Calculation of the Transient Response of Long Chains of Slightly Lossy Coupled Resonators

Methods of calculating and of illustrating the transient response of chains of coupled resonators are discussed. Such calculations are particularly useful in understanding the rf field behavior in linear accelerator structures, both of the drift tube and waveguide or coupled cavity types. Resonator chains are also employed in certain kinds of filters and delay lines; the methods to be discussed are applicable in these areas, as well. A frequency adjustment is presented which permits difference equations with a large time step to accurately represent the differential equations for slightly lossy coupled resonators.