Particle acceleration and fast magnetic reconnection

Abstract

Mathematics demonstrates that the exponential separation of neighboring magnetic field lines, which naturally increases during an ideal evolution in three dimensions, leads to an exponentially increasing connection-breaking nonideal magnetic field. On a time scale that depends only logarithmically on the magnitude of the nonideal terms, a fast magnetic reconnection will generally occur, which has a rate determined by Alfvénic, not resistive, physics. The traditional assumption that the reconnecting flux must be dissipated by an electric field is false. In three dimensions, an ideal evolution can spatially mix the magnetic flux. Flux mixing conserves magnetic helicity, which limits the energy that can be transferred from the magnetic field to the plasma. The magnetic evolution is quasi-ideal during a fast magnetic reconnection, and the energy loss is given by the dot product of the magnetic field line velocity u→⊥ with the j→×B→ Lorentz force. Energy loss occurs through Alfvén waves and two other effects, which are also present in an ideal evolution. One is an effective parallel electric field E||, which can accelerate particles despite the particle acceleration due to the true parallel electric field E|| being negligible, and a coefficient νK, which gives a rate for exponentiation of the kinetic energy of particle motion along the magnetic field.