The results of a spatial stability analysis of a two-dimensional slab
jet, in which optically thin radiative cooling is dynamically importan
t, are presented. We study both magnetized and unmagnetized jets at ex
ternal Mach numbers of 5 and 20. We model the cooling rate by using tw
o different cooling curves: one appropriate to interstellar gas, and t
he other to photoionized gas of reduced metallicity. Thus, our results
will be applicable to both protostellar (Herbig-Haro) jets and optica
l jets from active galactic nuclei. We present analytical solutions to
the dispersion relations in useful limits and solve the dispersion re
lations numerically over a broad range of perturbation frequencies. We
find that the growth rates and wavelengths of the unstable Kelvin-Hel
mholtz (K-H) modes are significantly different from the adiabatic limi
t, and that the form of the cooling function strongly affects the resu
lts. In particular, if the cooling curve is a steep function of temper
ature in the neighborhood of the equilibrium state, then the growth of
K-H modes is reduced relative to the adiabatic jet. On the other hand
, if the cooling curve is a shallow function of temperature, then the
growth of K-H modes can be enhanced relative to the adiabatic jet by t
he increase in cooling relative to heating in overdense regions. Inclu
sion of a dynamically important magnetic held does not strongly modify
the important differences between an adiabatic jet and a cooling jet,
provided the jet is highly supermagnetosonic and not magnetic pressur
e-dominated. In the latter case, the unstable modes behave more like t
he transmagnetosonic magnetic pressure-dominated adiabatic limit. We a
lso plot fluid displacement surfaces associated with the various waves
in a cooling jet in order to predict the structures that might arise
in the nonlinear regime. This analysis predicts that low-frequency sur
face waves and the lowest order body modes will be the most effective
at producing observable features in the jet.