Decay of trefoil and other magnetic knots

AbstractTwo setups with interlocked magnetic flux tubes are used to study the evolution of magnetic energy and helicity on magnetohydrodynamical (MHD) systems like plasmas. In one setup the initial helicity is zero while in the other it is finite. To see if it is the actual linking or merely the helicity content that influences the dynamics of the system we also consider a setup with unlinked field lines as well as a field configuration in the shape of a trefoil knot. For helical systems the decay of magnetic energy is slowed down by the helicity which decays slowly. It turns out that it is the helicity content, rather than the actual linking, that is significant for the dynamics.

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Ion velocity distributions within the LLBL and their possible implication to multiple reconnections

Annales Geophysicae ◽

10.5194/angeo-22-213-2004 ◽

2004 ◽

Vol 22 (1) ◽

pp. 213-236 ◽

Cited By ~ 4

Author(s):

O. L. Vaisberg ◽

L. A. Avanov ◽

T. E. Moore ◽

V. N. Smirnov

Keyword(s):

Magnetic Field ◽

Magnetic Flux ◽

Flux Tube ◽

Magnetic Flux Tube ◽

Flux Tubes ◽

Different Types ◽

Subsolar Point ◽

Magnetic Flux Tubes ◽

Ion Velocity ◽

Field Lines

Abstract. We analyze two LLBL crossings made by the Interball-Tail satellite under a southward or variable magnetosheath magnetic field: one crossing on the flank of the magnetosphere, and another one closer to the subsolar point. Three different types of ion velocity distributions within the LLBL are observed: (a) D-shaped distributions, (b) ion velocity distributions consisting of two counter-streaming components of magnetosheath-type, and (c) distributions with three components, one of which has nearly zero parallel velocity and two counter-streaming components. Only the (a) type fits to the single magnetic flux tube formed by reconnection between the magnetospheric and magnetosheath magnetic fields. We argue that two counter-streaming magnetosheath-like ion components observed by Interball within the LLBL cannot be explained by the reflection of the ions from the magnetic mirror deeper within the magnetosphere. Types (b) and (c) ion velocity distributions would form within spiral magnetic flux tubes consisting of a mixture of alternating segments originating from the magnetosheath and from magnetospheric plasma. The shapes of ion velocity distributions and their evolution with decreasing number density in the LLBL indicate that a significant part of the LLBL is located on magnetic field lines of long spiral flux tube islands at the magnetopause, as has been proposed and found to occur in magnetopause simulations. We consider these observations as evidence for multiple reconnection Χ-lines between magnetosheath and magnetospheric flux tubes. Key words. Magnetospheric physics (magnetopause, cusp and boundary layers; solar wind-magnetosphere interactions)

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Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer

Journal of Plasma Physics ◽

10.1017/s0022377820000641 ◽

2020 ◽

Vol 86 (4) ◽

Author(s):

Muni Zhou ◽

Nuno F. Loureiro ◽

Dmitri A. Uzdensky

Keyword(s):

Magnetic Flux ◽

Time Evolution ◽

Magnetic Energy ◽

Numerical Study ◽

Three Dimensional ◽

Early Time ◽

Small Scale ◽

Flux Tubes ◽

Seed Field ◽

Magnetic Flux Tubes

We report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers, and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants, viz. the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in a critically balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.

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Particle acceleration in relativistic magnetic flux-merging events

Journal of Plasma Physics ◽

10.1017/s002237781700071x ◽

2017 ◽

Vol 83 (6) ◽

Cited By ~ 18

Author(s):

Maxim Lyutikov ◽

Lorenzo Sironi ◽

Serguei S. Komissarov ◽

Oliver Porth

Keyword(s):

Magnetic Field ◽

Particle Acceleration ◽

Magnetic Flux ◽

Power Law ◽

Magnetic Energy ◽

Thermal Power ◽

Local Magnetic Field ◽

Flux Tubes ◽

Maximal Energy ◽

Magnetic Flux Tubes

Using analytical and numerical methods (fluid and particle-in-cell simulations) we study a number of model problems involving merger of magnetic flux tubes in relativistic magnetically dominated plasma. Mergers of current-carrying flux tubes (exemplified by the two-dimensional ‘ABC’ structures) and zero-total-current magnetic flux tubes are considered. In all cases regimes of spontaneous and driven evolution are investigated. We identify two stages of particle acceleration during flux mergers: (i) fast explosive prompt X-point collapse and (ii) ensuing island merger. The fastest acceleration occurs during the initial catastrophic X-point collapse, with the reconnection electric field of the order of the magnetic field. During the X-point collapse, particles are accelerated by charge-starved electric fields, which can reach (and even exceed) values of the local magnetic field. The explosive stage of reconnection produces non-thermal power-law tails with slopes that depend on the average magnetization $\unicode[STIX]{x1D70E}$. For plasma magnetization $\unicode[STIX]{x1D70E}\leqslant 10^{2}$ the spectrum power-law index is $p>2$; in this case the maximal energy depends linearly on the size of the reconnecting islands. For higher magnetization, $\unicode[STIX]{x1D70E}\geqslant 10^{2}$, the spectra are hard, $p<2$, yet the maximal energy $\unicode[STIX]{x1D6FE}_{\text{max}}$ can still exceed the average magnetic energy per particle, ${\sim}\unicode[STIX]{x1D70E}$, by orders of magnitude (if $p$ is not too close to unity). The X-point collapse stage is followed by magnetic island merger that dissipates a large fraction of the initial magnetic energy in a regime of forced magnetic reconnection, further accelerating the particles, but proceeds at a slower reconnection rate.

