BEM-FEM coupling for the electromagnetic simulation of superconducting accelerator magnets

The European Centre for Nuclear Research CERN develops and maintains the world's biggest particle accelerator complex. Particles are guided along a circular path by a magnet system, and once per round they are accelerated in so-called cavities. Two counter-rotating particle beams are intersected at maximum kinetic moment. Elementary particles are produced in the collisions, which had existed in our universe only fractions of a second after the Big Bang. The detection of these particles, and thus the validation of theoretical models of the fundamental laws of physics, is the actual goal of the CERN laboratory.

Superconducting magnets for accelerators weigh several dozens of tons and must be manufactured in tolerances below 20 micrometers. Prototypes cost several hundred thousand swiss francs. Comprehensive simulation and mathematical optimization are therefore indispensable for an economic design process. The required relative accuracy of 1e-6 in magnetic-field calculations cannot be achieved with commercially available finite-element software. We show that the use of BEM-FEM coupling is a natural choice for the simulation of superconducting magnets.