WARM-FLUID DESCRIPTION OF INTENSE BEAM EQUILIBRIUM AND ELECTROSTATIC STABILITY PROPERTIES

A nonrelativistic warm-fluid model is employed in the electrostatic ap proximation to investigate the equilibrium and stability properties of an unbunched, continuously focused intense ion beam. A closed macrosc opic 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 c orresponding to thermal equilibrium, the Kapchinskij-Vladimirskij (KV) equilibrium, and the waterbag equilibrium. Linearized fluid equations are derived that describe the evolution of small-amplitude perturbati ons about an arbitrary equilibrium. Electrostatic stability properties are analyzed in detail for a cold beam with step-function density pro file, and then for axisymmetric flute perturbations with partial deriv ative/partial derivative theta = 0 and partial derivative/partial deri vative z = 0 about a warm-fluid KV beam equilibrium. The radial eigenf unction describing axisymmetric flute perturbations about the KV equil ibrium 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 instabilit ies that are present in a kinetic description are obtained in the flui d model. A careful comparison of he mode oscillation frequencies assoc iated with the fluid and kinetic models is made in order to delineate which stability features of a KV beam are model-dependent and which ma y have general applicability. (C) 1998 American Institute of Physics.