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The plasma wake field excitation: Recent developments from thermal to quantum regime

Published online by Cambridge University Press:  08 January 2014

RENATO FEDELE,
FATEMA TANJIA,
SERGIO DE NICOLA and
DUŠAN JOVANOVIĆ
RENATO FEDELE
Affiliation:
Dipartimento di Fisica, Università di Napoli “Federico II”, Napoli, Italy (renato.fedele@na.infn.it)INFN Sezione di Napoli, Napoli, Italy
FATEMA TANJIA
Affiliation:
Dipartimento di Fisica, Università di Napoli “Federico II”, Napoli, Italy (renato.fedele@na.infn.it)INFN Sezione di Napoli, Napoli, Italy
SERGIO DE NICOLA
Affiliation:
SPIN-CNR, Complesso Universitario di M.S. Angelo, Napoli, ItalyINFN Sezione di Napoli, Napoli, Italy
DUŠAN JOVANOVIĆ
Affiliation:
Institute of Physics, University of Belgrade, Belgrade, SerbiaINFN Sezione di Napoli, Napoli, Italy
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Abstract

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To describe the transverse nonlinear and collective self-consistent interaction of a long relativistic electron or positron beam with an unmagnetized plasma, a pair of coupled nonlinear differential equations were proposed by Fedele and Shukla in 1992 (Fedele, R. and Shukla, P. K. 1992a Phys. Rev. A 45, 4045). They were obtained within the quantum-like description provided by the thermal wave model and the theory of plasma wake field excitation. The pair of equations comprises a 2D Schrödinger-like equation for a complex wave function (whose squared modulus is proportional to beam density) and a Poisson-like equation for the plasma wake potential. The dispersion coefficient of the Schrödinger-like equation is proportional to the beam thermal emittance. More recently, Fedele–Shukla equations have been further applied to magnetized plasmas, and solutions were found in the form of nonlinear vortex states and ring solitons. They have been also applied to plasma focusing problems and extended from thermal to quantum regimes. We present here a review of the original approach, and subsequent developments.

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