TY - JOUR
T1 - Constructing Current Singularity in a 3D Line-tied Plasma
AU - Zhou, Yao
AU - Huang, Yi Min
AU - Qin, Hong
AU - Bhattacharjee, A.
N1 - Funding Information:
This research was supported by the U.S. Department of Energy under Contract No. DE-AC02-09CH11466, and used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.
Funding Information:
Finally, we emphasize that the Parker problem is still open and of practical relevance, by echoing the latest review by Zweibel & Yamada (2016, p. 11): “It is important to determine whether the equilibrium of line-tied magnetic fields has true current singularities or merely very large and intermittent currents, to characterize the statistical properties of the sheets and to determine how the equilibrium level and spatial and temporal intermittency of energy release depend on S.” We thank E.G.Zweibel for helpful discussions and comments on an early version of this manuscript. This research was supported by the U.S.Department of Energy under Contract No.DE-AC02-09CH11466, and used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S.Department of Energy under Contract No.DE-AC05-00OR22725.
Publisher Copyright:
© 2017. The American Astronomical Society. All rights reserved.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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. 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.
AB - 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. 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.
KW - Sun: corona
KW - magnetic fields
KW - magnetohydrodynamics (MHD)
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U2 - 10.3847/1538-4357/aa9b84
DO - 10.3847/1538-4357/aa9b84
M3 - Article
AN - SCOPUS:85040229679
SN - 0004-637X
VL - 852
JO - Astrophysical Journal
JF - Astrophysical Journal
IS - 1
M1 - 3
ER -