  We study the collimation of a highly magnetized jet by a surrounding cocoon
that forms as a result of the interaction of the jet with the external medium.
We show that in regions where the jet is well confined by the cocoon,
current-driven instabilities should develop over timescales shorter than the
expansion time of the jet's head. We speculate that these instabilities would
give rise to complete magnetic field destruction, whereby the jet undergoes a
transition from high-to-low sigma above the collimation zone. Using this
assumption, we construct a self-consistent model for the evolution of the
jet-cocoon system in an ambient medium of arbitrary density profile. We apply
the model to jet breakout in long GRBs, and show that the jet is highly
collimated inside the envelope of the progenitor star, and is likely to remain
confined well after breakout. We speculate that this strong confinement may
provide a channel for magnetic field conversion in GRB outflows, whereby the
hot, low-sigma jet section thereby produced is the source of the photospheric
emission observed in many bursts.
