  We present the results of a series of axisymmetric time-dependent
magnetohydrodynamic (MHD) simulations of the propagation of cooling, overdense
jets, motivated by the properties of outflows associated with young stellar
objects. A variety of initial field strengths and configurations are explored
for both steady and time-variable (pulsed) jets. Even apparently weak magnetic
fields with strengths B < 60 micro-G in the pre-shocked jet beam can have a
significant effect on the dynamics, for example by altering the density, width,
and fragmentation of thin shells formed by cooling gas. A linear analysis
predicts that axisymmetric pinch modes of the MHD Kelvin-Helmholtz instability
should grow only slowly for the highly supermagnetosonic jets studied here; we
find no evidence for them in our simulations. Some of our models appear
unstable to current-driven pinch modes, however the resulting pressure and
density variations induced in the jet beam are not large, making this mechanism
an unlikely source of emission knots in the jet beam. In the case of pulsed
jets, radial hoop stresses confine shocked jet material in the pulses to the
axis, resulting in a higher density in the pulses in comparison to purely
hydrodynamic models.
