Optimal positioning of a single local magnetic sensor for integrated dipole measurements

In this report, we seek the optimal position inside a dipole magnet where a single, small magnetic field sensor such as a Hall probe should be installed to derive with best accuracy the field integral along the magnet’s axis. An effective installation criterion would be useful for many real-time field monitoring and control applications in both synchrotron main rings and transfer lines, such as those found at CERN and in hadrontherapy centres. The main quantity of interest is the so-called magnetic length, i.e. the ratio between integral and local field measured at any given position inside the gap. First, we present a simple mathematical model which proves that, under certain conditions, an optimal position exists where the magnetic length is a constant with respect to excitation current, irrespective of the degree of saturation of the iron yoke. We then investigate analytically the impact of perturbations such as remanent field and eddy currents, which cause the magnetic length to be only approximately constant at best. Next, we analyze the computed field profiles of two representative magnets, the ISR and the ELENA bending dipoles, finding that the simulations qualitatively agree with expectations based on the analytical model. Finally, we analyze measurements of the ELENA and the HIE ISOLDE bending dipoles, finding that the ELENA results match reasonably well predictions. We conclude by summarizing the advantages and drawbacks of the solution proposed and outlining possible objectives of future work.