Theoretical modeling of electron mobility in superfluid 4He

Abstract

The Orsay-Trento bosonic density functional theory model is extended to include dissipation due to the viscous response of superfluid (4)He present at finite temperatures. The viscous functional is derived from the Navier-Stokes equation by using the Madelung transformation and includes the contribution of interfacial viscous response present at the gas-liquid boundaries. This contribution was obtained by calibrating the model against the experimentally determined electron mobilities from 1.2 K to 2.1 K along the saturated vapor pressure line, where the viscous response is dominated by thermal rotons. The temperature dependence of ion mobility was calculated for several different solvation cavity sizes and the data are rationalized in the context of roton scattering and Stokes limited mobility models. Results are compared to the experimentally observed "exotic ion" data, which provides estimates for the corresponding bubble sizes in the liquid. Possible sources of such ions are briefly discussed.

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

“…At the same time, direct numerical modelling of the problem has been hindered by the lack of an accurate microscopic model that can be used to study the complex spatio-temporal dynamics of the ion interacting with the superfluid. Relatively recently, there has been some work employing density-functional theories [9][10][11] , that can accurately reproduce the equation of state (as well as the roton dispersion relation), in order to study the dynamics of the electron bubble. However, given the complexity of these models, simulations were restricted to axisymmetric configurations which we believe to be inadequate in representing some of the key physics such as the mechanism of asymmetric capture of the ion by nucleated vortex rings.…”

Atomic fluorescence emitted from a corona discharge in helium above and below saturated vapour pressure

“…Higher temperatures show higher singlettriplet conversion rates. Given that the process appears to be more efficient in the gas phase at similar densities, a possible interpretation is that fewer particles are solvated at 5.0 K than at 3.8 K. At higher temperatures, the He 2 + , He 3 + and He 4 + in gas bubbles would have a greater chance to recombine with electrons than at lower temperatures because solvated ions and electrons have lower mobility in liquid helium [98][99][100][101].…”

Density functional theory modeling of vortex shedding in superfluid He4

“…(1) imposes constant velocity rather than constant force employed in previous calculations. 7,10 The latter case would apply, for example, to modeling ion mobilities in the presence of an external electric field whereas our present aim is to characterize the liquid flow as a function of velocity and other system parameters. The GP theory can be obtained as a special case of Eq.…”

“…Based on an extended version of this method, where viscous dissipation was added to the hydrodynamic version of the He-DFT equations, the above force balance condition has been used to compute the electron mobility in superfluid helium above 1.4 K temperature. 7 The main contribution to the viscous drag was found to arise from continuous collisions between the ion and thermal rotons. The employed roton continuum approximation was observed to break down below 1.4 K where the mobility is determined by continuous interaction with thermal phonons as well as discrete roton collisions ("roton gas").…”