Exact Solutions for Steady State, Spine, and Fan Magnetic Reconnection

Craig, I. J. D.; Fabling, R.B.

doi:10.1086/177210

Cited by 93 publications

(94 citation statements)

References 4 publications

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“…1 t lnjjDx 0f tx0 ðÞ jj; (22) where jj Á jj is defined as the Euclidean norm. Equation (22) provides us with only one LCE since we have only considered a single tangent vectorũ 0 .…”

Section: A Calculating the Complete Lyapunov Spectrummentioning

confidence: 99%

Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos

Gascoyne

2015

Physics of Plasmas

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Using a full orbit test particle approach, we analyse the motion of a single proton in the vicinity of magnetic null point configurations which are solutions to the kinematic, steady state, resistive magnetohydrodynamics equations. We consider two magnetic configurations, namely, the sheared and torsional spine reconnection regimes [E. R. Priest and D. I. Pontin, Phys. Plasmas 16, 122101 (2009); P. Wyper and R. Jain, Phys. Plasmas 17, 092902 (2010)]; each produce an associated electric field and thus the possibility of accelerating charged particles to high energy levels, i.e., > MeV, as observed in solar flares [R. P. Lin, Space Sci. Rev. 124, 233 (2006)]. The particle's energy gain is strongly dependent on the location of injection and is characterised by the angle of approach b, with optimum angle of approach b opt as the value of b which produces the maximum energy gain. We examine the topological features of each regime and analyse the effect on the energy gain of the proton. We also calculate the complete Lyapunov spectrum for the considered dynamical systems in order to correctly quantify the chaotic nature of the particle orbits. We find that the sheared model is a good candidate for the acceleration of particles, and for increased shear, we expect a larger population to be accelerated to higher energy levels. In the strong electric field regime (E 0 ¼ 1500 V/m), the torsional model produces chaotic particle orbits quantified by the calculation of multiple positive Lyapunov exponents in the spectrum, whereas the sheared model produces chaotic orbits only in the neighbourhood of the null point. V C 2015 AIP Publishing LLC.

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“…1 t lnjjDx 0f tx0 ðÞ jj; (22) where jj Á jj is defined as the Euclidean norm. Equation (22) provides us with only one LCE since we have only considered a single tangent vectorũ 0 .…”

Section: A Calculating the Complete Lyapunov Spectrummentioning

confidence: 99%

Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos

Gascoyne

2015

Physics of Plasmas

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“…1,2002 CURRENT SHEET FORMATION IN CORONAL LOOPour model found. A more careful analysis of this approach will appeal to the dynamic response of a magnetic null point, a topic of ongoing investigation (Hassam 1992;Craig & Fabling 1996). In order to specify a field-line mapping, we assumed the chromosphere to be in force-free equilibrium.…”

Section: The Boundary Conditionmentioning

confidence: 99%

A Three‐dimensional Dynamical Model of Current Sheet Formation in a Coronal Loop

Longcope

Ballegooijen

2002

ApJ

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We develop a three-dimensional model for the time evolution of a slender coronal loop anchored in multiple isolated photospheric flux elements. As a result of the composite photospheric boundaries, the coronal field comprises multiple flux domains. The model shows that motion at the footpoints results in current singularities developing along separators between domains. Motion at one end of the loop creates a nonsingular Alfvénic pulse. Repeated reflections from the complex photospheric boundaries change the pulse's current into a surface singularity traveling along the separator ribbon. Final relaxation leads to an equilibrium that is current-free within all of the coronal domains and contains a separator current sheet. The relation of the equilibrium current to the footpoint displacements confirms previous quasi-static models of threedimensional separator current sheets.

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“…At this point there is still significant current in the system which slowly reduces through magnetic diffusion. Such fan plane perturbations are reminiscent of the radially symmetric non-reconnecting m = 0 spine mode of Craig & Fabling (1996) hinting that such solutions could be utilized to analyze such oscillations in the future. For much longer time frames this oscillatory motion will damp out (which we see begins to occur around t = 10 in Fig.…”

Section: Temporal Variation: Relaxation Phasementioning

confidence: 99%

“…Subsequently it has been shown that twisting motions about the spine/fan create a current sheet along the fan/spine leading to Torsional fan/spine respectively (Priest & Pontin 2009). Shearing motions of the spine or fan in the incompressible situation give rise to current accumulation at the fan and spine respectively (Priest & Titov 1996;Craig & Fabling 1996) known as fan and spine reconnection. When finite plasma compressibility is invoked the plasma pressure gradient is too weak within the planar current sheets of both cases to resist the Lorentz force driven spine-fan collapse and a current sheet forms at an angle to the spine and fan within which "spine-fan" reconnection takes place (Priest & Pontin 2009;Pontin et al 2007a,b).…”

Section: Introductionmentioning

confidence: 99%

Spine-fan reconnection

Wyper

Jain

Pontin

2012

A&A

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Context. From observations, the atmosphere of the Sun has been shown to be highly dynamic with perturbations of the magnetic field often lacking temporal or spatial symmetry. Despite this, studies of the spine-fan reconnection mode at 3D nulls have so far focused on the very idealised case with symmetric driving of a fixed spatial extent. Aims. We investigate the spine-fan reconnection process for less idealised cases, focusing on asymmetric driving and drivers with different length scales. We look at the initial current sheet formation and whether the scalings developed in the idealised models are robust in more realistic situations. Methods. The investigation was carried out by numerically solving the resistive compressible 3D magnetohydrodynamic equations in a Cartesian box containing a linear null point. The spine-fan collapse was driven at the null through tangential boundary driving of the spine foot points. Results. We find significant differences in the initial current sheet formation with asymmetric driving. Notable is the displacement of the null point position as a function of driving velocity and resistivity (η). However, the scaling relations developed in the idealised case are found to be robust (albeit at reduced amplitudes) despite this extra complexity. Lastly, the spatial variation is also shown to play an important role in the initial current sheet formation through controlling the displacement of the spine foot points. Conclusions. We conclude that during the early stages of spine-fan reconnection both the temporal and spatial nature of the driving play important roles, with the idealised symmetrically driven case giving a "best case" for the rate of current development and connectivity change. As the most interesting eruptive events occur in relatively short time frames this work clearly shows the need for high temporal and spatial knowledge of the flows for accurate interpretation of the reconnection scenario. Lastly, since the scalings developed in the idealised case remain robust with more complex driving we can be more confident of their use in interpreting reconnection in complex magnetic field structures.

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Exact Solutions for Steady State, Spine, and Fan Magnetic Reconnection

Cited by 93 publications

References 4 publications

Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos

Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos

A Three‐dimensional Dynamical Model of Current Sheet Formation in a Coronal Loop

Spine-fan reconnection

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