  The dispersion law of plasmons running along thin wires with radius $a$ is
known to be practically linear. We show that in a wire with a dielectric
constant $\kappa$ much larger than that of its environment $\kappa_e$, such
dispersion law crosses over to a dispersionless three-dimensional-like law when
the plasmon wavelength becomes shorter than the length $(a/2)
\sqrt{(\kappa/\kappa_e)\ln(\kappa/2\kappa_e)}$ at which the electric field
lines of a point charge exit from the wire to the environment. This happens
both in trivial semiconductor wires and wires of three-dimensional topological
insulators.
