Quantum ring solitons and nonlocal effects in plasma wake field excitations

Journal Article · Mon Oct 15 00:00:00 EDT 2012 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4757214· OSTI ID:22068798

Fedele, R; Tanjia, F ^[1]; De Nicola, S ^[1]; Jovanovic, D ^[2]; Shukla, P K ^[3]

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1. Dipartimento di Scienze Fisiche, Universita di Napoli 'Federico II', and INFN, Napoli (Italy)
2. Institute of Physics, University of Belgrade, Belgrade (Serbia)
3. Center of Advanced Studies in Physical Sciences, Ruhr-Universitaet Bochum, Bochum (Germany)

A theoretical investigation of the quantum transverse beam motion for a cold relativistic charged particle beam travelling in a cold, collisionless, strongly magnetized plasma is carried out. This is done by taking into account both the individual quantum nature of the beam particles (single-particle uncertainty relations and spin) and the self consistent interaction generated by the plasma wake field excitation. By adopting a fluid model of a strongly magnetized plasma, the analysis is carried out in the overdense regime (dilute beams) and in the long beam limit. It is shown that the quantum description of the collective transverse beam dynamics is provided by a pair of coupled nonlinear governing equations. It comprises a Poisson-like equation for the plasma wake potential (driven by the beam density) and a 2D spinorial Schroedinger equation for the wave function, whose squared modulus is proportional to the beam density, that is obtained in the Hartree's mean field approximation, after disregarding the exchange interactions. The analysis of this pair of equations, which in general exhibits a strong nonlocal character, is carried out analytically as well as numerically in both the linear and the nonlinear regimes, showing the existence of the quantum beam vortices in the form of Laguerre-Gauss modes and ring envelope solitons, respectively. In particular, when the relation between the plasma wake field response and the beam probability density is strictly local, the pair of the governing equations is reduced to the 2D Gross-Pitaevskii equation that allows one to establish the conditions for the self focusing and collapse. These conditions include the quantum nature of the beam particles. Finally, when the relation between the plasma wake field response and the beam probability density is moderately nonlocal, the above pair of equations permits to follow the spatio-temporal evolution of a quantum ring envelope soliton. Such a structure exhibits small or violent breathing, but it remains very stable for long time.

• OSTI ID: 22068798
• Journal Information: Physics of Plasmas, Vol. 19, Issue 10; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BEAM DYNAMICS
BEAM-PLASMA SYSTEMS
BEAMS
CHARGED PARTICLES
EXCHANGE INTERACTIONS
EXCITATION
MEAN-FIELD THEORY
NONLINEAR PROBLEMS
POISSON EQUATION
RELATIVISTIC PLASMA
RELATIVISTIC RANGE
SCHROEDINGER EQUATION
SOLITONS
TWO-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS