Theoretical and simulation study of dispersive electron cooling

In electron cooling, the transverse cooling rate is usually smaller than the longitudinal rate, especially at high energies. By introducing dispersive cooling, it is possible to redistribute the cooling rate between longitudinal and transverse planes. Theoretically, achieving dispersive electron cooling requires an ion dispersion and a transverse gradient of longitudinal friction force. The latter depends on many factors such as the relative momentum offset, transverse displacement, e-beam density distribution, and space charge effect. Therefore, several methods can be employed to achieve dispersive electron cooling based on these factors. Based on the dc electron beam, these factors and their respective impacts on the cooling rate are discussed and analyzed. For the first time, we propose a new mechanism to achieve dispersive cooling for a uniform electron beam by placing part of the ion beam outside of the electron beam. Based on a linear friction force model, we propose a simple formula to numerically estimate the cooling rate redistribution effect of these methods. The analytical results are in good agreement with Monte Carlo calculation and numerical simulation.