Resistivity-independent dissipation of magnetohydrodynamic waves in an inhomogeneous plasma

The heating of high temperature plasmas by magnetohydrodynamic (MHD) waves is one of the most interesting and challenging problems of plasma physics especially when the energy is injected into the system at length scales much larger than the dissipative ones. It has been conjectured that in two-dimensional MHD systems the possibility exists of establishing a state in which energy is dissipated at a rate that is independent of the Ohmic resistivity and that the time needed to reach such a state is finite and independent of resistivity as well. In this paper we prove that this is actually possible as a result of the nonlinear interaction of long-wavelength, "small" amplitude perturbations with a constant, inhomogeneous magnetic field, at least in the relatively moderate Lundquist number (magnetic Reynolds) range 100< or =S< or=3200.