  Relativistic charged particles (CR for cosmic-rays) produced by Supernova
explosion of the first generation of massive stars that are responsible for the
re-ionization of the universe escape into the intergalactic medium, carrying an
electric current. Charge imbalance and induction give rise to a return current,
$\vec j_t$, carried by the cold thermal plasma which tends to cancel the CR
current. The electric field, $\vec E=\eta \vec j_t$, required to draw the
collisional return current opposes the outflow of low energy cosmic rays and
ohmically heats the cold plasma. Owing to inhomogeneities in the resistivity,
$\eta(T)$, caused by structure in the temperature, $T$, of the intergalactic
plasma, the electric field possesses a rotational component which sustains
Faraday's induction. It is found that magnetic field is robustly generated
throughout intergalactic space at rate of 10$^{-17}-10^{-16}$ Gauss/Gyr, until
the temperature of the intergalactic medium is raised by cosmic reionization.
The magnetic field may seed the subsequent growth of magnetic fields in the
intergalactic environment.
