Collective Instabilities and Collisional Effects for a 2D Model of a Beam in a Storage Ring

We consider a collisional 2D model for a beam in a ring. In the smooth focus-ing approximation the relaxation time scales according to Landau’s theory, but the p.d.f of momentum jumps has a power law decaying queue. A new hybrid regime is found for the equipartitioning due to the interplay between collisional and collective effects. The moments equations of a small perturbation to the KV distribution are analytically determined and the stability conditions follow from Floquet’s theory.