  In a previous paper we presented an updated magnetic field map for the
chemically peculiar star Alpha 2 CVn using ESPaDOnS and Narval time-resolved
high-resolution Stokes $IQUV$ spectra. In this paper we focus on mapping
various chemical element distributions on the surface of Alpha 2 CVn. With the
new magnetic field map and new chemical abundance distributions we can
investigate the interplay between the chemical abundance structures and the
magnetic field topology on the surface of Alpha 2 CVn.
  Previous attempts at chemical abundance mapping of Alpha 2 CVn relied on
lower resolution data. With our high resolution (R=65,000) dataset we present
nine chemical abundance maps for the elements O, Si, Cl, Ti, Cr, Fe, Pr, Nd and
Eu. We also derive an updated magnetic field map from Fe and Cr lines in Stokes
$IQUV$ and O and Cl in Stokes $IV$. These new maps are inferred from line
profiles in Stokes $IV$ using the magnetic Doppler imaging code Invers10. We
examine these new chemical maps and investigate correlations with the magnetic
topology of Alpha 2 CVn. We show that chemical abundance distributions vary
between elements, with two distinct groups of elements; one accumulates close
to the negative part of the radial field, whilst the other group shows higher
abundances located where the radial magnetic field is on the order of 2 kG
regardless of the polarity of the radial field component. We compare our
results with previous works which have mapped chemical abundance structures of
Ap stars. With the exception of Cr and Fe, we find no clear trend between what
we reconstruct and other mapping results. We also find a lack of agreement with
theoretical predictions. This suggests that there is a gap in our theoretical
understanding of the formation of horizontal chemical abundance structures and
the connection to the magnetic field in Ap stars.
