Sm. Lund et Rc. Davidson, WARM-FLUID DESCRIPTION OF INTENSE BEAM EQUILIBRIUM AND ELECTROSTATIC STABILITY PROPERTIES, Physics of plasmas, 5(8), 1998, pp. 3028-3053
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.