Nonparallel wave propagation in an asymmetric magnetic slab

Theoretical and numerical analyses of the behavior of magnetohydrodynamic (MHD) waves in solar atmospheric structures have a vital role in understanding the plasma dynamics of the Sun. Magneto-helioseismology is indebted to the insight gained from simple magnetic slab structures accompanied by varying conditions within the slab and its environment. This paper builds on the existing literature on these structures by presenting an analytical approach to deriving the dispersion relation for MHD wave propagation in a nonparallel case. Analogous to the parallel case, a plethora of modes emerges that can be classified into quasi-kink or quasi-sausage, body or surface, as well as fast or slow waves. The slab itself can be viewed as thin or wide similarly to previous works, however due to the nonparallel condition it can also be categorised as short or long in the direction of the tilt of the wavevector. This is the analog of the thin or wide slab classification in the parallel direction, expanding our established knowledge regarding propagating MHD waves in magnetic slabs. The variance of the wavenumber along the nonparallel dimension brings to light a number of intriguing features, such as modes changing character with variation of the angle of the wavevector while the propagation speed remains the same. Further new information is provided by the newly derived classification limits, u±, which act as a form of generalised Alfvén and sound speeds in the dispersion relation.