The effect of beam intensity on the estimation bias of beam position

For the signals of the beam position monitor (BPM), the signal-to-noise ratio (SNR) is directly related to the beam intensity. Low beam intensity results in poor SNR. The random noise has a modulation effect on both the amplitude and phase of the BPM signals. Therefore, the beam position measurement has a certain random error. In the currently used BPM, time-averaging and waveform clipping are used to improve the measurement. The nonlinear signal processing results in a biased estimate of beam position. A statistical analysis was made to examine the effect of the SNR, which is determined by the beam intensity, on the estimation bias. The results of the analysis suggest that the estimation bias has a dependence not only on the beam position but also on beam intensity. Specifically, the dependence gets strong as the beam intensity decreases. This property has set a lower limit of the beam intensity range which the BPM's can handle. When the beam intensity is below that limit the estimation bias starts to vary dramatically, resulting in the BPMs failure. According to the analysis, the lowest beam intensity is that at which the SNR of the generated BPM signal is about 15 dB. The limit for NSEP BPM, for instance, is about 6Ell. The analysis may provide the BPM designers with some idea about the potential of the current BPM'S