Simulations of rhic coherent stabilities due to wakefield and electron cooling

The electron cooling beam has both coherent and incoherent effects to the circulating ion beam. The incoherent longitudinal cooling could reduce the ion beam energy spread and hence cause ´over-cooling´ of the ion beam. Depending on the beam densities and cooling length, the coherent interaction between the ion and electron beam could either damp or anti-damp the ion coherent motions. Using the tracking codes, TRANFT, the threshold for ´over-cooling´ has been found and compared with theoretical estimation. The transverse coherent effect of electron cooling has been implemented into the codes and its effect for the bunched ion beam is shown.