A fit-based frequency programme for the PS

Since the probes in the PS reference magnet that generate the so-called B-train are fairly short, they cannot register any change in magnetic length due to saturation. Hence the idea to derive the effective dipole magnetic field seen by the beam from measurements of revolution frequency and mean radial position over an entire cycle, to fit a saturation law, and to use the result to make a new frequency programme. Although far from new, the idea has never been implemented due to the tacit assumption that any imperfections in the existing frequency programme are taken care of by the action of the servo loops of the various beam controls. More recently, the delivery of ions at low energy from LEIR has called into question the accuracy the raw frequency programme and the idea has been revisited in a brief parasitic MD.