Magnetic fields in the solar corona are braught into an endless evolution by the never-ceasing motions of the subphotospheric plasma in which the feet of their lines are anchored. It is generally thought that this evolution is essentially quasi-static, the field passing through a sequence of force-free equilibrium states. Sporadically, however, the equilibrium is broken in a region of limited extent, and during a relatively short interval of time a catastrophic highly dynamic evolution takes place, giving rise to such wellknown phenomena as flares or coronal transients. Understanding the factors which determine if a magnetohydrostatic coronal equilibrium is maintained or, on the contrary, destroyed, when boundary conditions change at the photospheric level, then appears as a central theoretical problem of solar physics. In this Communication, we report some recent results which shed some new light onto this old problem.

In this Communication, we consider in the half-space {z > 0} a fully 3-D force-free magnetic field B˷ embedded in a perfectly conducting plasma and its quasi-static evolution driven by motions imposed to the feet of its lines on the boundary {z = 0}. Assuming that the field lines of B˷ have a simple topology - i.e. that it is possible to choose a (non-unique) set of nested magnetic surfaces which are either “arcade-like” or “tube-like” - we first establish a global representation of B˷ in terms of two Euler potentials u and v (with v multivalued) and derive new formulae giving in particular the relative helicity end the energy of B˷ as functions of the values of u and v (and of their derivatives) on {z = 0}. We thus establish analytically some general qualitative features of the behaviour of B˷.

In order to understand how prominences are supported in the solar corona, we have recently developed several 2D models describing x-invariant equilibrium configurations of a plasma occupying a half-space {z > 0} and submitted to a magnetic field then of the form

(1)

We describe a mechanism for coronal heating. The basic idea is that since the photospheric flux is observed to consist of a complex pattern of positive and negative polarity regions, the topology of the coronal magnetic field (in particular the connectivity) must be discontinuous over a complex network of surfaces and magnetic null points in the corona. Consequently, photospheric motions of the field line footpoints, even if arbitrarily smooth, result in discontinuous stressing of the field. This produces coronal current sheets, reconnection at the null points, and rapid heating.

A two dimensional MHD code is used to study the nonlinear evolution of the Parker instability in isolated horizontal magnetic flux imbedded in (or below) the solar photosphere. It is found that the magnetic loop expands self-similarly in the nonlinear stage. Numerical results explain many features observed in emerging flux regions.

A two-dimensional sheet model for solar filaments (Kippenhahn and Schluter configuration) is considered. We investigate, the quasi-static evolution of gravito-magnetohydrostatic equlibria in exploring the response of massive current sheets to a slow continuous variation of the mass/flux ratio with fixed boundary conditions. A catastrophic behavior of the field topology is found to occur in the sequence following the formation of a cusp point (bifurcation).

We determine the electron distribution function within a hot coronal loop using a hybrid numerical scheme which couples the Spitzer-Härm method at low velocities with the solution to the high velocity form of the Landau-Fokker-Planck equation. From this we calculate the heat flux throughout the loop and compare it with the classical fourier law of Spitzer and Härm(1953).

We discuss a mechanism whereby a current loop embedded in plasmas such as the solar and stellar coronae can dissipate magnetic energy without resistive effects or reconnection. This mechanism arises from the motion of magnetic/current structures driven by “toroidal forces”. Using a simple model loop, we show that it can exhibit a wide range of motion with correspondingly wide range of magnetic energy dissipation rates. For example, a loop with ~20G can attain expansion velocities of ~1200km s–1 under solar coronal conditions, dissipating ~1032erg in a few tens of minutes.

The arguments in favour of that the primary heating of the gas at the impulsive phase of stellar flares is caused by charged particles of higher energies than in the solar flares are given. It is shown that the model of the deep heating by high energy protons (E ≃ 10 MeV) or electrons (E ≃ 100 keV) with taken into account of the radiative transfer in flare region explane the main properties of the optical continuum of the flare.

