Reflection symmetry effects in the perturbation series of an action integral for the field line displacement in an ELMO Bumpy Torus

Deviations from this ideal geometry and less-than-perfect alignment of the field coils in an ELMO Bumpy Torus generate perturbations to the ideal magnetic field configuration, resulting generally in failure of the field lines to close on themselves and thereby causing degradation in plasma confinement. The sensitivity of the field line displacement to certain types of errors in coil parameters is studied by means of a perturbation formalism developed for an action integral representing the longitudinal adiabatic invariant. Reflection symmetry properties satisfied by the magnetic field and the vector potential are derived, and it is demonstrated both analytically and numerically that the leading term of the field line displacement per period of 2π around the major axis is second order in the perturbation parameter if the coil planes remain invariant under the perturbation. Numerical analyses for the field line displacement also reveal some more useful properties for the first- and second-order terms in the perturbation series