Stability of two-dimensional pre-flare structures

Several theoretical approaches to the problem of the onset of solar flares identify the point of onset as a ‘critical’ point, where the solution curve turns back. In other theories, a flare occurs at a conventional transition from stability to instability. The present paper provides stability results relevant for both types of approaches. Restricting the discussion to two-dimensional configurations (e.g. models for two-ribbon flares) stability is discussed in the framework of ideal magnetohydrodynamics, resistive magnetohydrodynamics and Vlasov theory. In most (but not all) cases the perturbation modes considered are restricted to two spatial dimensions in the same sense as the equilibrium. Several rather general criteria for stability of the lower part of the solution curve (‘minimal solutions’) are derived. Our results provide support to the concept of flare onset at a critical point.