Formation of singularities on the charged surface of a liquid-helium layer with a finite depth

The dynamics of the development of an instability of a charged surface of a liquid-helium layer with a finite depth is investigated. The equations describing the evolution of the free surface are derived with the use of conformal variables for the case in which the charge completely screens the electric field above the liquid. A model of the evolution of a spatially localized perturbation of a liquid-helium surface is proposed for the strong-field limit where the dynamics of the liquid is predominantly determined by the effect of electrostatic forces. This model describes the development of an instability of the initially planar boundary to the point of the formation of cuspidal dimples. The limit of an infinitely deep liquid is considered. The stability of the previously revealed liquid flow regime described by the Laplacian growth equations is proved without significant constraints on the surface geometry.     

Instability of equilibrium of the liquid dielectric surface and formation of regular cellular structures in the field of a corona discharge

It has been established experimentally that the equilibrium of the plane surface of transformer oil under a corona electrode (needle) becomes unstable when the critical voltage, which increases with the oil layer thickness, is attained at the corona point. When the voltage at the needle exceeds the critical value, regular static cells are formed on the oil surface with characteristic sizes decreasing upon an increase in voltage. The theoretically estimated parameters of the experiment are found to be close to the experimental data. Comparison of the parameters corresponding to the occurrence of instability in the equilibrium of the oil surface in the field of the corona discharge with the parameters of instability in the equilibrium of the charged surface of liquid helium in a uniform electric field [7] demonstrates the similarity of the effects.     

Stationary soliton on a charged surface of liquid helium and hydrogen films

A change in the shape of a charged surface of liquid hydrogen and helium — the formation of a solitary wave (a positively charged hump for hydrogen and a negatively charged dimple for helium)-is observed in an electric field exceeding a critical value under conditions of total compensation of the applied field by the surface charge. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 547–552 (10 April 1997)     

On the time evolution of the liquid meniscus at the end of a capillary placed in an external electric field

Using a linearized set of equations of electrodynamics, the stability of the uniformly charged meniscus of a viscous conducting incompressible liquid at the end of a capillary is investigated and analytical expressions are derived for the electric field outside the meniscus, velocity fields in the liquid flow and meniscus, and generatrix of the meniscus shape. It is found that, if an external electric field near the meniscus exceeds that at which the free liquid surface becomes unstable against the surface charge, a finite number of longest waves become unstable with their instability growth rates nonmonotonically depending on the wavenumber. Analysis of the time evolution of the meniscus shape under various initial conditions shows that cylindrical waves with the highest instability growth rates play a decisive role in this process, while the influence of the initial deformation amplitude is insignificant.     

Exact partial solutions for the surface dynamics of a dielectric liquid with a charged surface in the gravitational field

We study the evolution of instability in the boundary of a perfect dielectric liquid with a free surface charge in an external electric field. Conformal variables are used to find exact partial solutions to the equations of motion for the case when the charge completely shields the field above the liquid, the electrostatic and gravitational forces being taken into account. The solutions describe the development of instability of the initially planar boundary until sharp dimples are formed on it.     

Effect of tilted electrostatic field on the Kelvin–Helmholtz instability in a liquid dielectric and gas flow

The effect of surface ponderomotive forces on the Kelvin–Helmholtz instability is studied in the linear formulation based on the equations and boundary conditions of the electrostatics and fluid dynamics of an ideal incompressible fluid. Conditions to be satisfied by the values of determining parameters of the problem for the transition of an unstable flow in zero electric field into a stable regime after the application of a horizontal electric field have been written in the form of inequalities. It has been shown that, at the stability bound, the wavelength of the most instable mode is independent of the ponderomotive forces. In case of a liquid with large permittivity a stable flow regime exists for which the stability condition only differs in small dimensionless values from the stability condition for the charged surface of a quiescent liquid conductor in contact with a gas at rest.     

Electric dispersion of fluid under the oscillatory instability of its free surface

A semiphenomenological analysis is performed of possible modes of electric dispersion of drops and menisci at the end of the capillary used to deliver the liquid into the discharge system under an oscillatory instability of the charged liquid surface. The instability is assumed to be induced by a time-dependent external force acting on the liquid surface, a finite rate of charge redistribution over the surface under virtual deformations, and tangential discontinuity of the velocity field across the interface.     

