Theory of electron cooling using electron cooling as an intrabeam scattering process

Electron cooling that results when a bunch of electrons overlaps a bunch of ions , with both bunches moving at the same velocity, may be considered to be an intrabeam scattering process. The process is similar to the usual intrabeam scattering, where the ions scatter from each other and usually results in beam growth. An important difference is that in electron cooling the mass of the ion is different from and much larger than the mass of the electron. This difference considerably complicates the intrabeam scattering theory. It introduces a new term in the emittance growth rate, which vanishes when the particles are identical and their masses are equal, and can give rise to emittance cooling of the heavier particles. The term that gives rise to beam growth for the usual intrabeam scattering is also present but is much smaller than the cooling term when one particle is much heavier than the other. This paper derives the results found for the emittance cooling rates due to the scattering of the ions in the ion bunch by the electons in the electron bunch.