Boundary-Element Methods for Field Reconstruction in Accelerator Magnets

Magnetic fields in the aperture of particle accelerator magnets can be represented by boundary potentials, exploiting Kirchhoff’s integral equation. Depending on the formulation, magnetic measurement data can be represented by the discrete approximations of Dirichlet or Neumann data at the domain boundary. The missing Cauchy data, which are related to the tangential-field components, can then be computed by the boundary-element method (BEM) in a numerical post-processing step. Evaluating the integral equation for field reconstruction inside the domain of interest will reduce measurement uncertainties and approximation errors due to the smoothing property of Green’s kernel. Applications to the reconstruction of 2-D fields (integrated quantities from stretched-wire measurements) and 3-D fields (local quantities from measurements with moving induction-coil magnetometers) are presented.