  Stabilizing vortex solitons with high values of the topological charge, S, is
a challenging issue in optics, studies of Bose-Einstein condensates (BECs) and
other fields. To develop a new approach to the solution of this problem, we
consider a two-dimensional dipolar BEC under the action of an axisymmetric
radially periodic lattice potential, $V(r)\sim \cos (2r+\delta )$, with dipole
moments polarized perpendicular to the system's plane, which gives rise to
isotropic repulsive dipole-dipole interactions (DDIs). Two radial lattices are
considered, with $\delta =0$ and $\pi $, i.e., a potential maximum or minimum
at $r=0$, respectively. Families of vortex gapsoliton (GSs) with $S=1$ and
$S\geq 2$, the latter ones often being unstable in other settings, are
completely stable in the present system (at least, up to $S=11$), being trapped
in different annular troughs of the radial potential. The vortex solitons with
different $S$ may stably coexist in sufficiently far separated troughs.
Fundamental GSs, with $S=0$, are found too. In the case of $\delta =0$, the
fundamental solitons are ring-shaped modes, with a local minimum at $r=0.$At
$\delta =\pi $, they place a density peak at the center.
