Pure multipoles from strong permanent magnets: analytic and experimental results

We present the construction of arbitrary multipole field configurations from strong permanent magnets for trapping charged or neutral particles. A general analytic method for the design of three-dimensional magnetic multipoles is discussed for an idealized continuously varying magnetisation taking advantage of the superposition principle. Simple recipes for constructing magnetic dipole and quadrupole fields are given with two types of elements, axially and radially magnetised rings. Cylindrical magnet components not only give free access to the experimental region of interest, but also allow for some tunability to reduce undesirable higher multipole orders. Measurements confirm theoretical predictions achieving useful magnetic fields of 1 T and steep gradients of 3 T/cm with high purity over several ccm.