Adiabatic warm-fluid equilibrium theory of thermal charged-particle beams in alternating-gradient focusing fields

Abstract

An adiabatic warm-fluid equilibrium theory for a thermal charged-particle beam in an alternating-gradient focusing field is presented. Warm-fluid equilibrium equations are solved in the paraxial approximation. The theory predicts that the four-dimensional rms thermal emittance of the beam is conserved, but the two-dimensional rms thermal emittances are not constant. The rms beam envelope equations and the self-consistent Poisson equation, governing the beam density and potential distributions, are derived. Although the presented rms beam envelope equations have the same form as the previously known rms beam envelope equations, the evolution of the rms emittances in the present theory is given by analytical expressions. The density does not have the simplest elliptical symmetry, but the constant-density contours are ellipses, and the aspect ratio of the elliptical constant-density contours decreases as the density decreases along the transverse displacement from the beam axis. For high-intensity beams, the beam density profile is flat in the center of the beam and falls off rapidly within a few Debye lengths, and the rate at which the density falls is approximately isotropic in the transverse directions.