Numerical investigation of a three-dimensional four field model for collisionless magnetic reconnection

Grasso, D.; Borgogno, Dario; Tassi, Emanuele

doi:10.1016/j.cnsns.2011.06.013

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…This can indeed be seen as a limitation of the present analysis. However, numerical simulations [36][37][38] show that, for instance, secondary instabilities due to colliding jets, can originate inside a magnetic island, and the subsequent turbulent evolution of the instability remains confined within the island. Therefore, in addition to the above mentioned technical argument related to the Poincaré inequality, restricting the analysis to the region enclosed by the separatrices does not appear to rule out all physically relevant processes.…”

Section: The Domain Of Analysismentioning

confidence: 99%

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

Granier¹,

Tassi²

2020

J. Phys. A: Math. Theor.

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The linear stability of chains of magnetic vortices in a plasma is investigated analytically in two dimensions by means of a reduced fluid model assuming a strong guide field and accounting for equilibrium electron temperature anisotropy. The chain of magnetic vortices is modeled by means of the classical 'cat's eyes' solutions and the linear stability is studied by analysing the second variation of a conserved functional, according to the energy-Casimir method. The stability analysis is carried out on the domain bounded by the separatrices of the vortices. Two cases are considered, corresponding to a ratio between perpendicular equilibrium ion and electron temperature much greater or much less than unity, respectively. In the former case, equilibrium flows depend on an arbitrary function. Stability is attained if the equilibrium electron temperature anisotropy is bounded from above and from below, with the lower bound corresponding to the condition preventing the firehose instability. A further condition sets an upper limit to the amplitude of the vortices, for a given choice of the equilibrium flow. For cold ions, two sub-cases have to be considered. In the first one, equilibria correspond to those for which the velocity field is proportional to the local Alfvén velocity. Stability conditions imply: an upper limit on the amplitude of the flow, which automatically implies firehose stability, an upper bound on the electron temperature anisotropy and again an upper bound on the size of the vortices. The second sub-case refers to equilibrium electrostatic potentials which are not constant on magnetic flux surfaces and the resulting stability conditions correspond to those of the first sub-case in the absence of flow.

show abstract

Section: The Domain Of Analysismentioning

confidence: 99%

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

Granier¹,

Tassi²

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…This can indeed be seen as a limitation of the present analysis. However, numerical simulations [39,40,41] show that, for instance, secondary instabilities due to colliding jets, can originate inside a magnetic island, and the subsequent turbulent evolution of the instability remains confined within the island. Therefore, in addition to the above mentioned technical argument related to the Poincaré inequality, restricting the analysis to the region enclosed by the separatrices does not appear to rule out all physically relevant processes.…”

Section: The Domain Of Analysismentioning

confidence: 99%

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

Granier,

Tassi

2020

Preprint

Self Cite

View full text Add to dashboard Cite

The linear stability of chains of magnetic vortices in a plasma is investigated analytically in two dimensions by means of a reduced fluid model assuming a strong guide field and accounting for equilibrium electron temperature anisotropy. The chain of magnetic vortices is modelled by means of the classical "cat's eyes" solutions and the linear stability is studied by analysing the second variation of a conserved functional, according to the Energy-Casimir method. The stability analysis is based on a fluid model obtained from a gyrofluid model by means of a simple Hamiltonian reduction and is carried out on the domain bounded by the separatrices of the vortices. Two cases are considered, corresponding to a ratio between perpendicular equilibrium ion and electron temperature much greater or much less than unity, respectively. In the former case, equilibrium flows depend on an arbitrary function. Stability is attained if the equilibrium electron temperature anisotropy is bounded from above and from below, with the lower bound corresponding to the condition preventing the firehose instability. A further condition sets an upper limit to the amplitude of the vortices, for a given choice of the equilibrium flow. For cold ions, two sub-cases have to be considered. In the first one, equilibria correspond to those for which the velocity field is proportional to the local Alfvén velocity. Stability conditions imply: an upper limit on the amplitude of the flow, which automatically implies firehose stability, an upper bound on the electron temperature anisotropy and again an upper bound on the size of the vortices. The second sub-case refers to equilibrium electrostatic potentials which are not constant on magnetic flux surfaces and the resulting stability conditions correspond to those of the first sub-case in the absence of flow.

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A two-fluid study of oblique tearing modes in a force-free current sheet

et al. 2016

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Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Since kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless tearing instability in a force-free current sheet with a two-fluid model and fully kinetic simulations. Our results indicate that the most unstable modes are oblique for guide fields larger than the reconnecting field, in agreement with the kinetic results. The standard two-fluid tearing theory is extended to address the tearing instability at oblique angles. The resulting theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.

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Numerical investigation of a three-dimensional four field model for collisionless magnetic reconnection

Cited by 6 publications

References 21 publications

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

A two-fluid study of oblique tearing modes in a force-free current sheet

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