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Hu, Yaozhong; Xia, Li; Li, X.; Wang, J. X.; Ai, Guoxiang

doi:10.1023/a:1004905230866

Cited by 29 publications

(11 citation statements)

References 11 publications

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“…The microscopic processes by which the energy is thermalised may include Ohmic dissipation within current sheets, viscosity (as the evolving magnetic field generates plasma flows) or even non-MHD processes such as ion cyclotron waves. This tendency to relax to a minimum energy state is well confirmed by experiments in laboratory plasmas (Heidbrink & Dang 2000;Ji et al 1995;Taylor 1986) as well as by numerical simulations of coronal plasmas (Hu et al 1997;Kusano et al 1994). …”

Section: Introductionsupporting

confidence: 63%

Solar coronal heating by relaxation events

Browning¹,

Linden²

2003

A&A

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Abstract.A coronal heating model is proposed which predicts heating by a series of discrete events of various energies, analogous to the observed range of events from large scale flares through various transient brightening phenomena down to the often discussed "nanoflares". We suggest that an energy release event occurs when a field becomes linearly unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to reconnection in fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parameterised by two values of α (the ratio of current density to field strength). Different initial α profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes, but our model predicts an observationally realistic minimum size for these events.

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Section: Introductionsupporting

confidence: 63%

Solar coronal heating by relaxation events

Browning¹,

Linden²

2003

A&A

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“…The relative helicity, introduced by Berger & Field (1984), must be used instead of the total helicity. For our cylindrical flux rope, the total relative helicity per unit length of the rope is, in the notations of Hu et al (1997) and Zhang et al (2006),…”

Section: Taylor Relaxationmentioning

confidence: 99%

Coronal hydromagnetic implosions

Janse

Low

2007

A&A

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Aims. The released magnetic energy in coronal events, i.e. in flares and coronal mass ejections (CMEs), is believed to have been stored locally in the coronal magnetic field. The energy in a magnetic field B is distributed in space with densitythat is also the isotropic magnetic pressure at each point in space. A localized release of magnetic energy would therefore imply a localized reduction of magnetic pressure. Hence, such a release could lead to an implosion of the magnetic structure as its atmospheric surrounding pushes inward. Whether an implosion would take place immediately depends on how fast the released energy can escape, through optically-thin radiation, thermal conduction, hydromagnetic waves, and, the magnetic channeling of high-energy particles. Methods. We determined whether an expansion or an implosion would occur when cylindrical tubes of twisted flux relaxed to lower energy states. Depending on the dynamical nature of the relaxation we assumed, relevant dynamical invariants were invoked to relate a particular end state to the given initial state. Results. Comparing the initial and the end state, we found that when most of the liberated energy escaped the cylinder imploded. The results suggest that implosions may take place simultaneously with flares and CMEs.

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“…101 for a Cartesian field. This helicity can also be shown to be the relative helicity of Berger and Field, 42 except for a free additive constant.…”

Section: Appendix A: Generalized Helicities and Energy Extrema: Axisymentioning

confidence: 99%

Topological complexity and tangential discontinuity in magnetic fields

2010

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This is a study of the topological magnetostatic problem. A magnetic field embedded in a perfectly conducting fluid and rigidly anchored at its boundary has a specific topology invariant for all time. Subject to that topology, the force-free state of such a field generally requires the presence of tangential discontinuities ͑TDs͒. This property proposed and demonstrated by Parker ͓Spontaneous Current Sheets in Magnetic Fields ͑Oxford University Press, New York, 1994͔͒ is explained in terms of ͑i͒ the overdetermined nature of the magnetostatic partial differential equations nonlinearly coupled to the integral equations imposing the field topology and ͑ii͒ the hyperbolic nature of the partial differential equation for the twist function ␣ of the force-free field. The mathematical analysis elucidates a basic incompatibility between preserving a complex field topology and attaining equilibrium, if analyticity is assumed. Physics avoids this incompatibility via TD formation as a natural consequence of perfect conductivity. The study relates TD formation to topological complexity in two-dimensional and three-dimensional fields, as well as the topological connectivity and geometric shape of the field domain. Mathematical points made are given physical interpretations, but important topological concepts for understanding spontaneous TDs have remained incomplete. As an application, examples are presented to define twisted and untwisted potential fields found in simply and multiply connected domains, clarifying a confusion in several recent publications. Appendix A treats the expression of the frozen-in condition by a continuum of conserved, total generalized helicities. Appendix B reports briefly on concurrent developments showing that a published objection to the theory of spontaneous TDs is based upon a misunderstanding of the theory.

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Untitled

Cited by 29 publications

References 11 publications

Solar coronal heating by relaxation events

Solar coronal heating by relaxation events

Coronal hydromagnetic implosions

Topological complexity and tangential discontinuity in magnetic fields

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