Aperture Limits Due to the Presence of Higher Magnetic Field Multipoles

Superconducting magnets tend to produce magnetic fields which have larger higher systematic multipoles and larger random multipoles than conventional magnets. The current carrying coils in superconducting magnets are usually not shielded by the iron yoke, and thus the magnetic field shape is determined by the current distribution rather than the shape of an iron surface. Higher systematic magnetic field multipoles are then generated by necessary deviations of the current distribution from the ideal desired distribution; random multipoles are generated by errors in the location of the current carrying conductors. The presence of these undesired field multipoles will limit the good field aperture of the accelerator. One effect of these multipoles is that they will distort the working line, the dependencies of the ν-values, ν
_X
ν
_y
, on the momentum Δp/p. Another effect of these multipoles is to produce linear and non-linear stop bands. This paper is concerned primarily with aperture limits due to the distortion of the working line. Distortion of the working line produced by the lower field multipoles is usually corrected with a correction coil system provided for that purpose. The working line distortion that remains is that due to higher field multipoles that cannot be corrected with the correction coil system. The magnetic field due to the higher multipoles vary like some high power of r, the radial distance from the magnet center, like at least r6 in the case of the CBA (Colliding Beam Accelerator at BNL).