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-β, resistive plasma using an implicit integration scheme. The numerical simulations demonstrate that the dissipation on inhomoge-neities 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 ～ k_y~(-1.03) when k_z = 0.1, and as H_r ～ 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 ～ k_y~(-1.8) for k_z = 0.75 and as Q ～ 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, υ_A = 2000-4000 km s~(-1)), the Alfven waves can supply the required heating in a low-Q loops.
展开▼
