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In this work we report a numerical study of the cosmic magnetic fieldamplification due to collisionless plasma instabilities. The collisionlessmagnetohydrodynamic equations derived account for the pressure anisotropy thatleads, in specific conditions, to the firehose and mirror instabilities. Westudy the time evolution of seed fields in turbulence under the influence ofsuch instabilities. An approximate analytical time evolution of magnetic fieldis provided. The numerical simulations and the analytical predictions arecompared. We found that i) amplification of magnetic field was efficient infirehose unstable turbulent regimes, but not in the mirror unstable models, ii)the growth rate of the magnetic energy density is much faster than theturbulent dynamo, iii) the efficient amplification occurs at small scales. Theanalytical prediction for the correlation between the growth timescales withpressure anisotropy ratio is confirmed by the numerical simulations. Theseresults reinforce the idea that pressure anisotropies - driven naturally in aturbulent collisionless medium, e.g. the intergalactic medium -, couldefficiently amplify the magnetic field in the early Universe(post-recombination era), previous to the collapse of the first large-scalegravitational structures. This mechanism, though fast for the small scalefields ($\sim$kpc scales), is however unable to provide relatively strongmagnetic fields at large scales. Other mechanisms that were not accounted here(e.g., collisional turbulence once instabilities are quenched, velocity shear,or gravitationally induced inflows of gas into galaxies and clusters) couldoperate afterwards to build up large scale coherent field structures in thelong time evolution.

Fast magnetic field amplification in the early Universe: growth of collisionless plasma instabilities in turbulent media