Orbital stability of the high-current betatron

Orbital stability of the high-current betatron is analyzed. In this modified betatron a toroidal magnetic field is added to the conventional betatron magnetic field. This increases substantially the space charge limit during injection. It gives rise, however, to new problems during acceleration, such as ring stability, Fermi drift, and orbital resonances. A detailed analysis is presented showing that two serious problems may arise: (i) The beam becomes highly unstable when the net focusing force on it becomes zero. The dominant instability in this region is the Fermi drift. This may, however, be utilized in extracting the beam. (ii) Errors in the vertical (betatron) magnetic field result in driven resonances that must be crossed during acceleration. The amplitude growth of the transverse betatron oscillations due to these resonances is negligible up to very high γ (low n resonances). In practice, it may become very difficult to cross the n=1 resonance. Thus, extracting the beam again making use of the Fermi drift while n>1 is preferable.