Transition from isotropic to anisotropic beam profiles in a uniform linear focusing channel

Abstract

This paper examines the transition from isotropic to anisotropic beam profiles in a linear focusing channel. Considering a high-intensity ion beam in space-charge dominated regime and large mismatched RMS beam size initially, observe a fast anisotropy situation of the beam, characterized for a transition of the transversal section round to elliptical with a coupling of transversal emittance driven for instabilities of nonlinear space-charge forces. Space-charge interactions in high-intensity linear accelerator can lead to equipartitioning of energy between the degrees of freedom. The anisotropization phenomena suggest a kind of route to equipartition. In order to understand the initial dynamical behavior of an anisotropic beam, in particular, to study possible mechanisms of equipartition connected with phase space we have to know how we can compute the variables (volume, area of surface, and area projected) that characterize the anisotropic beam in phase space. The beam began in a nonequilibrium state evolved toward a metaequilibrium in which the particle orbits filled an invariant measure of phase space. We shall call this subspace of the phase space " ξ ", where ξ is the ratio of oscillations energies in the x and y directions. It is well-know [38] that an isolated difference ressonance of the form lωx − mωy = 0, where ωx is single particle frequency along of x-direction and ωy is single particle frequency along of y-direction, lead to the motion bounded in both directions and " ξ "remains unchanged. The purpose of this paper is to propose one definiton of the anisotropic equipartition [84]. Anisotropic equipartition corresponds to a phase space density uniform on the surface invariant of the ξ, a version of the ergodic hypothesis where the ξ invariant play the role of the conserved energy [62]. In the state of anisotropic equipartition, the beam temperature is stationary, the entropy grows in the cascade form, there is a coupling of transversal emittance, the beam develops an elliptical shape with a increase in its size along one direction and there is halo formation along one direction preferential.