Finite Ion Orbit Effects on Magnetic Islands in Toroidal Plasmas

POSTER

Abstract

A kinetic theory for the interaction of ions with an isolated magnetic island in tokamak plasma is presented. We examine islands whose characteristic widths are larger than ion gyro radius but comparable to the ion banana width. In this regime, the ion response to the island has a non-local feature due to the banana drifts. When solving the drift kinetic equation for ions, a change in coordinates is used to account for this behavior. A bounce averaging procedure is developed to separate out and solve the lower order distribution function. Constraint relationships found from transport equations and collision operators are used to determine the distribution function, which is treated in different velocity regions. A self-consistent calculation for the electrostatic potential is proposed. The perturbed current is composed of the bootstrap current and the perpendicular neoclassical enhanced ion polarization current. The closure parallel current is calculated and compared with some recent numerical results. Using this current in Rutherford equation, the island width evolution equation is determined. A pair of self-consistent equations for the island width and rotation frequency is to be derived. The results are to be compared with calculations for large island width so as to yield a description of magnetic island width evolution from sub-banana width to macroscopic scale lengths.

Authors

  • Xinzheng Liu

    UW-Madison

  • Barbara Jacak

    Texas A\&M University, University of Minnesota, Radiation Monitoring Devices, Inc., Livermore National Laboratory, MIT, Association EUTRATOM-CEA, CEA/DSM/DRFC, CEA Cadarache, 13108 St Paul Lez Durance France, University of Munich, Germany, LNS Catania, Italy, NASA Langley Research Center, Fermilab, University of Florida, Princeton Plasma Physics Laboratory, Princeton, NJ, U.S.A., Courant Institute, New York University, New York, U.S.A., Department of Physics, Harvard University, Department of Physics, McGill University, University of Illinois at Chicago, for the LIGO Scientific Collaboration, Stanford University, DESY, LPSC, Grenoble, France, University of Arizona, Cornell University, University of Wisconsin -- Milwaukee, Case Western Reserve University, Space Science Center and Department of Physics, University of New Hampshire, University of Chicago, Fermi National Accelerator Laboratory, University of Wisconsin, Lawrence Livermore National Laboratory, Princeton Plasma Physics Lab., ORNL, Politecnico diTorino, Max-Planck Institute for Plasma Physics, MIT-PSFC, UCLA Physics Department, Abastumani Astrophysical Observatory, A. Kazbegi 2a, Tbilisi 0160, Georgia, NYU, PPPL, Columbia University, UC-Davis, UCLA, UC-Irvine, Culham Science Centre, Massachusetts Institute of Technology, Fusion Research Center, Univ. of Texas at Austin, Institute for Fusion Studies, Univ. of Texas at Austin, Institute for Fusion Studies, Chalmers University of Technology, G\"{o}teborg, Sweden, Princeton Plasma Physics Lab, ANL, LLNL, Politecnico de Torino, Italy, UCSD, Lodestar Research Corp., Saclay, France, California Institute of Technology, NASA/GSFC, NRC, NASA/GSFC, Oslo, Mississippi State, Massachusetts-Lowell, NBI, Tennessee, Argonne National Lab, Florida State, US Naval Academy, Petersburg Nuclear Physics Institute, Dept. of Physics and Astronomy, Ohio Univ., Los Alamos National Laboratory, Ohio State University, University of Glasgow, Jet Propulsion Lab, Pasadena CA, U. of Minnesota, Minneapolis MN, Caltech, Pasadena CA, Washington U., St. Louis MO, NASA/GSFC, Greenbelt MD 20771, University of Michigan, Indiana University, Pennsylvania State University, Purdue University, CalTech, University of