Radiation damping partitions and RF-fields

In his classical paper “Radiation Effects in Circular Accelerators” K.W. Robinson (1958) has shown that the damping partitions in a circular machine cannot be changed by a radio-frequency field. The proof given there is quite general and valid for any RF-field, provided it is not so strong that it changes the equilibrium orbit appreciably. However, the physical mechanisms which prevent the possibility to alter the damping partitions is not very transparent. As a consequence, so-called “damping cavities” are still proposed from time to time. Here we want to illustrate the underlying physical principles by going in detail through the beam dynamics for the simple case of a cavity operating in a dipole (deflecting) mode and which is located in a region of finite dispersion in a storage ring