  A local magnetic equilibrium solution is sought around the magnetic axis in
order to identify the key parameters defining the magnetic-surface's up-down
asymmetry in the core of tokamak plasmas. The asymmetry is found to be
determined essentially by the ratio of the toroidal current density flowing on
axis to the fraction of the external field's odd perturbation that manages to
propagate from the plasma boundary into the core. The predictions are tested
and illustrated first with an analytical Solovev equilibrium and then using
experimentally relevant numerical equilibria. Hollow current-density
distributions, and hence reverse magnetic shear, are seen to be crucial to
bring into the core asymmetry values that are usually found only near the
plasma edge.
