Induced Deposition of Magnetic Energy in the Solar Corona

In this paper a numerical study of the propagation and dissipation properties of magnetohydro-dynamic waves in an incompressible magnetized plasma is presented. The magnetic field is assumed to be unidirectional, but its magnitude varies in a direction perpendicular to the field. The analysis concerns both linear and nonlinear waves. The main findings are the following. Among the waves whose amplitude never exceeds the linear limit, short-wavelength waves dissipate more efficiently than those of long wavelength. The dissipated energy is at most the energy initially injected into the system in the form of waves, the background magnetic field remaining unaltered. When the initial amplitude is significantly increased from very small values, but remains still substantially lower than the background field, a nonlinear cascade is excited and dissipation is greatly enhanced in the long-wavelength limit. The dissipated energy in this case exceeds that contained in the waves initially injected into the system, which shows that also part of the unperturbed field is actually dissipated. A second important point concerns the formation of localized current sheets in a finite time as a result of the propagation of the waves. Such current sheets are formed in a nonlinear process triggered by the same mechanism responsible for the formation of linear resonant normal modes. The dissipation rate of such modes is known to be independent of the Reynolds number. By analogy, it is conjectured that the time of formation of current sheets might not depend on the magnetic Reynolds number.