Plasma cooling by thermal conduction in the magnetically closed solar corona with large spatial variations in the magnetic field strength

Plasma cooling by thermal conduction is considered for solar coronal magnetic loops that have large variations in their magnetic field strength and hence cross-sectional area. In terms of a “cooling time”, for all cases considered an increase in the cross sectional area from base to apex leads to longer cooling times than for a loop with uniform area. Although this result is expected, this paper reveals, for the first time, a vast range of different cooling outcomes that depend on the details of the prescribed loop geometry. While a simple approach suggests that the cooling time could scale with the average area, 〈A〉, this only holds when the region of the most significant area variation and the hottest plasma coincide. Instead, analytic and quasi-analytic solutions show that this scaling can greatly exaggerate the effect of 〈A〉 on the cooling time. For example, there are cases in which the cooling time scales as ln (〈A〉). Thus, conductive cooling needs to be considered on a case-by-case basis. The results can be understood in terms of an artificial “heating” associated with a non-uniform loop area.