Homoclinic tangles in the DIIID divertor tokamak
Abstract
A new approach was developed for the calculation of homoclinic tangles of the primary unperturbed separatrix in divertor tokamaks. This new approach is different than calculating tangles by following single trajectories in phase space [M. V. Berry, Topics in Nonlinear Dynamics (Ed. S. Jorna), Am. Inst. Phys. Conf. Proc. 46, 16120 (1978)] or calculating the trajectories asymptotically in canonical time [R. K. W. Roeder, B. I. Rapoport, and T. E. Evans, Phys. Plasmas 10, 3796 (2003)]. The approach is to consider an equilibrium manifold as a whole and to calculate how the entire manifold evolves in phase space in time under the influence of perturbations. When the forward moving and the backward moving manifolds meet in a poloidal plane and intersect, they form tangles to preserve the topological invariance of the Hamiltonian system. This approach was applied to the DIIID tokamak. The low mn, the high mn, the peelingballooning modes, and topological noise and field error perturbations were considered. The results of the peelingballooning modes were analyzed. It was found that the perturbations create very complicated structures in phase space [A. Punjabi and A. Boozer, Phys. Lett A 378, 24102416 (2014); A. Punjabi, Phys. Plasmas 21, 122516 (2014)]. The structuremore »
 Authors:

 Hampton Univ., Hampton, VA (United States)
 Publication Date:
 Research Org.:
 Hampton Univ., Hampton, VA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1570386
 Report Number(s):
 DOEHAMPTONU04ER54793
TRN: US2000164
 DOE Contract Number:
 FG0204ER54793; FG0201ER54624; AC02 05CH11231
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
PUNJABI, ALKESH, and ALI, HALIMA. Homoclinic tangles in the DIIID divertor tokamak. United States: N. p., 2019.
Web. doi:10.2172/1570386.
PUNJABI, ALKESH, & ALI, HALIMA. Homoclinic tangles in the DIIID divertor tokamak. United States. https://doi.org/10.2172/1570386
PUNJABI, ALKESH, and ALI, HALIMA. Wed .
"Homoclinic tangles in the DIIID divertor tokamak". United States. https://doi.org/10.2172/1570386. https://www.osti.gov/servlets/purl/1570386.
@article{osti_1570386,
title = {Homoclinic tangles in the DIIID divertor tokamak},
author = {PUNJABI, ALKESH and ALI, HALIMA},
abstractNote = {A new approach was developed for the calculation of homoclinic tangles of the primary unperturbed separatrix in divertor tokamaks. This new approach is different than calculating tangles by following single trajectories in phase space [M. V. Berry, Topics in Nonlinear Dynamics (Ed. S. Jorna), Am. Inst. Phys. Conf. Proc. 46, 16120 (1978)] or calculating the trajectories asymptotically in canonical time [R. K. W. Roeder, B. I. Rapoport, and T. E. Evans, Phys. Plasmas 10, 3796 (2003)]. The approach is to consider an equilibrium manifold as a whole and to calculate how the entire manifold evolves in phase space in time under the influence of perturbations. When the forward moving and the backward moving manifolds meet in a poloidal plane and intersect, they form tangles to preserve the topological invariance of the Hamiltonian system. This approach was applied to the DIIID tokamak. The low mn, the high mn, the peelingballooning modes, and topological noise and field error perturbations were considered. The results of the peelingballooning modes were analyzed. It was found that the perturbations create very complicated structures in phase space [A. Punjabi and A. Boozer, Phys. Lett A 378, 24102416 (2014); A. Punjabi, Phys. Plasmas 21, 122516 (2014)]. The structure of tangles gives a possible cause for generation of radial electric fields in divertor tokamaks, and the possible consequent drifts, currents, shears, and curvature effects from the resulting complicated electric fields can possibly indicate a path to L to H mode transition [F. Wagner F et al, Phys. Rev. Lett. 49, 1408 (1982)] in divertor tokamaks. During the present period, four (4) refereed paper were published; six (6) contributed papers were presented at the EPS Conference on Plasma Physics and published in the EPS conference proceedings; six (6) contributed poster papers, coauthored with HU undergraduate students, were presented at APS/DPP Annual Meetings; three contributed papers were presented at HU School of Science Annual Research Symposia; four (4) invited talks were given; one talk, coauthored by Dr. Allen Boozer and the PI, was given by Dr. Boozer at the 20th International StellaratorHeliotron Workshop 2015, in Greifswald, Germany; and four (4) graduate students and nine (9) undergraduate students were mentored and provided research experience in fusion science. For the renewal period, it is planned to work on four (4) new problems. These are: Homoclinic tangles of the separatrices of the DIIID and the simple map, magnetic topology and homoclinic tangles of separatrices in divertor tokamaks, resonant stellarator divertors, and nonresonant stellarator divertors.},
doi = {10.2172/1570386},
url = {https://www.osti.gov/biblio/1570386},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {7}
}