• W. Simeoni
  IF-UFRGS, Porto Alegre

The question is whether an anisotropic system of collisionless particles coupled by long-range space-charge forces will equipartition and, if so, how. Results show that collective effects tend to cause an initial beam with strongly nonuniform density to relax, rapidly, to a state that is equlibrium-like. In order to understand the initial dynamical behavior of an anisotropic beams, 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 purpose of this paper is to propose one definiton of the anisotropic equipartition. In the state of anisotropic equipartition, the 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.