Standing MHD waves in a magnetic slab embedded in an asymmetric magnetic plasma environment: surface waves

Building on a previous study that analyzed standing surface waves in magnetic slabs embedded in a non-magnetic external environment, in this study the model is generalized and external magnetic fields are added. The slab is assumed to be thin, with weak magnetic asymmetry. The frequencies of the standing harmonic modes are derived to leading order in the small quantities representing the thin slab width and the weak asymmetry. It is found that the frequencies are more sensitive to changes to the width of the slab than changes in the magnetic asymmetry. The frequency ratio of the first harmonic to the fundamental mode is derived, along with the amplitude difference between the two sides of the slab, as these may be observable quantities that can be compared with observational results and applied to carry out solar magnetoseismology.