Coaxial Wire Method Adapted to Weakly Coupled Resonator Mode for LHC RF Fingers Evaluation

In high intensity particle accelerators, RF contact fingers are commonly used to carry the beam induced image current. In addition, they reduce beam impedance by shielding the outer bellows required to compensate mechanical displacements between components. In order to assess the resulting beam impedance from a specific bellow/RF finger configuration, RF measurements are routinely carried out. During these measurements, it was observed that cavity modes in the volume between the fingers and the bellow undulation arise. These resonances occur at significantly higher frequencies than the expected frequency range of interest. Due to their broadband nature, the tails of the imaginary part of these resonances reach into the lower frequency range of interest where it contributes to the beam coupling impedance of the device. For proper evaluation of this contribution, a time domain delay technique in TDT (time domain transmissiometry) was used in order to overcome shortcomings that arise if the classical coaxial wire method is applied to these structures. We present the theory of our method and discuss it in view of the data measured on deformable fingers that were studied for the LHC.