Stability of a force‐free Hall equilibrium and release of magnetic energy

Kitchatinov, L. L.

doi:10.1002/asna.201913644

Cited by 6 publications

(6 citation statements)

References 23 publications

(38 reference statements)

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“…This heuristic condition for the instability is satisfied by any force-free field of ∇ × B = α(r)B. Instability of a 1-D force-free field with maximum helicity was confirmed by Kitchatinov (2019). The instability can be active with the force-free fields of the solar corona where the Hall number R H ∼ 10 7 is large.…”

Section: Discussionmentioning

confidence: 78%

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Hall instability: origin, properties and asymptotic theory for its tearing mode

Kitchatinov

2021

J. Plasma Phys.

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Hall instability in electron magnetohydrodynamics is interpreted as the shear-Hall instability driven jointly by helicoidal oscillations and shear in the electron current velocity. This explanation suggests an antiparallel orientation of the background magnetic field and vorticity of the current velocity as the necessary condition for Hall instability. The condition is tested and generally confirmed by numerical computations in plane slab geometry. Unstable eigenmodes are localized in the spatial regions of the antiparallel field and vorticity. Computations of the tearing-type mode of the instability are complemented by (and generally agree with) asymptotic analytical estimations for large Hall numbers. The stabilizing effect of perfect conductor boundary conditions is found and explained. For large Hall numbers, the growth rates approach the power-law dependence $\sigma \propto B^\alpha \eta ^{1-\alpha }$ on the magnetic field ( $B$ ) and diffusivity ( $\eta$ ). Almost all computations give the power index $\alpha = 3/4$ with one exception of the tearing-type mode with vacuum boundary conditions for which case $\alpha = 2/3$ .

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Section: Discussionmentioning

confidence: 78%

“…A decrease of the field scale cannot therefore be balanced by diffusion. Release of magnetic energy on the nonlinear stage of the instability proceeds in a sequence of spikes or bursts, where each spike releases several percent of magnetic energy (Kitchatinov 2017(Kitchatinov , 2019.…”

Section: Discussionmentioning

confidence: 99%

Hall instability: origin, properties and asymptotic theory for its tearing mode

Kitchatinov

2021

J. Plasma Phys.

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“…Closely related to this feature is the idea of a Hall equilibrium-a magnetic field configuration where the Hall term is identically equal to zero. Such equilibria were first proposed by [71], and have been extensively studied further [65,66,72,73]. In most of these works, the field is computed directly from the requirement that the Hall term ∇ × 1 4πen e (∇ × B) × B = 0, in which case one must additionally consider the question of whether the solution is stable or not.…”

Section: Hall Evolutionmentioning

confidence: 99%

Evolution of Neutron Star Magnetic Fields

2021

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Neutron stars are natural physical laboratories allowing us to study a plethora of phenomena in extreme conditions. In particular, these compact objects can have very strong magnetic fields with non-trivial origin and evolution. In many respects, its magnetic field determines the appearance of a neutron star. Thus, understanding the field properties is important for the interpretation of observational data. Complementing this, observations of diverse kinds of neutron stars enable us to probe parameters of electro-dynamical processes at scales unavailable in terrestrial laboratories. In this review, we first briefly describe theoretical models of the formation and evolution of the magnetic field of neutron stars, paying special attention to field decay processes. Then, we present important observational results related to the field properties of different types of compact objects: magnetars, cooling neutron stars, radio pulsars, and sources in binary systems. After that, we discuss which observations can shed light on the obscure characteristics of neutron star magnetic fields and their behaviour. We end the review with a subjective list of open problems.

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“…These models have successfully addressed observational properties of NSs and they have revealed, moreover, rich effects in terms of magnetohydrodynamical evolution, arising from the non-linear nature of the equations. These effects include instabilities and turbulent cascades and are of broader applications within the realm of magnetohydrodynamics [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68].…”

Section: Introductionmentioning

confidence: 99%

Magnetic Field Evolution in Neutron Star Crusts: Beyond the Hall Effect

Gourgouliatos

Grandis²,

Igoshev

2022

Symmetry

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Neutron stars host the strongest magnetic fields that we know of in the Universe. Their magnetic fields are the main means of generating their radiation, either magnetospheric or through the crust. Moreover, the evolution of the magnetic field has been intimately related to explosive events of magnetars, which host strong magnetic fields, and their persistent thermal emission. The evolution of the magnetic field in the crusts of neutron stars has been described within the framework of the Hall effect and Ohmic dissipation. Yet, this description is limited by the fact that the Maxwell stresses exerted on the crusts of strongly magnetised neutron stars may lead to failure and temperature variations. In the former case, a failed crust does not completely fulfil the necessary conditions for the Hall effect. In the latter, the variations of temperature are strongly related to the magnetic field evolution. Finally, sharp gradients of the star’s temperature may activate battery terms and alter the magnetic field structure, especially in weakly magnetised neutron stars. In this review, we discuss the recent progress made on these effects. We argue that these phenomena are likely to provide novel insight into our understanding of neutron stars and their observable properties.

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Stability of a force‐free Hall equilibrium and release of magnetic energy

Cited by 6 publications

References 23 publications

Hall instability: origin, properties and asymptotic theory for its tearing mode

Hall instability: origin, properties and asymptotic theory for its tearing mode

Evolution of Neutron Star Magnetic Fields

Magnetic Field Evolution in Neutron Star Crusts: Beyond the Hall Effect

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