L. Sparks

Radiative instabilities in a sheared magnetic field

The structure and growth rate of the radiative instability in a sheared magnetic field B have been calculated analytically using the Braginskii fluid equations. In a shear layer, temperature and density perturbations are linked by the propagation of sound waves parallel to the local magnetic field. As a consequence, density clumping or condensation plays an important role in driving the instability. Parallel thermal conduction localizes the mode to a narrow layer where k∥ =k⋅B/‖B‖ is small and stabilizes short wavelengths k>kc, where kc depends on the local radiation and conduction rates. Thermal coupling to ions also limits the width of the unstable spectrum. It is shown that a broad spectrum of modes is typically unstable in tokamak edge plasmas and it is argued that this instability is sufficiently robust to drive the large‐amplitude density fluctuations often measured there.

Nonlinear radiative condensation in a sheared magnetic field

A well-resolved two-dimensional nonlinear numerical simulation of the radiative/thermal instability in a sheared magnetic field is described which leads to filament formation. The condensation is initiated by a linearly unstable mode and widens until it is slowed by thermal conduction parallel to B. During the nonlinear evolution, the minimum temperature falls from 10 to the 6th K to 10 to the 4th K and eventually reaches a state of local thermal equilibrium in about five e-folding times. 13 references.

Ideal condensations due to perpendicular thermal conduction in a sheared magnetic field

Cool condensations generated by a radiative thermal instability in a sheared magnetic field have previously been the bases of solar filament formation models. Through the assumption of fully anisotropic heat flow, a new set of condensation modes are here obtained which become singular in the limit of vanishing perpendicular thermal conductivity. The growth rates are noted to typically be greater than those reported previously for sheared field condensations. The fastest growth is exhibited by modes possessing the fewest oscillations.

The physics of thermal instability in two dimensions

Previous studies of a thermal (radiative) instability in a sheared magnetic field have shown that, under solar coronal conditions, cool condensations can form in a small neighborhood about the shear layer. Such results have served to model the formation of solar filaments (or prominences) observed to occur above photospheric magnetic polarity-inversion lines. A surprising conclusion of these studies is that the width of the condensation does not depend on the thermal conductivity (κ∥). By examining the mass-flow patterns of two-dimensional condensations in the absence of thermal conduction, we demonstrate that local plasma dynamics and the constraints imposed by boundary conditions are together sufficient to explain the size of the condensation width. In addition we present the results of a series of numerical calculations which illustrate the characteristic mode structure of sheared-field condensations.

The nonlinear evolution of magnetized solar filaments

Thermal instability driven by optically thin radiation is believed to initiate the formation of plasma filaments in the solar corona. The fact that filaments are observed generally to separate regions of opposite, line-of-sight, magnetic polarity in the underlying photosphere suggests that filament formation requires the presence of a highly sheared, local magnetic field. Two-dimensional, nonlinear, magnetohydrodynamic simulations of the local genesis and growth of solar filaments in a force-free, sheared, magnetic field were performed, and the evolution of generic perturbations possessing broad spatial profiles was traced. It was found that simulations of the evolution of initial random-noise perturbations produce filamentary plasma structures that exhibit densities and temperatures characteristic of observed solar filaments. Furthermore, in each of these simulations, the filament axis lies at a finite angle with respect to the local magnetic field, consistent with solar observations. 28 refs.

Thermal instability of a radiative and resistive coronal plasma

Thermal instability is believed to determine the evolution and formation of cool structures in the solar atmosphere such as the transition region and prominences (or filaments). The linear modes that arise in a sheared, force-free, magnetic field due to thermal instability are studied numerically. Previous studies have considered separately modes that arise due to the effects of radiation, compression, anisotropic thermal conduction, and ohmic heating. Here the results of such studies are integrated, first by presenting simple arguments that illustrate the essential physics of ideal, sheared-field, condensation modes, and second by showing numerically how finite resistivity affects the condensational instability in parameter regimes applicable to the solar corona. 21 references.

Resistive‐heating instability of a compressible, force‐free plasma

The thermal stability of a resistive, force‐free plasma in a two‐dimensional, slab geometry is investigated numerically. Linearly unstable modes that arise as an energetic consequence of Ohmic heating are examined in relation to the dynamic magnetic‐tearing instability. Plasma compression is found to give rise to a set of unstable thermal modes not seen in previous incompressible studies. Such modes can occur in parameter regimes where no purely growing tearing mode exists.