Analytical estimates of halo current loss rates in space charge dominated beams

In this paper, we investigate the dynamical behaviours of a continuous intense charged particle beam in a transport system. It is assumed that fermion particles, such as electron and proton, in the beam follow Fermi-Dirac statistics in the equilibrium state. The halo particles executing stochastic motions due to the envelope oscillation induced nonlinear resonances are investigated. Analytical formulae for the halo current and halo current loss rate on the beam pipe wall are established