Signal processing for beam position measurement

The spectrum of the signals generated by beam position monitors can be very large. It is the convolution product of the bunch spectrum and the transfer function of the monitor including the transmission cable. The rate of information flow is proportional to the bandwidth and the maximum amplitude rating of monitor complex. Technology is progressing at a good pace and modern acquisition capabilities are such that nearly all the information contained in the spectrum can be acquired with a reasonable resolution [1]. However, the cost of such a system is enormous and a major part of the information is superfluous. The objective of a beam position measurement system is generally restricted to trajectory measurements of a portion of the beam that is much larger than the finer details that can be observed with the bare signal generated by the position monitor. Closed orbit measurements are a simple derivation product of the trajectory and will not be considered further. The smallest beam portion that is of practical interest is one bunch. Hence the maximum frequency is in the order of the bunch repetition rate. Lower frequencies than the bunching frequency may be chosen either to obtain better resolution, either because it is technically easier to accomplish. The sensitivity of beam position monitors degrades quickly at low frequencies. Therefore, signals are selected at some convenient multiple of the bunching frequency and are shifted to so called baseband to match the capabilities of the acquisition system. The task of signal processing is to make a selection among the many frequencies that are available and prepare the signals for acquisition. The signal selection is done by filtering, a vast subject but it will not be treated in this paper. Three signal processing techniques will be examined from the point of view of (amplitude) resolution of a single acquisition of the beam position, dynamic range and operational frequency. They are the following: the homodyne receiver, the phase processor and the logarithmic detector. Baseband techniques are also used in practice and will be briefly mentioned to start.