New state of a 2D electron crystal above liquid helium

A transition to a new, presumably unstable, state of a two-dimensional (2D) electron crystal above liquid helium has been discovered at temperatures well below the melting point. The transition is manifested as an abrupt increase in the active component of the inverse conductivity of the crystal with a decrease in the potential pressing of the electrons to the surface. The state can be destroyed by the in-plane electric field of a sufficiently high amplitude. The new state is supposed to be a 2D electron glass.     

Negative Ca− and Ba− ions of large radius on the surface and in the volume of liquid helium

Negative Ca⁻ and Ba⁻ ions of large radii on the surface of and in bulk liquid helium have been studied. Our results indicate that these ions are adsorbed on the helium surface. Ions on free liquid helium surfaces have not been studied previously because it was thought impossible to confine them on the surface. Ca⁻ and Ba⁻ ions have very low binding energies, therefore, like electrons, they form a bubble of large radius in bulk helium, whose energy is higher than on the surface. The behavior of ions on the surface exhibits a number of previously unknown features owing to their large masses and strong localization in the horizontal plane. Even in the absence of confining electric field, a hole is formed under an ion due to the polarization attraction between the liquid helium and the charged ion. This hole formation reduces the ion mobility by several orders of magnitude and increases its effective mass severalfold. The critical density of electrons and ions is approximately the same on the surfaces of thin and thick helium films. Zh. éksp. Teor. Fiz. 115, 593–604 (February 1999)     

Effect of tangential electric field on the evolution of the Rayleigh-Taylor instability of a dielectric liquid film

The effect of surface ponderomotive forces produced by a uniform tangential electric field on the evolution of the Rayleigh-Taylor instability of an isothermal film of a homogeneous incompressible dielectric liquid coating the lower surface of a horizontal insulating plate is studied in the long-wavelength approximation for the hydrodynamic equations and a simplified system of electrostatics equations. The lower boundary of the liquid is the interface with a stationary gas. It is shown in the framework of the linear theory that during the disruption of the continuous film, ponderomotive forces induce the formation of liquid billows extended along the applied field lines.     

Negative ions Ar<Superscript>−</Superscript>, Kr<Superscript>−</Superscript>, and Xe<Superscript>−</Superscript> in superfluid helium

The catalogue of negative ions in superfluid helium has been extended using the example of Ar⁻, Kr⁻, and Xe⁻. Such objects cannot exist in vacuum, since the polarization attraction of an electron to the inert A atom is insufficient for the formation of the bound state A⁻. However, these objects exist in helium as stable or metastable with a very long lifetime. The effect is due to the electron localization in liquid helium. If a mixture of excited A* atoms and electrons is prepared in the gas phase above liquid helium, the reaction A* + e = A*⁻ becomes possible for all atoms of the periodic table. Such charges can be immersed into liquid helium by the electric field. In this case, the radiative decay A*⁻ = A + e allowed in vacuum can be forbidden in liquid. This leads to the formation of the new unique objects A⁻, which can exist in liquid helium but are absent in nature. The size of such charged formations has been determined and is close the radius of a usual electron bubble in helium.     

Electrostatic instability of a heavily charged conducting liquid jet

The effect of electric charge on the jet surface on the capillary instability of the jet and its disintegration into drops is analyzed. A theoretical explanation is given for the electrostatic mechanism of instability development and jet disintegration that is akin to the mechanisms behind the instability of a heavily charged drop (Rayleigh instability) and flat uniformly charged liquid surface (Tonks-Frenkel instability) but differs qualitatively from the conventional capillary mechanism of instability and disintegration.     

Voltage–current characteristics and current instability conditions of a high-temperature superconductor in non-uniform temperature distribution

The influence of non-uniform temperature distribution in the cross section of a high-temperature superconductor (thermal size effect) on its voltage–current characteristic and the instability conditions of charged current is investigated. The boundary values of the electric field and the current above which the charged current is unstable are defined taking into account the size effect. It is shown that the calculated current of the instability determining the maximum allowable value of the charged current is reduced, if the thermal heterogeneity of the electrodynamics states is taken into consideration in the theoretical analysis of the stability conditions. As a result, the limiting stable values of the electric field and current depend nonlinearly on the thickness of the superconductor, its critical properties as well as on the external cooling conditions. Therefore, the current of instability will not increase proportionally to the increase in the thickness of superconductor or its critical current density at the intensive cooling conditions.     

