Collisionless magnetic reconnection: Flux quanta, field lines, `composite electrons' -- Is the quantum-Hall effect involved in its micro-scale physics?

Abstract

Microscopically, collisionless reconnection in thin current sheets is argued to involve `composite electrons' in the ion inertial (Hall current) domain, a tiny fraction of electrons only. These `composite electrons' are confined to lower Landau levels $\epsilon_L\ll T_e$ (energy much less than temperature). They demagnetise by absorbing magnetic flux quanta $\Phi_0=h/e$, decouple from the magnetic field, transport the attached magnetic flux into the non-magnetic centre of the current layer, where they release the flux in the form of micro-scale magnetic vortices, becoming ordinary electrons. The newly born micro-scale magnetic vortices reconnect in their strictly anti-parallel sections when contacting other vortices, ultimately producing the meso-scale reconnection structure. We clarify the notions of magnetic field lines and field line radius, estimate the power released when two oppositely directed flux quanta annihilate, and calculate the number density and Landau-level filling-factor of `composite electrons' in the Hall domain. As side product we find that the magnetic diffusion coefficient in plasma also appears in quanta $D_0^m=e\Phi_0/m_e=h/m_e$, yielding that the bulk perpendicular plasma resistivity is quantised, with quantum (lowest limit) $\eta_{\,0\perp}=\mu_0 e\Phi_0/m_e=\mu_0h/m_e\sim 10^{-9}$ Ohm m. Keywords: Reconnection, thin current sheets, quantum Hall effect, quantised diffusivity, quantised plasma resistivity, composite electrons