Stability of solar coronal loops

Abstract

The equations of magnetohydrodynamics do not contain an intrinsic length scale determining the size of phenomena. Hence, size only enters through the external geometrical properties of the configurations considered. This is one of the reasons why tokamaks and solar coronal loops may be considered as similar objects. The equations of MHD do not distinguish between the two. It is only the geometry and, hence, the boundary conditions that discriminate between them. Whereas for tokamaks toroidal periodicity and normal confinement provide the appropriate boundary conditions, for coronal loops line-tying at the photosphere and some prescription for the behavior across the “edge” of the loop determine the solutions. The latter is a more complicated problem and gives rise to even more complex dynamics than encountered in tokamaks. Here, we consider the influence of the two mentioned groups of boundary conditions for the problem of the stability and disruption of a solar coronal loop.We consider the stability properties of a single loop with twisted magnetic field lines under the simultaneous influence of photospheric line-tying and constraining by neighboring flux loops. The loops would be violently unstable without these two ingredients (i.e. for the corresponding tokamak problem). It is shown that line-tying alone in not sufficient for stability, but the neighboring flux tubes provide a normal boundary condition similar to a conducting shell in tokamaks. This stabilization gets lost on the time scale associated with reconnection of the tangetial magnetic field discontinuities present in the many-loop system. On this time scale the magnetic energy, which has been built up during the twisting of the field lines, gets released, resulting in a disruption of the loop. This process may be considered as the single loop variant of Parker's solar flare model.