Optimum lattice functions for electron cooling

Cooling down time measurements carried out at LEAR with 4.2 MeV/nucleon Pb54+ ions and various combinations of lattice functions led to unexpected results. Notably, a finite dispersion was found to decrease strongly the horizontal cooling down times. Furthermore, intermediate betatron functions yielded shorter cooling down times than large ones and an increase of the cooler length by a factor 2 did not lead to the expected increase in the cooling rate. The aim of this report is to explain, at least qualitatively, the experimental observations.