Landau damping of collective betatron oscillation in a quasi-isochronous electron storage ring

This paper shows the derivation of analytical formula for the damping of collective betatron oscillation by longitudinal radiation excitation. The betatron phase spread is produced by radiation excitation in energy, in combination with a finite chromaticity. This spread damps the collective betatron oscillation through Landau damping. Especially in quasi-isochronous operation, this can be much stronger than radiation damping. We expect strong damping when the chromaticity is large, whether its sign is positive or negative.