Cooling of ions and antiprotons with magnetized electrons

Electron cooling is a well-established method to improve the phase space quality of ion beams in storage rings. More recently antiprotons have been cooled in traps, first by electrons and then by positrons in order to produce antihydrogen atoms as simplest form of antimatter for CPT-tests. During these cooling processes the light particles are guided by strong external magnetic fields which imposes a challenge to the theoretical description. Within the binary collision model we treat the Coulomb interaction as second-order perturbation to the helix motion of the light particles and also by numerical simulations. In the complementary dielectric theory we calculate the polarization of the light particles by solving the nonlinear Vlasov–Poisson equation as well as linear response. It turns out that the linearization becomes dubious at low ion velocities. In the presence of a strong magnetic field the numerically expensive solution of the Vlasov–Poisson equation is the method of choice, alternatively one may employ the binary collision model. Within this approach simulations must be employed for a repulsive interaction, e.g. antiproton–electron, or for highly charged ions. Drag forces F→ are given as functions of the ion velocity v→i and can be used as input for codes to calculate cooling times.