Elementary Heating Events - Magnetic Interactions Between Two Flux Sources. III Energy Considerations

The magnetic field plays a crucial role in heating the solar corona, but the exact energy release mechanism(s) is(are) still unknown. Here, we investigate in detail, the process of magnetic energy release in a situation where two initially independent flux systems are forced into each other. Work done by the foot point motions goes in to building a current sheet in which magnetic reconnection takes place. The scaling relations of the energy input and output are determined as functions of the driving velocity and the strength of fluxes in the independent flux systems. In particular, it is found that the energy injected into the system is proportional to the distance travelled not the rate of travel. Similarly, the rate of Joule dissipation is related to the distance travelled. Hence, rapidly driven foot points lead to bright, intense, but short-lived events, whilst slowly driven foot points produce weaker, but longer-lived brightenings. Integrated over the lifetime of the events both would produce the same heating if all other factors were the same. A strong overlying field has the affect of creating compact flux lobes from the sources. These appear to lead to a more rapid injection of energy, as well as a more rapid release of energy. Thus, the stronger the overlying field the more compact and more intense the heating. This means observers must know the rate of movement of the magnetic fragments involved in an events, as well as determine the strength and orientation of the surrounding field to be able to predict anything about the energy dissipated.