Abstract
Coupling impedance values of accelerator components can be obtained from standard bench measurements based on the coaxial wire method. Longitudinal impedance is obtained with one wire and the transverse impedance with a twin wire inserted into the ``device under test.'' The coupling impedance follows from the interpretation of the scattering coefficients from a network analyzer. In this paper, models and formulas applicable to the interpretation of the data are collected and reviewed. The paper is focused on lumped and distributed kicker magnets, for which a simulated measurement is numerically analyzed with the results graphically presented. This study suggests that the application of the standard lumped formula or the simple log formula for distributed impedances is appropriate.
Highlights
The driving terms of instabilities in accelerators/storage rings always depend on the beam surroundings which are conveniently described by impedances [1,2].Establishing and maintaining a coupling impedance budget becomes an important part of designing a high current accelerator
In the application of the above formulas it is assumed that the characteristic impedance RC of the reference wire/beam tube is fully matched to the network analyzer impedance R0
The improved impedance expressions require the knowledge of the electrical length of the device under test and one would expect that its accuracy decreases for shorter devices due to the signal noise
Summary
Storage rings always depend on the beam surroundings which are conveniently described by impedances [1,2]. The estimates need to be confirmed by impedance bench measurements [6]. Coupling impedance bench measurements discussed here are performed with a network analyzer which provides the scattering coefficients, S21 and S11 , of the DUT and the reference. The standard formulas used to interpret the measured data were all derived in the framework of transmission line theory. Notwithstanding its limitations, transmission line analysis represents the proper framework for the interpretation of coupling impedance bench measurements. The model of a transmission line kicker magnet is developed and several formulas intended for a distributed wall impedance are collected and discussed. The theoretical forward scattering coefficients of prototypical models of a lumped kicker and of a transmission line kicker magnet are in a simulated wire measurement numerically interpreted via the various formulas. Hahn and Pedersen (HP) formula [16] for lumped and to the simple Walling et al [17] log formula as appropriate for the interpretation of the wire measurements
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