Transverse profiles and stability limits with electron cooler and target

We determine action dependent damping coefficients for electron coolers with cylindrical and hollow beams and action dependent diffusion coefficients from the interaction with a target and a simple model of intrabeam scattering. We use these coefficients to numerically solve the time-dependent Fokker–Planck equation and present simulations of the transient cooling down. An efficient integrator makes it possible to simulate long times (hours) very efficiently and quickly. Moreover we determine a maximum acceptable limit of the cooling time to provide stable operation.