Hyperbolic extensions of free groups from atoroidal ping-pong

We prove that all atoroidal automorphisms of Out (F-N) act on the space of projectivized geodesic currents with generalized north-south dynamics. As an application, we produce new examples of nonvirtually cyclic, free and purely atoroidal subgroups of Out (F-N) such that the corresponding free group extension is hyperbolic. Moreover, these subgroups are not necessarily convex cocompact.