The ideal magnetohydrodynamic stability of a line-tied coronal magnetohydrostatic equilibrium

An energy method is used to determine a condition for local instability of field lines in magnetohydrostatic equilibrium which are rooted in the photosphere. The particular equilibrium studied is isothermal and two-dimensional and may model a coronal arcade of loops where varitions along the axis of the arcade are weak enough to be ignorable. It is found that when β <0.34 the equilibrium is stable. When β = 0.34 a magnetic neutral line appears at the photosphere and it is marginally stable. When β > 0.34 a magnetic island is present and all the field lines inside the island are unstable as well as some beyond it. As β increases, the size of the island and the extent of unstable field lines increase. The effect of the instability is likely to be to create small-scale filamentation in the solar corona and to enhance the global transport coefficients.