  Jet driving and fragmentation process in collapsing primordial cloud are
studied using three-dimensional MHD nested grid simulations. Starting from a
rotating magnetized spherical cloud with the number density of n=10^3 cm^-3, we
follow the evolution of the cloud up to the stellar density n=10^22 cm^-3. We
calculate 36 models parameterizing the initial magnetic and rotational energies
(\gamma_0, \beta_0). In the collapsing primordial clouds, the cloud evolutions
are characterized by the ratio of the initial rotational to magnetic energy,
\gamma_0/\beta_0. The Lorentz force significantly affects the cloud evolution
when \gamma_0 > \beta_0, while the centrifugal force is more dominant than the
Lorentz force when \beta_0 > \gamma_0. When the cloud rotates rapidly with
angular velocity of \Omega_0 > 10^-17 (n/10^3 cm^-3)^2/3 s^-1 and \beta_0 >
\gamma_0, fragmentation occurs before the protostar is formed, but no jet
appears after the protostar formation. On the other hand, a strong jet appears
after the protostar formation without fragmentation when the initial cloud has
the magnetic field of B_0 > 10^-9 (n/10^3 cm^-3)^2/3 G and \gamma_0 > \beta_0.
Our results indicate that proto-Population III stars frequently show
fragmentation and protostellar jet. Population III stars are therefore born as
binary or multiple stellar systems, and they can drive strong jets, which
disturb the interstellar medium significantly, as well as in the present-day
star formation, and thus they may induce the formation of next generation
stars.
