Intrabeam scattering on halo formation

The effect of the Coulombian collision between particles of a beam (intra-beam scattering) is investigated. Starting from the basic two-bodies cross section formula in the centre of mass referential, the maximum energy gain that can be caught by a particle along one direction is calculated as a function of the equipartition factor. Then, assuming that particle trajectories are ellipses in (x, x´) phase-space (linear force-no space charge forces), the intra-beam scattering halo magnitude is calculated and shown to be very small. These calculations are done with different beam distribution functions and equipartition factor. The effect of space-charge is then investigated