force for moving electron bunches with beam modulation frequency. The electromagnetic radiation emitted by the beam in a plasma is a superposition of vacuum Coulomb field of moving bunches and of polarization wave excited by this field in a plasma. Under the resonance when modulation frequency is close to the Langmuir frequency, focusing polarization field dominates and plasma-beam instability leads to spatial (longitudinal and transversal) compression of bunches under the action of collective field in plasma.