  We study baryon asymmetry generation originated from the leptogenesis in the
presence of hypermagnetic fields in the early Universe plasma before the
electroweak phase transition (EWPT). For the simplest Chern-Simons (CS) wave
configuration of hypermagnetic field we find the baryon asymmetry growth when
the hypermagnetic field value changes due to alpha^2-dynamo and the lepton
asymmetry rises due to the Abelian anomaly. We solve the corresponding
integro-differential equations for the lepton asymmetries describing such
self-consistent dynamics for lepto- and baryogenesis in the two scenarios : (i)
when a primordial lepton asymmetry sits in right electrons e_R; and (ii) when,
in addition to e_R, a left lepton asymmetry for e_L and nu_eL arises due to
chirality flip reactions provided by inverse Higgs decays at the temperatures,
T<T_RL ~ 10 TeV. We find that the baryon asymmetry of the Universe (BAU) rises
very fast through such leptogenesis, especially, in strong hypermagnetic
fields. Varying (decreasing) the CS wave number parameter k_0 < 10^-7 T_EW one
can recover the observable value of BAU, eta_B ~ 10^-9, where k_0 = 10^-7 T_EW
corresponds to the maximum value for CS wave number surviving ohmic dissipation
of hypermagnetic field. In the scenario (ii) one predicts the essential
difference of the lepton numbers of right - and left electrons at EWPT time,
L_eR - L_eL ~ (mu_eR - mu_eL) / T_EW = Delta mu / T_EW ~ 10^-5 that can be used
as an initial condition for chiral asymmetry after EWPT.
