Longitudinal profile and effective length of a conventional dipole magnet

Magnetic saturation in the vicinity of longitudinal edges results in a small decrease in effective length with increasing excitation current. This phenomenon does not pose any problem in a machine where all dipoles are identical. In the Fermilab Main Injector lattice, dipoles of two different physical lengths are used. The effective length variation is caused by end effects and is essentially independent of the physical length of each type of magnet. However, the relative variation is larger for the short magnets. Since all dipole magnets are on a common bus, the closed orbit is modified in an energy dependent way. Although this effect can be compensated with corrector magnets, a better approach is to design the dipole magnets so as to minimize absolute effective length variations. This can be accomplished with a suitable longitudinal pole profile in the end region. Theoretical considerations and numerical calculations leading to the choice of this profile are presented