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The radiation pressure inside an RF cavity resonator, resulting from theLorentz force, couples the fundamental electromagnetic mode to the mechanicalmodes and may lead to static and dynamic ponderomotive instability. Theanalysis for generator driven (GD) cavity and for self-excited (SEL) cavity wasgiven 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 fromthe analysis for multiple (N) cavities (GD or SE) powered from a single sourceand regulated in vector sum. The system behaves as N virtual cavities, one withall loops present and N-1 with no loops except the tuner. After reviewingstability threshold criteria for these systems, difference control in thetuning loops is proposed as means for extending the stability range.Counter-tuning of alternating cavities is also discussed.

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