  We apply the time dependent Ginzburg-Landau equations (TDGL) to study small
ac currents of frequency $\omega$ in superconducting channels narrow on the
scale of London penetration depth. We show that TDGL have $t$-dependent and
spatially uniform solutions that describe the order parameter with an
oscillating part of the double frequency coexisting with an ac electric field.
We evaluate the Ohmic losses (related neither to the flux flow nor to the phase
slips) and show that the resistivity reduction on cooling through the critical
temperature $T_c$ should behave as $(T_c-T)^2/\omega^2$. If the channel is cut
out of an anisotropic material in a direction other than the principal axes,
the transverse phase difference and the Josephson voltage between the channel
sides are generated.
