  Stellar dynamos are affected by boundary conditions imposed by stellar
coronae. Under some approximations it is possible to find analytical solutions.
Interior dynamo models often consider a current-free coronae without taking
into account the constraints imposed by the presence of currents in the corona.
We aim to analytically evaluate the effect of coronal currents and of an outer
boundary condition on the efficiency of an $\alpha^2$ dynamo. We intend to
estimate the change in geometry and dinamo excitation numbers with respect to
the current-free case. We analytically solve the turbulent dynamo induction
equation for a homogeneous, non-mirror symmetric turbulence, in a spherical
domain surrounded by a linear force-free corona with magnetic field B
satisfying curl B = \beta B. The main result is that the dynamo number is a
decreasing function of \beta. Moreover, if the current is parallel to the field
(\beta > 0) the dynamo number is smaller than in the force-free case. On the
contrary (\beta < 0) the dynamo number is greater than the in force-free case.
We conclude that the presence of currents in the corona needs to be taken into
account because it affects the condition for excitation of a dynamo.
