Damping/cooling sum rules in accelerators

I remark that, when formulated appropriately, the damping sum rules for many beam cooling phenomena are in fact particular instances of the same general sum rule. I draw attention to the formulas of Csonka and of Derbenev and Skrinsky, who both showed that under very general circumstances, the total damping rate for a Hamiltonian system acted on by frictional forces is the divergence in momentum space of the frictional force: the individual formulas for radiation damping, ionization cooling, electron cooling and laser cooling are all special cases of this general formula. This places the damping sum rules in a broader context, and gives a deeper understanding of beam cooling.