Thermodynamic bounds on nonlinear electrostatic perturbations in intense charged particle beams

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 T /T ⊥ < 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.