Shear wave dissipation in planar magnetic X-points

The resistive dissipation of nonlinear shear wave disturbances is discussed. We consider an incompressible, ''open'' X-point geometry, in which mass and energy are free to enter and leave the reconnection region. An analytic treatment is possible which unifies many of the dynamic and steady-state X-point solutions obtained previously. We show that while field disturbances in the plane of the X-point have the potential for rapid energy release when suitably driven, perpendicular shear disturbances dissipate slowly, at a rate similar to eta(1/2), where eta is the plasma resistivity. This behavior can be understood in terms of the absence of flux pileup in nonplanar shear wave disturbances. We conclude that only planar shear waves have the potential for fast magnetic energy release.