  Quasi-one dimensional electron systems have been created using a suspended
helium film on a structured substrate. The electron mobility along the channel
is calculated by taking into account the essential scattering processes of
electrons by helium atoms in the vapor phase, ripplons, and surface defects of
the film substrate. It is shown that the last scattering mechanism may dominate
the electron mobility in the low temperature limit changing drastically the
temperature dependence of the mobility in comparison with that controlled by
the electron-ripplon scattering.
