Two-fluid magnetic island dynamics in slab geometry: I - Isolated   islands
  A set of reduced, 2-D, two-fluid, drift-MHD equations is derived. Using these equations, a complete and fully self-consistent solution is obtained for an isolated magnetic island propagating through a slab plasma with uniform but different ion and electron fluid velocities. The ion and electron fluid flow profiles around the island are uniquely determined, and are everywhere continuous. Moreover, the island phase-velocity is uniquely specified by the condition that there be zero net electromagnetic force acting on the island. Finally, the ion polarization current correction to the Rutherford island width evolution equation is evaluated, and found to be stabilizing provided that the anomalous perpendicular ion viscosity significantly exceeds the anomalous perpendicular electron viscosity. 
Richard Fitzpatrick and Francois L. Waelbroeck