On the performance characteristics of electron ring accelerators

On the basis of our present understanding of the physical phenomena involved in an electron ring accelerator (ERA), a theoretical study is made of the performance which might be expected for an ERA. Rigorous upper bounds are obtained on the rate of energy gain, from which it is shown that, in order to prevent azimuthal instability, parameters must be selected such that (for reasonable fields, injector properties, etc., but with no safety factors) the proton energy gain is less than 80 MeV/m. Numerical examples and approximate formulas are given for the properties of rings satisfying the stability conditions for both azimuthal oscillations and ion-electron oscillations. It is found that for reasonable fields and injector properties, but without safety factors, the useable proton energy gain is less than 45 MeV/m.