2017/05/31 by Yao Zhou, Yi-Min Huang, Hong Qin +1 · 10 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Current (fluid) #Geometry #Ionosphere and magnetosphere dynamics #Line (geometry) #Magnetic confinement fusion research #Magnetohydrodynamics #Mathematical analysis #Mathematics #Nonlinear system #Physics #Plasma #Singularity #Solar and Space Plasma Dynamics #astro-ph.SR #physics.plasm-ph
paper · pdf · doi:10.3847/1538-4357/aa9b84
published in The Astrophysical Journal 852(1), 3 (IOP Publishing)
openalex publication_date 2017/12/27 · arxiv created 2018/01/02 · arxiv updated 2018/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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. 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.