  We analyse solutions of the MHD equations around the electroweak transition
taking into account the effects of the chiral anomaly. It is shown that a
transition that is not of the first order has direct consequences on the
evolution of the asymmetry between left- and right-handed leptons. Assuming an
initial chiral asymmetry in the symmetric phase at temperatures higher than the
transition temperature, as well as the existence of magnetic fields, it is
demonstrated that the asymmetry typically grows with time, until it undergoes a
fast decrease at the transition, and then eventually gets damped at lower
temperatures in the broken phase. We argue that it is unlikely to have any
significant magnetic field amplification as a consequence of the electroweak
transition in the Standard model, even when the chiral anomaly is introduced.
The presence of a chiral asymmetry between left- and right-handed charge
carriers naturally leads to the creation of helical magnetic fields from
non-helical fields and this can have consequences on their subsequent
evolution.
