Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams
Authors: Nikolas C. Logan and Ronald C. Davidson
Abstract: This paper places a lowest upper bound on the field energy in electrostatic perturbations
in single-species charged particle beams with initial temperature anisotropy (TllT⊥
< 1). The result applies to all electrostatic perturbations driven by the natural
anisotropies that develop in accelerated particle beams, including Harris-type
electrostatic instabilities, known to limit the luminosity and minimum spot size attainable
in experiments. The thermodynamic bound on the field perturbation energy
of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an
arbitrary initial distribution function, including the effects of intense self-fields, finite
geometry and nonlinear processes. This paper also includes analytical estimates of the
nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic
bi-Maxwellian distributions.
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Submitted to: Physics of Plasmas (May 2012)
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Download PPPL-4783 (pdf 632 KB 14 pp)
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