Ponderomotive Instability of RF Cavities with Vector Sum Control, and Cure By Difference Control

Abstract

The radiation pressure inside an RF cavity resonator, resulting from the Lorentz force, couples the fundamental electromagnetic mode to the mechanical modes and may lead to static and dynamic ponderomotive instability. The analysis for generator driven (GD) cavity and for self-excited (SEL) cavity was given by Schulze in 1971 and by Delayen in 1978, respectively. Since that time, little or no new analytical work - until now. Here are presented results from the analysis for multiple (N) cavities (GD or SE) powered from a single source and regulated in vector sum. The system behaves as N virtual cavities, one with all loops present and N-1 with no loops except the tuner. After reviewing stability threshold criteria for these systems, difference control in the tuning loops is proposed as means for extending the stability range. Counter-tuning of alternating cavities is also discussed.