A Mathematical Formulation to Predict the Harmonics of the Superconducting LHC Magnets

CERN is currently assembling the LHC (Large Hadron Collider) that will accelerate and bring in collision 7 Tev protons for high energy physics. Such a superconducting magnet-based accelerator can be controlled only when the field errors of production and installation of all magnetic elements are known to the required accuracy. The ideal way to compensate the field errors obviously is to have direct diagnostics on the beam. For the LHC, however, a system solely based on beam feedback may be too demanding. The present baseline for the LHC control system hence requires an accurate forecast of the magnetic field and the multipole field errors to reduce the burden on the beam-based feed-back. The Field Model is the core of this magnetic prediction system, that we call the Field Description for the LHC (FiDeL). The model will provide the forecast of the magnetic field at a given time, magnet operating current, magnet ramp rate, magnet temperature and magnet powering history. The model is based on the identification and physical decomposition of the effects that contribute to the total field in the magnet aperture of the LHC dipoles. Each effect is quantified using data obtained from series measurements, and modelled theoretically or empirically depending on the complexity of the physical phenomena involved. This paper presents the developments of the new finely tuned magnetic field model and, using the data accumulated through series tests to date, evaluates its accuracy and predictive capabilities over a sector of the machine.