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Magnetic Fields from QCD Phase Transitions

We study the evolution of QCD phase transition-generated magnetic fields in freely decaying MHD turbulence of the expanding Universe. We consider a magnetic field generation model that starts from basic non-perturbative QCD theory and predicts stochastic magnetic fields with an amplitude of the order of 0.02 $μ$G and small magnetic helicity. We employ direct numerical simulations to model the MHD turbulence decay and identify two different regimes: "weakly helical" turbulence regime, when magnetic helicity increases during decay, and "fully helical" turbulence, when maximal magnetic helicity is reached and an inverse cascade develops. The results of our analysis show that in the most optimistic scenario the magnetic correlation length in the comoving frame can reach 10 kpc with the amplitude of the effective magnetic field being 0.007 nG. We demonstrate that the considered model of magneto-genesis can provide the seed magnetic field for galaxies and clusters.