The Protogalactic Origin for Cosmic Magnetic Fields
  It is demonstrated that strong magnetic fields are produced from a zero initial magnetic field during the pregalactic era, when galaxies are first forming. Their development proceeds in three phases. In the first phase, weak magnetic fields are created by the Biermann battery mechanism, acting in shocked parts of the intergalactic medium where caustics form and intersect. In the second phase, these weak magnetic fields are amplified to strong magnetic fields by the Kolmogoroff turbulence endemic to gravitational structure formation of galaxies. During this second phase, the magnetic fields reach saturation with the turbulent power, but they are coherent only on the scale of the smallest eddy. In the third phase, the magnetic field strength increases to equipartition with the turbulent energy, and the coherence length of the magnetic fields increases to the scale of the largest turbulent eddy, comparable to the scale of the entire galaxy. The resulting magnetic field represents a galactic magnetic field of primordial origin. No further dynamo action is necessary, after the galaxy forms, to explain the origin of magnetic fields. However, the magnetic field may be altered by dynamo action once the galaxy and the galactic disk have formed. It is first shown by direct numerical simulations, that thermoelectric currentsassociated with the Biermann battery, build the field up from zero to $10^{-21}$ G in the regions about to collapse into galaxies, by $z\sim3$. For weak fields, in the absence of dissipation, the cyclotron frequency ${\bf \omega_{cyc}}=e{\bf B } /m_H c $ and $ {\bf \omega}/(1+ \chi )$, where ${\bf \omega = \nabla \times v }$ is the vorticity and $\chi$ is the degree of ionization, satisfy the same equations, and initial conditions ${\bf \omega_{cyc}=\omega}=0$, so that, ${\bf \omega_{cyc}}({\bf 
Russell M. Kulsrud, Renyue Cen, Jeremiah P. Ostriker and Dongsu Ryu