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 dri ven by turbulent photospheric motions which twist and shear the magnet ic footpoints of loops. Fine-scale structure in the corona is required in order to dissipate the currents rapidly enough to account for coro nal heating. A long-standing controversy surrounds the question: is th e fine-scale filamentation the result of magnetohydrodynamic (MI-ID) i nstabilities, or of dynamical nonequilibrium, or is it merely the dire ct 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 cons ists of a three-mode truncation of the ''reduced'' MHD equations. One mode is driven by a stationary velocity held at the footpoints; the ot her two modes, of different spatial frequencies, are amplified through interaction with the driven mode. After approximately one photospheri c turnover time, the coronal field loses equilibrium, and evolves rapi dly to a new configuration, transferring energy to the two nondriven m odes. 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 ta u(p) is the photospheric turnover time. Regarding this simple model as a building block of a much more complex process, we see that dynamica l nonequilibrium should be able to produce a cascade of free energy to fine spatial scales where it can be dissipated rapidly enough to acco unt for coronal heating, as envisioned by Parker.