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Title: Near equilibrium distributions for beams with space charge in linear and nonlinear periodic focusing systems

A procedure to obtain a near equilibrium phase space distribution function has been derived for beams with space charge effects in a generalized periodic focusing transport channel. The method utilizes the Lie transform perturbation theory to canonically transform to slowly oscillating phase space coordinates. The procedure results in transforming the periodic focusing system to a constant focusing one, where equilibrium distributions can be found. Transforming back to the original phase space coordinates yields an equilibrium distribution function corresponding to a constant focusing system along with perturbations resulting from the periodicity in the focusing. Examples used here include linear and nonlinear alternating gradient focusing systems. It is shown that the nonlinear focusing components can be chosen such that the system is close to integrability. The equilibrium distribution functions are numerically calculated, and their properties associated with the corresponding focusing system are discussed.
Authors:
;  [1]
  1. Center for Integrated Plasma Studies and Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States)
Publication Date:
OSTI Identifier:
22408357
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BEAMS; DISTRIBUTION FUNCTIONS; DISTURBANCES; FOCUSING; NONLINEAR PROBLEMS; PERIODICITY; PERTURBATION THEORY; PHASE SPACE; SPACE CHARGE