  We carry out an extensive linear stability analysis of magnetized cylindrical
jets in a global framework. Foregoing the commonly invoked force-free limit, we
focus on the small-scale, internal instabilities triggered in regions of the
jet dominated by a toroidal magnetic field, with a weak vertical field and
finite thermal pressure gradient. Such regions are likely to occur far from the
jet source and boundaries, and are potential sites of magnetic energy
dissipation that is essential to explain the particle acceleration and
radiation observed from astrophysical jets. We validate the local stability
analysis of Begelman by verifying that the eigenfunctions of the most unstable
modes are radially localized. This finding allows us to propose a generic
stability criterion in the presence of a weak vertical field. A stronger
vertical field with a radial gradient complicates the stability criterion, due
to the competition between the destabilizing thermal pressure gradient and
stabilizing magnetic pressure gradients. Nevertheless, we argue that the jet
interiors generically should be subject to rapidly growing, small-scale
instabilities, capable of producing current sheets that lead to dissipation. We
identify some new instabilities, not predicted by the local analysis, which are
sensitive to the background radial profiles but have smaller growth rates than
the local instabilities, and discuss the relevance of our work to the findings
of recent numerical jet simulations.
