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Phys. Rev. ST Accel. Beams 10, 064203 (2007) [3 pages]

Proof that stable monotonic equilibrium distributions in a continuous-focusing channel are necessarily axisymmetric

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Steven M. Lund*
Lawrence Livermore National Laboratory, Livermore, California 94550, USA

Received 29 March 2007; published 21 June 2007

The transverse Vlasov equilibrium distribution function of an unbunched ion beam propagating in a continuous-focusing channel is specified by a function f(H), where H is the single-particle Hamiltonian. In standard treatments of continuous-focusing equilibria in Vlasov-Poisson electrostatic models, it is assumed that a stable beam equilibrium specified by monotonic f(H) with f(H)/∂H≤0 is axisymmetric (no variation in azimuthal angle, i.e., with ∂/∂θ=0). In this paper a simple, but rigorous, proof is presented that only axisymmetric equilibrium solutions are possible in Vlasov-Poisson models for any physical choice of f(H) with f(H)/∂H≤0 if the confining boundary of the system (the beam pipe) is axisymmetric or if the geometry is radially unbounded.

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© 2007 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevSTAB.10.064203
DOI:
10.1103/PhysRevSTAB.10.064203
PACS:
29.27.Bd, 41.75.−i, 52.59.Sa

*Electronic address: smlund@llnl.gov