Eur. Phys. J. D (2014) 68: 271
https://doi.org/10.1140/epjd/e2014-50220-6

Regular Article

Vlasov’s kinetic theory of the collective charged particle beam transport through a magnetized plasma in the strongly nonlocal regime^*

¹ Dipartimento di Fisica, Università di Napoli Federico II, Complesso Universitario di M.S. Angelo, Napoli, Italy
² INFN Sezione di Napoli, Complesso Universitario di M.S. Angelo, Napoli, Italy
³ Dipartimento di Matematica e Fisica, Seconda Università degli Studi di Napoli, Sede di Caserta, Caserta, Italy
⁴ SPIN-CNR, Complesso Universitario di M.S. Angelo, Napoli, Italy
⁵ Institute of Physics, University of Belgrade, Belgrade, Serbia

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

Received: 17 March 2014
Received in final form: 10 July 2014
Published online: 25 September 2014

Abstract

Within the Vlasov’s kinetic theory, describing the plasma wake field interaction, the collective transport of a warm nonlaminar relativistic charged particle beam is analyzed in the strongly nonlocal regime, where the beam spot-size is much less than the plasma wavelength. This is done in the overdense regime, i.e., the beam density is much less than the plasma density. The beam is supposed to be sufficiently long to experience the adiabatic shielding by the plasma. In these conditions, we neglect the longitudinal beam dynamics and focus on the transverse one only. We derive the virial description (envelope description) from the 2D Vlasov-Poisson-type system of equations that governs the transverse self-consistent plasma wake field excitation. The resulting envelope equation is then reduced, in the aberration-less approximation, to a differential equation for the beam spot size, where the role of the ambient magnetic field is evaluated in both laboratory and astrophysical environments. An analysis of the beam envelope self-modulation is then carried out and the criteria for the occurrence of the instability are found.