Two kinds of MHS equilibrium are studied; isothermal and nonisothermal. The onsets of two - ribbon flares and flare - loops are explained by this study.

A detailed analysis of the kink instability in finite length (inertially line-tied), cylindrically symmetric coronal loops is presented. The correct line-tying boundary conditions within the framework of ideal and resistive magnctohydrodynamics are discussed, and the growth rates of unstable modes and corresponding eigenfunctions are calculated. Resistive kink modes are found to be unstable in configurations where the axial magnetic field undergoes an inversion, resistive effects being confined to a small region around the loop vertex.

We investigate numerically the effect of a finite density gradient on the Langmir wavelevel produced by an electron beam in the flaring solar corona. The energy losses and associated plasma heating resulting from the presence of a beam-neutralizing reverse current are taken into account. The density and temperature structure of the background plasma are determined self-consistently, assuming steady state energy balance and hydrostatic equilibrium. The implications of our results for flare acceleration mechanisms are discussed.

We consider the problem of ion-acoustic wave generation, and resultant anomalous Joule heating, by a return current driven unstable by a small-area thick-target electron beam in solar flares. We find that, contrary to the usual assumption, the hard X-ray bremsstrahlung emission may actually be enhanced in comparison to conventional thick-target models. This present paper is a summary of the work of Cromwell, McQuillan and Brown (1988).

A model for the acceleration of electrons in a flaring coronal loop is described. The mechanism is stochastic acceleration by resonant interactions with a spectrum of conipressive magnetosonic waves. Current results of test particle calculations examining the feasibility of this model are presented.

The proposed model of particles transport in the solar atmosphere during flares consists in a low density plasmoid originating deep in the atmosphere and rising under magnetic and buoyancy forces. Confined particles are selectively released during the ascent and their interaction with the solar atmosphere produces X and γ bremsstrahlung. The characteristics of high energy particles released in the interplanetary medium are found to agree with observations.

Recent observations suggest that the energy release in solar flares may occur in many small bursts. If these bursts give rise to plasma heating, a large number of collisionless shocks will be generated. These shocks can individually heat plasma and accelerate particles, but the interaction of particles with many shocks as well, as of shocks with each other can give rise to further heating and acceleration.

The emission mechanism studied here, the synchrotron maser instability is based on a gyroresonance of highly energetic electrons. Compared to the cyclotron maser, this mechanism has the great advantage to be a direct amplification process even if the ratio ωp/ωc is not very small; a situation relevant to stellar flares.The high efficiency of the process can be confirm by the non linear study of its saturation.

The propagation and absorption of the maser radiation emitted during solar flares are examined through linear theory and electromagnetic particle simulations. While linear theory predicts complete absorption of the maser radiation at the second harmonic layer (where the local cyclotron frequency is roughly one-half the frequency of the maser radiation), particle simulations indicate that some radiation escapes clue to reemission of absorbed energy by the ambient plasma. Strong perpendicular heating of the ambient electrons occurs as well.

A simple impulsive event observed at microwave frequencies between 3.2 and 50 GHz is simulated with a homogeneous source model. Intensity and polarization of the 1984 April 26 event are shown in fig. 1a and 1b, respectively. The spectral maximum is close to the observing frequency of 11.8 GHz.

The time profiles of the intensity I and the circular polarization ρc at this frequency as well as the spectrum at different characteristic phases (rise, maximum and decay) are calculated and compared with the observation in order to deduce parameters of the microwave source.

The investigations of plasma motions at the initial phases of solar flares (Antonucci and Dennis, 1983; Doschek, 1983; Watanabe, 1987) suggest evaporation from the chromospheric flaring area. According to de Jager (1983) when seen at the limb the evaporated plasma will look like a “convective plume” and it can be seen separated from heated footpoint areas.

The subject of this work is the study of the possibility of forming hydrodynamic structures o-f thermal and starting plume's kind at the time of evaporation of the upper chromosphere in a flaring area. Also the possibility of increasing an initial magnetic field by a periodically moving vortex in a plume structure is investigated.