Magnet end design: The main injector dipoles

From the accelerator designer standpoint, one of the quantities of interest in a magnet is the axially integrated transverse field. It is easily shown that the latter satisfies the equations of 2D magnetostatics. This is the basic theoretical result needed to design accelerator magnet ends. Unfortunately, axially integrated fields must be obtained from accurate 3D field maps and magnets ends have historically been designed using a cut and try approach. To a certain extent, this remains true even today; however, the advent of reliable 3D magnet design codes now permits to substantially reduce the costs associated with the construction of various prototypes. In this paper, the theory of magnet end design is reviewed. The design of the end of the dipole magnets of the proposed Fermilab Main Injector is analyzed in a detailed manner using TOSCA, a well-established 3D finite element code. Provided the limitations of the code are well understood by the user, the integrated field profile is satisfactorily predicted