Evaluation of magnetic forces in permanent magnets

The numerical evaluation of magnetic forces exerted by permanent magnets is usually performed by two methods, the integration of the Maxwell stress tensor or by means of virtual displacements and energy balance. In this paper, we will review previous works on this subject, where controversy exists due to the sign of the magnetic energy stored in the magnet itself. We will check the theoretical work in the matter with numerical results from a number of FEM codes, as Ansys, Opera and Quickfield. Several examples of application will be provided. One of those will be the particular case of a phase shifter under development for the XFEL (European X-Ray Free Electron Laser) project. Its purpose is to adjust the phase between two consecutive undulator segments. The magnetic field is obtained in this device through a Halbach hybrid configuration with Nd-Fe-B permanent magnets and Fe-Co poles.