Primordial Magnetic Fields from Cosmological First Order Phase Transitions

We give an improved estimate of primordial magnetic elds generated during cosmological rst order phase transitions. We examine the charge distribution at the nucleated bubble wall and its dynamics. We consider instabilities on the bubble walls developing during the phase transition. It is found that damping of these instabilities due to viscosity and heat conductivity caused by particle di usion can be important in the QCD phase transition, but is probably negligible in the electroweak transition. We show how such instabilities together with the surface charge densities on bubble walls excite magnetic elds within a certain range of wavelengths. We discuss how these magnetic seed elds may be ampli ed by MHD e ects in the turbulent uid. The strength and spectrum of the primordial magnetic eld at the present time for the cases where this mechanism was operative during the electroweak or the QCD phase transition are estimated. On a 10Mpc comoving scale, eld strengths of the order 10 G for electroweak and 10 20 G for QCD, could be attained for reasonable phase transition parameters.