A field-cancellation algorithm for constructing economical planar permanent magnet (PM) multipoles with large high-quality field apertures

In recent years studies have been initiated on a new class of multipole field generators consisting of cuboid planar permanent magnet (PM) pieces arranged in biplanar arrays of 2-fold rotational symmetry. These structures, first introduced for free electron laser (FEL) applications, are based on reducing the rotational symmetry of conventional N-pole field generators from N-fold to 2-fold. One consequence of this reduction is a large higher-multipole content in a planar PM multipole´s field at distances relatively close to the structure´s axis, making it generally unsuitable for applications requiring a large high-quality field aperture. In this paper we outline an economical field-cancellation algorithm that can substantially decrease the harmonic content of a planar PM´s field without breaking its biplanar geometry or 2-fold rotational symmetry