  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.
