  In the presence of strong density stratification, turbulence can lead to a
large-scale instability of a horizontal magnetic field if its strength is in a
suitable range (within a few percent of the turbulent equipartition value).
This instability is related to a suppression of the turbulent pressure so that
the turbulence contribution to the mean magnetic pressure becomes negative.
This results in the excitation of a negative effective magnetic pressure
instability (NEMPI). This instability has so far only been studied for an
imposed magnetic field. We want to know how NEMPI works when the mean magnetic
field is generated self-consistently by an $\alpha^2$ dynamo, whether it is
affected by global spherical geometry, and whether it can influence the
properties of the dynamo itself. We adopt the mean-field approach which has
previously been shown to provide a realistic description of NEMPI in direct
numerical simulations. We assume axisymmetry and solve the mean-field equations
with the Pencil-Code for an adiabatic stratification at a total density
contrast in the radial direction of approximately 4 orders of magnitude. NEMPI
is found to work when the dynamo-generated field is about 4% of the
equipartition value, which is achieved through strong $\alpha$ quenching. This
instability is excited in the top 5% of the outer radius provided the density
contrast across this top layer is at least 10. NEMPI is found to occur at lower
latitudes when the mean magnetic field is stronger. For weaker fields, NEMPI
can make the dynamo oscillatory with poleward migration. NEMPI is a viable
mechanism for producing magnetic flux concentrations in a strongly stratified
spherical shell in which a magnetic field is generated by a strongly quenched
$\alpha$ effect dynamo.
