Nonlinear fast magnetosonic waves in solar coronal holes

A coronal hole is modeled as a slab of cold plasma threaded by a vertical, uniform magnetic field. A periodic driver acting at the coronal base is assumed to drive the velocity component normal to the equilibrium magnetic field. Previous works indicate that, in the linear regime, only fast mode perturbations propagate, since Alfven waves are excluded from the model and the slow wave is absent in the cold plasma limit. However, in this work, it is shown that nonlinear terms in the magnetohydrodynamic (MHD) equations give rise to excitation of the velocity component parallel to the equilibrium B, with a lower amplitude than the normal component. Another consequence of nonlinearities is the generation of higher-frequency Fourier modes, which can be detected by Fourier analyzing the velocity variations above the photosphere. The nature of the nonlinear interactions in the MHD equations determines the frequency of those modes. These interactions are quadratic in the case of the parallel component, while they are cubic in the case of the normal component. Therefore, nonlinearly excited frequencies 2w(d), 4w(d), 6w(d), : : : are present in the parallel velocity, whereas frequencies 3w(d), 5w(d), 7w(d), : :: are present in the normal velocity, with w(d) the driving frequency.