Homoclinic tangles in the DIII-D tokamak from the map equations in natural canonical coordinates*

Punjabi, Alkesh; Boozer, Allen

doi:10.1080/10420150.2017.1290632

Title: Homoclinic tangles in the DIII-D tokamak from the map equations in natural canonical coordinates*

Journal Article · Wed Feb 01 00:00:00 EST 2017 · Radiation Effects and Defects in Solids

DOI:https://doi.org/10.1080/10420150.2017.1290632· OSTI ID:1523276

Punjabi, Alkesh ^[1]; Boozer, Allen ^[2]

Hampton Univ., Hampton, VA (United States). Department of Mathematics
Columbia Univ., New York, NY (United States). Dept. of Applied Physics and Applied Mathematics

Trajectories of magnetic field lines are a 1½ degree of freedom Hamiltonian system. The unperturbed separatrix and the perturbed separatrix in a divertor tokamak are fundamentally different. Magnetic asymmetries cause the separatrix to form extremely complicated structures known as homoclinic tangles. After each toroidal circuit, the perturbed separatrix manifolds meet in a fixed poloidal plane and intersect to form homoclinic tangle in order to preserve the topological invariants. This tangle becomes extremely complicated as the magnetic field lines take more and more toroidal turns. This effect is most pronounced near the X-point. The homoclinic tangles of the DIII-D tokamak separatrix from the magnetic perturbation representing the peeling-ballooning modes are studied. The homoclinic tangles can have important implications for the edge physics in divertor tokamaks.

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Research Organization:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

Sponsoring Organization:: USDOE

DOE Contract Number:: AC02-05CH11231

OSTI ID:: 1523276

Journal Information:: Radiation Effects and Defects in Solids, Vol. 172, Issue 1-2; ISSN 1042-0150

Country of Publication:: United States

Language:: English

References (16)

Symplectic approach to calculation of magnetic field line trajectories in physical space with realistic magnetic geometry in divertor tokamaks Punjabi, Alkesh; Ali, Halima Physics of Plasmas, Vol. 15, Issue 12 https://doi.org/10.1063/1.3028310	journal	December 2008
Evaluation of the structure of ergodic fields Boozer, Allen H. Physics of Fluids, Vol. 26, Issue 5 https://doi.org/10.1063/1.864289	journal	January 1983
Homoclinic tangle of the ideal separatrix in the DIII-D tokamak from (30, 10) + (40, 10) perturbation Punjabi, Alkesh Physics of Plasmas, Vol. 21, Issue 12 https://doi.org/10.1063/1.4904305	journal	December 2014
Loss of relativistic electrons when magnetic surfaces are broken Boozer, Allen H.; Punjabi, Alkesh Physics of Plasmas, Vol. 23, Issue 10 https://doi.org/10.1063/1.4966046	journal	October 2016
Homoclinic tangle in tokamak divertors Punjabi, Alkesh; Boozer, Allen Physics Letters A, Vol. 378, Issue 32-33 https://doi.org/10.1016/j.physleta.2014.06.027	journal	June 2014
Footprint structures due to resonant magnetic perturbations in DIII-D Wingen, A.; Evans, T. E.; Spatschek, K. H. Physics of Plasmas, Vol. 16, Issue 4 https://doi.org/10.1063/1.3099053	journal	April 2009
Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter Kroetz, T.; Roberto, M.; da Silva, E. C. Physics of Plasmas, Vol. 15, Issue 9 https://doi.org/10.1063/1.2988335	journal	September 2008
Experimental signatures of homoclinic tangles in poloidally diverted tokamaks Evans, T. E.; Roeder, R. K. W.; Carter, J. A. Journal of Physics: Conference Series, Vol. 7 https://doi.org/10.1088/1742-6596/7/1/015	journal	January 2005
Tokamak magnetic field lines described by simple maps: Dedicated to Professor Celso Grebogi on the occasion of his 60th birthday Portela, J. S. E.; Caldas, I. L.; Viana, R. L. The European Physical Journal Special Topics, Vol. 165, Issue 1 https://doi.org/10.1140/epjst/e2008-00863-y	journal	December 2008
Explicit calculations of homoclinic tangles in tokamaks Roeder, R. K. W.; Rapoport, B. I.; Evans, T. E. Physics of Plasmas, Vol. 10, Issue 9 https://doi.org/10.1063/1.1592515	journal	September 2003
Stochastic broadening of the separatrix of a tokamak divertor Punjabi, Alkesh; Verma, Arun; Boozer, Allen Physical Review Letters, Vol. 69, Issue 23 https://doi.org/10.1103/PhysRevLett.69.3322	journal	December 1992
An area-preserving mapping in natural canonical coordinates for magnetic field line trajectories in the DIII-D tokamak Punjabi, Alkesh Nuclear Fusion, Vol. 49, Issue 11 https://doi.org/10.1088/0029-5515/49/11/115020	journal	September 2009
Homoclinic tangles, bifurcations and edge stochasticity in diverted tokamaks Evans, T. E.; Roeder, R. K. W.; Carter, J. A. Contributions to Plasma Physics, Vol. 44, Issue 13 https://doi.org/10.1002/ctpp.200410034	journal	April 2004
Noncanonical Hamiltonian mechanics and its application to magnetic field line flow Cary, John R.; Littlejohn, Robert G. Annals of Physics, Vol. 151, Issue 1 https://doi.org/10.1016/0003-4916(83)90313-5	journal	November 1983
Escape patterns, magnetic footprints, and homoclinic tangles due to ergodic magnetic limiters da Silva, Elton C.; Caldas, Iberê L.; Viana, Ricardo L. Physics of Plasmas, Vol. 9, Issue 12 https://doi.org/10.1063/1.1518681	journal	December 2002
Traces of stable and unstable manifolds in heat flux patterns Wingen, A.; Jakubowski, M.; Spatschek, K. H. Physics of Plasmas, Vol. 14, Issue 4 https://doi.org/10.1063/1.2715548	journal	April 2007

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