Abstract
This paper is organized into two parts. In the first one we analyze the equipartitioning process in the presence of collisions for a Gaussian anisotropic beam. Far from instabilities the equipartition process can be described correctly by using Landau's collisional theory, whereas when the dynamics of the system is strongly nonlinear (e.g. in the vicinity of a resonance) a hybrid dynamical–collisional equipartition mechanism occurs. In the second part of the paper we discuss shortly a systematic study of the collective instabilities in a symmetric periodic focusing channel for a KV beam by using the moments method. We emphasize differences occurring when the periodic focusing lattice is replaced by the corresponding constant focusing one.
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