Numerical simulations of MHD wave excitation in bounded plasma slabs

Numerical simulations are performed in the framework of nonlinear resistive 2.5-dimensional magnetohydrodynamics to investigate the response of a coronal loop to shearing motions of the footpoints. A simple slab plasma with straight magnetic field lines is used to model the coronal loop, with the photospheric ends represented by impermeable walls. The hot, dense loop plasma is approximated by smoothed step-function profiles. The results show that an initially excited Alfvén wave reveals a 1/x-type singularity, which is characteristic of the linear Alfvén resonances, smoothed by the resistive dissipation. Both fast and slow magnetosonic waves are driven by the nonlinear Alfvén wave. The slow magnetosonic waves concentrate their energies in resonance layers, and their associated flows exhibit singularities of the 1/x-type. The Alfvén resonances, which are absent from the system in the case of linear waves, develop late in time as the Alfvén-wave amplitude grows into the nonlinear regime, and their development is accelerated for larger-amplitude driving forces. The resultant heating associated with the resonances phase mixing of the waves is concentrated in the region of large Alfvén-speed gradients.