Constructing Current Singularity in a 3D Linetied Plasma
We revisit Parker's conjecture of current singularity formation in 3D linetied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozenin equation builtin, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D linetied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. Finally, with the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.
 Authors:

^{[1]}
;
^{[1]}
;
^{[2]};
^{[1]}
 Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences and Plasma Physics Lab.
 Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences and Plasma Physics Lab.; Univ. of Science and Technology of China, Hefei (China). Dept. of Modern Physics
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725; AC0209CH11466
 Type:
 Accepted Manuscript
 Journal Name:
 The Astrophysical Journal (Online)
 Additional Journal Information:
 Journal Name: The Astrophysical Journal (Online); Journal Volume: 852; Journal Issue: 1; Journal ID: ISSN 15384357
 Publisher:
 Institute of Physics (IOP)
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 79 ASTRONOMY AND ASTROPHYSICS; magnetohydrodynamics (MHD); magnetic fields; Sun: corona
 OSTI Identifier:
 1430536
Zhou, Yao, Huang, YiMin, Qin, Hong, and Bhattacharjee, A. Constructing Current Singularity in a 3D Linetied Plasma. United States: N. p.,
Web. doi:10.3847/15384357/aa9b84.
Zhou, Yao, Huang, YiMin, Qin, Hong, & Bhattacharjee, A. Constructing Current Singularity in a 3D Linetied Plasma. United States. doi:10.3847/15384357/aa9b84.
Zhou, Yao, Huang, YiMin, Qin, Hong, and Bhattacharjee, A. 2017.
"Constructing Current Singularity in a 3D Linetied Plasma". United States.
doi:10.3847/15384357/aa9b84. https://www.osti.gov/servlets/purl/1430536.
@article{osti_1430536,
title = {Constructing Current Singularity in a 3D Linetied Plasma},
author = {Zhou, Yao and Huang, YiMin and Qin, Hong and Bhattacharjee, A.},
abstractNote = {We revisit Parker's conjecture of current singularity formation in 3D linetied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozenin equation builtin, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D linetied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. Finally, with the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.},
doi = {10.3847/15384357/aa9b84},
journal = {The Astrophysical Journal (Online)},
number = 1,
volume = 852,
place = {United States},
year = {2017},
month = {12}
}