Eur. Phys. J. D (2014) 68: 210
https://doi.org/10.1140/epjd/e2014-50219-y

Regular Article

Transverse evolution of a long relativistic electron beam governed by the Vlasov-Poisson-type pair of equations within the plasma wake field dynamics in the local regime^*

¹ Dipartimento di Fisica, Università di Napoli “Federico II”, Napoli, Italy
² INFN Sezione di Napoli, Napoli, Italy
³ Institute of Physics, University of Belgrade, Belgrade, Serbia
⁴ SPIN-CNR Napoli, Napoli, Italy
⁵ Dipartimento di Matematica e Fisica, Seconda Università degli Studi di Napoli, Italy

^a e-mail: akhter@na.infn.it

Received: 17 March 2014
Received in final form: 12 May 2014
Published online: 29 July 2014

Abstract

An analysis of the transverse plasma wake field dynamics excited by a long relativistic electron beam is carried out in a purely local regime, in which the transverse beam spot-size is much bigger than the plasma wavelength. This is done by using the Vlasov equation, that governs the kinetic spatiotemporal evolution of the transverse paraxial beam transport. A self-consistent description of the beam dynamics is then provided by coupling the Vlasov equation with a Poisson-type equation. Furthermore, the latter relates the beam density with the plasma wake potential energy. Remarkably, the approach here proposed seems to be suitable for describing the beam self-modulation and the prediction of the beam collapse.