The mechanisms that generate “seed” magnetic fields in our Universe and that amplify them throughout cosmic time remain poorly understood. By means of fully kinetic particle-in-cell simulations of turbulent, initially unmagnetized plasmas, we study the genesis of magnetic fields via the Weibel instability and follow their dynamo growth up to near-equipartition levels. In the kinematic stage of the dynamo, we find that the rms magnetic field strength grows exponentially with rate ${\gamma }_B\simeq 0.4u_{\mathrm{rms}}/L$, where $L/2\pi$ is the driving scale and $u_{\mathrm{rms}}$ is the rms turbulent velocity. In the saturated stage, the magnetic field energy reaches about half of the turbulent kinetic energy. Here, magnetic field growth is balanced by dissipation via reconnection, as revealed by the appearance of plasmoid chains. At saturation, the integral-scale wave number of the magnetic spectrum approaches $k_{\mathrm{int}}\simeq 12\pi /L$. Our results show that turbulence—induced by, e.g., the gravitational buildup of galaxies and galaxy clusters—can magnetize collisionless plasmas with large-scale near-equipartition fields.

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• Dynamo theory
• Magnetic field generation & plasma dynamo
• Plasma instabilities
• Space & astrophysical plasma
• Weibel instability