  We study the properties of the chromohydrodynamical instabilities induced by
a relativistic jet that crosses the quark-gluon plasma. Assuming that the jet
of particles and the plasma can be described using a hydrodynamical approach,
we derive and discuss the dispersion laws for the unstable collective modes. In
our analysis the chromohydrodynamical equations for the collective modes are
tackled in the linear response approximation. Such an approximation, valid for
short time scales, allows to study in a straightforward way the dependence of
the dispersion laws of the collective modes on the velocity of the jet, on the
magnitude of the momentum of the collective mode and on the angle between these
two quantities. We find that unstable modes arise for velocity of the jet
larger than the speed of the sound of the plasma and only modes with momenta
smaller than a certain values are unstable. Moreover, for ultrarelativistic
velocities of the jet the longitudinal mode becomes stable and the most
unstable modes correspond to relative angles between the velocity of the jet
and momentum of the collective mode larger than $\sim \pi/8$. Our results
suggest an alternative mechanism for the description of the jet quenching
phenomenon, where the jet crossing the plasma loses energy exciting colored
unstable modes.
