CORONAL HEATING BY THE RESONANT ABSORPTION OF ALFVEN WAVES - WAVE-NUMBER SCALING LAWS

The importance of global modes in coronal loop heating is well established. In the present work the scaling of the global-mode resonant heating rate with the perturbation wavenumbers is studied with the numerical solution of the linearized time-dependent MHD equations for a full compressible, low-beta, resistive plasma using an implicit integration scheme. The numerical simulations demonstrate that the dissipation on inhomogeneities in the background Alfven speed occurs in narrow resonant layer with the highest heating rate at the global-mode frequency. The global-mode heating rate H-r was found to scale as H-r similar to k(y)(-1.03) when k(z) = 0.1, and as H-r similar to k(y)(-1.93) when k(z) = 0.75, where k(y) and k(z) are the wavenumbers in the perpendicular and parallel to the magnetic field directions, respectively, while the dependence of H-r on k(z) is more complex. The ''quality factor'' Q of the MHD resonance cavity scales as Q similar to k(y)(-1.8) for k(z) = 0.75 and as Q similar to k(y)(-1.46) for k(z) = 0.1 The numerically determined heating rate scaling, the global-mode frequency, and the ''quality factor'' are in good agreement with the analytical linear theory. The magnitude of the perturbed velocities was found to decrease with k(y). Assuming typical coronal loop parameters (B-0 = 100-200 G, upsilon(A) 2000-4000 km s(-1)), the Alfven waves can supply the required heating in a low-Q loops.