<pre>In the present-day star formation, strong magnetic fields control
circumstellar disc and binary formation through the angular momentum
transport by magnetic braking or outflows. While only a much weaker field
has been believed to exist in the early universe, recent theoretical
studies suggested that turbulent dynamo can amplify them to a strong field
during the collapse phase. Here we investigate the gravitational collapse
of a cloud core (~$10^{3}$ $cm^{-3}$) up to protostar formation
(~$10^{20}$ $cm^{-3}$) by performing non-ideal magnetohydrodynamic
simulations considering ambipolar diffusion, which has been believed to be an
important diffusion process in the primordial gas. We find that the
ambipolar diffusion heating cannot affect the temperature evolution, since
the heating rate is always smaller than compression heating. We also find
that the inefficiency of ambipolar diffusion allows the dynamo to amplify
the fields around protostars as strong as $10^{3}-10^{5}$ G, much stronger
than in the present-day cases. The amplified strong fields affect the
inflow motion to protostars, although they cannot launch winds. This
implies that the amplified fields have smaller impact on the dynamics in
the later accretion phase than other processes such as ionization
feedback.</pre>