No abstract

No abstract

No abstract

Solar coronal loops are observed to be remarkably stable structures. A magnetohydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. In addition to such line-tying, the effect of a radial pressure gradient is incorporated in the analysis.Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. This value depends on the aspect ratio of the loop, the ratio of the plasma to magnetic pressure and the detailed transverse magnetic structure. For a force-free field of uniform twist the critical twist is 3.3 ~r, and for other fields it is typically between 2~" and 6~r. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability.

The remarkable magnetohydrodynamic stability of solar coronal loops has been attributed lo the anchoring of the ends of loops in the dense photosphere. However, all the previous analyses of such line-tying have been approximate, in the sense that they give only upper or lower bounds on the critical amount of twist (or the critical looplength) required for the breakdown of stability. The object of the present paper is to remove these approximations and determine the exact value for the critical twist. When it is exceeded the magnetic field becomes kink unstable and a flare may be initiated.A simple analytic stability calculation is described for an idealised loop. This is followed by the development of a general numerical technique for any loop profile, which involves solving the partial differential equations of motion. It is found, for example, that a force-free field of uniform twist possesses a critical twist of 2.4971. by comparison with the previous bounds of 2n, for stability, and 3.3 n, for instability.