We investigate a model for the excitation of high-order oscillations in roA
p stars. In this model we assume that the strong concentration of magnetic
field about the magnetic poles is enough to suppress convection. Thus the m
odel considered is composed of two polar regions, in which convection is pr
esumed to be suppressed totally, and an equatorial region, where the convec
tion is unaffected. This model is generated by building pairs of locally sp
herically symmetrical equilibria to represent the polar and equatorial regi
ons of the star, which are patched together below the base of the, convecti
on zone. Gravitational settling of heavy elements is taken into account by
choosing appropriate chemical composition profiles for both the polar and e
quatorial regions. Our results indicate that the composite model is unstabl
e against axisymmetric non-radial high-order modes of pulsation that are al
igned with the magnetic poles. The oscillations are excited by the kappa me
chanism acting principally in the hydrogen ionization zones of the polar re
gions. The effect of the lateral inhomogeneity on the second frequency diff
erences is also investigated; we find that the perturbation to them by the
inhomogeneity is of the same order as the second differences themselves, th
ereby hindering potential attempts to use such differences to identify the
degrees of the modes in a straightforward way.