NONLINEAR ENERGY-TRANSFER IN SOLAR MAGNETIC LOOPS

Active region coronal loops are widely believed to be heated by ohmic dissipation of field-aligned electric currents. These currents are driven by turbulent photospheric motions which twist and shear the magnetic footpoints of loops. Fine-scale structure in the corona is required in order to dissipate the currents rapidly enough to account for coronal heating. A long-standing controversy surrounds the question: is the fine-scale filamentation the result of magnetohydrodynamic (MI-ID) instabilities, or of dynamical nonequilibrium, or is it merely the direct product of the turbulent footpoint motions themselves? We present a simple model for the evolution of the coronal magnetic field, with no fine-scale structure in the imposed footpoint motions. The model consists of a three-mode truncation of the ''reduced'' MHD equations. One mode is driven by a stationary velocity held at the footpoints; the other two modes, of different spatial frequencies, are amplified through interaction with the driven mode. After approximately one photospheric turnover time, the coronal field loses equilibrium, and evolves rapidly to a new configuration, transferring energy to the two nondriven modes. The timescale of rapid nonequilibrium evolution is (tau(A),tau(p))(1/2), where tau(A) is the Alfven transit time along the loop and tau(p) is the photospheric turnover time. Regarding this simple model as a building block of a much more complex process, we see that dynamical nonequilibrium should be able to produce a cascade of free energy to fine spatial scales where it can be dissipated rapidly enough to account for coronal heating, as envisioned by Parker.