"Anomalous," Nonlinearly Current-Dependent Damping in CESR

In multibunch operation of the e+e- storage ring CESR, a long-range interbunch coupling force reveals itself by causing coherent transverse instabilities. We measure the damping time constant of the beam\´s coherent response to shock excitation, using single beams of 1, 3, 5, 7, or 8 bunches of e+; frequency-selective observation of a pickup signal permits identification of the multibunch modes. The long-range force predominates at low frequencies, like the effect of a resistive wall impedance, but two orders of magnitude larger; it exhibits a strongly nonlinear current dependence. Because of this, and because the source of the coupling is as yet unknown, we call the damping" anomalous." The resulting multibunch instabilities can be controlled by use of head-tail damping (positive chromaticity) and narrowband feedback.