Application of modern mathematical concepts to plasma confinement

Progress in four research areas has been achieved. A second-order symplectic integration algorithm has been developed and tested. Use of this algorithm allows integration of systems of Hamiltonian equations of motion to be carried out with much less computation. Vacuum field optimization techniques have been improved. One result of this work is a simple method for calculating magnetic island widths. Studies of alpha particle transport in toroidal confinement systems were initiated. This has been used as a test bed for studies of symplectic integrators. Quantum modifications of separatrix crossing theory were calculated. In addition the principal investigator is organizing a U.S.-Japan conference concerning the use of modern techniques for the study of plasma confinement.