In the presence of cosmic chiral asymmetry, chiral-vorticity and chiral-magnetic effects can play an important role in the generation and evolution of magnetic fields in the early universe. We include these chiral effects in the magnetic field equations and find solutions under simplifying assumptions. Our numerical and analytical results show the presence of an attractor solution in which chiral effects produce a strong, narrow, Gaussian peak in the magnetic spectrum and the magnetic field becomes maximally helical. The peak in the spectrum shifts to longer length scales and becomes sharper with evolution. We also find that the dynamics may become non-linear for certain parameters, pointing to the necessity of a more complete analysis.

17 pages, 6 figures