%0 Generic %1 citeulike:12280783 %A Campanelli, Leonardo %D 2013 %K imported %T Evolution of primordial magnetic fields in mean-field approximation %U http://arxiv.org/abs/1304.4044 %X We study the evolution of phase-transition-generated cosmic magnetic fields coupled to the primeval cosmic plasma in turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and correlation length, both in helical and non-helical cases, are found by solving the autoinduction and Navier-Stokes equations in mean-field approximation. Analytical results are derived in Minkowski spacetime and then extended to the case of a Friedmann universe with zero spatial curvature, both in radiation and matter dominated eras. The three possible viscous free-streaming phases are characterized by a drag term in the Navier-Stokes equation which depends on the free-steaming properties of neutrinos, photons, or hydrogen atoms, respectively. In the case of non-helical magnetic fields, the magnetic intensity \$B\$ and the magnetic correlation length \$\xi\_B\$ evolve asymptotically with the temperature \$T\$ as \$B(T) \kappa\_B (N\_i v\_i)^\varrho\_1 (T/T\_i)^\varrho\_2\$ and \$\xi\_B(T) \kappa\_(N\_i v\_i)^\varrho\_3 (T/T\_i)^\varrho\_4\$. Here, \$T\_i\$, \$N\_i\$ and \$v\_i\$ are, respectively, the temperature, the number of magnetic domains per horizon, and the bulk velocity at the onset of the particular regime. The coefficients \$\kappa\_B\$, \$\kappa\_\xi\$, \$\varrho\_1\$, \$\varrho\_2\$, \$\varrho\_3\$, and \$\varrho\_4\$, depend on the index of the assumed initial power-law magnetic spectrum, \$p\$, and on the particular regime, with the order-one constants \$\kappa\_B\$ and \$\kappa\_\xi\$ depending also on the cut-off adopted for the initial magnetic spectrum. In the helical case, the quasi-conservation of the magnetic helicity implies, apart from logarithmic corrections and a factor proportional to the initial fractional helicity, power-like evolution laws equal to those in the non-helical case, but with \$p\$ equal to zero.

@misc{citeulike:12280783, abstract = {We study the evolution of phase-transition-generated cosmic magnetic fields coupled to the primeval cosmic plasma in turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and correlation length, both in helical and non-helical cases, are found by solving the autoinduction and Navier-Stokes equations in mean-field approximation. Analytical results are derived in Minkowski spacetime and then extended to the case of a Friedmann universe with zero spatial curvature, both in radiation and matter dominated eras. The three possible viscous free-streaming phases are characterized by a drag term in the Navier-Stokes equation which depends on the free-steaming properties of neutrinos, photons, or hydrogen atoms, respectively. In the case of non-helical magnetic fields, the magnetic intensity \$B\$ and the magnetic correlation length \$\xi\_B\$ evolve asymptotically with the temperature \$T\$ as \$B(T) \simeq \kappa\_B (N\_i v\_i)^{\varrho\_1} (T/T\_i)^{\varrho\_2}\$ and \$\xi\_B(T) \simeq \kappa\_\xi (N\_i v\_i)^{\varrho\_3} (T/T\_i)^{\varrho\_4}\$. Here, \$T\_i\$, \$N\_i\$ and \$v\_i\$ are, respectively, the temperature, the number of magnetic domains per horizon, and the bulk velocity at the onset of the particular regime. The coefficients \$\kappa\_B\$, \$\kappa\_\xi\$, \$\varrho\_1\$, \$\varrho\_2\$, \$\varrho\_3\$, and \$\varrho\_4\$, depend on the index of the assumed initial power-law magnetic spectrum, \$p\$, and on the particular regime, with the order-one constants \$\kappa\_B\$ and \$\kappa\_\xi\$ depending also on the cut-off adopted for the initial magnetic spectrum. In the helical case, the quasi-conservation of the magnetic helicity implies, apart from logarithmic corrections and a factor proportional to the initial fractional helicity, power-like evolution laws equal to those in the non-helical case, but with \$p\$ equal to zero.}, added-at = {2019-03-25T08:20:55.000+0100}, archiveprefix = {arXiv}, author = {Campanelli, Leonardo}, biburl = {https://www.bibsonomy.org/bibtex/2533b7cff945d48de0599ee5ea2a54645/ericblackman}, citeulike-article-id = {12280783}, citeulike-linkout-0 = {http://arxiv.org/abs/1304.4044}, citeulike-linkout-1 = {http://arxiv.org/pdf/1304.4044}, day = 15, eprint = {1304.4044}, interhash = {ba3232fa06e07698c47267be90393a13}, intrahash = {533b7cff945d48de0599ee5ea2a54645}, keywords = {imported}, month = apr, posted-at = {2013-04-21 08:26:05}, priority = {2}, timestamp = {2019-03-25T08:20:55.000+0100}, title = {{Evolution of primordial magnetic fields in mean-field approximation}}, url = {http://arxiv.org/abs/1304.4044}, year = 2013 }