Refinement of the Hamilton-Jacobi solution using a second canonical transformation

Two canonical transformations are implemented to find approximate invariant surfaces for a nonlinear time-periodic Hamiltonian. The first transformation is found from the nonperturbative, iterative solution of the Hamilton-Jacobi equation. The residual angle dependence remaining after performing the transformation is mostly eliminated by a second, perturbative transformation. This refinement can improve the accuracy or the speed, of the invariant surface calculation. The motion of a single particle in one transverse dimension is studied in a storage ring example where strong sextupole magnets are the source of the nonlinearity.<>