STUDIES OF TRANSVERSE ELECTRON COOLING

We have used a transverse instability that can be excited in an electron-cooled ion beam in order to produce beams with well-defined emittances. These beams have been cooled and the transverse cooling times have been stud- ied as functions of the emittance. Ions of different charge states (D+ ,F 6+ and Pb54+) have been used for the mea- surements to investigate the charge-state dependence of the cooling time. Comparisons are also made with numerical simulations of the cooling process. Electron cooling is a technique for reducing the emittance of stored ion beams that works best for beams of small emittances. More precisely, typical quantities like emit- tances, beam diameters, etc., shrink approximately expo- nentially with time if the velocity spread of the ion beam is small compared to that of the electron beam (and intrabeam scattering is neglected). At higher velocity spreads, the de- crease is slower than in the exponential regime. To know the cooling rate as a function of the emittance of the ion beam is important for applications of electron cooling, and in this paper this emittance-dependent rate is discussed. A method to achieve an ion beam with a transverse pro- file of a particular kind, namely a hollow beam where all particles perform betatron oscillations with the same ampli- tude, is introduced. This method allows us to measure the cooling rate as a function of the betatron amplitude of the ions. Since, in principle, any transverse beam profile can be constructed by superimposing these "elementary beams" with definite betatron amplitudes, the measurements make it possible to predict how the cooling will proceed for a beam with an arbitrary profile.