  In the context of the white dwarf asteroseismology, we investigate
vibrational properties of a non-convective solid star with an axisymmetric
purely toroidal intrinsic magnetic field of two different shapes. Focus is laid
on regime of node-free global Lorentz-force-driven vibrations about symmetry
axis at which material displacements have one and the same form as those for
nodeless spheroidal and torsional vibrations restored by Hooke's force of
elastic shear stresses. Particular attention is given to the even-parity
poloidal Alfven modes whose frequency spectra are computed in analytic form
showing how the purely toroidal magnetic fields completely buried beneath the
star surface can manifest itself in seismic vibrations of non-magnetic white
dwarfs. The obtained spectral formulae are discussed in juxtaposition with
those for Alfven modes in the solid star model with the poloidal, homogeneous
internal and dipolar external, magnetic field whose inferences are relevant to
Alfven vibrations in magnetic white dwarfs.
