Instabilities of cooled antiproton beam in recycler

The more beam is cooled, the less stable it is. In the 3.3 km Recycler Ring, stacked 8 GeV antiprotons are cooled both with stochastic (transversely) and electron (3D) cooling. Since the machine is staying near the coupling resonance, coupled optical functions should be used for stability analysis. To stabilize beam against the resistive wall instability, a digital damper is used. Digital dampers can be described as linear operators with explicit time dependence, and that makes a principle difference with analogous dampers. Theoretical description of the digital dampers is presented. Electron cooling makes possible a two-beam instability of the cooled beam with the electron beam. Special features of this instability are described, and the remedy is discussed.