Finite-Element Simulation of an Accelerator Magnet: an Exercise

TL;DR

This paper presents an educational exercise where students learn to construct, simulate, and analyze an accelerator magnet using finite-element methods with freely available software, enhancing understanding of FE theory and implementation.

Contribution

It introduces a comprehensive exercise for students to build and simulate an FE model of an accelerator magnet, including implementing core FE algorithms and developing post-processing routines.

Findings

Students gain practical understanding of FE simulation of magnets.

Implementation of a simple FE solver enhances learning.

The exercise provides freely available resources for education.

Abstract

This note describes an extended exercise on the finite-element (FE) simulation of an accelerator magnet. The students construct and simulate a magnet model using the FEMM freeware. They get the opportunity to exercise on the theory of FEs, including Maxwell equations, magnetoquasistatic formulation, weighted residual approach, choice of appropriate FE shape functions and algebraic system of equations, thereby guided by fill-in sheets. They are invited to implement the most crucial parts of a simple FE solver. Finally, the own software is used to simulate the magnet once more and to develop some problem-dedicated post-processing routines. The exercise educates students in accelerator physics and electrical engineering on the construction and simulation of accurate and manageable FE models, the algorithms behind a standard FE solver and some ideas to extend a FE solver for own purposes. All necessary files to carry out the exercise are freely available.