IMP/CAS, Lanzhou, People’s Republic of China
We develop a formula including the low-beta effect and the influence of long cable issues for estimating the original signal of cold BPMs. A good agreement between the numerical and the measured signal with regard to two kinds of beam commissioning, helium and proton beams, in a low-beta helium and proton superconducting linac, proves that the developed numerical model could accurately estimate the output signal of cold button BPMs. Analysing the original signal between the first and the last cold BPM in the cryomodule, it is found that the signal voltage in the time domain is increased with the accelerated beam energy. However, the amplitude spectra in the frequency domain has more high frequency Fourier components and the amplitude at the first harmonic frequency reduces a lot. It results in a decline of the summed value from the BPM electronics. The decline is not proportional to a variety of the beam intensity. This is the reason why BPMs give only relative intensity and not absolute value for low-beta beams with a Gaussian distribution.
