Magnetic field evolution and reconnection in low resistivity plasmas

The mathematics and physics of each of the three aspects of magnetic field evolution—topology, energy, and helicity—are remarkably simple and clear. When the resistivity η is small compared to an imposed evolution, a/v, timescale, which means R m ≡ μ 0 v a / η ≫ 1, magnetic field-line chaos dominates the evolution of field-line topology in three-dimensional systems. Chaos has no direct role in the dissipation of energy. A large current density, j η ≡ v B / η, is required for energy dissipation to be on a comparable timescale to the topological evolution. Nevertheless, chaos plus Alfvén wave damping explain why both timescales tend to be approximately an order of magnitude longer than the evolution timescale a/v. Magnetic helicity is injected onto tubes of field lines when boundary flows have vorticity. Chaos can spread but not destroy magnetic helicity. Resistivity has a negligible effect on helicity accumulation when R m ≫ 1. Helicity accumulates within a tube of field lines until the tube erupts and moves far from its original location.