Exact Steady State Reconnection Solutions in Weakly Collisional Plasmas

Watson, P.G.; Porcelli, Francesco

doi:10.1086/425646

Cited by 8 publications

(5 citation statements)

References 20 publications

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“…These effects have already been examined in the related problem of weakly collisional reconnection in the limit of a strong guide field. 21 In this problem there are two main regimes: a regime where finite Larmor radius effects dominate, and growing oscillatory solutions, much like those found in Craig and Watson,6 develop; and an electron inertia dominated regime, where a single peak localized solution naturally saturates. Watson and Porcelli 21 found that the oscillatory solutions become unstable, and the same is probably true of the oscillatory solutions found in the work by Craig and Watson 6 and discussed here in Sec.…”

Section: Discussionmentioning

confidence: 95%

“…6,13 To what extent the inclusion of a generalized Ohm's law, or a truly collisionless description of the reconnecting current layer, modifies these conclusions is largely unknown at present. Related work on reconnection in weakly collisional plasmas with strong guide fields 21 suggests that in some regimes the large scale quasi-one-dimensional sheets can become unstable. This transition may signal the switch over from one-dimensional current sheets to the cross shaped current structures observed in Hall MHD reconnection.…”

Section: More General Solutions and The Breakdown Of The Analyticmentioning

confidence: 99%

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Exact models for Hall current reconnection with axial guide fields

Craig

Watson

2005

Physics of Plasmas

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This paper employs an analytic reconnection model to investigate the conditions under which Hall currents can influence reconnection and Ohmic dissipation rates. It is first noted that time dependent magnetohydrodynamic systems can be analyzed by decomposing the magnetic and velocity fields into guide field and reconnecting field components. A formally exact solution shows that Hall currents can speed up or slow down the reconnection rate depending on the strength and orientation of the axial guide field. In particular, merging solutions are developed in which the axial guide field is the dominant driver of the reconnection. The extent to which Hall currents can alleviate the buildup of back pressures in flux pile-up reconnection models is also examined. The analysis shows that, although enhancements of the merging rate can be expected under certain conditions, it is unlikely that Hall currents can completely undo the fundamental pressure limitations associated with flux pile-up reconnection.

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Section: Discussionmentioning

confidence: 95%

Section: More General Solutions and The Breakdown Of The Analyticmentioning

confidence: 99%

Exact models for Hall current reconnection with axial guide fields

Craig

Watson

2005

Physics of Plasmas

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“…Refs. [23,24]). The results of the previous section provide strong evidence that in a fully dynamic and fully 3D (yet incompressible) system, the fan current sheet solutions are indeed dynamically accessible.…”

Section: Relation To Analytical Solutions a Dynamic Accessibilitymentioning

confidence: 99%

Current sheets at three-dimensional magnetic nulls: Effect of compressibility

2007

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The nature of current sheet formation in the vicinity of three-dimensional (3D) magnetic null points is investigated. The particular focus is upon the effect of the compressibility of the plasma on the qualitative and quantitative properties of the current sheet. An initially potential 3D null is subjected to shearing perturbations, as in a previous paper [Pontin et al., Phys. Plasmas, in press (2007)]. It is found that as the incompressible limit is approached, the collapse of the null point is suppressed, and an approximately planar current sheet aligned to the fan plane is present instead. This is the case regardless of whether the spine or fan of the null is sheared. Both the peak current and peak reconnection rate are reduced. The results have a bearing on previous analytical solutions for steady-state reconnection in incompressible plasmas, implying that fan current sheet solutions are dynamically accessible, while spine current sheet solutions are not.In astrophysical plasmas, such as the solar corona, the three-dimensional (3D) magnetic field topology is often highly complex. In such complex 3D magnetic fields, where traditional two-dimensional (2D) X-point magnetic reconnection models may no longer be applicable, determining the sites at which dynamic phenomena and energy release may occur is a crucial and non-trivial problem. Due to the typically very high Lundquist number, such events occur only at locations where intense currents (singular under an ideal MHD evolution) may form.One such site is a 3D magnetic null point (e.g. Refs. [1,2,3,4,5]). The nature of current sheet formation at such 3D nulls is investigated here.3D null points are predicted to be present in abundance in the solar corona (e.g. Refs. [6,7]). Furthermore, there is observational evidence that reconnection at a 3D null may be important in some solar flares 8 , as well as in eruptive phenomena in active regions 9 . In addition, the first in situ observation 10 of reconnection occurring at a 3D null point in the Earth's magnetotail has recently been made by the Cluster spacecraft. Moreover, current growth at 3D nulls has been observed in the laboratory 11 .The magnetic field topology and geometry in the vicinity of such a null can be described by the two sets of field lines which asymptotically approach, or recede from, the null. A pair of field lines approach (recede from) the null from opposite directions, defining the 'spine' (or γ-line) of the null. In addition, an infinite family of field lines recede from (approach) the null in a surface known as the fan (or Σ-) plane (see Refs. [2,12]).To this point, many studies of the MHD behaviour of 3D nulls have been kinematic, see e.g. Refs. [2,13,14,15]. However, a few solutions to the full set of MHD equations do exist for reconnection at current sheets located at 3D nulls, in incompressible plasmas. These incompressible solutions are based upon the technique first proposed by Craig & Henton 16 for the 2D reconnection problem. The solutions describe steady-state current sheets aligned...

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“…Craig and coworkers obtained more general solutions that describe magnetic reconnection in two and three dimensions Craig & Fabling 1996;Craig et al , 1997. More recent models incorporated various physical effects, such as the Hall electric field (Dorelli 2003), electron inertia (Watson & Porcelli 2004), and viscosity (Besser et al 1990;Litvinenko 2005; for a recent summary, see Craig & Litvinenko 2012).…”

Section: Introductionmentioning

confidence: 99%

An Exact Solution for Magnetic Annihilation in a Curved Current Sheet

Litvinenko

2013

ApJ

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An exact magnetohydrodynamic solution is presented for steady magnetic annihilation (merging) in an incompressible resistive viscous plasma. The merging, driven by an axisymmetric stagnation flow on a cylinder, takes place in a curved current sheet that is perpendicular to the plane in which the plasma flow stagnates. The new solution extends earlier models of flux pileup merging in a flat current sheet, driven by stagnation-point flows. The new solution remains valid in the presence of both the isotropic and anisotropic (parallel) plasma viscosity. The geometry of the solution may make it useful in modeling the photospheric flux cancellation on the Sun.

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Exact Steady State Reconnection Solutions in Weakly Collisional Plasmas

Cited by 8 publications

References 20 publications

Exact models for Hall current reconnection with axial guide fields

Exact models for Hall current reconnection with axial guide fields

Current sheets at three-dimensional magnetic nulls: Effect of compressibility

An Exact Solution for Magnetic Annihilation in a Curved Current Sheet

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