Algorithm comparison for the determination of toroidal harmonics


The classical way of expressing the field uniformity in accelerator magnets is by means of the Fourier coefficients of the trigonometric eigenfunctions of the Laplace equation also known as multipoles. When the magnets are curved (Fig. 1), higher-order terms appear and the scaling laws derived for straight magnets are no more applicable. The field reconstruction from field simulations or magnetic measurements should therefore be based on the eigenfunctions of the Laplace equation in the toroidal coordinate system, so called toroidal harmonics.

TU Darmstadt, together with the European Organization for Nuclear Research (CERN) formulated a linear inverse problem to determine the toroidal harmonics from the magnetic flux density.

In this thesis, different algorithms to solve this inverse problem shall be studied and compared on magnetic flux density measurements.