Theory of Electron Cooling in a Magnetic Field

Abstract

We shall discuss the phase space compression of a “beam of antiprotons thermalizing in a continuously renewed, cold, dense electron beam moving parallel to the antiprotons with the same average velocity. The electrons are guided and confined throughout the interaction region “by a homogeneous, longitudinal magnetic field. In previous discussions of this so-called electron cooling effect the interaction of an antiproton with the cooling electron gas has “been treated as a series of independent two-body collisions.^1–4 This leads to logarithmic divergences at large impact parameters, due to the neglect of polarization forces, and the difficulties are particularly severe because of the presence of the magnetic field. In this paper we shall briefly outline how these problems may be avoided through the application of a dielectric description of the electron gas. A comprehensive treatment of the cooling process containing a detailed discussion of both the binary and the dielectric description will be published in the very near future.⁵