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Warm-fluid description of intense beam equilibrium and electrostatic stability properties

### Abstract

A nonrelativistic warm-fluid model is employed in the electrostatic approximation to investigate the equilibrium and stability properties of an unbunched, continuously focused intense ion beam. A closed macroscopic model is obtained by truncating the hierarchy of moment equations by the assumption of negligible heat flow. Equations describing self-consistent fluid equilibria are derived and elucidated with examples corresponding to thermal equilibrium, the Kapchinskij–Vladimirskij (KV) equilibrium, and the waterbag equilibrium. Linearized fluid equations are derived that describe the evolution of small-amplitude perturbations about an arbitrary equilibrium. Electrostatic stability properties are analyzed in detail for a cold beam with step-function density profile, and then for axisymmetric flute perturbations with and about a warm-fluid KV beam equilibrium. The radial eigenfunction describing axisymmetric flute perturbations about the KV equilibrium is found to be *identical* to the eigenfunction derived in a full kinetic treatment. However, in contrast to the kinetic treatment, the warm-fluid model predicts stable oscillations. None of the instabilities that are present in a kinetic description are obtained in the fluid model. A careful comparison of the mode oscillation frequencies associated with the fluid and kinetic models is made in order to delineate which stability features of a KV beam are model-dependent and which may have general applicability.

© 1998 American Institute of Physics

Received 30 March 1998
Accepted 16 April 1998

/content/aip/journal/pop/5/8/10.1063/1.873027

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55.The authors wish to thank Ed Lee for bringing to our attention energy arguments analogous to those employed in magnetohydrodynamics [see, for example, G. Schmidt, Physics of High Temperature Plasmas (Academic, New York, 1979)] can be used in the present warm-fluid model to bound perturbations for rigidly-rotating fluid equilibria with radial profiles satisfying certain derivative conditions. This can be used to show that the macroscopic profiles for a KV beam equilibrium satisfy a sufficient condition for fluid stability.

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