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| Titel |
The non-linear evolution of magnetic flux ropes: 3. effects of dissipation |
| VerfasserIn |
C. J. Farrugia, V. A. Osherovich, L. F. Burlaga |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
0992-7689
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| Digitales Dokument |
URL |
| Erschienen |
In: Annales Geophysicae ; 15, no. 2 ; Nr. 15, no. 2, S.152-164 |
| Datensatznummer |
250012624
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| Publikation (Nr.) |
 copernicus.org/angeo-15-152-1997.pdf |
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| Zusammenfassung |
| We study the evolution (expansion or
oscillation) of cylindrically symmetric magnetic flux ropes when the energy
dissipation is due to a drag force proportional to the product of the plasma
density and the radial speed of expansion. The problem is reduced to a single,
second-order, ordinary differential equation for a damped, non-linear
oscillator. Motivated by recent work on the interplanetary medium and the solar
corona, we consider polytropes whose index, γ, may be less than
unity. Numerical analysis shows that, in contrast to the small-amplitude case,
large-amplitude oscillations are quasi-periodic with frequencies substantially
higher than those of undamped oscillators. The asymptotic behaviour described by
the momentum equation is determined by a balance between the drag force and the
gradient of the gas pressure, leading to a velocity of expansion of the flux
rope which may be expressed as (1/2γ)r/t, where r is the
radial coordinate and t is the time. In the absence of a drag force, we
found in earlier work that the evolution depends both on the polytropic index
and on a dimensionless parameter, κ. Parameter κ was
found to have a critical value above which oscillations are impossible, and
below which they can exist only for energies less than a certain energy
threshold. In the presence of a drag force, the concept of a critical
κ remains valid, and when κ is above critical, the
oscillatory mode disappears altogether. Furthermore, critical κ
remains dependent only on γ and is, in particular, independent of
the normalized drag coefficient, ν*. Below critical
κ, however, the energy required for the flux rope to escape to
infinity depends not only on κ (as in the conservative force case)
but also on ν*. This work indicates how under certain
conditions a small change in the viscous drag coefficient or the initial energy
may alter the evolution drastically. It is thus important to determine ν*
and κ from observations. |
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