A magnetic quadrupole from rectangular permanent magnets

An analytical model of iron-free pure permanent magnet (PPM) quadrupole consisting of rectangular magnets is presented. Its strength is tunable via the retraction of four magnet arms so that it can be axially compact also. Its working principle is given by a theory of ideal rectangular PPM quadrupole developed from the theory of planar PPM undulators. It is simple to build and tune for minimization of the undesired higher harmonics arising in practice. It has demagnetizing fields limited to the linear region of the B–H curve. Its field quality is not degraded by anisotropic nonunit permeability of rare-earth alloys (like NdFeB, SmCo). Its parameters are suitable between ultra-compact high-gradient Halbach quadrupoles and low-gradient-medium-aperture iron pole current-fed quadrupoles. It can be suitable for applications like focussing inside a free electron laser cavity, horizontal focussing between contiguous undulators in XFELs or final focussing in scattering experiments.