Supersonic drift-tearing magnetic islands in tokamak plasmas*

A two-fluid theory of long wavelength, supersonic, drift-tearing magnetic islands in low collisionality, low-$\beta$ plasmas possessing relatively weak magnetic shear is developed. The model assume s both slab geometry and cold ions, and neglects electron temperature and equilibrium current gradient effects. The problem is solved in two asymptotically matched regions. The ``inner region'' contains the island. However, the island emits electrostatic drift-acoustic waves which propagate into the surrounding ``outer region'', where they are absorbed by the plasma. Since the waves carry momentum, the inner region exerts a net force on the outer region, and {\em vice versa}, giving rise to strong velocity shear in the region immediately surrounding the island. Isolated supersonic islands propagate with a velocity which lies between those of the unperturbed local ion and electron fluids, but is much closer to the latter. The ion polarization current is {\em stabilizing}, and {\em increases}\/ with increasing is land width. Finally, the supersonic branch of isolated island solutions {\em ceases to exist}\/ above a certain critical island width. Supersonic islands whose widths exceed the critical width are hypothesized to bifurcate to the so-called ``subsonic'' solution branch.