During the design of a magnet, people generally
pay particular attention to get the largest
transverse section with small contribution of
undesirable multipoles, and the 2D cross-section
is adjusted in that way with a good accuracy. But
the poles are often cut with sharp ends in the
beam direction. Otherwise, in order to minimize
the stray field to avoid interaction with other
elements on the beam lines and corner saturation,
it is common to define a simple 45° chamfer. The
such truncated poles will create an amount of
multipolar components that could exceed the
magnet required tolerances. The magnetic length
is also affected by the way that the truncation
is done. This problem is all the more crucial
since the magnet is short and/or the order of the
desired multipole is low. We propose in this
paper a handy analytical model that allows both
to control integrated focusing forces and magnetic
lengths for each type of conventional magnets
(dipole, quadripole, sextupole). The different end
pole profiles are simulated with the 3D-program
TOSCA for the dipole and the quadrupole cases. To
estimate a possible damaging of optical qualities
introduced by the end pole profile, we compare
the multipolar components obtained by a 2D
harmonic analysis at the magnet center, with an
integrated one along the beam axis, taking into
account the entire stray field. The results are
then compared with those of the sharp end case. |
