Circular attractors as heating mechanism in coherent electron cooling

Abstract

We show that under certain conditions a longitudinal mismatch between an electron and a hadron beam in a coherent electron cooling (CeC) scheme creates a circular attractor in the longitudinal phase space of the cooled hadrons. Formation of an attractor completely stops the cooling and results in anticooling (“heating”) causing small synchrotron amplitudes to grow to the attractor’s radius, rather than being damped. We present a theory of this effect, compare the analytical results with simulations and derive tolerances to possible sources of the longitudinal mismatch. We further show that under certain conditions a “weak” attractor, affecting hadrons with large synchrotron amplitudes, can appear in the hadrons’ longitudinal phase space and explain that formation of such an attractor does not require the presence of any mismatches.