Apsimon, Robert James and Burt, Graeme Campbell (2017) An improved equivalent circuit model of a four rod deflecting cavity. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 847. pp. 52-60. ISSN 0168-9002
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Abstract
In this paper we present an improved equivalent circuit model for a four rod deflecting cavity which calculates the frequencies of the first four modes of the cavity as well as the $\frac{R_{T}}{Q}$ for the deflecting mode. Equivalent circuit models of RF cavities give intuition and understanding about how the cavity operates and what changes can be made to modify the frequency, without the need for RF simulations, which can be time-consuming. We parameterise a generic four rod deflecting cavity into a geometry consisting of simple shapes. Equations are derived for the line impedance of the rods and the capacitance between the rods and these are used to calculate the resonant frequency of the deflecting dipole mode as well as the lower order mode and the model is bench-marked against two test cases; the CEBAF separator and the HL-LHC 4-rod LHC crab cavity. CST and the equivalent circuit model agree within $4\%$ for both cavities with the LOM frequency and within 1$\%$ for the deflecting frequency. $\frac{R_{T}}{Q}$ differs between the model and CST by $37\%$ for the CEBAF separator and $25\%$ for the HL-LHC 4-rod crab cavity; however this is sufficient for understanding how to optimise the cavity design. The model has then been utilised to suggest a method of separating the modal frequencies in the HL-LHC crab cavity and to suggest design methodologies to optimise the cavity geometries.