Computation of ChargedParticle Transfer Maps for General Fields and Geometries Using Electromagnetic BoundaryValue Data
Abstract
Threedimensional field distributions from realistic beamline elements can be obtained only by measurement or by numerical solution of a boundaryvalue problem. In numerical chargedparticle map generation, fields along a reference trajectory are differentiated multiple times. Any attempt to differentiate directly such field data multiple times is soon dominated by "noise" due to finite meshing and/or measurement errors. This problem can be overcome by the use of field data on a surface outside of the reference trajectory to reconstruct the fields along and around the reference trajectory. The integral kernels for Laplace's equation that provide interior fields in terms of boundary data or boundary sources are smoothing: interior fields will be analytic even if the boundary data or source distributions fail to be differentiable or are even discontinuous. In our approach, we employ all three components of the field on the surface to find a superposition of singlelayer and doublelayer surface source distributions that can be used together with simple, surfaceshapeindependent kernels for computing vector potentials and their multiple derivatives (required for a Hamiltonian map integration) at interior points. These distributions and kernels are found by the aid of Helmholtz's theorem (or equivalently, by Green's theorem). A novel application of the Diracmonopole vector potential is used to find a kernel for the singlelayer distribution. These methods are the basis for mapgenerating modules that can be added to existing numerical electromagnetic fieldsolving codes and would produce transfer maps to any order for arbitrary static chargedparticle beamline elements.
 Publication:

arXiv eprints
 Pub Date:
 December 2010
 arXiv:
 arXiv:1012.1647
 Bibcode:
 2010arXiv1012.1647D
 Keywords:

 Physics  Accelerator Physics
 EPrint:
 Paper presented at the 2000 International Computational Accelerator Conference, Darmstadt, Germany, Sept. 1114, 2000