  In this paper, we study the spontaneous scalarization of an extended,
self-gravitating system which is static, cylindrically symmetric and possesses
electromagnetic fields. We demonstrate that a real massive scalar field
condenses on this Melvin magnetic universe solution when introducing a
non-minimal coupling between the scalar field and (a) the magnetic field and
(b) the curvature of the space-time, respectively. We find that in both cases,
the solutions exist on a finite interval of the coupling constant and that
solutions with a number of nodes $k$ in the scalar field exist. For case (a) we
observe that the intervals of existence are mutually exclusive for different
$k$.
