  We study the effect a guiding magnetic field has on the formation and
structure of a pair jet that propagates through a collisionless electron-proton
plasma at rest. We model with a PIC simulation a pair cloud with the
temperature 400 keV and mean speed 0.9c. The cloud propagates through a
spatially uniform, magnetized and cool ambient electron-proton plasma that is
at rest. Its mean velocity vector is aligned with the background magnetic
field. A jet forms in time. Its outer cocoon consists of jet-accelerated
ambient plasma and is separated from the inner cocoon by an electromagnetic
piston with a thickness that is comparable to the thermal gyroradius of jet
particles. A supercritical fast magnetosonic shock will form between the
pristine ambient plasma and the jet-accelerated one on a time scale that
exceeds our simulation time by an order of magnitude. The inner cocoon is pair
plasma that lost its directed flow energy while it swept out the background
magnetic field. A beam of electrons and positrons moves along the jet spine at
its initial speed. Its electrons are slowed down and some positrons are
accelerated as they cross the jet's head. The latter escape upstream along the
magnetic field, which yields an excess of MeV positrons ahead of the jet. Some
of the protons, which were located behind the electromagnetic piston at the
time it formed, are accelerated to MeV energies
