Phase mixing and island saturation in Hamiltonian reconnection

The nonlinear evolution of a Hamiltonian magnetic field line reconnection in a two-dimensional fluid plasma leads to a macroscopic equilibrium with a finite-size island and fine-scale spatial structures. The latter arise from the phase mixing of the Lagrangian invariant fields. This equilibrium is the analog of the Bernstein-Greene-Kruskal equilibrium solution for electrostatic Langmuir waves.