The strength and astounding simplicity of certain permanent magnet mat
erials allow a wide variety of simple, compact configurations of high
field strength and quality multipole magnets. Here we analyze the impo
rtant class of iron-free permanent magnet systems for charged particle
beam optics. The theory of conventional segmented multipole magnets f
ormed from uniformly magnetized block magnets placed in regular arrays
about a circular magnet aperture is reviewed. Practical multipole con
figurations resulting are presented that are capable of high and inter
mediate aperture field strengths. A new class of elliptical aperture m
agnets is presented within a model with continuously varying magnetiza
tion angle. Segmented versions of these magnets promise practical high
field dipole and quadrupole magnets with an increased range of applic
ability.