  We present a new study of the nonlinear transport of a two-dimensional
electron crystal on the surface of liquid helium confined in a 10
micrometer-wide channel in which the effective length of the crystal can be
varied from 10 to 215 micrometers. At low driving voltages, the moving electron
crystal is strongly coupled to deformation of the liquid surface arising from
resonant excitation of surface capillary waves, ripplons, while at higher
driving voltages the crystal decouples from the deformation. We find strong
dependence of the decoupling threshold of the driving electric field acting on
the electrons, on the size of the crystal. In particular, the threshold
electric field significantly decreases when the length of the crystal becomes
shorter than 25 micrometers. We explain this effect as arising from weakening
of surface deformations due to radiative loss of resonantly-excited ripplons
from an electron crystal of finite size, and we account for the observed effect
using an instructive analytical model.
