  The protostellar jets driven by the formation of the first stars are studied
by using MHD nested grid simulations. Starting from a slowly rotating spherical
cloud of 5.1 times 10^4 Msun permeated by a uniform magnetic field, we follow
the evolution from the central number density n = 10^3 cm^-3 to n simeq 10^23
cm^-3. We calculate four models that differ in initial magnetic field strengths
and angular velocities. In all models, protostars of simeq 10^-3 Msun are
formed at n simeq 10^22 cm^-3 in accordance with one-dimensional calculations.
By this epoch, the magnetic flux density is amplified by 10 orders of magnitude
from the initial value. Consequently, the formed protostar possesses the
magnetic field of \sim 10^6 G that is much larger than the flux density of the
present counterparts, reflecting the fact that the dissipation of a magnetic
field is ineffective in primordial gas clouds. If the initial magnetic field B
> 10^-9 (n/10^3 cm^-3)^2/3 G, the protostellar jet is launched and its
velocities reaches \sim 70 km s^-1 by the time the protostellar mass becomes
(4-6) times 10^-3 Msun, and a fraction (3-10%) of the accreting matter is blown
off from the central region. Owing to the interaction of these ejecta with
surrounding matter, expanding bow shocks are created at both heads of the jet.
If this jet continues to sweep out the surrounding gas that otherwise accretes
onto the central star or circumstellar disk, the final mass of the first star
can be substantially reduced. In addition, dense post-shock regions behind the
bow shocks are expected to promote the chemical reactions (formation of H_2 and
HD), and this provides possible environments for subsequent low-mass star
formation in the early universe.
