Electronic damping of microphonics in superconducting cavities

In previous applications of high-velocity superconducting cavities, the accelerated beam currents were sufficiently high that the microphonics-induced frequency excursions were significantly less than the loaded bandwidth, and the power absorbed by the beam dominated the total power requirement. In new applications (CEBAF Upgrade, RIA) the beam currents will be sufficiently low that the rf power requirements will be dominated by the control of the cavity fields in the presence of microphonics. Active electronic damping of microphonics by modulation of the cavity field amplitude has been occasionally used in the past in small, low-velocity, low-gradient superconducting structures; its application to much larger, high-velocity, high-gradient structures could result in a substantial reduction of the rf power requirements. This paper presents an analytical study of various schemes for electronic damping and presents formulae to quantify the reduction of microphonics as a function of rf field modulation