{'fraction_non_alphanumeric': 0.01728276524243879, 'fraction_numerical': 0.0, 'mean_word_length': 5.129411764705883, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Longitudinal Beam Transfer Function Measurement with Parametric System Identification

Collisions of particles of high kinetic energy are used as a tool for research in Particle Physics, where their kinetic energy is retrieved in specially designed accelerators. A way of retrieving information about the momentum distribution of a coasting particle beam in such an accelerator is the Beam Transfer Function (BTF) measurement, which is widely used for storage rings. When the BTF is applied to a beam that is kept stable for a rather short time period in the Proton Synchrotron Booster at CERN, structures in the injected beam add a substantial amount of noise to the measurements, which specifically leads to fluctuating asymptotic values of the integrated real part, here called the Base-Line Offset (BLO). In this report, it is demonstrated how the BTF and its integrated real part are influenced by noise and by some physical parameters. The procedure of external excitation of the sensitive beam is analysed to find good conditions for the BTF measurements in order to reduce the impact of the noise. Measurements reveals a relationship between the excitation power and the time at which an alteration of the momentum distribution can be detected. This suggests that a restricted measurement time is not a problem. The report compares a number of non-parametric methods common for BTF measurements with black-box Prediction Error Methods (PEMs) in theory, simulations and measurements at the PSB. In particular, a general expression for the BLO variance is retreived. The PEMs show the best results and a model of the measurement environment further motivates their usage. The investigations also find that the time-gated estimate is closely related to another smoothed non-parametric estimate and that it has exactly the same BLO as the empirical transfer function estimate. A relation between two common measures of the momentum spread (standard deviation and FWHM) is derived for some common distributions. CERN = European Laboratory for Particle Physics, Geneva, Switzerland