Experimental studies of circular attractors in the first rf-based electron cooler

In electron coolers, under certain conditions, a circular attractor (CA) can appear in either a longitudinal or a transverse phase space of cooled ion bunches. In the presence of an attractor, ions with small amplitudes of synchrotron or betatron oscillations are getting excited rather than being damped. This effect was observed at several nonrelativistic electron coolers with a direct current electron beam. Experimental studies of circular attractors at electron coolers utilizing rf-accelerated electron bunches, where this effect becomes particularly important, are lacking. We report CA studies at the low energy RHIC electron cooler (LEReC)-the first rf-based relativistic electron cooler. We derive formulas defining conditions for a CA appearance, perform dedicated experiments, and compare the measurements' results to the theoretical predictions.