A stability property of a force-free  surface 
 bounding a vacuum gap

Aly, J. J.

doi:10.1051/0004-6361:20041624

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…The quasi-static dynamics of coronal fields is often modeled as a sequence of instabilities followed by relaxation and current sheets formation (Ng & Bhattacharjee 1998), in which equilibria play an important role (Aly 2005).…”

Section: Discussionmentioning

confidence: 99%

Current Sheets Formation in Tangled Coronal Magnetic Fields

Rappazzo

Parker

2013

ApJ

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We investigate the dynamical evolution of magnetic fields in closed regions of solar and stellar coronae. To understand under which conditions current sheets form, we examine dissipative and ideal reduced magnetohydrodynamic models in cartesian geometry, where two magnetic field components are present: the strong guide field B 0 , extended along the axial direction, and the dynamical orthogonal field b. Magnetic field lines thread the system along the axial direction, that spans the length L, and are line-tied at the top and bottom plates. The magnetic field b initially has only large scales, with its gradient (current) length-scale of order ℓ b . We identify the magnetic intensity threshold b/B 0 ∼ ℓ b /L. For values of b below this threshold, field-line tension inhibits the formation of current sheets, while above the threshold they form quickly on fast ideal timescales. In the ideal case, above the magnetic threshold, we show that current sheets thickness decreases in time until it becomes smaller than the grid resolution, with the analyticity strip width δ decreasing at least exponentially, after which the simulations become under-resolved.

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Section: Discussionmentioning

confidence: 99%

Current Sheets Formation in Tangled Coronal Magnetic Fields

Rappazzo

Parker

2013

ApJ

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“…Note that Eq. (15) imposes σE < 0 just above Σ (with E the component of E along B), while in a true equilibrium electrosphere we would have µE > 0 just above the upper surface of the equatorial belt (approximated by Σ in our model) where the volume charge density is µ (see Aly 2005, for a general proof of this statement). However, this should not cause too much trouble here, as the problems we are interested in are essentially dominated by the radial structure of the electric field (remember that we do not allow vertical distortions of Σ).…”

Section: Some Relations For the Electrostatic Potential And Fieldmentioning

confidence: 84%

Conservation laws and theorems of confinement and stability for a charged equatorial disk in a pulsar magnetosphere

Aly¹

2005

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Abstract. For studying the nonaxisymmetric stability of the bounded electrosphere of an "aligned pulsar" (Michel's structure with polar domes and equatorial belt), Pétri et al. (2002) recently introduced a simplified but useful model in which all the charge-separated plasma located outside the magnetized rotating star is concentrated into a thin equatorial disk. In this paper, some aspects of this model are investigated analytically. It is shown that the equations governing the behaviour of the disk -in the case where there are no sources of particles feeding it -imply a series of conservation laws (for energy, angular momentum,...), and that there is a non-canonical Hamiltonian structure hidden behind them. The conservation laws are used to prove that: (i) for any initial conditions imposed on the disk, its evolution cannot lead to charges escaping to infinity (confinement theorem); (ii) a disk steady state with a possibly rotating pattern is nonlinearly stable if the charge density per unit of magnetic flux is a decreasing function of the electrostatic potential in the rotating frame (stability theorem).

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“…On the force-free side, the charges ensure that E = 0 (and if any lapse in shielding occurs, the electric field direction is such that it drives charges towards the trap surface, which is why the cloud fills at least up to this surface), but on the vacuum side, E is non-vanishing and points in the expedient direction to collect and transport stray particles of the same (sign of) charge into the force-free side, while repelling particles of the undesirable opposite charge. This ensures that the charge clouds, and in turn the electrosphere solutions, are stable [120,126] 12 . Such a self-maintenance feature also prevents clouds from dissipating if they spill over beyond the trap surfaces, as would be the case when there is too much charge and the electric repulsion is severe.…”

Section: Appendix A3 With Plasma: the Charge-separated Electrospheresmentioning

confidence: 99%

A Magnetospheric Dichotomy for Pulsars with Extreme Inclinations

Zhang

2021

Universe

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In this work, we expand on a comment by Lyne et al. (2017), that intermittent pulsars tend to congregate near a stripe in the logarithmic period versus period-derivative diagram. Such a stripe represents a small range of polar cap electric potential. Taking into account also the fact (already apparent in their Figure 7, but not explicitly stated there) that high-fraction nulling pulsars also tend to reside within this and an additional stripe, we make the observation that the two stripes further match the “death lines” for double- and single-pole interpulses, associated with nearly orthogonal and aligned rotators, respectively. These extreme inclinations are known to suffer from pair production deficiencies, so we propose to explain intermittency and high-fraction nulling by reinvigorating some older quiescent (no pulsar wind or radio emission) “electrosphere” solutions. Specifically, as the polar potential drops below the two threshold bands (i.e., the two stripes), corresponding to the aligned and orthogonal rotators, their respective magnetospheres transition from being of the active pair-production-sustained-type into becoming the electrospheres, in which charges are only lifted from the star. The borderline cases sitting in the gap outside of the stable regime of either case manifest as high-fraction nullers. Hall evolution of the magnetic field inside orthogonally rotating neutron stars can furthermore drive secular regime changes, resulting in intermittent pulsars.

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A stability property of a force-free surface bounding a vacuum gap

Cited by 4 publications

References 15 publications

Current Sheets Formation in Tangled Coronal Magnetic Fields

Current Sheets Formation in Tangled Coronal Magnetic Fields

Conservation laws and theorems of confinement and stability for a charged equatorial disk in a pulsar magnetosphere

A Magnetospheric Dichotomy for Pulsars with Extreme Inclinations

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