Analytical calculation of three-dimensional magnetic fields for insertion devices

To analyze how insertion devices affect electron beam dynamics, it is necessary to know the three-dimensional distribution of the magnetic field. This is of particular value for non-standard wiggler designs, such as with trapezoidal or staggered magnetic blocks, or with alternate pole canting. It is generally shown in this paper that by knowing the two-dimensional distribution of the magnetic field at the median plane of the insertion device, it is possible to calculate the three-dimensional distribution of this field over all space. The analytical expressions for the magnetic field components are derived for the general case, both for planar and non-planar insertion devices. The obtained magnetic field satisfies Maxwell equations