Resistive Magnetic Field Generation at Cosmic Dawn

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.