  In the paradigm of magnetic acceleration of relativistic outflows, a crucial
point is identifying a viable mechanism to convert the Poynting flux into the
kinetic energy of the plasma, and eventually into the observed radiation. Since
the plasma is hardly accelerated beyond equipartition, MHD instabilities are
often invoked to explain the dissipation of the magnetic energy. Motivated by
the fast variability that is shown by the gamma-ray flares of both AGN and
PWNe, different authors have proposed the Poynting flux to be dissipated in a
region where the flow is converging. Here we perform a linear stability
analysis of ultra-relativistic, highly magnetised outflows with such a
recollimation nozzle, showing that MHD instabilities are indeed induced by the
convergence of the flow. The amplitude of the perturbations increases while
recollimation gets stronger, and eventually diverges when the flow is focused
to a single point. Hence, depending on the geometry of the outflow,
instabilities excited while the flow is converging may play an important role
to dissipate the magnetic energy of the plasma.
