Building the Impedance Model of a Real Machine

Longitudinal impedance and coherent synchrotron radiation models for ThomX storage ring

“…Ideally the line impedance should be much higher than the DUT impedance. However, there is a compromise to be made between the frequency precision and attenuation of the signal with respect to the wire diameter which will be explain briefly in the measurements section [33,34]. Firstly, we started to do measurements with a wire diameter of d = 1 mm which gives a line impedance of Z L = 205.7 ± 6.0 Ω.In this case, the matching is done using a resistor of R s = Z L − Z 0 ≈ 150 Ω.…”

“…With the 0.1 mm wire, the frequency shift with respect to the impedance calculations was reduced significantly as it can be seen in Figure 10 however the attenuation gets bigger with the thinner wire [36]. Also the strong field distortion due to the insertion of the wire creates frequency shifts in impedance spectrum decreasing when the wire diameter gets smaller [33,34]. In the measurement, the peaks are broader than in the simulations as all the components of the real bellows do not resonate at the same frequency due to small variations in the bellows period which do not exist in the perfect model used for simulations.…”