The stability of a magnetic flux element in a horizontally stratified compressible plasma

The configuration of a magnetic flux element in a static, compressible, gravitationally stratified plasma is considered. Under isothermal conditions an exact force-free solution is given for a two-dimensional cartesian flux sheath but for an axi-symmetric element, i.e. a flux tube, approximate solutions, applicable only to thin flux tubes, are obtained.When the isothermal condition is relaxed within the flux tube, non-force-free solutions are obtained exhibiting either a temperature excess or deficit on the axis of the flux tube. Using these solutions, the total potential energy of such a tube and its surroundings may be calculated. By comparing this with the total energy of an equivalent system ofn flux tubes the temperature excess or deficit in these tubes corresponding to the adiabatic subdivision of the single tube is determined.It is shown that under non-adiabatic conditions the subdivision process must be endothermic (i.e., external energy is required) if the temperature within the original tube is significantly less than its surroundings but exothermic if the temperatures are comparable. Thus it is conjectured that magnetic structures are less susceptible to subdivision if they are significantly cooler than their surroundings.