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| Titel |
Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo |
| VerfasserIn |
R. Hide |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 4, no. 4 ; Nr. 4, no. 4, S.201-205 |
| Datensatznummer |
250001808
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| Publikation (Nr.) |
 copernicus.org/npg-4-201-1997.pdf |
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| Zusammenfassung |
In the interpretation of geomagnetic polarity reversals
with their highly variable frequency over geological time it is necessary, as with other
irregularly fluctuating geophysical phenomena, to consider the relative importance of
forced contributions associated with changing boundary conditions and of free
contributions characteristic of the behaviour of nonlinear systems operating under fixed
boundary conditions. New evidence -albeit indirect- in favour of the likely
predominance of forced contributions is provided by the discovery reported here of the
possibility of complete quenching by nonlineax effects of current fluctuations in a
self-exciting homopolar dynamo with its single Faraday disk driven into rotation with
angular speed y(τ) (where τ denotes time) by a steady applied couple. The
armature of an electric motor connected in series with the coil of the dynamo is driven
into rotation' with angular speed z(τ) by a torque xf
(x) due to Lorentz forces associated with the electric current x(τ)
in the system (just as certain parts of the spectrum of eddies within the liquid outer
core are generated largely by Lorentz forces associated with currents generated by the
self-exciting magnetohydrodynamic (MHD) geodynamo). The discovery is based on
bifurcation analysis supported by computational studies of the following (mathematically
novel) autonomous set of nonlinear ordinary differential equations:
dx/dt = x(y - 1) - βzf(x),
dy/dt = α(1 - x²) - κy,
dz/dt = xf (x) -λz, where f (x) = 1
- ε + εσx,
in cases when the dimensionless parameters
(α, β, κ, λ, σ) are all positive and 0
≤ ε ≤ 1. Within
those regions of
(α, β, κ, λ, σ) parameter space where the applied couple, as measured by
α, is
strong enough for persistent dynamo action (i.e. x ≠ 0) to occur at all, there are in
general extensive regions where x(τ) exhibits large amplitude regular or irregular
(chaotic) fluctuations. But these fluctuating régimes shrink in size as increases
from zero, and they disappear altogether when ε = 1, leaving only steady régimes of dynamo
action. |
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