Numerical Modeling in Magnetism Macro-Magnetism: Solution of Maxwell´s Equations – Engineering of (electro)magnetic devices Atomic Magnetism: Instrinsic Magnetic Properties Micromagnetism: Domain Dynamics, Hysteresis MFM image Micromagnetic simulation.

Macro-Magnetism Calculate Magnetic Fields and Forces BIOT-SAVART Law Maxwells Laws in Matter Vector Potential...if j=0, determination of H with „Magnetic Charges“

Boundary Element Method (BEM) The Boundary Element Method solves field problems by solving an equivalent source problem. In the case of electric fields it solves for equivalent charge, while in the case of magnetic fields it solves for equivalent currents. BEM also uses an integral formulation of Maxwell's Equations, which allow for very highly accurate field calculations. The formulations are such that differentiating the field is not a problem. Problem

Finite Element Method (FEM) Finite elements solve by breaking up a problem into small regions and solutions are found for each region taking into account only the regions that are right next to the one being solved. In the case of magnetic fields where FEM is often used, the vector potential is what is solved for in these regions. Magnetic field solutions are derived from the vector potential through differentiating the solution. This can cause problems in smoothness of field solutions. Theoretically, any partial differential equation class of problem can be solved using FEM (although some types will do better than others.) Problem

BEM AdvantagesFEM Advantages Open regions not a problem Extreme aspect ratios not a problem World space is not truncated Perfectly smooth field solutions Non linear problems easily solved Easy formulations allow many different types of problems to be solved BEM DisadvantagesFEM Disadvantages Non linear problems difficult to solve Some problem formulations are not possible Not well suited for open region problems Extreme aspect ratios can cause problems Truncated world space Fields can be noisy

Hybrid BE-FE Method When you compare the advantages and disadvantages (below), you can see that an ideal method would be to combine both methods to form a hybrid of the two. The hybrid solver takes the strengths of both methods and uses them to an advantage. The BEM handles the open regions and linear solution while the FEM handles the non-linear areas. The results are excellent open region solutions with no non-linear convergence problems.

EXAMPLE FORCES ON CRYOMAGNET OF PANDA vertical field H max = 15T

PANDA – general view beam-channel monochromator- shielding with platform Cabin with computer work-places and electronics secondary spectrometer with surrounding radioprotection

PANDA – general view

Costs Cryomagnet: € 100% stainless steel concrete screening: approx € Concrete screening with magnetic steel: €