A semi-analytical method to generate an arbitrary 2D magnetic field and determine the associated current distribution

This reports describes a novel method based on polynomial algebra techniques which aims to determine the transverse position of N current wires perpendicular to a plane in which the induced 2D magnetic field map shall exhibit a given multipole expansion at one or several specified locations. Rather than a case-by-case comparative study of the method with other existing ones, we will insist on the details of the method itself and then illustrate its potential to the design of many magnet classes, from very pure 2n-pole magnets to more exotic components producing a magnetic field with more complex characteristics, such as FFAG magnets, mass-less septa or magnetic collimators.