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Title: Current sheet formation and nonideal behavior at three-dimensional magnetic null points

Abstract

The nature of the evolution of the magnetic field, and of current sheet formation, at three-dimensional (3D) magnetic null points is investigated. A kinematic example is presented that demonstrates that for certain evolutions of a 3D null (specifically those for which the ratios of the null point eigenvalues are time-dependent), there is no possible choice of boundary conditions that renders the evolution of the field at the null ideal. Resistive magnetohydrodynamics simulations are described that demonstrate that such evolutions are generic. A 3D null is subjected to boundary driving by shearing motions, and it is shown that a current sheet localized at the null is formed. The qualitative and quantitative properties of the current sheet are discussed. Accompanying the sheet development is the growth of a localized parallel electric field, one of the signatures of magnetic reconnection. Finally, the relevance of the results to a recent theory of turbulent reconnection is discussed.

Authors:
; ;  [1];  [2]
  1. Space Science Center and Center for Magnetic Self-Organization, University of New Hampshire, Durham, New Hampshire 03824 (United States)
  2. (Denmark)
Publication Date:
OSTI Identifier:
20974966
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 5; Other Information: DOI: 10.1063/1.2722300; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOUNDARY CONDITIONS; EIGENVALUES; ELECTRIC FIELDS; MAGNETIC FIELDS; MAGNETIC RECONNECTION; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA SHEATH; PLASMA SIMULATION; SHEAR; THREE-DIMENSIONAL CALCULATIONS; TIME DEPENDENCE; TURBULENCE

Citation Formats

Pontin, D. I., Bhattacharjee, A., Galsgaard, K., and Niels Bohr Institute, University of Copenhagen, Copenhagen. Current sheet formation and nonideal behavior at three-dimensional magnetic null points. United States: N. p., 2007. Web. doi:10.1063/1.2722300.
Pontin, D. I., Bhattacharjee, A., Galsgaard, K., & Niels Bohr Institute, University of Copenhagen, Copenhagen. Current sheet formation and nonideal behavior at three-dimensional magnetic null points. United States. doi:10.1063/1.2722300.
Pontin, D. I., Bhattacharjee, A., Galsgaard, K., and Niels Bohr Institute, University of Copenhagen, Copenhagen. Tue . "Current sheet formation and nonideal behavior at three-dimensional magnetic null points". United States. doi:10.1063/1.2722300.
@article{osti_20974966,
title = {Current sheet formation and nonideal behavior at three-dimensional magnetic null points},
author = {Pontin, D. I. and Bhattacharjee, A. and Galsgaard, K. and Niels Bohr Institute, University of Copenhagen, Copenhagen},
abstractNote = {The nature of the evolution of the magnetic field, and of current sheet formation, at three-dimensional (3D) magnetic null points is investigated. A kinematic example is presented that demonstrates that for certain evolutions of a 3D null (specifically those for which the ratios of the null point eigenvalues are time-dependent), there is no possible choice of boundary conditions that renders the evolution of the field at the null ideal. Resistive magnetohydrodynamics simulations are described that demonstrate that such evolutions are generic. A 3D null is subjected to boundary driving by shearing motions, and it is shown that a current sheet localized at the null is formed. The qualitative and quantitative properties of the current sheet are discussed. Accompanying the sheet development is the growth of a localized parallel electric field, one of the signatures of magnetic reconnection. Finally, the relevance of the results to a recent theory of turbulent reconnection is discussed.},
doi = {10.1063/1.2722300},
journal = {Physics of Plasmas},
number = 5,
volume = 14,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • Asymmetric current sheets are likely to be prevalent in both astrophysical and laboratory plasmas with complex three dimensional (3D) magnetic topologies. This work presents kinematic analytical models for spine and fan reconnection at a radially symmetric 3D null (i.e., a null where the eigenvalues associated with the fan plane are equal) with asymmetric current sheets. Asymmetric fan reconnection is characterized by an asymmetric reconnection of flux past each spine line and a bulk flow of plasma across the null point. In contrast, asymmetric spine reconnection is characterized by the reconnection of an equal quantity of flux across the fan planemore » in both directions. The higher modes of spine reconnection also include localized wedges of vortical flux transport in each half of the fan. In this situation, two definitions for reconnection rate become appropriate: a local reconnection rate quantifying how much flux is genuinely reconnected across the fan plane and a global rate associated with the net flux driven across each semi-plane. Through a scaling analysis, it is shown that when the ohmic dissipation in the layer is assumed to be constant, the increase in the local rate bleeds from the global rate as the sheet deformation is increased. Both models suggest that asymmetry in the current sheet dimensions will have a profound effect on the reconnection rate and manner of flux transport in reconnection involving 3D nulls.« less
  • The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D andmore » 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed.« less
  • The ideal three-dimensional incompressible magnetohydrodynamics equations are analyzed at magnetic null points using a generalization of a method from fluid dynamics. A closed system of ordinary differential equations governing the evolution of traces of matrices associated with the fluid velocity and magnetic field gradients are derived using a model for the pressure Hessian. It is shown rigorously that the eigenvalues of the magnetic field gradient matrix are constant in time and that, in the model, a finite time singularity occurs with characteristics similar to the magnetic field-free case. {copyright} {ital 1996 American Institute of Physics.}
  • Magnetic reconnection around three dimensional (3D) magnetic null points is the natural progression from X-point reconnection in two dimensions. In 3D the separator field lines of the X-point are replaced with the spine line and fan plane (the field lines which asymptotically approach or recede from the null). In this work analytical models are developed for the newly classified torsional spine and torsional fan reconnection regimes by solving the steady state, kinematic, resistive magnetohydrodynamic equations. Reconnection is localized to around the null through the use of a localized field perturbation leading to a localized current while a constant resistivity ismore » assumed. For the torsional spine case current is found to localize around the spine leading to a spiraling slippage of the field around the spine and out along the fan. For the torsional fan case current is found to be localized to the fan plane leading again to a spiraling slippage of the field. In each case no flux is transported across either the spine or the fan. An intermediate twist is then introduced and a link is established between the two regimes. We find that for a general twist plasma flows associated with both torsional spine and fan appear in distinct regions. As such we suggest that the ''pure'' flows of each are extreme cases.« less