Magnetic Helicity Flux and the Nonlinear Galactic Dynamo

Kleeorin, N.; Moss, D.; Sokoloff, Dmitry

doi:10.1007/978-94-010-0788-7_29

Cited by 73 publications

(120 citation statements)

References 6 publications

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“…where F = Cχ v φ v (B)B 2 η A (B)(∇ρ)/ρ is the nonadvective flux of the magnetic helicity which serves as an additional nonlinear source in the equation for χ c , Vχ c is the advective flux of the magnetic helicity and −κ∇χ c is the diffusive flux of the magnetic helicity (see Kleeorin & Rogachevskii 1999;Kleeorin et al 2000Kleeorin et al , 2002, V = e φ Ω r is the differential rotation, and T = (1/3)(l/h) 2 Rm. Equation (15) was obtained using arguments based on the magnetic helicity conservation law (see Kleeorin & Rogachevskii 1999).…”

Section: The Dynamical Equation For the Function χ C (B)mentioning

confidence: 99%

“…The governing equation for magnetic helicity was suggested by Kleeorin & Ruzmaikin (1982; see also the discussion by Zeldovich et al 1983) for an isotropic turbulence, and investigated by Kleeorin et al (1995) for stellar dynamos, and self-consistently derived by Kleeorin & Rogachevskii (1999) for an arbitrary anisotropic turbulence. A quantitative model for the flux of magnetic helicity was proposed by Kleeorin & Rogachevskii (1999) and Kleeorin et al (2000). Note that Schmalz & Stix (1991), Covas et al (1998) and Blackman & Brandenburg (2002) have also investigated related solar dynamo models that included a dynamical equation describing the evolution of magnetic helicity.…”

Section: Introductionmentioning

confidence: 99%

“…We stress that the scenario of Kleeorin et al (2000Kleeorin et al ( , 2002 does not include all possible types of nonlinear processes which can occur at the nonlinear dynamo stage (see, e.g., Brandenburg & Subramanian 2000;Brandenburg & Dobler 2001), but rather is restricted by a minimal number of processes involved in the magnetic helicity conservation. In particular, we consider transport of mean helicity of small-scale magnetic field only and note that this helicity may be transported out of the galactic disc without significant loss of large-scale magnetic field.…”

Section: Introductionmentioning

confidence: 99%

“…In the spirit of the basic ideas about the nonlinear saturation of galactic dynamos, the analysis presented by Kleeorin et al (2000Kleeorin et al ( , 2002 was restricted to the evolution of α only, while a detailed simulation (e.g. Brandenburg & Sokoloff 2002) also demonstrates a quenching of the turbulent magnetic diffusivity.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear magnetic diffusion and magnetic helicity transport in galactic dynamos

Kleeorin¹,

Moss²,

Rogachevskii³

et al. 2003

A&A

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Abstract.We have extended our previous mean-field galactic dynamo model which included algebraic and dynamic alpha nonlinearities (Kleeorin et al. 2002), to include also a quenching of the turbulent diffusivity. We readily obtain equilibrium states for the large-scale magnetic field in the local disc dynamo model, and these fields have strengths that are comparable to the equipartition field strength. We find that the algebraic nonlinearity alone (i.e. quenching of both the α effect and turbulent magnetic diffusion) cannot saturate the growth of the mean magnetic field; only the combined effect of algebraic and dynamic nonlinearities can limit the growth of the mean magnetic field. However, in contrast to our earlier work without quenching of the turbulent diffusivity, we cannot now find satisfactory solutions in the no-z approximation to the axisymmetric galactic dynamo problem.

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Section: The Dynamical Equation For the Function χ C (B)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear magnetic diffusion and magnetic helicity transport in galactic dynamos

Kleeorin¹,

Moss²,

Rogachevskii³

et al. 2003

A&A

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“…This was shown in direct numerical simulations of a twisted magnetic flux tube by Blackman & Brandenburg (2003), in good agreement with observations of sigmoid loops in the solar corona. However, the smallscale magnetic helicity backreacts on the helical turbulence and quenches the dynamo (Blackman & Field 2000;Kleeorin et al 2000).…”

Section: Introductionmentioning

confidence: 99%

Magnetic helicity fluxes in interface and flux transport dynamos

Chatterjee

Gómez

Brandenburg

2010

A&A

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Context. Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism. Aims. In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we aim to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation. Methods. We consider a model with only radial shear confined to a thin layer (tachocline) at the bottom of the convection zone. The kinetic α owing to helical turbulence is assumed to be localized in a region above the convection zone. The dynamical quenching formalism is used to describe the build-up of mean magnetic helicity in the model, which results in a magnetic α effect that feeds back on the kinetic α effect. In some cases we compare these results with those obtained from a model with a simple algebraic α quenching formula.Results. In agreement with earlier findings, the magnetic α effect has the opposite sign compared with the kinetic α effect and leads to a catastrophic decrease of the saturation field strength proportional to the inverse magnetic Reynolds number. At high latitudes this quenching effect can lead to secondary dynamo waves that propagate poleward because of the opposite sign of α. These secondary dynamo waves are driven by small-scale magnetic helicity instead of the small-scale kinetic helicity. Magnetic helicity fluxes both from turbulent mixing and from meridional circulation alleviate catastrophic quenching. Interestingly, supercritical diffusive helicity fluxes also give rise to secondary dynamo waves and grand minima-like episodes.

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Solar and stellar dynamos – latest developments

Brandenburg

Dobler

2002

Astron. Nachr.

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Recent progress in the theory of solar and stellar dynamos is reviewed. Particular emphasis is placed on the mean-field theory which tries to describe the collective behavior of the magnetic field. In order to understand solar and stellar activity, a quantitatively reliable theory is necessary. Much of the new developments center around magnetic helicity conservation which is seen to be important in numerical simulations. Only a dynamical, explicitly time dependent theory of α-quenching is able to describe this behavior correctly.

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Magnetic Helicity Flux and the Nonlinear Galactic Dynamo

Cited by 73 publications

References 6 publications

Nonlinear magnetic diffusion and magnetic helicity transport in galactic dynamos

Nonlinear magnetic diffusion and magnetic helicity transport in galactic dynamos

Magnetic helicity fluxes in interface and flux transport dynamos

Solar and stellar dynamos – latest developments

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