Beam impedance measurement by the wire method using a synthetic pulse technique

The coaxial wire method is widely used to simulate the image current and the electromagnetic field of a bunch. Measurements are usually performed in frequency (impedance) or time-domain (k-parameter). Some limits of validity and possible sources of error applying this simulation method are discussed. In general one may expect correct results if measurements are restricted to single localized impedances much smaller than the characteristic impedance of the coaxial line (beampipe with center wire). In case of more than one localised small impedance in a given beampipe time-filtering can be applied, provided there is sufficient spatial separation to reduce the problem to the case of isolated single impedances and to eliminate multiple reflections from nonmatched 50 ohm transitions at the end of the beampipe. The technique consists in generating a synthetic pulse in time domain via FFT, from measurements taken in the frequency domain. This leads to higher spectral power density than realtime or sampling pulse measurements thus giving higher dynamic range and better reproducibility. The impedance Z(ω) as well as the loss parameter k as a function of the bunch length l can then be deduced by computations