A self‐consistent treatment of the electromotive force in magnetohydrodynamics for large diffusivities

Courvoisier, Alice; Hughes, David W.; Proctor, M. R. E.

doi:10.1002/asna.201011358

Cited by 10 publications

(12 citation statements)

References 5 publications

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“…Given the rather immense size of the calculation without such effects, it seemed prudent to ignore these. possible that there are important interactions between U and B that lead to other instabilities [33], we leave their systematic study to future work.…”

Section: Fundamentals Of Mean-field Electrodynamicsmentioning

confidence: 99%

Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence

Squire¹,

Bhattacharjee²

2015

Phys. Rev. E

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This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of α effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of α, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.

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Section: Fundamentals Of Mean-field Electrodynamicsmentioning

confidence: 99%

Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence

Squire¹,

Bhattacharjee²

2015

Phys. Rev. E

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“…With the pattern in the disc halo being unchanged in the presence of a dead zone, this picture possibly has to be amended. Naively, for a positive α effect in the halo (as found by Gressel 2010), one would not expect an outward butterfly diagram from classical theory – demonstrating the need for non‐linear feedback both in the diagnostics (Rheinhardt & Brandenburg 2010) as well as in the modelling (Brandenburg, Candelaresi & Chatterjee 2009; Courvoisier, Hughes & Proctor 2010).…”

Section: Disc Model Propertiesmentioning

confidence: 99%

On the dynamics of planetesimals embedded in turbulent protoplanetary discs with dead zones

Gressel

Nelson

Turner

2011

Monthly Notices of the Royal Astronomical Society

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Accretion in protoplanetary discs is thought to be driven by magnetohydrodynamic (MHD) turbulence via the magnetorotational instability. Recent work has shown that a planetesimal swarm embedded in a fully turbulent disc is subject to strong excitation of the velocity dispersion, leading to collisional destruction of bodies with radii Rp < 100 km. Significant diffusion of planetesimal semimajor axes also arises, leading to large‐scale spreading of the planetesimal population throughout the inner regions of the protoplanetary disc, in apparent contradiction of constraints provided by the distribution of asteroids within the asteroid belt. In this paper, we examine the dynamics of planetesimals embedded in vertically stratified turbulent discs, with and without dead zones. Our main aims are to examine the turbulent excitation of the velocity dispersion, and the radial diffusion, of planetesimals in these discs. We employ 3D MHD simulations using the shearing box approximation, along with an equilibrium chemistry model that is used to calculate the ionization fraction of the disc gas as a function of time and position. Ionization is assumed to arise because of stellar X‐rays, galactic cosmic rays and radioactive nuclei. In agreement with our previous study, we find that planetesimals in fully turbulent discs develop large random velocities that will lead to collisional destruction/erosion for bodies with sizes below 100 km, and undergo radial diffusion on a scale ∼2.5 au over a 5 Myr disc lifetime. But planetesimals in a dead zone experience a much reduced excitation of their random velocities, and equilibrium velocity dispersions lie between the disruption thresholds for weak and strong aggregates for sizes Rp≤ 100 km. We also find that radial diffusion occurs over a much reduced length‐scale ∼0.25 au over the disc lifetime, this being consistent with Solar system constraints. We conclude that planetesimal growth via mutual collisions between smaller bodies cannot occur in a fully turbulent disc. By contrast, a dead zone may provide a safe haven in which km‐sized planetesimals can avoid mutual destruction through collisions.

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“…Finding a simple interpretation of these four tensors is even more difficult than for the purely kinematic problem, in which one has only the tensor α B . As in the kinematic case however, some progress can be made in the limit of small Rm (Courvoisier et al 2010a); under this restriction, the (dimensionless) e.m.f. can be approximated at leading order by…”

Section: Mean Field Instabilities Of Mhd Statesmentioning

confidence: 99%

“…For example, one might ask whether such instabilities can result from the saturated state of a small-scale dynamo, driven by some forcing . Somewhat surprisingly, these ideas have been explored only fairly recently (Courvoisier, Hughes & Proctor 2010 a , b ).…”

Section: The Dynamical Regimementioning

confidence: 99%

Mean field electrodynamics: triumphs and tribulations

Hughes

2018

J. Plasma Phys.

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The theory of mean field electrodynamics, now celebrating its fiftieth birthday, has had a profound influence on our modelling of cosmical dynamos, greatly enhancing our understanding of how such dynamos may operate. Here I discuss some of its undoubted triumphs, but also some of the problems that can arise in a mean field approach to dynamos in fluids (or plasmas) that are both highly turbulent and also extremely good electrical conductors, as found in all astrophysical settings. †

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A self‐consistent treatment of the electromotive force in magnetohydrodynamics for large diffusivities

Cited by 10 publications

References 5 publications

Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence

Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence

On the dynamics of planetesimals embedded in turbulent protoplanetary discs with dead zones

Mean field electrodynamics: triumphs and tribulations

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