International Journal of Numerical Modelling vol:27 issue:3 pages:472-484
A Stern–Gerlach magnet applies a field gradient in order to deflect particles such that their magnetic moment can
be determined. The design of such magnets is based on finite-element (FE) simulations of the magnetic field and
its gradient. However, inaccuracies arise when these quantities are calculated from an FE solution for the magnetic
vector potential by numerical differentiation. For first-order FE shape functions, the discretisation error for the
field gradient may even fail to converge. An improved post-processing approach marks a region in the magnet
aperture where the field is post-processed by matching a local analytical solution with the obtained FE solution.
The local solution allows to derive values for the magnetic field and its gradient without reducing the convergence
order of the discretisation error. The method is validated against the analytic solution for a two-wire configuration
and is applied for the design of a Rabi-type Stern–Gerlach magnet.