Motion of negative ions at supercritical drift velocities in liquidHe4at low temperatures

The motion of negative ions at supercritical drift velocities in pressurized liquid helium is governed at low temperatures by the spontaneous emission of rotons. Assuming a constant matrix element the transition probability for two-roton emission processes is calculated using perturbation theory. The effect of recoil on the ionic motion is studied qualitatively by means of a simple kinetic approach and quantitative calculations are performed using the Boltzmann equation. The calculated dependence of drift velocity on electric field $E$ shows that an $E^{\frac{1}{3}}$ variation occurs over a substantial range of fields as found experimentally. Comparison with experimental data for fields $2<E<\mathrm{}{10}^3$ kV ${\mathrm{m}}^{-1\mathrm{}}$ is made and deviations from the $E^{\frac{1}{3}}$ law at high fields are accurately accounted for. The role of vortex nucleation is discussed and further experiments are suggested.