Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields

Taylor, J. B.

doi:10.1103/physrevlett.33.1139

Cited by 1,867 publications

(1,271 citation statements)

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“…Using a variational principle calculation, Woltjer (1958a) found that the answer is a configuration for which J = c 4π ∇×B = f (x)B, where f (x) is a scalar function that must therefore satisfy B · ∇f = 0. Taylor (1974Taylor ( ,1986 considered the same question but assumed that magnetic helicity is approximately conserved when averaged over sufficiently large scales even in the presence of a small but finite resistive dissipation . Essentially, f becomes a measure of the inverse gradient scale of the helical magnetic field and so minimizing the energy means decreasing f as much as possible.…”

Section: Minimum Energy State Of Helical Magnetic Fieldsmentioning

confidence: 99%

“…4) shows a simple helicity conserving relaxation process where reconnection is not actually needed.) The arguments of Woltjer (1958a) and Taylor (1974) essentially assumed that R > 1. The previous section shows the specific spectral conditions for this to be viable, and solidifies the assumptions on which these results were based.…”

Section: Minimum Energy State Of Helical Magnetic Fieldsmentioning

confidence: 99%

See 1 more Smart Citation

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Blackman¹

2016

Space Sciences Series of ISSI

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Magnetic fields of laboratory, planetary, stellar, and galactic plasmas commonly exhibit significant order on large temporal or spatial scales compared to the otherwise random motions within the hosting system. Such ordered fields can be measured in the case of planets, stars, and galaxies, or inferred indirectly by the action of their dynamical influence, such as jets. Whether large scale fields are amplified in situ or a remnant from previous stages of an object's history is often debated for objects without a definitive magnetic activity cycle. Magnetic helicity, a measure of twist and linkage of magnetic field lines, is a unifying tool for understanding large scale field evolution for both mechanisms of origin. Its importance stems from its two basic properties: (1) magnetic helicity is typically better conserved than magnetic energy; and (2) the magnetic energy associated with a fixed amount of magnetic helicity is minimized when the system relaxes this helical structure to the largest scale available. Here I discuss how magnetic helicity has come to help us understand the saturation of and sustenance of large scale dynamos, the need for either local or global helicity fluxes to avoid dynamo quenching, and the associated observational consequences. I also discuss how magnetic helicity acts as a hindrance to turbulent diffusion of large scale fields, and thus a helper for fossil remnant large scale field origin models in some contexts. I briefly discuss the connection between large scale fields and accretion disk theory as well. The goal here is to provide a conceptual primer to help the reader efficiently penetrate the literature.

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Section: Minimum Energy State Of Helical Magnetic Fieldsmentioning

confidence: 99%

Section: Minimum Energy State Of Helical Magnetic Fieldsmentioning

confidence: 99%

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Blackman¹

2016

Space Sciences Series of ISSI

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“…In strong contrast to IMHD, Taylor's relaxed equilibrium model, Taylor (1974), relaxes all the IMHD constraints save for conservation of toroidal magnetic flux and global magnetic helicity (which are IMHD invariants), leading to a very low-energy 'relaxed' equilibrium state. Such a 'Taylor state' is a special static solution of the IMHD equations, but is dynamically inaccessible via IMHD from arbitrary initial states because of IMHD's infinity of extra constraints.…”

Section: Introductionmentioning

confidence: 99%

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

et al. 2015

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Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor relaxation model for formation of macroscopically self-organized plasma equilibrium states, all these constraints are relaxed save for the global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, relaxed magnetohydrodynamics (RxMHD), such that all static solutions are Taylor states but also allows state with flow. By postulating that some long-lived macroscopic current sheets can act as barriers to relaxation, separating the plasma into multiple relaxation regions, a further generalization, multi-region relaxed magnetohydrodynamics (MRxMHD) is developed.

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“…In the limit of vanishing resistivity, this not only implies that the volume integrated magnetic helicity vanishes, it also implies that the magnetic helicity of any individual flux tube is separately conserved [79]. For a non-zero, but very small, η, we can transfer magnetic helicity from one flux tube to another.…”

Section: Magnetic Helicity Conservation Constraintmentioning

confidence: 99%

“…On the other hand, the conservation of magnetic helicity for individual flux tubes is completely lost. The implication is that global magnetic helicity conservation is a good approximation for laboratory plasmas, a point that was originally stressed by Taylor [79], and an even better one for astrophysical systems.…”

Section: Magnetic Helicity Conservation Constraintmentioning

confidence: 99%

Problems and Progress in Astrophysical Dynamos

Vishniac

Lazarían²,

Cho³

Turbulence and Magnetic Fields in Astrophysics

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Abstract. Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux threading a fluid element, or the field topology. Classical dynamo theory evades this limit by assuming that magnetic reconnection is fast, even for vanishing resistivity, and that the large scale field can be generated by the action of kinetic helicity. Both these claims have been severely criticized, and the latter appears to conflict with strong theoretical arguments based on magnetic helicity conservation and a series of numerical simulations. Here we discuss recent efforts to explain fast magnetic reconnection through the topological effects of a weak stochastic magnetic field component. We also show how mean-field dynamo theory can be recast in a form which respects magnetic helicity conservation, and how this changes our understanding of astrophysical dynamos. Finally, we comment briefly on why an asymmetry between small scale magnetic and velocity fields is necessary for dynamo action, and how it can arise naturally.

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Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields

Cited by 1,867 publications

References 8 publications

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

Problems and Progress in Astrophysical Dynamos

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