  The collective excitation spectra are studied for a multisubband
quasi-one-dimensional electron gas on the surface of liquid helium. Different
intersubband plasmon modes are identified by calculating the spectral weight
function of the electron gas within a 12 subband model. Strong intersubband
coupling and depolarization shifts are found. When the plasmon energy is close
to the energy differences between two subbands, Landau damping in this finite
temperature system leads to plasmon gaps at small wavevectors.
