Abstract
We evaluate the large‐scale energy budget of magnetic reconnection utilizing an analytical time‐dependent impulsive reconnection model and a numerical 2‐D MHD simulation. With the generalization to compressible plasma, we can investigate changes in the thermal, kinetic, and magnetic energies. We study these changes in three different regions: (a) the region defined by the outflowing plasma (outflow region, OR), (b) the region of compressed magnetic fields above/below the OR (traveling compression region, TCR), and (c) the region trailing the OR and TCR (wake). For incompressible plasma, we find that the decrease inside the OR is compensated by the increase in kinetic energy. However, for the general compressible case, the decrease in magnetic energy inside the OR is not sufficient to explain the increase in thermal and kinetic energy. Hence, energy from other regions needs to be considered. We find that the decrease in thermal and magnetic energy in the wake, together with the decrease in magnetic energy inside the OR, is sufficient to feed the increase in kinetic and thermal energies in the OR and the increase in magnetic and thermal energies inside the TCR. That way, the energy budget is balanced, but consequently, not all magnetic energy is converted into kinetic and thermal energies of the OR. Instead, a certain fraction gets transfered into the TCR. As an upper limit of the efficiency of reconnection (magnetic energy → kinetic energy) we find η eff=1/2. A numerical simulation is used to include a finite thickness of the current sheet, which shows the importance of the pressure gradient inside the OR for the conversion of kinetic energy into thermal energy.
Highlights
Magnetic reconnection is seen as the responsible process for huge energy releases in the universe, such as during solar flares or in the context of geomagnetic storms and substorms.Reconnection leads to the conversion of previously stored magnetic energy into kinetic and thermal plasma energy and a topological reconfiguration of magnetic field lines
At this stage no more reconnected flux is added to the system, but the volume of the outflow region (OR) grows during their propagation as more and more plasma gets accelerated over the shocks and energy conversion continues
For the two areas of the IR, the thermal energy behaves differently. While it decreases in the wake, it increases inside the TCR. This can be understood by the following: The TCR corresponds to a compression of magnetic field lines and plasma, which leads to an increase in the magnetic and thermal energies therein
Summary
Magnetic reconnection is seen as the responsible process for huge energy releases in the universe, such as during solar flares or in the context of geomagnetic storms and substorms. In the Earth’s magnetotail these regions are frequently observed and known as travelling compression regions (TCRs, Slavin et al, 1984) Another domain, absent in steady–state reconnection, but implemented in time–dependent models, is the wake of the outflowing plasma. The outflow regions are no longer connected to the initial reconnection site and they propagate in opposite directions along the current sheet (Figure 1c) At this stage no more reconnected flux is added to the system, but the volume of the OR grows during their propagation as more and more plasma gets accelerated over the shocks and energy conversion continues (see Figure 2). Using a time–dependent reconnection model allows us to include the TCR and assess the energy changes and transfers in that region
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