  We carry out numerical and mathematical investigations of shear Alfven waves
inside of a spherical shell filled with an incompressible conducting fluid, and
bathed in a strong dipolar magnetic field. We focus on axisymmetric toroidal
and non-axisymmetric modes, in continuation of a previous work by Rincon &
Rieutord (2003, A&A, 398, 663). Analytical expressions are obtained for
toroidal eigenmodes and their corresponding frequencies at low diffusivities.
These oscillations behave like magnetic shear layers, in which the magnetic
poles play a key role, and hence become singular when diffusivities vanish. It
is also demonstrated that non-axisymmetric modes are split into two categories,
namely poloidal or toroidal types, following similar asymptotic behaviours as
their axisymmetric counterparts when the diffusivities become arbitrarily
small.
