Stability conditions for a neutralised electron cooling beam

Charge neutralisation of the cooling electron beam, e.g. by stationary ions produced from the residual gas, is desirable to compensate the space-charge induced velocity spread which tends to reduce the cooling force. However, it has been demonstrated by Parkhomchuk and collaborators (1993) that two-stream instabilities, especially transverse dipole modes, are a serious threat to the stability. In the present report we analyse stabilising mechanisms including Landau damping, external feedback and clearing of reflected electrons. Experimental results at LEAR (the Low Energy Antiproton Ring at CERN) are discussed in a companion paper at this conference.