Diffractive model of the high-frequency impedance

Abstract

High-frequency diffraction can be described by iterations based on an approximate formulation of the boundary conditions. The method formulated is analogous to the Born series of scattering theory. It is used to study the interaction of short bunches with the beam environment in terms of the impedances. The impedances of typical elements of an accelerator structure are obtained. The crosstalk between elements, the impedance of a periodic array, and the effect of a taper are discussed. The method can be applied to a cavity of an arbitrary shape.

Coupling impedance for modern accelerators

“…The integral equation that is equivalent to Maxwell's equations is solved by iteration using approximate boundary conditions [42,89]. This approach is very close to the diffraction models discussed by Bane and Sands [6,7] and by Palmer [90,92,93].…”

“…This assumption is probably also unsatisfactory if the modes are to be understood as those of a closed cavity unperturbed by the beam pipe openings [41].…”

“…Trapped modes are narrow resonances observed above the cutoff frequency both in experiments [28] and in numerical calculations [41]. Their field pattern corresponds to modes localized within a cavity with a relatively large Q-factor.…”

“…For an array of cavities with a large number of cavities, the interference can drastically change the impedance. Another example where the interference is important (two adjacent cavities) is considered by Heifets [42].…”

“…Effectively, only the modes that have frequencies below or comparable to the cutoff frequency w,.,. N c/u of the beam pipe with radius a contribute to the narrow-band impedance [42]. The widths of the resonance peaks above the cutoff frequencies rapidly become large and their height decreases.…”