Ionization degree and magnetic diffusivity in the primordial
  star-forming clouds
  Magnetic fields play such roles in star formation as the angular momentum
transport in star-forming clouds, thereby controlling circumstellar disc
formation and even binary star formation efficiency. The coupling between the
magnetic field and gas is determined by the ionization degree in the gas. Here,
we calculate the thermal and chemical evolution of the primordial gas by
solving chemical reaction network where all the reactions are reversed. We find
that at ~ 10^14-10^18 /cm^3, the ionization degree becomes 100-1000 times
higher than the previous results due to the lithium ionization by thermal
photons trapped in the cloud, which has been omitted so far. We construct the
minimal chemical network which can reproduce correctly the ionization degree as
well as the thermal evolution by extracting 36 reactions among 13 species.
Using the obtained ionization degree, we evaluate the magnetic field
diffusivity. We find that the field dissipation can be neglected for global
fields coherent over > a tenth of the cloud size as long as the field is not so
strong as to prohibit the collapse. With magnetic fields strong enough for
ambipolar diffusion heating to be significant, the magnetic pressure effects to
slow down the collapse and to reduce the compressional heating become more
important, and the temperature actually becomes lower than in the no-field
case.
