Cosmological magnetic field generation by the Weibel instability

Hydrodynamical simulations of a cold dark matter universe imply relative motion of fully ionized gaseous baryonic matter. Using the dispersion relation for the Weibel instability in unmagnetized plasmas with colliding ion-electron streams, we investigate the instability threshold conditions for the Weibel instability. The intense relative streaming is subject first to the longitudinal two-stream instability resulting in an anisotropic bi-Maxwellian electron-ion distribution function. The Weibel instability operates as a secular instability of this bi-Maxwellian in high Mach number (M > 43) flows, and it generates magnetic fields as purely growing modes. The maximum cosmological field strength generated by this mechanism is 3.4 x 10(-7) G.