Theory, Design and Measurement of the Brookhaven Narrow Quadrupoles

A novel approach is presented which results in mechanically simple quadrupoles producing high field gradients with modest power consumption and with very small aberrations. These lenses can be assembled either in four-fold geometrically symmetrical versions or in narrow "septum" versions without side yokes. The asymmetrical version conserves the very valuable space available for small angle secondary beams. There is no deterioration of optical properties since the four-fold magnetic symmetry is maintained in the aperture region. In addition, the fringing field is quite small. A unique magnet profile was adopted. Most general purpose iron quadrupoles are derived from the concept of four identical hyperbolic pole profiles which are quadrupole equipotentials. However, for a practical design this geometry must be severely distorted to provide space for reasonable current density coils. The present conceptual approach is to abandon the hyperbolic idea completely and treat the problem from the viewpoint of its four-fold symmetry which permits only r2 sin 2¿, r6 sin 6¿, r10 sin 10¿, etc., potential terms. Since these terms increase as the fourth power in their spatial variations, their magnitudes can be separately controlled with properly chosen physical perturbations. Using this method a quadrupole of high optical purity was produced employing a simple iron profile composed only of plane surfaces.