  We use the quasiclassical theory of superconductivity to calculate the
response of the currents in the core of a vortex to an alternating electric
field. We consider relatively clean superconductors with a mean free path
larger than the coherence length (but still not in the 'superclean limit'). The
current response of the core is dominated by the bound states of Caroli, de
Gennes and Matricon, and differs significantly from the response obtained from
the model of a ``normal core'' introduced by Bardeen and Stephen. The model of
Bardeen and Stephen describes the limit of a dirty core and fails for a clean
superconductor. The response of the bound states includes non-dissipative
acceleration of the charge carriers as well as dissipative currents.
Dissipation dominates at low frequencies and the real part of the conductivity
greatly exceeds the normal state conductivity. These dissipative currents have
a dipolar structure superimposed on an oscillating supercurrent in the
direction of the electric field. We attribute the anomalous dissipation to the
zero-energy bound state broadened by lifetime effects.
