  Several observations of stellar jets show evidence of X-ray emitting shocks
close to the launching site. In some cases, the shocked features appear to be
stationary, also for YSOs at different stages of evolution. We study the case
of HH 154, the jet originating from the embedded binary Class 0/I protostar IRS
5, and the case of the jet associated to DG Tau, a more evolved Class II
disk-bearing source or Classical T Tauri star (CTTS), both located in the
Taurus star-forming region. We aim at investigating the effect of perturbations
in X-ray emitting stationary shocks in stellar jets; the stability and
detectability in X-rays of these shocks; and explore the differences in jets
from Class 0 to Class II sources. We performed a set of 2.5-dimensional
magnetohydrodynamic numerical simulations that modelled supersonic jets ramming
into a magnetized medium. The jet is formed by two components: a continously
driven component that forms a quasi-stationary shock at the base of the jet;
and a pulsed component constituted by blobs perturbing the shock. We explored
different parameters for both components. We studied two cases: a jet less
dense than the ambient medium (light jet), representing the case of HH 154; and
a jet denser than the ambient (heavy jet), associated with DG Tau. We
synthesized the count rate from the simulations and compared with available
Chandra observations. Our model explains the formation of X-ray emitting
quasi-stationary shocks observed at the base of jets in a natural way, being
able to reproduce the observed jet properties at different evolutionary phases
(in particular, for HH 154 and DG Tau). The jet is collimated by the magnetic
field forming a quasi-stationary shock at the base which emits in X-rays even
when perturbations formed by a train of blobs are present. We found similar
collimation mechanisms dominating in both heavy and light jets...
