In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated selfsimilarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of a universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two-dimensionality and the shallower k 2 subinertial range spectrum of kinetic energy forcing the magnetic field with a k 4 subinertial range to attain larger-scale coherence. The inertial range shows a clear k −2 spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling.

We consider the evolution of primordial magnetic fields generated during cosmological, electroweak or QCD, phase transitions. We assume that the magnetic field generation can be described as an injection of magnetic energy to cosmological plasma at a given scale determined by the moment of magnetic field generation. A high Reynolds number ensures strong coupling between magnetic field and fluid motions. The subsequent evolution of the magnetic field is governed by decaying hydromagnetic turbulence. Both our numerical simulations and a phenomenological description allow us to recover "universal" laws for the decay of magnetic energy and the growth of magnetic correlation length in the turbulent (low viscosity) regime. In particular, we show that during the radiation dominated epoch, energy and correlation length of non-helical magnetic fields scale as conformal time to the powers −1/2 and +1/2, respectively. For helical magnetic fields, energy and correlation length scale as conformal time to the powers −1/3 and +2/3, respectively. The universal decay law of the magnetic field implies that the strength of magnetic field generated during the QCD phase transition could reach ∼ 10 −9 G with the present day correlation length ∼ 50 kpc. The fields generated at the electroweak phase transition could be as strong as ∼ 10 −10 G with correlation lengths reaching ∼ 0.3 kpc. These values of the magnetic fields are consistent with the lower bounds of the extragalactic magnetic fields.PACS numbers: 98.70. Vc,

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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 µG 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.