  We compute numerically the topological charge distribution in the initial
stage of a high energy heavy ion collision. This charge distribution is
generated by Chern-Simons number fluctuations associated with the dynamics of
strong classical fields in the initial state. The distribution is found to be
quite narrow at RHIC and LHC energies reflecting a small value of the
topological susceptibility. Thus the effective potential of classical fields is
shallow in the $\theta$-direction likely creating favorable conditions for the
subsequent generation of P-odd bubbles.