Supercooling molecular hydrogen down through the superfluid transition

Recent calculations by Vorobev and Malyshenko [JETP Lett. 71, 39 (2000)] show that molecular hydrogen may stay liquid and superfluid in strong electric fields of the order of 4x10(7) V/cm. I demonstrate that strong local electric fields of similar magnitude exist beneath a two-dimensional layer of electrons localized in the image potential above the surface of solid hydrogen. Even stronger local fields exist around charged particles (ions or electrons) if the surface or bulk of a solid hydrogen crystal is statically charged. Measurements of the frequency shift of the 1 --> 2 photoresonance transition in the spectrum of a two-dimensional layer of electrons above a positively or negatively charged solid hydrogen surface performed in the temperature range 7-13.8 K support the prediction of electric field induced surface melting. The range of surface charge density necessary to stabilize the liquid phase of molecular hydrogen at the temperature of superfluid transition is estimated.     

On the stability of a weakly charged surface of liquid helium

The traditional approach to the development of instability of a weakly charged helium surface needs correction. It is shown that the well-known electrostatically “equipotential” Frenkel-Tonks scenario should be transformed to a more general sequence of events that would remain reasonable when the 2D charge density tends to zero. Under these conditions, the priorities change and the instability development through nucleation (with the formation of separate multicharged dimples) becomes preferable. The experiment qualitatively confirms the predictions of the theory.     

New phase nucleation in electric fields

The formation of vapor bubbles in a superheated liquid or of liquid drops in a superheated vapor in a uniform electric field and at a charged center is considered. The work done for the formation of drops as well as their critical size decrease in all cases. The critical size of bubbles always increases, while the work decreases at a charged center and in a uniform field. An explanation is offered for the results of experiments on the initiation of boiling of a superheated liquid by electric field pulses.     

Influence of charge relaxation on the capillary disintegration of a jet of a viscous dielectric liquid placed in an electrostatic field collinear with the axis of the jet

A dispersion relation is derived for capillary waves with an arbitrary symmetry on the surface of a charged jet of a finite-conductivity viscous liquid placed in an electric field collinear with the axis of the jet. Analytical calculations are carried out in an approximation that is linear in dimensionless wave amplitude. In the case of axisymmetric waves, the instability of which causes disintegration of the jet into drops, the finiteness of the potential equalization rate has a noticeable effect only for jets of poorly conducting liquids. The charge relaxation shows up in that “purely relaxation” periodic and aperiodic liquid flows arise. When the conductivity of the liquid declines, the instability growth rates for unstable waves increase and their spectrum extends toward short waves. A charge present on the surface of the jet enhances its instability. An increase in the charge surface diffusion coefficient variously influences the capillary and relaxation branches of the solution: the damping ratio increases in the former case and decreases in the latter. As the diffusion coefficient rises, relaxation flows may become unstable.     

Convective flows in a layer of a viscous liquid with the uniformly charged free surface

It is found theoretically that the critical conditions under which a charged liquid surface becomes unstable against the electric charge relax as a result of interaction between capillary-gravitational and convective flows in the liquid. As the surface charge density approaches a value critical in terms of development of Tonks-Frenkel instability, convection in the liquid arises at a temperature gradient however small, this effect depending on the liquid layer thickness.     

Formation of electric discharges above the free surface of a current-carrying liquid

The study is devoted to analysis of the formation of high-current electric discharges developing above the free surface of a liquid metal, deformed as a result of the interaction of the electric current passing through the liquid metal with the intrinsic magnetic field. We report on the electric characteristics of discharges and parameters of their initiation, consider the patterns of deformation of the free surface and the formation of electric discharges, describe the processes occurring in the system, and discuss the mechanism of cyclic formation of discharges above the liquid metal surface.