Asymptotic properties of disk dynamo

Isakov, R. V.; Ruzmaikin, A.; Sokoloff, D.; Faminskaya, M.V.

doi:10.1007/bf00649143

Cited by 8 publications

(10 citation statements)

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“…It is easy to see from the asymptotic solution (3) that in fact this means that the field being generated is not concentrated in the vicinity of maximum generation (to, 0o), but it is carried away from there by the differential rotation. Similar effects are known for solutions of mean field dynamo equations (Isakov et aL, 1981;Zeldovich et aL, 1983), however, at present, they have no sufficient mathematical justification. In particular, it is not clear how to construct the solution far from the generation region and to find the next members of the asymptotic expansion.…”

Section: R?mentioning

confidence: 87%

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Excitation of non-axially symmetric modes of the Sun's mean magnetic field

1988

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The kinematic dynamo equations for the mean magnetic field are solved with an asymptotic method of the WKB type. The excitation conditions and main characteristics of the non-axially symmetric modes for a given distribution of the sources are obtained. Utilization of the helioseismologic data on the Sun's internal rotation permits an explanation, within the framework of dynamo theory, of the excitation of the main non-axially symmetric modes revealed in the Sun's magnetic field sector structure.

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Section: R?mentioning

confidence: 87%

“…is a complex number. One can easily determine that any other representation of solution (3) having a different power of e is impossible, since it will either damp out with time or will not satisfy the boundary conditions at infinity due to the different order of the main terms in (2) (Isakov et aL, 1981).…”

Section: The Form Of the Asymptotic Solutionmentioning

confidence: 99%

Excitation of non-axially symmetric modes of the Sun's mean magnetic field

1988

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“…Again, the numerical results agree well with the asymptotic scaling b r /b φ ∝ |D| −1/2 . In their analytic study, Isakov et al (1981) assumed that the eigenfunctions of b φ and b r differed only by a constant of proportionality. This assumption allowed these authors to reduce dash-dotted.…”

Section: The Eigenfunctionsmentioning

confidence: 99%

“…A deeper insight into the nature of the eigensolutions and their dependence upon the distribution of α(z) has been provided by approximate and asymptotic solutions. Isakov et al (1981) developed boundary-layer asymptotics for an αω-dynamo in a slab for |D| 1. Adopting a definition for the dynamo number that is consistent with that given below (see equation ( 5)), these authors were able to show that the growth rate of the leading mode, which has quadrupolar parity, has the form…”

Section: Introductionmentioning

confidence: 99%

Asymptotic solutions for mean-field slab dynamos

Cole

Bushby

et al. 2014

Geophysical & Astrophysical Fluid Dynamics

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We discuss asymptotic solutions of the kinematic αω-dynamo in a thin disc (slab) surrounded by an electric insulator. Focusing upon the strong dynamo regime, in which the dynamo number D satisfies |D| 1, we resolve uncertainties in the earlier treatments and conclude that some of the simplifications that have been made in previous studies are questionable. Having abandoned these simplifications, we show, by comparing numerical solutions with complementary asymptotic results obtained for |D| 1 and |D| 1, that the asymptotic solutions give a reasonably accurate description of the dynamo even far beyond their formal ranges of applicability. Indeed, our results suggest a simple analytical expression for the growth rate of the mean magnetic field that remains accurate across the wide range of values for D that are typical of spiral galaxies and accretion discs. Finally, we analyse the role of various terms in the governing equations to clarify the fine details of the dynamo process. In particular, in the case of the radial magnetic field equation, we have shown that the α ∂ B φ /∂z term (where B φ is the azimuthal magnetic field, α is the mean-field dynamo coefficient and z is measured across the slab), which is neglected in some of the earlier asymptotic studies, is essential for the dynamo as it drives a flux of magnetic energy away from the dynamo region towards the surface of the slab.

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Current results on the asymptotics of dynamo models

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Asymptotic properties of disk dynamo

Cited by 8 publications

References 2 publications

Excitation of non-axially symmetric modes of the Sun's mean magnetic field

Excitation of non-axially symmetric modes of the Sun's mean magnetic field

Asymptotic solutions for mean-field slab dynamos

Current results on the asymptotics of dynamo models

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