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Title: Hall assisted forced magnetic reconnection

Abstract

The role of the Hall effect in forced magnetic reconnection is investigated analytically for the so-called Taylor problem. In the latter, a tearing stable slab plasma equilibrium, which is chosen here to be a simple magnetic field reversal, is subjected to a small-amplitude boundary deformation that drives magnetic reconnection (hence the adjective 'forced') at the neutral surface within the plasma. It is shown that such reconnection becomes substantially accelerated by the Hall effect when the nondimensional parameter d{sub i}=(c/{omega}{sub pi})/a exceeds S{sup -1/5}. Here, c/{omega}{sub pi} is the ion inertial skin depth, a is the width of the plasma slab, and S>>1 is the Lundquist number of a highly conducting plasma. Two different types of external perturbation are considered. In the case of continuous quasistatic driving, with a frequency {omega} such that {omega}{tau}{sub A}<<1, {tau}{sub A} being the Alfven transit time, various reconnection regimes are identified. The corresponding heating rates, which are determined by the parameters d{sub i}, S, and {omega}{tau}{sub A}, are derived. In the case of a 'one-off' reconnection event, we demonstrate when and how the transition from the Hall regime to the magnetohydrodynamic regime occurs in the course of the reconnection process. It is found that themore » peak instantaneous reconnection rate scales as d{psi}{sub 1}(0)/dt{approx}d{sub i}{sup 1/2}S{sup -1/2}(B{sub 0}{delta}{sub 0}/{tau}{sub A}), where {psi}{sub 1}(0) is the reconnected magnetic flux, B{sub 0} is the magnetic field strength, and {delta}{sub 0} is the amplitude of the boundary deformation.« less

Authors:
;  [1]
  1. School of Physics and Astronomy, University of Manchester, Manchester M60 1QD (United Kingdom)
Publication Date:
OSTI Identifier:
20860422
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 12; Other Information: DOI: 10.1063/1.2398933; (c) 2006 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; ALFVEN WAVES; AMPLITUDES; BOUNDARY LAYERS; DEFORMATION; DISTURBANCES; EQUILIBRIUM; HALL EFFECT; HEATING RATE; MAGNETIC FIELD REVERSAL; MAGNETIC FIELDS; MAGNETIC FLUX; MAGNETIC RECONNECTION; MAGNETOHYDRODYNAMICS; PLASMA; RADIATION TRANSPORT; TEARING INSTABILITY

