Shunt impedance concept in RF cavity-moving charge electrodynamics
Cavity eigen functions for vector potential make it possible to determine completely the differential equations for amplitudes of the fields induced by charged particle traversing the cavity. For many accelerator based applications such detailed description of cavity excitation problem is not necessary. It is quite sufficient to have expressions or equations for cavity voltage induced by the charge and its phase as well, maximum particle energy gain after RF cavity passage expressed in voltage unites being assumed as voltage amplitude. Usually, equivalent electrical circuit is used instead of RF cavity to make appropriate calculation, stability analysis etc., resonance frequency, quality factor and shunt impedance of the circuit being equal to appropriate parameters of the RF cavity. In this paper, the attempt is undertaken to associate cavity excitation equations with beam charge and its velocity and cavity shunt impedance as well, the deduction being made on the basis of electrodynamics equations. It is shown that complex shunt impedance concept is quite natural generalization of usual shunt impedance for electrical charge-accelerating RF cavity interaction problem. Both shunt impedance module and its phase can be calculated or measured experimentally.
CYBERNETICS AND PHYSICS, Vol. 3, No. 3. 2014, 119-123.