Modeling s-dependent magnetic fields

Xsuite provides two elements for modeling magnetic fields that vary along the longitudinal coordinate: xtrack.SplineBoris and xtrack.BFieldExpansion. They reconstruct the off-axis magnetic field from longitudinal profiles of the field and its transverse derivatives on the reference axis. These models can describe devices such as undulators, wigglers, magnets with fringe fields, and solenoids, for which a constant multipolar description is not sufficient.

• xtrack.SplineBoris uses fourth-order polynomial profiles specified through xtrack.Spline4 objects, with field data in SI units. It tracks particles in a straight reference frame using a second-order spatial Boris integrator. The examples in Magnetic fields with SplineBoris show how to build an undulator from a field map and install it in a ring.

• xtrack.BFieldExpansion accepts polynomial coefficients normalized by the signed reference magnetic rigidity and supports straight and curved reference frames. It tracks particles using fourth-order Runge–Kutta integration. See Magnetic fields with BFieldExpansion for field specification, geometry, field evaluation, and integration settings.

The reconstruction of the three-dimensional field is described in the Modeling s-dependent magnetic fields chapter of the Physics Guide.

• Magnetic fields with SplineBoris
  • Overview
  • Building an undulator from a field map
  • Installing the undulator in a ring
• Magnetic fields with BFieldExpansion
  • Specifying the field
  • Additional strengths and scaling
  • Longitudinal coordinate and geometry
  • Evaluating fields and potentials
  • Integration and boundary momenta
  • Updating coefficients and using an Environment