Hydromagnetic Dynamo Models.

Parker, E. N.

doi:10.1086/146087

Cited by 1,852 publications

(1,380 citation statements)

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“…The standard physical explanation for the solar activity cycle is that the phenomenon underlying the cycle is the propagation of a wave of quasi-stationary magnetic field which in turn is excited by the solar dynamo. The classical explanation of the solar dynamo (Parker, 1955) is that solar differential rotation produces toroidal magnetic field from poloidal, while mirror-asymmetric convective flows produce poloidal field from toroidal (the "α-effect"), thus closing the chain of magnetic field self-excitation. This scheme results in latitudinal propagation of a wave of toroidal magnetic field (the dynamo wave).…”

Section: The General Form Of the Record Of Solar Activitymentioning

confidence: 99%

Sunspot cycles and Grand Minima

Sokoloff¹,

Arlt²,

Moss³

et al. 2009

Proc. IAU

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Abstract. Observational data concerning the long-term history of cyclic solar activity as recorded in sunspot and isotopic data are discussed in the context of solar dynamo theory. In particular, a simple dynamo model based on differential rotation and the mirror asymmetry of convection with random fluctuations of dynamo governing parameters is shown to reproduce some basic features of the solar magnetic activity evolution.

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Section: The General Form Of the Record Of Solar Activitymentioning

confidence: 99%

Sunspot cycles and Grand Minima

Sokoloff¹,

Arlt²,

Moss³

et al. 2009

Proc. IAU

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“…With the development of mean-field theory (Parker 1955;Steenbeck et al 1966), this complicated threedimensional process became amenable to simpler analytic and numerical treatments in one and two dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…The earliest model of a dynamo for the Sun goes back to Parker (1955), who considered the additional presence of differential rotation, which is referred to as the Ω affect. In the presence of both α and Ω effects, there are self-excited oscillatory plain wave solutions in unbounded domains.…”

Section: Introductionmentioning

confidence: 99%

Analytic solution of an oscillatory migratoryα²stellar dynamo

Brandenburg

2017

A&A

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Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α. Aims. We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant α, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. Methods. We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. Results. The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of α. Conclusions. The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant α.

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“…The essential idea about the operation of the solar dynamo came from Parker (1955), who developed the notion that cyclonic events would tilt a toroidal field systematically in the poloidal direction, closing thereby a critical step in the dynamo cycle. While this concept is still valid today, it still required the existence proof by Herzenberg (1958) that began to convince critics that Cowling's antidynamo theorem does not extend to the general case of three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Simulations of astrophysical dynamos

Brandenburg

2010

Proc. IAU

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Abstract. Numerical aspects of dynamos in periodic domains are discussed. Modifications of the solutions by numerically motivated alterations of the equations are being reviewed using the examples of magnetic hyperdiffusion and artificial diffusion when advancing the magnetic field in its Euler potential representation. The importance of using integral kernel formulations in mean-field dynamo theory is emphasized in cases where the dynamo growth rate becomes comparable with the inverse turnover time. Finally, the significance of microscopic magnetic Prandtl number in controlling the conversion from kinetic to magnetic energy is highlighted.

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Hydromagnetic Dynamo Models.

Cited by 1,852 publications

References 0 publications

Sunspot cycles and Grand Minima

Sunspot cycles and Grand Minima

Analytic solution of an oscillatory migratoryα²stellar dynamo

Simulations of astrophysical dynamos

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Hydromagnetic Dynamo Models.

Cited by 1,852 publications

References 0 publications

Sunspot cycles and Grand Minima

Sunspot cycles and Grand Minima

Analytic solution of an oscillatory migratoryα2stellar dynamo

Simulations of astrophysical dynamos

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Analytic solution of an oscillatory migratoryα²stellar dynamo