Analytic representation of cyclotron magnetic field

A model has been developed for the rapid but accurate calculation of the static magnetic field in the Chalk River cyclotron. The field is expressed in terms of elementary functions which can be handled efficiently in differential-algebra trajectory integrations. Maxwell´s equations are satisfied exactly. Each of seven subdivisions of the superconducting coils is treated by a moment expansion about a central circle. Each pole is modeled as a uniformly magnetized semi-infinite prism. Monopoles and dipoles at the vertices of the polygonal pole faces correct for departures from the true pole shape. Uniform distributions of dipole strength along the edges of the pole-face polygons correct for the local inappropriateness of the assumption of uniform magnetization. The contributions of the yoke and of other relatively distant parts of the structure to the held in the region of particle acceleration are represented by low-order polynomials. Some of the source parameters are obtained by fitting to the measured values of B_z in the horizontal plane of symmetry