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Title: Novel Hamiltonian method for collective dynamics analysis of an intense charged particle beam propagating through a periodic focusing quadrupole lattice

Abstract

Identifying regimes for quiescent propagation of intense beams over long distances has been a major challenge in accelerator research. In particular, the development of systematic theoretical approaches that are able to treat self-consistently the applied oscillating force and the nonlinear self-field force of the beam particles simultaneously has been a major challenge of modern beam physics. In this paper, the recently developed Hamiltonian averaging technique [E. A. Startsev, R. C. Davidson, and M. Dorf, Phys. Rev. ST Accel. Beams 13, 064402 (2010)] which incorporates both the applied periodic focusing force and the self-field force of the beam particles, is generalized to the case of time-dependent beam distributions. The new formulation allows not only a determination of quasi-equilibrium solutions of the non-linear Vlasov-Poison system of equations but also a detailed study of their stability properties. The corrections to the well-known ''smooth-focusing'' approximation are derived, and the results are applied to a matched beam with thermal equilibrium distribution function. It is shown that the corrections remain small even for moderate values of the vacuum phase advance {sigma}{sub {upsilon}}. Nonetheless, because the corrections to the average self-field potential are non-axisymmetric, the stability properties of the different beam quasi-equilibria can change significantly.

Authors:
;  [1]
  1. Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
Publication Date:
OSTI Identifier:
21537910
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 18; Journal Issue: 5; Other Information: DOI: 10.1063/1.3589441; (c) 2011 American Institute of Physics; Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOLTZMANN-VLASOV EQUATION; CHARGED PARTICLES; DISTRIBUTION FUNCTIONS; FOCUSING; HAMILTONIANS; PARTICLE BEAMS; POISSON EQUATION; THERMAL EQUILIBRIUM; BEAMS; DIFFERENTIAL EQUATIONS; EQUATIONS; EQUILIBRIUM; FUNCTIONS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS

Citation Formats

Startsev, Edward A, and Davidson, Ronald C. Novel Hamiltonian method for collective dynamics analysis of an intense charged particle beam propagating through a periodic focusing quadrupole lattice. United States: N. p., 2011. Web. doi:10.1063/1.3589441.
Startsev, Edward A, & Davidson, Ronald C. Novel Hamiltonian method for collective dynamics analysis of an intense charged particle beam propagating through a periodic focusing quadrupole lattice. United States. https://doi.org/10.1063/1.3589441
Startsev, Edward A, and Davidson, Ronald C. 2011. "Novel Hamiltonian method for collective dynamics analysis of an intense charged particle beam propagating through a periodic focusing quadrupole lattice". United States. https://doi.org/10.1063/1.3589441.
@article{osti_21537910,
title = {Novel Hamiltonian method for collective dynamics analysis of an intense charged particle beam propagating through a periodic focusing quadrupole lattice},
author = {Startsev, Edward A and Davidson, Ronald C},
abstractNote = {Identifying regimes for quiescent propagation of intense beams over long distances has been a major challenge in accelerator research. In particular, the development of systematic theoretical approaches that are able to treat self-consistently the applied oscillating force and the nonlinear self-field force of the beam particles simultaneously has been a major challenge of modern beam physics. In this paper, the recently developed Hamiltonian averaging technique [E. A. Startsev, R. C. Davidson, and M. Dorf, Phys. Rev. ST Accel. Beams 13, 064402 (2010)] which incorporates both the applied periodic focusing force and the self-field force of the beam particles, is generalized to the case of time-dependent beam distributions. The new formulation allows not only a determination of quasi-equilibrium solutions of the non-linear Vlasov-Poison system of equations but also a detailed study of their stability properties. The corrections to the well-known ''smooth-focusing'' approximation are derived, and the results are applied to a matched beam with thermal equilibrium distribution function. It is shown that the corrections remain small even for moderate values of the vacuum phase advance {sigma}{sub {upsilon}}. Nonetheless, because the corrections to the average self-field potential are non-axisymmetric, the stability properties of the different beam quasi-equilibria can change significantly.},
doi = {10.1063/1.3589441},
url = {https://www.osti.gov/biblio/21537910}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 5,
volume = 18,
place = {United States},
year = {Sun May 15 00:00:00 EDT 2011},
month = {Sun May 15 00:00:00 EDT 2011}
}