Equilibrium configurations of the conducting liquid surface in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid deformed by a nonuniform external electric field are investigated. The liquid rests on an electrode that has the shape of a dihedral angle formed by two intersecting equipotential half-planes (conducting wedge). It is assumed that the problem has plane symmetry: the surface is invariant under shift along the edge of the dihedral angle. A one-parametric family of exact solutions for the shape of the surface is found in which the opening angle of the region above the wedge serves as a parameter. The solutions are valid when the pressure difference between the inside and outside of the liquid is zero. For an arbitrary pressure difference, approximate solutions to the problem are constructed and it is demonstrated the approximation error is small. It is found that, when the potential difference exceeds a certain threshold value, equilibrium solutions are absent. In this case, the region occupied by the liquid disintegrates, the disintegration scenario depending on the opening angle.     

Dynamics of the free surface of a conducting liquid in a near-critical electric field

Near-critical behavior of the free surface of a perfectly conducting liquid in an external electric field is considered. Based on an analysis of three-wave processes using the method of integral estimates, sufficient criteria for hard instability of a planar surface are formulated. It is shown that the higher-order nonlinearities do not saturate the instability, for which reason the growth of disturbances has an explosive character.     

On the equilibrium shapes of a conducting drop in a uniform and nonuniform electric field

The equilibrium shape of a drop in the electrostatic field of a point charge and a point dipole is asymptotically calculated in terms of the dimensionless deformation of the shape and a ratio between the drop’s radius and the distance to the point charge (dipole). Irrespective of the degree of nonuniformity of the field, the prolate spheroidal deformation (typical of the uniform field) is shown to be the main reason for the change in the equilibrium shape of the spherical drop. When the nonuniformity of the field grows, the equilibrium shape becomes more and more asymmetric and different from the spheroidal one. This, all other things being equal, may influence the critical conditions for the instability of the drop’s surface against an induced charge. It follows from the aforesaid that the drop in the field of the dipole will be the first to undergo instability with the electrostatic pressure on the drop being the same.     

Exact solutions to the problem on the shape of an uncharged conducting liquid jet in a transverse electric field

Exact solutions are obtained for the problem of an equilibrium configuration of an uncharged cylindrical jet of a conducting liquid in a transverse electric field. The transverse cross section of the jet moving between two planar electrodes is deformed under the action of electrostatic forces (capillary forces play a stabilizing role). According to the solutions obtained, the initially circular cross section of the jet may be significantly (formally, unboundedly) stretched along the lines of forces of the field, and the boundaries of the jet asymptotically approach the electrodes.     

Equilibrium configurations of uncharged conducting liquid jets in a transverse electric field

Solutions for the problem on the equilibrium configurations of uncharged conducting liquid jets in a transverse electric field are obtained. These solutions correspond to finite-amplitude non-axisymmetric azimuthal deformations of the surface of a round jet: the jet is stretched along the field in its cross-section. The range of electric fields is determined for which solutions of the problem exist. If the electric field strength is over some critical value, the electrostatic equations have no solution, and the jet splits. The obtained solutions are qualitatively examined for stability under small azimuthal perturbations.     

Effect of the electric field on the shape of a bubble in a conducting liquid

Technical Physics - It is found that a bubble in a conducting liquid is stretched in the direction of the electric field. Expressions are derived for the extension coefficient of the bubble as a...     

Equilibrium configurations of a jet of an ideally conducting liquid in an external nonuniform magnetic field

Possible equilibrium configurations of the free surface of a jet of an ideally conducting liquid placed in a nonuniform magnetic field are considered. The magnetic field is generated by two thin wires that are parallel to the jet and bear oppositely directed currents. Equilibrium is due to a balance between capillary and magnetic forces. For the plane symmetric case, when the jet deforms only in the plane of its cross section, two one-parameter families of exact solutions to the problem are derived using the method of conformal mapping. According to these solutions, a jet with an initially circular cross section deforms up to splitting into two separate jets. A criterion for jet splitting is derived by analyzing approximate two-parameter solutions.     

Instability of a spherical drop in a nonuniform electric field

Analytical calculation in the first order of smallness shows that the equilibrium shape of a drop in the field of a point charge is axisymmetric about the plane passing through the center of mass of the drop normally to the axis connecting the center of mass with the point charge. Whether the equilibrium shape of the drop is stable or not depends on the value of the field parameter, which, in turn, depends on the point charge and the distance to it. There is an asymptotic value of the critical parameter above which all modes become unstable. In the field of the point charge, the mode coupling grows; that is, a mode excited at the zero time generates oscillations of the six nearest modes with amplitudes proportional to that of the initially excited mode. If the initially excited mode loses stability, all the modes coupled with it also become unstable. The surface instability of the drop also develops when the initially excited mode is stable but at least one of the modes coupled with it is unstable.     

