A constrained tectonics model for coronal heating

An analytical and numerical treatment is given of a constrained version of the tectonics model developed by Priest et al.. We begin with a uniform magnetic field B = B_oẐ that is line-tied at the surfaces z = 0 and z = L. This initial configuration is twisted by photospheric footpoint motion that is assumed to depend on only one coordinate (x) transverse to the initial magnetic field. The geometric constraints imposed by our assumption preclude the occurrence of reconnection and secondary instabilities but enable us to follow for long times the dissipation of energy due to the effects of resistivity and viscosity. In this limit, we demonstrate that when the coherence time of random photospheric footpoint motion is much smaller by several orders of magnitude compared with the resistive diffusion time, the heating due to ohmic and viscous dissipation becomes independent of the resistivity of the plasma. Furthermore, we obtain scaling relations that suggest that even if reconnection and/or secondary instabilities were to limit the buildup of magnetic energy in such a model, the overall heating rate will still be independent of the resistivity.