Schottky Based Intensity Measurements and Errors Due to Statistical Fluctuations

The beam intensities at the Extra Low ENergy Antiproton ring ELENA are too low for standard beam current transformers and, thus, are measured with longitudinal Schottky diagnostics. This method is already successfully used at the Antiproton Decelerator since the commissioning of this machine. The fact that Schottky noise is a statistical phenomenon implies statistical errors of these measurements. Simple analytical formulas describing the statistical error to be expected as a function of the frequency spread of the band considered, the time resolution chosen and the background noise have been derived. On the one hand, low revolution harmonics and, in turn, frequency spread of the band analysed lead to large measurement errors as this situation corresponds to low momentum resolution of the resulting distribution describing the beam. At very large revolution harmonics and, thus, frequency spreads of the band analysed, the measurement error increases again due to additional contributions from the background noise.