String dynamics in an external field: A family of exact solutions

We formulate the problem of the motion of a closed string in an external field by analogy with classical electrodynamics. A two-parameter family of axially symmetric solutions is obtained when the field is static and uniform.     

High-pressure runaway-electron-preionized diffuse discharges in a nonuniform electric field

High-pressure nanosecond diffuse (volume) discharges in a nonuniform electric field are studied experimentally using a recording system with a ?100-ps time resolution. As the voltage pulse shrinks to a width of ≈100 ps, the initiation of a diffuse discharge without a source of additional ionization is facilitated; specifically, a runaway-electron-preionized diffuse discharge is ignited in atmospheric-pressure air in the case of short interelectrode gaps. It is found that a major energy deposit into the plasma of this discharge is from an abnormal glow discharge following a maximum of the gap voltage.     

Nonlinear waves on the surface of a dielectric liquid in a horizontal electric field in 3D geometry: Exact solutions

It has been shown that waves of arbitrary configuration in 3D geometry may propagate without distortion along the surface of a dielectric liquid in the direction of a horizontal electric field. This situation occurs for the high-permittivity liquids in the case of a sufficiently high external field when the effect of electrostatic forces dominates. A general solution of the equations of motion that describes the interaction of counterpropagating waves of a small but finite amplitude has been obtained.     

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.     

Formation of root singularities on the free surface of a conducting fluid in an electric field

The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.     

Effect of an electric field on the orientation of a liquid crystal in a cell with a nonuniform director distribution

The electric field-induced reorientation of a nematic liquid crystal in cells with a planar helicoidal or a homeoplanar structure of a director field is studied theoretically and experimentally. The dependences of the capacitances of these systems on the voltage in an applied electric field below and above the Fréedericksz threshold are experimentally obtained and numerically calculated. The calculations use the director distribution in volume that is obtained by direct minimization of free energy at various voltages. The inhomogeneity of the electric field inside a cell is taken into account. The calculation results are shown to agree with the experimental data.     

Properties of exact solutions for a massive classical Yang-Mills field

Exact solutions for a massive Yang-Mills field are found and solutions of classical Wong equations and quantum Dirac equations are discussed for the field configurations obtained. A procedure for constructing constant fields is given and transition to solutions of the Yang-Mills equations in the case of a massless field is discussed.Translated from Izvestriya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 96–100, May, 1986.In conclusion, the authors express their gratitude to V. Ch. Zhukovskii and V. R. Khalilov for valuable remarks and discussions.     

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is established that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time. Zh. éksp. Teor. Fiz. 114, 2043–2054 (December 1998)     

New exact solutions in a chiral model for a planar-symmetry gravitational field

New exact solutions are derived to the dynamic equations for an effective nonlinear sigma model NSM for a vacuum planar-symmetry gravitational field by the use of a functional-parameter method. The solutions are Backlund transformations of solutions to D'Alembert's and Einstein's equations. Ul'yanov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 102–107, November, 1998.     

Conditions for runaway electrons in a gas diode with a strongly nonuniform electric field

The dynamics of runaway electrons in a gas diode in a sharply nonuniform electric field determined by the geometry of electrodes is considered. The analytical solution of the equation of motion of electrons for an edge cathode shows that their runaway at the periphery in the region of weak field is possible only if the applied potential difference exceeds a certain threshold determined by the interelectrode distance and the parameters of the gas. This condition supplements a classical runaway condition that the field strength at the emission edge of the cathode should be higher than a threshold value depending only on the parameters of the gas. According to our estimates, this new condition imposes higher requirements than the classical condition on the field strength in the limit of the strongly sharp edge of the cathode.     

Nonlinear surface magnetic polaritons in a nonuniform magnetic field

High-frequency surface magnetic polaritons of finite amplitude propagating along the interface between a ferrite and a nonlinear insulator in a weakly nonuniform, shaft-shaped external magnetic field are investigated theoretically. The analysis is based on employment of the variational method together with bilinear relations having the form of Lorentz’s lemma. It is shown that the wave dispersion and the transverse profile of a wave along the field nonuniformity depend significantly on the amplitude of the wave. Zh. Tekh. Fiz. 68, 92–95 (September 1998)     

On the instability of conical protrusions of liquid surface in electric field

Electric field is analyzed at the tip of the conical protrusion of a conductive liquid surface that forms as the field strength approaches certain threshold values. When the field exceeds the threshold, the cone tip generally becomes unstable and emits a slender jet. The field strength at the sharp tip of a conducting liquid cone tends to infinity. Even though the field has a singularity, the cone tip becomes unstable only if the semi-cone angle decreases below the Taylor angle, which is the same for all conducting liquids. It is shown that similar conical protrusions can form if the liquid is a dielectric and its permittivity is sufficiently high. In this case, the equilibrium cone angle depends on the permittivity. When the permittivity is lower than approximately 17.60, cones cannot form, and the ensuing phenomena do not occur.