Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Blackman, Eric G.

doi:10.1007/978-1-4939-3547-5_3

Cited by 15 publications

(16 citation statements)

References 121 publications

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“…In three‐dimensional MHD, the ideal invariants in the absence of dissipation are the total energy

E_{T} = E_{V} + E_{M} = 1 false/ 2 (⟨⟩, false| boldu |^{2} + false| boldB |^{2})

, the magnetic helicity

H_{M} = (⟨⟩, boldA \cdot boldB)

with B = ∇ × A (where A is the magnetic vector potential), and the cross correlation between the velocity and magnetic field,

H_{C} = (⟨⟩, boldu \cdot boldB)

(Blackman, ; Pouquet, ; Woltjer, ). The total energy cascades to small scales, both in two and in three dimensions, with a self‐similar spectrum whose spectral index might still be in dispute (Beresniak, ; Lee et al, ; Mininni & Pouquet, ; Perez et al, ), a matter that is rendered difficult (i) by the anisotropy of such flows especially in the small scales because of the presence of a uniform (or quasi‐uniform) strong magnetic field in the large scales, (ii) by the presence of nonzero correlations between the velocity and the magnetic field, and (iii) by intermittency effects leading to the steepening of these spectra.…”

Section: Coupling To a Magnetic Fieldmentioning

confidence: 99%

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Pouquet

Rosenberg

Stawarz

et al. 2019

Earth and Space Science

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We briefly review helicity dynamics, inverse and bidirectional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the nondissipative case, is transferred to small scales through nonlinear mode coupling. Fifty years ago, it was realized that, for a two‐dimensional fluid, energy cascades instead to larger scales and so does magnetic excitation in MHD. However, evidence obtained recently indicates that, in fact, for a range of governing parameters, there are systems for which their ideal invariants can be transferred, with constant fluxes, to both the large scales and the small scales, as for MHD or rotating stratified flows, in the latter case including quasi‐geostrophic forcing. Such bidirectional, split, cascades directly affect the rate at which mixing and dissipation occur in these flows in which nonlinear eddies interact with fast waves with anisotropic dispersion laws, due, for example, to imposed rotation, stratification, or uniform magnetic fields. The directions of cascades can be obtained in some cases through the use of phenomenological arguments, one of which we derive here following classical lines in the case of the inverse magnetic helicity cascade in electron MHD. With more highly resolved data sets stemming from large laboratory experiments, high‐performance computing, and in situ satellite observations, machine learning tools are bringing novel perspectives to turbulence research. Such algorithms help devise new explicit subgrid‐scale parameterizations, which in turn may lead to enhanced physical insight, including in the future in the case of these new bidirectional cascades.

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“…In three‐dimensional MHD, the ideal invariants in the absence of dissipation are the total energy

E_{T} = E_{V} + E_{M} = 1 false/ 2 (⟨⟩, false| boldu |^{2} + false| boldB |^{2})

, the magnetic helicity

H_{M} = (⟨⟩, boldA \cdot boldB)

with B = ∇ × A (where A is the magnetic vector potential), and the cross correlation between the velocity and magnetic field,

H_{C} = (⟨⟩, boldu \cdot boldB)

Section: Coupling To a Magnetic Fieldmentioning

confidence: 99%

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Pouquet

Rosenberg

Stawarz

et al. 2019

Earth and Space Science

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“…The same system averaged in different ways might lead to different explanations of the differently computed mean magnetic fields (Blackman 2015). Mean fields in shearing boxes are typically computed as x, y planar averages leaving quantities as a function of z (see § 4), whereas mean fields in MRI simulations in global cylindrical systems with conducting boundaries have invoked azimuthal and vertical (φ, z) averages (Ebrahimi & Bhattacharjee 2014).…”

Section: Role Of Large-scale Dynamos In Mri Simulations and Transportmentioning

confidence: 99%

“…The importance of E · B also highlights the utility of tracking the temporal and spatial evolution of magnetic helicity (a topological measure of magnetic field line linkage) because E · B can be written as the sum of a time derivative of the magnetic helicity density associated with the large-scale magnetic field, a spatial divergence of largescale magnetic helicity flux and a resistive term associated with the large-scale current helicity. This same E · B can also be written as the sum of a time derivative of mean small-scale helicity density plus a spatial divergence of mean small-scale magnetic helicity flux and a resistive term associated with the mean small-scale current helicity (see Brandenburg & Subramanian 2005;Blackman 2015 for reviews).…”

Section: Role Of Large-scale Dynamos In Mri Simulations and Transportmentioning

confidence: 99%

Motivation and challenge to capture both large-scale and local transport in next generation accretion theory

Blackman

Nauman

2015

J. Plasma Phys.

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Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate the insights gained from simulations into improving practical models for comparison with observations. What has been learned from simulations that can lead to improvements beyond SS73 in practical models? Here, we emphasize the need to incorporate the role of non-local transport more precisely. To show where large-scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura & Sunyaev (Astron. Astrophys., vol. 24, 1973, pp. 337-355, SS73) is necessarily a mean field theory, and one which does not include large-scale transport. Observations of coronae and jets, combined with the interpretation of results from shearing box simulations, of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large-scale contributions and that the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRI as it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations, but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona and outflow contributions. Finally, we note that any mean field theory, including that of SS73, has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

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“…Magnetic helicity is a volume integral of the dot product of the magnetic vector potential and the magnetic field. Depending on the geometry in question there can be contributions from both twist (rotation of the flux tube in a plane perpendicular to the field direction) and writhe (a large scale kink in the 3‐dim structure of the flux tube; Blackman, ). The observations available to us are at the solar surface and are essentially two‐dimensional so we focus on the twist.…”

Section: Methodsmentioning

confidence: 99%

Solar Sources of Interplanetary Magnetic Clouds Leading to Helicity Prediction

2018

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This study identifies the solar origins of magnetic clouds that are observed at 1 AU and predicts the helical handedness of these clouds from the solar surface magnetic fields. We started with the magnetic clouds listed by the Magnetic Field Investigation (MFI) team supporting NASA's Wind spacecraft in what is known as the MFI table and worked backward in time to identify solar events that produced these clouds. Our methods utilize magnetograms from the Helioseismic and Magnetic Imager instrument on the Solar Dynamics Observatory spacecraft so that we could only analyze MFI entries after the beginning of 2011. This start date and the end date of the MFI table gave us 37 cases to study. Of these we were able to associate only eight surface events with clouds detected by Wind at 1 AU. We developed a simple algorithm for predicting the cloud helicity that gave the correct handedness in all eight cases. The algorithm is based on the conceptual model that an ejected flux tube has two magnetic origination points at the positions of the strongest radial magnetic field regions of opposite polarity near the places where the ejected arches end at the solar surface. We were unable to find events for the remaining 29 cases: lack of a halo or partial halo coronal mass ejection in an appropriate time window, lack of magnetic and/or filament activity in the proper part of the solar disk, or the event was too far from disk center. The occurrence of a flare was not a requirement for making the identification but in fact flares, often weak, did occur for seven of the eight cases.

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Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Cited by 15 publications

References 121 publications

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Motivation and challenge to capture both large-scale and local transport in next generation accretion theory

Solar Sources of Interplanetary Magnetic Clouds Leading to Helicity Prediction

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