AbstractThe strength and astounding simplicity of certain permanent magnet materials allow a wide variety of simple, compact configurations of high field strength and quality multipole magnets. Here we analyze the important class of iron-free permanent magnet systems for charged particle beam optics. The theory of conventional segmented multipole magnets formed from uniformly magnetized block magnets placed in regular arrays about a circular magnet aperture is reviewed. Practical multipole configurations resulting are presented that are capable of high and intermediate aperture field strengths. A new class of elliptical aperture magnets is presented within a model with continuously varying magnetization angle. Segmented versions of these magnets promise practical high field dipole and quadrupole magnets with an increased range of applicability.