Exact models for Hall current reconnection with axial guide fields

Craig, I. J. D.; Watson, P.G.

doi:10.1063/1.1826094

Cited by 14 publications

(16 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They are also broadly consistent with exact steady incompressible Hall MHD solutions which suggest that Hall effects can both speed up and slow down magnetic reconnection, depending on the structure of the magnetic field (Dorelli 2003;Craig & Watson 2005). It should be emphasized that numerical (e.g., Morales et al 2005) and analytical (e.g., Craig et al 2003) time-dependent studies of Hall MHD reconnection often invoke plasma incompressibility.…”

Section: Discussionsupporting

confidence: 56%

“…This is why the system-size dependence remains a hotly debated topic in the literature. It is interesting that analytical Hall MHD models for steady incompressible reconnection (Dorelli 2003;Craig & Watson 2005) can be used to estimate p = −1, suggesting that Hall effects become less effective for larger scales. This result cannot be regarded as definitive, however, because steady analytical models indicate that the Hall term may either speed up or slow down the rate, depending on the orientation of an imposed axial guide field.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Influence of the Hall effect on the reconnection rate at line-tied magnetic X-points

Craig

Litvinenko²

2008

A&A

Self Cite

View full text Add to dashboard Cite

Context. The role of the Hall term in magnetic reconnection at line-tied planar magnetic X-points is explored. Aims. The goal is to determine the reconnection scaling laws and to investigate how the reconnection rate depends on the size of the system in Hall magnetohydrodynamics (MHD). Methods. The evolution of reconnective disturbances is determined numerically by solving the linearized compressible Hall MHD equations. Scaling laws are derived for the decay rate as a function of the dimensionless resistivity and ion inertial length. Results. Although the Hall effect leads to an increase in the decay rate, this increase is shown to be moderated in larger systems. A key finding is that the Hall term contribution to the decay rate, normalized by the resistive decay rate, scales inversely with the system size L, approximately as L −2 . Conclusions. The evidence suggests that decay rate enhancements due to Hall effects in line-tied X-points are weakened for largescale systems. The result may have important implications for modeling energy release in large-scale astrophysical plasma environments, such as solar flares.

show abstract

Section: Discussionsupporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

Influence of the Hall effect on the reconnection rate at line-tied magnetic X-points

Craig

Litvinenko²

2008

A&A

Self Cite

View full text Add to dashboard Cite

show abstract

“…15,16 It has also been incorporated into exact analytical solutions for steady reconnection. 3,5 These facts motivate the following forms for the axial velocity and magnetic field:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Exact global Hall MHD solutions for steady reconnection in incompressible plasmas have been discovered. [3][4][5] These analytical solutions incorporate both planar and axial components of the magnetic field and demonstrate the sensitivity of the reconnection rate to the imposed magnetic geometry: the Hall term can both speed up and slow down magnetic reconnection, depending on the structure of the axial field.…”

Section: Introductionmentioning

confidence: 99%

Current sheet formation at a magnetic neutral line in Hall magnetohydrodynamics

Litvinenko

2007

Physics of Plasmas

View full text Add to dashboard Cite

The inner structure of collisionless magnetic reconnection: The electron-frame dissipation measure and Hall fields Phys.The dynamics of a plasma in the vicinity of a neutral line of the magnetic field is considered in the framework of incompressible Hall magnetohydrodynamics ͑MHD͒. A self-similar solution for the collapse to a current sheet is obtained. Numerical and analytical results are presented. In contrast to the standard incompressible MHD model in two dimensions, the Hall effect leads to the formation of finite-time singularities of the velocity derivatives and the electric current density at the neutral line. Analytical expressions are derived for the collapse time and the form of the solution near the singularity, which agree closely with the numerical results. If the ion skin depth is set to zero, the singularity formation time becomes infinite, corresponding to the standard MHD result. Implications of the results for Hall MHD models of fast magnetic reconnection are discussed.

show abstract

“…These kinetic processes might enhance the resistivity significantly over the Spitzer resistivity based on collisions among particles (Spitzer, 1962). The coupling between macroscopic (MHD) and microscopic (kinetic) processes is important during magnetic reconnection, which has intensively been investigated by theory, simulation, and laboratory (Treumann and Baumjohann, 1997;Biskamp et al, 1995;Horiuchi and Sato, 1999;Yamada et al, 2000;Birn et al, 2001;Shay et al, 2001;Bhattacharjee et al, 2003;Drake et al, 2003;Hanasz and Lesch, 2003;Heitsch and Zweibel, 2003;Rogers et al, 2003;Ji et al, 2004;Craig and Watson, 2005).…”

Section: Living Reviews In Solar Physicsmentioning

confidence: 99%

Solar Flares: Magnetohydrodynamic Processes

Shibata

Magara

2011

Living Rev. Solar Phys.

752

647

View full text Add to dashboard Cite

This paper outlines the current understanding of solar flares, mainly focused on magnetohydrodynamic (MHD) processes responsible for producing a flare. Observations show that flares are one of the most explosive phenomena in the atmosphere of the Sun, releasing a huge amount of energy up to about 10 32 erg on the timescale of hours. Flares involve the heating of plasma, mass ejection, and particle acceleration that generates high-energy particles. The key physical processes for producing a flare are: the emergence of magnetic field from the solar interior to the solar atmosphere (flux emergence), local enhancement of electric current in the corona (formation of a current sheet), and rapid dissipation of electric current (magnetic reconnection) that causes shock heating, mass ejection, and particle acceleration. The evolution toward the onset of a flare is rather quasi-static when free energy is accumulated in the form of coronal electric current (field-aligned current, more precisely), while the dissipation of coronal current proceeds rapidly, producing various dynamic events that affect lower atmospheres such as the chromosphere and photosphere. Flares manifest such rapid dissipation of coronal current, and their theoretical modeling has been developed in accordance with observations, in which numerical simulations proved to be a strong tool reproducing the time-dependent, nonlinear evolution of a flare. We review the models proposed to explain the physical mechanism of flares, giving an comprehensive explanation of the key processes mentioned above. We start with basic properties of flares, then go into the details of energy build-up, release and transport in flares where magnetic reconnection works as the central engine to produce a flare.

show abstract

Exact models for Hall current reconnection with axial guide fields

Cited by 14 publications

References 26 publications

Influence of the Hall effect on the reconnection rate at line-tied magnetic X-points

Influence of the Hall effect on the reconnection rate at line-tied magnetic X-points

Current sheet formation at a magnetic neutral line in Hall magnetohydrodynamics

Solar Flares: Magnetohydrodynamic Processes

Contact Info

Product

Resources

About