Magnetic islands and singular currents at rational surfaces in threedimensional magnetohydrodynamic equilibria
Abstract
Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces in nonaxisymmetric ideal MHD equilibria. These include the forcefree singular current density represented by a Dirac δfunction, which presumably prevents the formation of islands, and the PfirschSchlüter 1/x singular current, which arises as a result of finite pressure gradient. An analytical model based on linearized MRxMHD is derived that can accurately (1) describe the formation of magnetic islands at resonant rational surfaces, (2) retrieve the ideal MHD limit where magnetic islands are shielded, and (3) compute the subsequent formation of singular currents. The analytical results are benchmarked against numerical simulations carried out with a fully nonlinear implementation of MRxMHD.
 Authors:
 MaxPlanckInstitut für Plasmaphysik, D17491 Greifswald (Germany)
 (United States)
 Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543 (United States)
 Publication Date:
 OSTI Identifier:
 22408096
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BENCHMARKS; COMPUTERIZED SIMULATION; CURRENT DENSITY; DIRAC EQUATION; EQUILIBRIUM; MAGNETIC ISLANDS; MAGNETOHYDRODYNAMICS; MODE RATIONAL SURFACES; NONLINEAR PROBLEMS; PRESSURE GRADIENTS; RELAXATION; THREEDIMENSIONAL CALCULATIONS
Citation Formats
Loizu, J., Email: joaquim.loizu@ipp.mpg.de, Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543, Hudson, S., Bhattacharjee, A., and Helander, P.. Magnetic islands and singular currents at rational surfaces in threedimensional magnetohydrodynamic equilibria. United States: N. p., 2015.
Web. doi:10.1063/1.4906888.
Loizu, J., Email: joaquim.loizu@ipp.mpg.de, Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543, Hudson, S., Bhattacharjee, A., & Helander, P.. Magnetic islands and singular currents at rational surfaces in threedimensional magnetohydrodynamic equilibria. United States. doi:10.1063/1.4906888.
Loizu, J., Email: joaquim.loizu@ipp.mpg.de, Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543, Hudson, S., Bhattacharjee, A., and Helander, P.. 2015.
"Magnetic islands and singular currents at rational surfaces in threedimensional magnetohydrodynamic equilibria". United States.
doi:10.1063/1.4906888.
@article{osti_22408096,
title = {Magnetic islands and singular currents at rational surfaces in threedimensional magnetohydrodynamic equilibria},
author = {Loizu, J., Email: joaquim.loizu@ipp.mpg.de and Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543 and Hudson, S. and Bhattacharjee, A. and Helander, P.},
abstractNote = {Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces in nonaxisymmetric ideal MHD equilibria. These include the forcefree singular current density represented by a Dirac δfunction, which presumably prevents the formation of islands, and the PfirschSchlüter 1/x singular current, which arises as a result of finite pressure gradient. An analytical model based on linearized MRxMHD is derived that can accurately (1) describe the formation of magnetic islands at resonant rational surfaces, (2) retrieve the ideal MHD limit where magnetic islands are shielded, and (3) compute the subsequent formation of singular currents. The analytical results are benchmarked against numerical simulations carried out with a fully nonlinear implementation of MRxMHD.},
doi = {10.1063/1.4906888},
journal = {Physics of Plasmas},
number = 2,
volume = 22,
place = {United States},
year = 2015,
month = 2
}

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