A Laplace expansion solution technique for 2D simulation of PPM fields

Summary for only given. The magnetic fields generated by periodic permanent magnet (PPM) stacks can be approximated at 2-dimensional with axial symmetry. For such systems with Laplacian fields, it is possible to obtain field solutions in the source-free region around the symmetry axis from a knowledge of the on-axis magnetic potential (or field) by application of the Laplace expansion solution method. This technique employs an incomplete power series expansion of a scalar potential function in the transverse variable where the series coefficients are axial derivatives of the on-axis potential (or field). By approximating a PPM stack with an equivalent system of magnetic coils, the Laplace expansion solution technique can be applied to accurately calculate the 2D off-axis magnetic field of the stack. This solution technique has been implemented in a compact, flexible, and extremely fast numerical code, lesPPM. The PPM stack geometry is used to construct an equivalent coil system, which can include key design elements such as end-effects and variation of PPM parameters (period, radius, magnet strength, number of periods, etc.).