Ballistic techniques for magnetic field calibration of large iron detectors operating in underground areas

The experimental problem of the calibration of magnetic field in large iron detectors located in underground areas is discussed. Emphasis is laid on techniques based on ballistic measurements as the ones employed by MINOS or OPERA. An experimental investigation of the precision achievable by these methods has been carried out using a full-scale prototype of the OPERA spectrometer built in Frascati in 2001. We demonstrate that a field calibration at the level of 3% can be reached and discuss in details the limiting systematics. Moreover, we provide analytical formulas to model the behaviour of the apparatus in the transient regime, keeping into account eddy current effects and the finite penetration velocity of the driving fields. These formulas ease substantially the design of the calibration apparatus. Finally, ballistic techniques are shown to match the requirements for field calibration at the next generation long-baseline neutrino experiments and are well-suited to operate in underground laboratories.