Energy conversion in magnetic reconnection

It is widely believed that magnetic reconnection automatically releases the stored magnetic energy and converts it into particle thermal or kinetic energy. Most theoretical or simulation studies in reconnection focus on the ``mechanism'' of reconnection under the assumption that magnetic-to-particle energy conversion is automatically implied. However, such an assumption has not been demonstrated in a rigorous mathematical sense thus far. In this paper, it is demonstrated on the basis of energy principle, which is derived from exact nonlinear Vlasov equation, that the change in magnetic topology (i.e., reconnection) in a finite closed system does indeed lead to the conversion of magnetic field energy to particle energy. However, it is also shown that the volume-averaged conversion efficiency is highly dependent on many geometrical factors which includes the system size. This principle is demonstrated by comparing the total energy content of the classical Harris current sheet versus that of Fadeev current sheet which features magnetic island structure.