Journal
PHYSICAL REVIEW D
Volume 86, Issue 10, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.86.103010
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Funding
- Deutsche Forschungsgemeinschaft through the collaborative research centre [SFB 676]
- Helmholtz Alliance for Astroparticle Phyics (HAP)
- Initiative and Networking Fund of the Helmholtz Association
- State of Hamburg, through the Collaborative Research program Connecting Particles with the Cosmos
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We present a derivation of the time evolution equations for the energy content of nonhelical magnetic fields and the accompanying turbulent flows from first principles of incompressible magnetohydrodynamics in the general framework of homogeneous and isotropic turbulence. This is then applied to the early Universe, i.e., the evolution of primordial magnetic fields. Numerically integrating the equations, we find that most of the energy is concentrated at an integral wavenumber scale k(I) where the turbulence turn over time equals the Hubble time. At larger length scales L, i.e., smaller wavenumbers q = 2 pi/L << k(I), independent of the assumed turbulent flow power spectrum, mode-mode coupling tends to develop a small q magnetic field tail with a Batchelor spectrum proportional to the fourth inverse power of L and therefore a scaling for the magnetic field of B similar to L-5/2.
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