Variable strength focussing with permanent magnet quadrupoles

Recent development of high field permanent magnet quadrupoles opens up their use in a variety of beam line applications. Various approaches have been suggested to adjust the quadrupole strength by rotation of the quadrupoles, but these have the undesirable feature of coupling the motion in the two transverse directions. In the present work, general symmetry arguments are used to derive the special form of the symplectic matrices which apply to configurations consisting of several rotated quadrupole disks. We show that a 'sandwich' of three rotated quadrupole disks lead to approximate decoupling of the motion in the two transverse directions, and a 'sandwich' of five rotated disks leads to exact decoupling. In addition, a simple rotatable doublet configuration is shown to lead to exact decoupling and is proposed as a basic 'building block' for adjustable doublet and triplet permanent magnet quadrupole combinations. Our conclusions are valid even if the basic quadrupole fringing fields are taken into account. (orig.)