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 – is remarkably simple and clear. When the resistivity $\eta$ is small compared to an imposed evolution, $a\mathrm{/}v$, timescale, which means $R_m\equiv {\mu }_{0}va\mathrm{/}\eta >>1$, 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, $j_{\eta }\equiv vB\mathrm{/}\eta$, is required for energy dissipation to be on a comparable time scale 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 $a\mathrm{/}v$. 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.