  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...