California, Berkeley and Lawrence Berkeley National Laboratory, University of Rochester, Washington University, St. Louis, University of Iowa, University of Kansas, University of Athens, Greece, Kent State University, Tenn Tech U., Oak Ridge Assoc. U., Colorado School of Mines, Rutgers, UNC - Chapel Hill, U. of Tenn, Oak Ridge National Laboratory, Ohio University, Cyclotron Institute, Texas A\&M University, Colorado College, Japanese Atomic Energy Agency, ORNL Physics Division, Universita' di Milano, Bordeaux Obs, UMRAO, WUSTL, Leeds, Laboratory for Elementary-Particle Physics, Cornell University, Senate Energy and Natural Resources Committee, CEA-Cadarache, France, SAIC-San Diego, University of Colorado at Boulder, University of Wisconsin-Madison, Princeton Plasma Physics Laboratory, Institute for Fusion Studies, University of Texas at Austin, M.I.T., National Institute for Fusion Science, Toki, Japan, U. Maryland, RRC Kurchatov Institute, Association EURATOM-CEA Cadarache, UKAEA Fusion Association, University of Colorado, Boulder, General Atomic, Columbia Univ., Caltech, UC Irvine, Univ. Colorado, CNR-IFP, Italy, Associazione Euratom-ENEA sulla Fusione, Italy, Office of Fusion Energy Sciences, US DoE, Fusion Research Center, Georgia Institute of Technology, Lawrence Livermore National Lab, Universidad Nacional de Cordoba, C.W. Post -- Long Island University, Brigham Young University, Louisiana State University, NSCL, Washington University in St. Louis, Cyclotron Institute Texas A\&M University, Cyclotron Institute, Texas A$\&$M University, College Station, TX 77843, Middle East Technical University/FNAL, INRNE-BAS/FNAL, Texas Tech University, FNAL, Cavendish Laboratory, University of Cambridge, UK, CIEMAT, Madrid, Spain, Center for Relativity, Department of Physics, University of Texas at Austin, Cyclotron Institute, Texas A\&M University, College Station, TX 77843, U. Sussex, Tulane U., NIST, U. Michigan, University of Winnipeg, Tohoku University, Dept. of Chemistry, Indiana Univ./IUCF, Washington University, Universidade Federal do Rio de Janeiro, Michigan State University, Boston University, Queen's University, National Institute for Standards and Technology, Yale University, Princeton University, University of California, Riverside, University of Surrey, LLNL and UC Berkeley, LBNL and UC Berkeley, LBNL, LBL, Dept. of Chemistry, Indiana University/IUCF, A. Soltan Institute for Nuclear Studies, Warsaw, Poland, CEA-Saclay, DSM/DAPNIA/SPhn, France, Florida State University, Department of Physics, University of California, Davis, Univ. of Arizona, INFN Pisa and University of Pisa, University of North Carolina at Wilmington, University of North Carolina at Chapel Hill and Triangle Universities Nuclear Laboratory, Rockefeller University, Northern Kentucky University, UNESCO Senior Program Specialist, CASS and Physics Dept., UCSD, Institute for Research in Electronics and Applied Physics,Univ. of Maryland,College Park,MD 20742, MPI for Plasma Physics, Greifswald, Germany, Emory University, University of Wisconsin-Madison and the Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin, Madison, Berkeley, E.N.S., Paris, Polymath Research Inc, Pleasanton CA, LPMIA, INRS Energie et Materiaux Quebec, LPMIA UMR 7040 UHP Nancy France, Pacific Northwest National Laboratory, Helmholtz Inst., Universitaet Bonn, D-53115 Bonn, Forschungszentrum Juelich, IKP, D-52425 Juelich, University of Michigan, Ann Arbor, MI 48109-1120, Helmholtz Inst., Univ. Bonn, D-53115 Bonn, IIT, Chicago, IL 60616, Univ. of Michigan, Ann Arbor, MI 48109-1120, Duke University, SDSU, Racah Institute of Physics, Univ. of Trento, Gesellschaft f\"ur Schwerionenforschung, Bowling Green State Univ., Dept. of Chemistry, Indiana University, SUNY, Stony Brook