3D simulation of accelerator conventional magnets with end pole defined by an analytical approach controlling multipoles and magnetic length

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/spl deg/ chamber. The such truncated poles will create an amount of multipoles that could exceed the magnet required tolerances. The magnetic length is also affected by the way that the truncation is done. 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, quadrupole, 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 multipole 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.