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Flux quanta, magnetic field lines, merging – some sub-microscale relations of interest in space plasma physics

Annales Geophysicae ◽

10.5194/angeo-29-1121-2011 ◽

2011 ◽

Vol 29 (6) ◽

pp. 1121-1127 ◽

Cited By ~ 3

Author(s):

R. A. Treumann ◽

R. Nakamura ◽

W. Baumjohann

Keyword(s):

Magnetic Field ◽

Magnetic Flux ◽

Quantum Mechanical ◽

Space Plasma Physics ◽

Flux Tubes ◽

Magnetic Diffusion ◽

Macro Scale ◽

Magnetic Flux Tubes ◽

Field Lines ◽

The Given

Abstract. We clarify the notion of magnetic field lines in plasma by referring to sub-microscale (quantum mechanical) particle dynamics. It is demonstrated that magnetic field lines in a field of strength B carry single magnetic flux quanta Φ0=h/e. The radius of a field line in the given magnetic field B is calculated. It is shown that such field lines can merge and annihilate only over the length &ell;&par; of their strictly anti-parallel sections, for which case we estimate the power generated. The length &ell;&par; becomes a function of the inclination angle θ of the two merging magnetic flux tubes (field lines). Merging is possible only in the interval 12πθ&leq;π. This provides a sub-microscopic basis for "component reconnection" in classical macro-scale reconnection. We also find that the magnetic diffusion coefficient in plasma appears in quanta D0m=eΦ0/me=h/me. This lets us conclude that the bulk perpendicular plasma resistivity is limited and cannot be less than η0⊥=μ0eΦ0/me=μ0h/me~10−9 Ohm m. This resistance is an invariant.

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Topological Transformations in Isolated Straight Magnetic Flux Tubes

The Astrophysical Journal ◽

10.1086/305740 ◽

1998 ◽

Vol 500 (2) ◽

pp. 966-977 ◽

Cited By ~ 7

Author(s):

Sergey Bazdenkov ◽

Tetsuya Sato

Keyword(s):

Magnetic Flux ◽

Flux Tubes ◽

Magnetic Flux Tubes ◽

Topological Transformations

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A Statistical Study on the Reconnection in Boundary Layers of Small-scale Magnetic Flux Tubes in Solar Winds

Chinese Astronomy and Astrophysics ◽

10.1016/j.chinastron.2013.04.005 ◽

2013 ◽

Vol 37 (2) ◽

pp. 163-174

Author(s):

Qi Yu ◽

Yao Shuo ◽

He Jian-sen ◽

Tian Hui ◽

Tu Chuan-yi

Keyword(s):

Magnetic Flux ◽

Boundary Layers ◽

Statistical Study ◽

Small Scale ◽

Flux Tubes ◽

Solar Winds ◽

Magnetic Flux Tubes

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The Influence of Binarity on Stellar Activity

Proceedings of the International Astronomical Union ◽

10.1017/s1743921307004425 ◽

2006 ◽

Vol 2 (S240) ◽

pp. 442-452 ◽

Cited By ~ 1

Author(s):

Katalin Oláh

Keyword(s):

Binary Systems ◽

Magnetic Energy ◽

Theoretical Calculations ◽

Deep Convection ◽

Magnetic Activity ◽

Close Binary ◽

Convective Envelope ◽

Flux Tubes ◽

Gravitational Forces ◽

Magnetic Flux Tubes

AbstractActivity of late type stars is enhanced by fast rotation, which is maintained in nearly synchronized close binary systems. Magnetic activity originates in the deep convection zones of stars from where magnetic flux tubes emerge to their surfaces. The gravitational forces in binaries help the clustering of activity features giving rise to active longitudes. These preferred longitudes are observed in binaries from dwarfs to giants. Differential rotation is found in many active stars that are components of binary systems. If these binaries are circularized and nearly synchronized, then there will be a corotation latitude in their surfaces, and its position can be determined by observations and by theoretical calculations. Enhanced activity in binaries could have a reverse effect as well: strong magnetism in a binary component can modify the orbital period by the cyclic exchange of kinetic and magnetic energy in its convective envelope.

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