Shunt impedance

The shunt impedance is a term used in radio frequency technology, specifically from the field of cavity resonators. Cavity resonators are often used in particle accelerators, they serve there the acceleration, and the position and intensity measurement of a particle.

A particle passes through a resonator, then the shunt impedance between the proportionality factor of the power which is withdrawn from or supplied to the beam, and the square of the beam current, which is suitably guided by the cavity:

The shunt impedance have the dimension of an electrical resistance.

Measurement of the shunt impedance by Störkörpermethode

For determining the shunt impedance of a cavity resonator, the so-called Störkörpermessung can be applied. The idea is that on a small dielectric object by the electric or magnetic field inside the resonator is polarized, thereby changing characteristics of the resonator. The bluff body is usually made of a material with high electrical permeability, for example, Teflon. There are various methods to obtain a value for the shunt impedance from this frequency reduction, which are known are the resonant and non-resonant Störkörpermethode.

Resonant Störkörpermessung

Here, the resonance frequency of the resonator in dependence on the position of the bluff body is considered. Assuming a very small bluff body that does not deform the field, the magnitude of the electric field at the position of the bluff body resulting from

In this case, refers to the stored energy in the cavity field, the actual resonance frequency of the resonator, the resonant frequency and the few Störkörperkonstante. This is given by

In this case, the volume of the bluff body, the dielectric constant and the electrical permeability of the bluff body.

Integrated to the electric field along the measured axis, one obtains the voltage of a charged particle passing through said axis.

From the relationship between power, voltage and resistance is given as the shunt impedance

It is the power loss that is lost due to resistive effects in the walls of the resonator.

Non-resonant Störkörpermessung

In contrast to the resonant method is not the resonant frequency, but the reflection factor is monitored at a fixed frequency in the non-resonant method. The reflection factor is the ratio of the amplitude of the resonator in the a - and the outgoing wave from the resonator and their phase relationship.

This is in general complex. From the deviation of the complex reflection coefficient at the passage of the bluff body to the undisturbed case, a value for the magnitude of the electric field can now be similar to the resonant method determined.

In this case, denotes the coupling coefficient that describes the adaptation of the characteristic impedance of the resonator to the connected cable. This results from the reflection factor at the resonant frequency.

Referred to the unloaded quality factor. The further calculation is analogous to the resonant measurement.