Ions and electrons in liquid helium

Abstract

In liquid helium, an electron is surrounded by a cavity called an electron bubble of 20 Ångstroms in diameter. A positive helium ion is solvated by an electrostriction induced solid helium-ice shell called a snowball of 7 Ångstroms in diameter. By studying their transport properties, these objects are well suited for the testing of the microscopic properties of superfluidity. At low temperatures and with small electric fields, the drift velocity of the charges depends on their interaction with the elementary excitations of the superfluid: phonons, rotons, and 3He atomic impurities. At higher fields, ions produce quantized vortex rings and vortex lines and studying these sheds light on quantum hydrodynamics. In the fermionic liquid, the 3He isotope ion transport properties display important pieces of information on the coupling of a charge to a Fermi liquid and on the richer topological structure of the superfluid phases appearing at ultralow temperatures. In the normal liquid phases of both isotopes, ions and electrons are used to probe classical hydrodynamics at the λ-transition and at the liquid-vapor transition at which long-range critical fluctuations of the appropriate order parameter occur. Several experiments have investigated the structure of electron bubbles. Electron drift velocity measurements in dense helium gas have elucidated the dynamics of electron bubble formation. This book provides a review of the more than forty-year-long experimental and theoretical research on the transport properties of electrons and ions in liquid and gaseous helium.

Vortex nucleation limited mobility of free electron bubbles in the Gross-Pitaevskii model of a superfluid

“…Electrically charged particles have been one of the most effective probes to study properties of 4 He in the superfluid state. Beginning with the pioneering works of Williams [1], Careri et al [2], and Reif and Mayer [3], it has been observed that ions moving through liquid helium due to an external applied electric field can interact with different types of excitations that act to produce a drag force on the ion [4].…”

“…By using the GrossClark model, in which a Gross-Pitaevskii equation for the superfluid wave function is coupled to a Schrödinger equation for the electron wave function, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid 4 He at a pressure of one bar. By performing fully three-dimensional spatiotemporal simulations of the superfluid coupled to an electron, that is modeled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form.…”

Theoretical modeling of ion mobility in superfluid4He

“…Atkins' snowball model for K + predicts an effective ion mass 45× the mass of a helium atom and a radius of 6Å. 9 Ion mobility in superfluid helium is essentially determined by the following aspects: 10 (i) the number of helium atoms dragged with the ion, (ii) dissipation of energy through emission of sound when the ion is accelerated in the liquid, (iii) roton emission when the Landau critical velocity is exceeded, (iv) vortex nucleation when the corresponding critical velocity is exceeded, and (v) interaction with thermal excitations when T > 0 K. The first effect is independent of the bubble radius (R b ) and does not depend strongly on temperature provided that the rigidly bound solvent atoms remain attached to the ion. The second effect depends on R b through ion acceleration (phonon emission), and for an inviscid liquid it is given by 1 2 Vρ 0 , where V is the bubble volume and ρ 0 is the bulk liquid density.…”

Electron mobility in liquid and supercritical helium measured using corona discharges: a new semi-empirical model for cavity formation

“…There, like in the normal liquid phase, the motion is governed by the laws of hydrodynamical (Stokes) flow, whereas in the superfluid state interactions with collective excitations (phonons, rotons and vortices) become dominant. 11 In all of these flow regimes the radius of the spherical cavities determines the mobility. In the gas phase at lower densities, cavities are not supported.…”