  The non-linear evolution of a magnetic island is studied using the Vlasov
gyro-kinetic code GKW. The interaction of electromagnetic turbulence with a
self-consistently growing magnetic island, generated by a tearing unstable
$\Delta' > 0$ current profile, is considered. The turbulence is able to seed
the magnetic island and bypass the linear growth phase by generating structures
that are approximately an ion gyro-radius in width. The non-linear evolution of
the island width and its rotation frequency, after this seeding phase, is found
to be modified and is dependent on the value of the plasma beta and equilibrium
pressure gradients. At low values of beta the island evolves largely
independent of the turbulence, while at higher values the interaction has a
dramatic effect on island growth, causing the island to grow exponentially at
the growth rate of its linear phase, even though the island is larger than
linear theory validity. The turbulence forces the island to rotate in the
ion-diamagnetic direction as opposed to the electron diamagnetic direction in
which it rotates when no turbulence is present. In addition, it is found that
the mode rotation slows as the island grows in size.
