Nanoflare Theory and Stochastic Reconnection

Local magnetic reversals are an inseparable part of MHD turbulence whose collective outcome on an arbitrary scale in the inertial range may lead to a global stochastic reconnection event with a rate independent of small scale physics. We show that this picture is intimately related to the nanoflare theory, proposed a long time ago to explain the solar coronal heating. We argue that due to stochastic flux freezing, generalized flux freezing in turbulence, the magnetic field follows the turbulent flow in a statistical sense. Bending and stretching an initially smooth field, therefore, the turbulence generally increases the magnetic spatial complexity — a measure of the geometric complexity of the field recently formulated in terms of renormalized field at different scales. Strong magnetic shears associated with such a highly tangled field can trigger local reversals and field annihilations that convert magnetic energy into kinetic and thermal energy respectively. The former maintains the turbulence, which incidentally continues to entangle the field completing the cycle, while the latter enhances the heat generation in the dissipative range. We support this theoretical picture invoking recent analytical and numerical studies which suggest a correlation between magnetic complexity and magnetic energy dissipation. The amplification of multiple local, in-phase reversals by super-linear Richardson diffusion may initiate a global reconnection at larger scales, however, even in the absence of such a global stochastic reconnection, the small scale reversals will continue to interact with the turbulence. We use scaling laws to illustrate that these local events are indeed efficient in both enhancing the turbulence and generating heat. Finally, using an MHD numerical simulation, we show that the time evolution of the magnetic complexity is statistically correlated with the kinetic energy injection rate and/or magnetic-to-thermal energy conversion rate.