Index Geophysics

The non-linear evolution of magnetic flux ropes: 3. effects of dissipation

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, <i>&#x03B3;</i>, 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 (1/2<i>&#x03B3;</i>)<i>r/t</i>, where <i>r</i> is the radial coordinate and <i>t</i> 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.

Farrugia, C. J.

Osherovich, V. A.

Burlaga, L. F.

2018-09-27

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application/pdf

10.1007/s00585-997-0152-9

https://angeo.copernicus.org/articles/15/152/1997/

eISSN: 1432-0576

eng