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Title: Constructing Current Singularity in a 3D Line-tied Plasma

Abstract

We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, 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 line-tied 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:
ORCiD logo [1]; ORCiD logo [1];  [2];  [1]
  1. Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences and Plasma Physics Lab.
  2. 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:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1430536
Grant/Contract Number:  
AC05-00OR22725; AC02-09CH11466
Resource 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 1538-4357
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 79 ASTRONOMY AND ASTROPHYSICS; magnetohydrodynamics (MHD); magnetic fields; Sun: corona

Citation Formats

Zhou, Yao, Huang, Yi-Min, Qin, Hong, and Bhattacharjee, A. Constructing Current Singularity in a 3D Line-tied Plasma. United States: N. p., 2017. Web. doi:10.3847/1538-4357/aa9b84.
Zhou, Yao, Huang, Yi-Min, Qin, Hong, & Bhattacharjee, A. Constructing Current Singularity in a 3D Line-tied Plasma. United States. doi:10.3847/1538-4357/aa9b84.
Zhou, Yao, Huang, Yi-Min, Qin, Hong, and Bhattacharjee, A. Wed . "Constructing Current Singularity in a 3D Line-tied Plasma". United States. doi:10.3847/1538-4357/aa9b84. https://www.osti.gov/servlets/purl/1430536.
@article{osti_1430536,
title = {Constructing Current Singularity in a 3D Line-tied Plasma},
author = {Zhou, Yao and Huang, Yi-Min and Qin, Hong and Bhattacharjee, A.},
abstractNote = {We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, 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 line-tied 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 = {10.3847/1538-4357/aa9b84},
journal = {The Astrophysical Journal (Online)},
number = 1,
volume = 852,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

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Cited by: 1 work
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Figures / Tables:

Figure 1 Figure 1: Numerical solutions of ξx(x0, 0, L/2) for L = 32 with N = 32, 64, and 128 converge to a smooth one. The solid line shows the 2D solution (7).

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