Prominence and flare fine structure from cross-field thermal conduction

Thermal conduction across a magnetic field is strongly suppressed compared with conduction along the field. However, if a flare is heated by a highly filamented beam directed along the field, then the array of heated cells in a cross-section of the flare will result in both small spatial scales (with consequently large temperature gradients) and a large surface area for the heated volume, providing a geometrical enhancement of the total cross-field energy flux. To investigate the importance of this filamentary geometry, we present a simple model of a single heated filament surrounded by an optically thin radiating shell, obtain an analytical expression for the stable equilibrium temperature profile within the shell, and use this to impose limits on the size of filament for which this model is appropriate. We find that this mechanism by itself is capable of transporting a power of the same order as a large flare, with a moderate range of filament sizes. The length scales are substantially smaller than can be resolved at present, although they should be regarded as underestimates.