A Two-Dimensional Non-Linear Magnetic Equivalent Circuit Model to Facilitate the Preliminary Design of a Normal Conducting Quadrupole

Normal conducting quadrupoles have been used to focus charged particle beams in synchrotrons, beam transfer lines, medical linacs, etc. for a long time. Optimization techniques based on analytical expressions combined with the use of a numerical field analysis tool exist in the literature for the design of an optimal pole tip shape. However, the initial shape and dimensions of the remaining yoke (including the pole itself and yoke base that act as the return path) are usually less well defined. This article discusses a design methodology for a normal conducting quadrupole based on a two-dimensional magnetic equivalent circuit. This approach considers the geometry of the entire magnet and the non-linear behavior of the yoke material, thereby eliminating the initial iterations. The design outcome of this exercise serves as a competent starting point and can then be used to refine the pole tip, pole taper, yoke size, and add other geometrical features to achieve the required field quality, gradient, coil considerations, etc. by employing a finite element analysis tool. An example design study to demonstrate the proposed methodology is presented.