  Within the Ginzburg-Landau theory we consider Abrikosov vortex pinning on a
columnar defect with the characteristic size of the cross-section much smaller
than the coherence length. We present an extension of the electrostatic
analogies method, which proved to be useful for calculations of the pinning
force for large cavities, to the case of small defects. The pinning potential
for an elliptic cavity is derived analytically. Also, we determine the
depinning current for a circular defect.
