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.     

A theory of the onset of solar eruptive processes

The present theory assumes that solar eruptive processes - such as flares or eruptive prominences - occur at a critical stage when a configuration evolves in a quasi-static way. The onset criterion is not based on standard linear stability considerations but on the fact that under suitable conditions static equilibrium configurations cease to exist. This starting point leads us to present a general discussion of existence properties of the corresponding set of equations. It turns out that the existing mathematical literature provides very useful pertinent information. In fact, some important questions of the existence can be answered without even solving the equations. Nevertheless, several explicit examples are discussed for reasons of illustration.For the major part of the paper the configurations are characterized by a single parameter. In a particularly simple (one-dimensional) case we also discuss solutions depending on two parameters. The results can be discussed in terms of catastrophe theory.The theory is valid for two space dimensions and contains topological changes of the magnetic field, although the latter feature is not necessary for the theory to apply. The theory of two-dimensional force-free fields is contained as a special case.     

Substorm observations in the early morning sector with Equator-S and Geotail

Data from Equator-S and Geotail are used to study the dynamics of the plasma sheet observed during a substorm with multiple intensifications on 25 April 1998, when both spacecraft were located in the early morning sector (03–04 MLT) at a radial distance of 10–11 R_E. In association with the onset of a poleward expansion of the aurora and the westward electrojet in the premidnight and midnight sector, both satellites in the morning sector observed plasma sheet thinning and changes toward a more tail-like field configuration. During the subsequent poleward expansion in a wider local time sector (20−04 MLT), on the other hand, the magnetic field configuration at both satellites changed into a more dipolar configuration and both satellites encountered again the hot plasma sheet. High-speed plasma flows with velocities of up to 600 km/s and lasting 2–5 min were observed in the plasma sheet and near its boundary during this plasma sheet expansion. These high-speed flows included significant dawn-dusk flows and had a shear structure. They may have been produced by an induced electric field at the local dipolarization region and/or by an enhanced pressure gradient associated with the injection in the midnight plasma sheet.     

Magnetotail stability and dynamics: Progress 1991–1993

The progress in investigations of magnetotail stability and dynamics is reviewed for the years 1991–1993. Major advances have been made in understanding magnetotail convection, near-tail properties relevant for substorm onset, the change of thermal plasma properties during substorms, and ion acceleration. Also, attempts have been made to integrate different aspects of substorms and different substorm models. Major outstanding problems concern the onset mechanism, electron energization, and substorm recovery.     

On sheared magnetic field structures containing neutral points

This paper discusses the occurence of current sheets near the separatrix in sheared magnetic field structures containing an x-type neutral point, as suggested by a number of previous authors. Our approach is based on selfconsistent theory. In analogy to the theory of quasistatic convection by Grad, we interpret the break-down of the quasistatic theory near the separatrix as evidence for the occurence of a boundary layer. In particular, this picture suggests large (however integrable) current sheets, with the current flowing parallel to the poloidal magnetic field. This concept is also tested by numerical computations. Here the discretization procedure simulates those physical effects that in a real case would keep the current from becoming infinitely large. The results fully confirm the formation of current sheets. Our findings have potential applications to energy storage for solar flares and to the heating of the solar corona.     

Open and closed magnetospheric tail configurations and their stability

The asymptotic theory valid for magnetospheric tail configurations that vary only weakly in the antisolar direction is used to derive a number of explicit properties. The conditions under which the magnetopause converges to form a closed magnetosphere or diverges (open magnetosphere) are identified and discussed. It is shown that the presence of the high latitude low pressure tail lobes guarantees the open solution. The large value of the Mach-number of the unperturbed solar wind is the reason for the slow variation of the plasma and field quantities along the tail. Criteria for (two-dimensional) stability are discussed and it is shown that they can be expressed in terms of simple topological properties of the equilibria. Closed magnetopheres turn out to be stable, open magnetospheres with sufficiently stretched field lines are subject to an instability which — as shown earlier —may be the cause of magnetospheric substorms.     

The evolution of line-tied coronal arcades including a converging footpoint motion

It has been demonstrated in the past that single, two-dimensional coronal arcades are very unlikely driven unstable by a simple shear of the photospheric footpoints of the magnetic field lines. By means of two-dimensional, time-dependent MHD simulations, we present evidence that a resistive instability can result if in addition to the footpoint shear a slow motion of the footpoints towards the photospheric neutral line is included. Unlike the model recently proposed by van Ballegooijen and Martens (1989), the photospheric footpoint velocity in our model is nonsingular and the shear dominates everywhere. Starting from a planar potential field geometry for the arcade, we find that after some time a current sheet is formed which is unstable with respect to the tearing instability. The time of its onset scales with the logarithm of the magnetic diffusivity assumed in our calculation. In its nonlinear phase, a quasi-stationary situation arises in the vicinity of the x-line with an almost constant reconnection rate. The height of the x-line above the photosphere and the distance of the separatrix footpoints remain almost constant in this phase, while the helical flux tube, formed above the neutral line, continuously grows in size.