Improvement of field quality in quadrupole magnets by optimizing the pole profile consisting of plane surfaces

Abstract

The pole profiles of quadrupole magnets are often made circular, with a radius that can be so chosen as to reduce the error in the field due to the 12-pole contribution. In some magnets the pole face consists entirely of a few plane surfaces. We have obtained an analytical procedure which optimizes the lengths and the angles of the straight lines to eliminate the 12-pole, 20-pole and 28-pole contributions to the field error.

New method of designing pole profile in combined function magnets of high field quality

“…Analytical methods based on the conformal mapping technique 27 and semianalytical methods are also sometimes used. which solve the Poisson's equation by the finite difference method or the finite element method.…”

A group of codes for finding the pole profile in quadrupoles with high field quality

“…The optimized values of the harmonics are found from eqn. (7). The calculation however is done iteratively.…”

“…The corresponding variation in the higher harmonics (∆C 18 , ∆C 22 , ∆C 26 , ∆C 30 ) are calculated by solving eqn. (7). A small fraction (r) of these error harmonics is fed back and the new profile is calculated again by solving eqn.…”

“…Some others truncate the hyperbolic profile with straight lines at the outer edges. Poles consisting entirely of plane surfaces are also used [6,7].…”