A system close to a one-dimensional (1D) electron system on superfluid heli
um is realized in the experiments. A profiled substrate with a small dielec
tric constant is used to create a set of parallel channels on the surface o
f liquid helium. The mobility of carriers was measured in this system in th
e temperature range 0.5-1.8 K. For clean substrates the electron mobility i
ncreases with decreasing temperature and reaches high values at low tempera
tures. The results of experiments are found to be in a good agreement with
the existing theory. (C), 2000 Elsevier Science B.V. All rights reserved.