Citation Formats

Vekstein, G., and Bian, N. H.. Hall assisted forced magnetic reconnection. United States: N. p., 2006. Web. doi:10.1063/1.2398933.
Vekstein, G., & Bian, N. H.. Hall assisted forced magnetic reconnection. United States. doi:10.1063/1.2398933.
Vekstein, G., and Bian, N. H.. Fri . "Hall assisted forced magnetic reconnection". United States. doi:10.1063/1.2398933.
@article{osti_20860422,
title = {Hall assisted forced magnetic reconnection},
author = {Vekstein, G. and Bian, N. H.},
abstractNote = {The role of the Hall effect in forced magnetic reconnection is investigated analytically for the so-called Taylor problem. In the latter, a tearing stable slab plasma equilibrium, which is chosen here to be a simple magnetic field reversal, is subjected to a small-amplitude boundary deformation that drives magnetic reconnection (hence the adjective 'forced') at the neutral surface within the plasma. It is shown that such reconnection becomes substantially accelerated by the Hall effect when the nondimensional parameter d{sub i}=(c/{omega}{sub pi})/a exceeds S{sup -1/5}. Here, c/{omega}{sub pi} is the ion inertial skin depth, a is the width of the plasma slab, and S>>1 is the Lundquist number of a highly conducting plasma. Two different types of external perturbation are considered. In the case of continuous quasistatic driving, with a frequency {omega} such that {omega}{tau}{sub A}<<1, {tau}{sub A} being the Alfven transit time, various reconnection regimes are identified. The corresponding heating rates, which are determined by the parameters d{sub i}, S, and {omega}{tau}{sub A}, are derived. In the case of a 'one-off' reconnection event, we demonstrate when and how the transition from the Hall regime to the magnetohydrodynamic regime occurs in the course of the reconnection process. It is found that the peak instantaneous reconnection rate scales as d{psi}{sub 1}(0)/dt{approx}d{sub i}{sup 1/2}S{sup -1/2}(B{sub 0}{delta}{sub 0}/{tau}{sub A}), where {psi}{sub 1}(0) is the reconnected magnetic flux, B{sub 0} is the magnetic field strength, and {delta}{sub 0} is the amplitude of the boundary deformation.},
doi = {10.1063/1.2398933},
journal = {Physics of Plasmas},
number = 12,
volume = 13,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}
  • A parametric study of forced magnetic reconnection using a 2D Hall magnetohydrodynamic (MHD) code based on the 'Newton Challenge' is presented. The 'Newton Challenge' defined a magnetic reconnection problem in which reconnection was initiated by a spatially and temporally dependent inflow velocity on the upstream boundary. In this study the magnitude and time dependence of the inflow velocity are varied, as well as the length of the system and the boundary conditions. The general conclusion is that reconnection occurs sooner and faster for stronger impulsive drives (e.g., larger inflow velocities and longer time scales). The results are fairly insensitive tomore » system length. Finally, the Hall MHD results are compared to results from a particle-in-cell simulation study.« less
  • Magnetic reconnection is a strong candidate for a coronal heating mechanism, and heating by forced magnetic reconnection is investigated here. Two dimensional, nonlinear magnetohydrodynamic simulations are used to investigate forced magnetic reconnection in a compressible plasma. The reconnection occurs when a sheared force-free field is perturbed by a slow disturbance (pulse) at the boundary which is representative of the solar corona where the reconnection is induced by the photospheric motions. The case of driving by successive pulses, which generate a series of heating events which may interact with each other, is considered. This is in order to model the heatingmore » of the corona by a series of nanoflare events. For small perturbations, the simulation results are consistent with the previous analytic theory based on linear approach where a current sheet is formed initially at the resonant surface followed by reconnection and then release of magnetic energy. For large amplitude perturbations, or close to the threshold for tearing instability, the system exhibits strong nonlinear aspects. Following the second driving pulse, the current sheet expands along the separatrix before relaxing to a reconnective equilibrium and releasing even more magnetic energy for the same amplitude perturbation.« less
  • During periods of southward interplanetary magnetic field (IMF) orientation the magnetic field geometry at the dayside magnetopause is susceptible to magnetic reconnection. It has been suggested that reconnection may occur in a localized manner at several patches on the magnetopause. A major problem with this picture is the interaction of magnetic flux ropes which are generated by different reconnection processes. An individual flux rope is bent elbowlike where it intersects the magnetopause and the magnetic field changes from magnetospheric to interplanetary magnetic field orientation. Multiple patches of reconnection can lead to the formation of interlinked magnetic flux tubes. Although themore » corresponding flux is connected to the IMF the northward and southward connected branches are hooked into each other and cannot develop independently. We have studied this problem in the framework of three-dimensional magnetohydrodynamic simulations. The results indicate that a singular current sheet forms at the interface of two interlinked flux tubes if no resistivity is present in the simulation. This current sheet is strongly tilted compared to the original current sheet. In the presence of resistivity the interaction of the two flux tubes forces a fast reconnection process which generates helically twisted closed magnetospheric flux. This linkage induced reconnection generates a boundary layer with layers of open and closed magnetospheric flux and may account for the brightening of auroral arcs poleward of the boundary between open and closed magnetic flux.« less
  • Two-dimensional, nonlinear magnetohydrodynamic simulations in a compressible plasma to investigate magnetic energy release during the process of forced magnetic reconnection are carried out. This is in order to study the heating of the Sun's corona where it is believed that reconnection is induced by the photospheric motions. A sheared force-free field is perturbed by a transitory slow disturbance (pulse) at the boundary. This disturbance triggers the formation of a current sheet that subsequently releases stored magnetic energy through magnetic reconnection. Previously, it has been shown that for small boundary perturbations, the simulation results are consistent with the previous analytic theorymore » based on a linear approach. For larger amplitude perturbations, or close to the threshold for tearing instability, the evolution shows nonlinear behavior. Solar coronal heating may arise due to a series of reconnection events, and a primary aim of this work is to study the interaction of such heating events. Thus, the perturbations are applied at the boundary by successive pulses. It is found that following the second driving pulse, the current sheet expands along the separatrix before relaxing to a reconnective equilibrium with magnetic islands and releasing even more magnetic energy for the same amplitude perturbation. Here, the previous work is extended to study long wavelength perturbations for which the system exhibits even stronger nonlinear aspects.« less
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