Using Magnetic Moment for Field Reconstruction in Accelerator Magnets and Particle Tracking

Achieving accurate transfer maps for realistic beamline elements hinges on obtaining precise 3-D magnetic field data for both straight and curved beamlines. Among various numerical methods for electromagnetic field calculations, boundary element methods can offer results that strictly comply with Maxwell’s equations. In this study, we use discrete magnetic moments for field reconstruction, storing magnetic field data locally using spherical harmonics conveniently without the need for integration. It shows efficient evaluation of arbitrary static magnetic fields, resulting in analytical representation of fields that can be differentiated and integrated. Leveraging the reconstructed field data, we use truncated power series algebra (TPSA) to compute precise design orbits and corresponding transfer maps.