Accurate computation of transfer maps from magnetic field data

Consider an arbitrary beamline magnet. Suppose one component (for example, the radial component) of the magnetic field is known on the surface of some imaginary cylinder coaxial to and contained within the magnet aperture. This information can be obtained either by direct measurement or by computation with the aid of some 3D electromagnetic code. Alternatively, suppose that the field harmonics have been measured by using a spinning coil. We describe how this information can be used to compute the exact transfer map for the beamline element. This transfer map takes into account all effects of real beamline elements including fringe-field, pseudo-multipole, and real multipole error effects. The method we describe automatically takes into account the smoothing properties of the Laplace-Green function. Consequently, it is robust against both measurement and electromagnetic code errors. As an illustration we apply the method to the field analysis of high-gradient interaction region quadrupoles in the Large Hadron Collider (LHC)