An orbit fit program for localizing errors in RHIC

Many errors in an accelerator are evidenced as transverse kicks to the beam which distort the beam trajectory. Therefore, the information of the errors are imprinted in the distorted orbits, which are different from what would be predicted by the optics model. In this note, we introduce an algorithm for fitting the orbit based on an on-line optics model. By comparing the measured and fitted orbits, we first present results validating the algorithm. We then apply the algorithm and localize the location of the elusive source of vertical diurnal variations observed in RHIC. The difference of two trajectories (linear accelerator) or closed orbits (storage ring) should match exactly a betatron oscillation, which is predictable by the optics model, in an ideal machine. However, in the presence of errors, the measured trajectory deviates from prediction since the model is imperfect. Comparison of measurement to model can be used to detect such errors. To do so the initial conditions (phase space parameters at any point) must be determined which can be done by comparing the difference orbit to prediction using only a few beam position monitors (BPMs). The fitted orbit can be propagated along the beam line based on the optics model. Measurement and model will agree up to the point of an error. The error source can be better localized by additionally fitting the difference orbit using downstream BPMs and back-propagating the solution. If one dominating error source exist in the machine, the fitted orbit will deviate from the difference orbit at the same point.