  The time-evolution of the magnetic field in hot homogeneous nuclear matter
has two qualitatively different stages separated by the sphaleron transition
time $\tau_c$. At early times the axial chemical potential and the
corresponding chiral conductivity $\sigma_\chi$ are slow functions of time. The
soft chiral modes $k<\sigma_\chi$ of the magnetic field grow exponentially with
time, which is known as the chiral instability. At later times $\sigma_\chi$
fluctuates due to the sphaleron transitions and can be regarded as a random
process. It is argued that the average magnetic field is exponentially damped
at later times. The time-evolution of the average magnetic energy is more
complicated and depends on the electrical conductivity of the chiral matter but
does not depend on chirality. It exhibits instability only if the matter is a
poor electrical conductor, such as the quark-gluon plasma near the critical
temperature. The precise conditions for the instability and the growth rate of
the unstable modes are derived.
