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Wave theories of non-laminar charged particle beams: from quantum to thermal regime

Published online by Cambridge University Press:  15 January 2014

Renato Fedele ,
Fatema Tanjia ,
Dusan Jovanović ,
Sergio De Nicola  and
Concetta Ronsivalle
Renato Fedele*
Affiliation:
Dipartimento di Fisica, Università di Napoli “Federico II” and INFN Sezione di Napoli, Italy
Fatema Tanjia
Affiliation:
Dipartimento di Fisica, Università di Napoli “Federico II” and INFN Sezione di Napoli, Italy
Dusan Jovanović
Affiliation:
Institute of Physics, University of Belgrade, Belgrade, Serbia
Sergio De Nicola
Affiliation:
Dipartimento di Fisica, Università di Napoli “Federico II” and INFN Sezione di Napoli, Italy SPIN-CNR, Complesso Universitario di M.S. Angelo, Napoli, Italy
Concetta Ronsivalle
Affiliation:
Centro Ricerche ENEA, Frascati, Italy
*
†Email address for correspondence: renato.fedele@na.infn.it
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Abstract

The standard classical description of non-laminar charged particle beams in paraxial approximation is extended to the context of two wave theories. The first theory that we discuss (Fedele R. and Shukla, P. K. 1992 Phys. Rev. A45, 4045. Tanjia, F. et al. 2011 Proceedings of the 38th EPS Conference on Plasma Physics, Vol. 35G. Strasbourg, France: European Physical Society) is based on the Thermal Wave Model (TWM) (Fedele, R. and Miele, G. 1991 Nuovo Cim. D13, 1527.) that interprets the paraxial thermal spreading of beam particles as the analog of quantum diffraction. The other theory is based on a recently developed model (Fedele, R. et al. 2012a Phys. Plasmas19, 102106; Fedele, R. et al. 2012b AIP Conf. Proc.1421, 212), hereafter called Quantum Wave Model (QWM), that takes into account the individual quantum nature of single beam particle (uncertainty principle and spin) and provides collective description of beam transport in the presence of quantum paraxial diffraction. Both in quantum and quantum-like regimes, the beam transport is governed by a 2D non-local Schrödinger equation, with self-interaction coming from the nonlinear charge- and current-densities. An envelope equation of the Ermakov–Pinney type, which includes collective effects, is derived for both TWM and QWM regimes. In TWM, such description recovers the well-known Sacherer's equation (Sacherer, F. J. 1971 IEEE Trans. Nucl. Sci.NS-18, 1105). Conversely, in the quantum regime and in Hartree's mean field approximation, one recovers the evolution equation for a single-particle spot size, i.e. for a single quantum ray spot in the transverse plane (Compton regime). We demonstrate that such quantum evolution equation contains the same information as the evolution equation for the beam spot size that describes the beam as a whole. This is done heuristically by defining the lowest QWM state accessible by a system of non-overlapping fermions. The latter are associated with temperature values that are sufficiently low to make the single-particle quantum effects visible on the beam scale, but sufficiently high to make the overlapping of the single-particle wave functions negligible. This lowest QWM state constitutes the border between the fundamental single-particle Compton regime and the collective quantum and thermal regimes at larger (nano- to micro-) scales. Comparing it with the beam parameters in the existing accelerators, we find that it is feasible to achieve nano-sized beams in advanced compact machines.

Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 2 , April 2014 , pp. 133 - 145
Copyright
Copyright © Cambridge University Press 2014 

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References

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