the inverse power of the resistivity (eq. (\[eq:hrdiff\])). In other words, the smaller the resistivity in the corona, the higher the power dissipated would be. But the amplitudes can not become arbitrarily large, because non-linear effects intervene to stop the increase in field amplitudes, increasing the effective dissipation at a given resistivity. Since the power can not continue to increase monotonically as the resistivity is decreased, it is clear that at some point non-linear interactions must limit the dissipated power to a finite value, regardless of the value of the resistivity. Finite dissipation at arbitrarily small values of dissipative coefficients is another definition of a turbulent system.

All this assuming that a statistically stationary state may be reached in a finite time, a question closely related to the presence of finite time singularities in 3D magnetohydrodynamics. It now appears that magnetic field relaxation in an unforced situation does not lead to the development of infinitely thin current sheets in a finite time, but rather the current development appears to be only exponential in time [@GRM00]. In forced numerical simulations, as the ones we will describe in detail here, this is a moot point: for all intents and purposes a statistically 