  In the presence of an anomalous CP phase in a U(1) gauge theory, a monopole
becomes a dyon via the Witten effect. When the anomalous CP phase is promoted
to a dynamical field, the axion, the electric charge of the dyon changes
according to the coherent motion of the axion oscillation. Once the electric
charge exceeds a certain threshold, the Schwinger pair production of charged
particles becomes efficient near the surface of the dyon. These
non-perturbative effects lead to the back reaction of the axion dynamics by
causing the dissipation of the axion oscillation energy and the change of the
effective potential due to the Witten effect. Taking these effects into
account, we consider the dynamics of the whole system, including the axion,
monopole, and charged heavy vector bosons, and discuss to what extent the axion
abundance is modified. We also discuss the electric dipole radiation from a
bound state of a monopole-anti-monopole pair due to the axion coherent
oscillations.
