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Wave propagation in magnetically structured atmospheres is a thoroughlystudied, yet practically inexhaustible well of investigations in the field ofsolar magneto-seismology. A simple but powerful example is the examination ofwave behaviour in a magnetic slab. Our previous study (Zs\'amberger, Allcockand Erd\'elyi, Astrophys. J., 853, p. 136, 2018) used an analytical approach toderive the general dispersion relation for magneto-acoustic waves in a magneticslab of homogeneous plasma, which was enclosed in an asymmetric magneticenvironment. In the present study, we focus on the analysis of wave propagationin various limiting cases applicable to solar and space plasma or astrophysics.The thin- and wide-slab approximations, as well as the limits of low and highplasma-beta values are considered. Utilising the fact that in a weaklyasymmetric slab, the dispersion relation can be decoupled, the behaviour ofquasi-sausage and quasi-kink modes is studied in further analytical andnumerical detail, and their avoided crossings are described. The resultshighlight how the asymmetry influences the wave properties, e.g. the phasespeed of eigenmodes, depending on the ratios of external-to-internal densitiesand magnetic fields on the two sides. Notably, the phase speeds of surfacemodes will converge to different values for quasi-sausage and quasi-kink modesin the wide-slab limit, and cut-off frequencies are introduced with respect toboth surface and body modes, in thin as well as wide slabs, beyond which thesolutions become leaky. These obtained properties of MHD wave behaviour couldbe measured with suitable high-resolution instruments in the future.

Magneto-acoustic waves in a magnetic slab embedded in an asymmetric magnetic environment II: Thin and wide slabs, hot and cold plasmas