Sensitivity of the magnetic axis to variations in the magnetic field

Lagrangian variational principles are used to locate the magnetic axis and to determine its sensitivity to variations in the magnetic field. Only the change in the magnetic field on axis is required to determine, to lowest order, the location of the new magnetic axis. Using a simple example, namely, the magnetic field produced by a set of current-carrying filaments (a.k.a. coils), the variation in the coil geometry that induces the largest change in the magnetic axis is determined using singular value decomposition.