  The long term magnetohydrodynamic stability of magnetized
transonic/supersonic jets is numerically investigated using a spatial approach.
We focus on two-dimensional linearly-unstable slab configurations where the jet
is embedded in a flow-aligned uniform magnetic field of weak amplitude. We
compare our results with previous studies using a temporal approach where
longitudinally periodic domains were adopted. The finite-volume based versatile
advection code (VAC) is used to solve the full set of ideal compressible MHD
equations. We follow the development of Kelvin-Helmholtz modes that are driven
by a white noise perturbation continuously introduced at the jet inlet. No
noticeable difference is observed in spatial simulations versus analogous
temporal ones during the linear and early non-linear evolution of the
configuration. However, in the case of transonic flows, a different long-term
scenario occurs in our spatial runs. Indeed, after the large-scale disruption
of the flow, a sheath region of enhanced magnetic field encompassing the jet
core forms along the whole flow. This provides a partial stabilization
mechanism leading to enhanced stability for later times, which is almost
independent of the initial magnitude of the magnetic field. The implication of
this mechanism for the stability of astrophysical jets is discussed.
