We present a model for protogalactic star forming regions that assumes that self-gravitating isothermal clouds form by gravitational instability of cooling, shocked gas layers in the protogalaxy. The shocked primordial gas cools down to a temperature of 100 K by nonequilibrium formation of H_2_. Cloud longevity is maintained by the suppression of efficient cooling in the absence of heavy elements and by the inability of gas with significant angular momentum to form stars in the absence of a magnetic field. The vorticity generated in oblique shocks and sustained by nonaxisymmetric instabilities in marginally stable cooling layers stimulates the generation of a strong magnetic field by dynamo action. Starting from a seed field of ~10^-19^ G driven by the Biermann battery effect operating in protogalactic gas, exponential growth by dynamo action generates a field of 10^-6^ G in 2 x 10^9^ yr (a free fall time in the outer halo) in cooling clouds. The fiducial primordial clouds have characteristic masses of ~4 x 10^6^ M_sun_, diameters ~300 pc, surface densities ~12 M_sun_ pc^-2^, and internal velocity dispersions ~2 km s^-1^. These dynamically significant magnetic fields solve the angular momentum problem for primordial stars by magnetic braking. The inferred redshifts at which subsequent star formation occurs are z <= 3 ({OMEGA} = 1) or z <= 7 ({OMEGA} = 0.1) with H_0_ = 75 km s^-1^ Mpc^-1^. The magnetic fields generated in these shocked clouds eventually fill the entire volume of the protogalactic halo as star formation disrupts the placental magnetized gas. The coherence scale for a field which has been swept up in shells of expanding material is several kiloparsecs in size. This model provides a possible explanation for the existence of strong magnetic fields in galactic halos, inferred from recent measurements of Faraday rotation toward radio-loud quasars.
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Pudritz et al. (1989) studied this question.