Extraction of 3D field maps of magnetic multipoles from 2D surface measurements with applications to the optics calculations of the large-acceptance superconducting fragment separator BigRIPS

Abstract

The fringing fields of magnets with large apertures and short lengths greatly affect ion-optical calculations. In particular, for a high magnetic field where the iron core becomes saturated, the effective lengths and shapes of the field distribution must be considered because they change with the excitation current. Precise measurement of the three-dimensional magnetic fields and the correct application of parameters in the ion-optical calculations are necessary. First we present a practical numerical method of extracting full 3D magnetic field maps of magnetic multipoles from 2D field measurements of the surface of a cylinder. Using this novel method, we extracted the distributions along the beam axis for the coefficient of the first-order quadrupole component, which is the leading term of the quadrupole components in the multipole expansion of magnetic fields and proportional to the distance from the axis. Higher order components of the 3D magnetic field can be extracted from the leading term via recursion relations. The measurements were done for many excitation current values for the large-aperture superconducting triplet quadrupole magnets (STQs) in the BigRIPS fragment separator at the RIKEN Nishina Center RI Beam Factory. These distributions were parameterized using the Enge functions to fit the fringe field shapes at all excitation current values, so that unmeasured values are interpolated. The extracted distributions depend only on the position along the beam axis, and thus the measured three-dimensional field can easily be parameterized for ion-optical calculations. We implemented these parameters in the ion-optical calculation code COSY INFINITY and realized a first-order calculation that incorporates the effect of large and varying fringe fields more accurately. We applied the calculation to determine the excitation current settings of the STQs to realize various optics modes of BigRIPS and the effectiveness of this approach has been demonstrated.