On the capillary stability of a cylindrical dielectric liquid jet in a longitudinal electrostatic field

A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a cylindrical jet of an ideal incompressible dielectric liquid subjected to an electrostatic field aligned with the symmetry axis of the jet. It is shown that only long axisymmetric waves can experience capillary instability in such a system. The wavenumber range into which unstable waves fall begins with a zero value, and its width depends on the permittivities of the liquid and ambient and on the electrostatic field strength squared. As the field strength grows, the wavenumber range for unstable waves rapidly narrows and the capillary instability growth rate, as well as the wavenumber of the wave with the greatest growth rate, decreases.     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

Instability of a charged spherical drop moving parallel to an external electrostatic field

It is shown that the pressure of electrostatic fields induced by the self-charge of a drop and by the polarization charge and aerodynamic pressure of a laminar gas flow around a moving charged drop acting simultaneously reduce the critical instability conditions for the surface of the drop. For these conditions, the spectrum of capillary oscillations of the drop is calculated. It is found that, at various values of the charge, field strength, and velocity of the drop, the vibrational instability of the drop surface develops through the interaction of different oscillation modes, namely, second and third, second and fourth, and third and fifth.     

Disintegration of a drop in an external electrostatic field

Regular features of the disintegration of both a drop of a perfectly conducting liquid and a drop of a dielectric liquid into two or three parts in an external uniform electric field are studied using the principle of minimizing the potential energy of the final state of a closed system with spontaneous processes.     

Nonlinear oscillations of a drop moving at a constant velocity in an insulating medium subjected to an electrostatic field

Nonlinear asymptotic calculations of the second order of smallness in the amplitude of the initial deformation of an ideally conducting liquid drop show that the laminar flow of an ideal conducting incompressible dielectric liquid flowing about the drop in an external electrostatic field parallel to the flow causes oscillation mode’s interaction in the first and second orders of smallness. Both linear and nonlinear interactions between the oscillation modes of the drop excite modes that are absent in the spectrum of modes governing the initial deformation of the drop’s equilibrium shape. In the second order of smallness, the mode interaction decreases the electrostatic field strength, as well as the velocity and density of the environment, that are critical for development of instability of the drop against the polarization charge.     

Polarization fluctuations in a dipolar medium in an electrostatic field

Radio Engineering and Electronics Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1113–1124, September, 1989.     

On propagation of high-energy photon in a medium in presence of an external field

The polarization tensor is calculated which originates from interaction of a photon with the electron–positron field. The effects of multiple scattering of electrons and positrons in a medium side by side with external fields are included. The corresponding general representation of polarization tensor is found in the form of two-dimensional integral. The both effects may be essential for propagation of high-energy photons in oriented single crystals.     

On the stability of acoustic waves propagating in a nonstationary moving medium

We analyze the stability of acoustic waves in a medium moving with a time-variable velocity. An instability criterion for these waves is obtained and analyzed for the weak modulation of medium velocity. The harmonics that emerge during the propagation under parametric resonance are shown to have an additional frequency shift.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1087–1090, September, 1996.This work was supported by the Russian Foundation for Fundamental Research under Projects 95-02-05001 (G. I. Grigor'ev and V. V. Tamoikin) and 96-05-64277 (O. N. Savina).     

Stability of a bubble in a dielectric liquid in an external electrostatic field

Critical instability conditions are found for a gas bubble in a liquid dielectric in a uniform external electrostatic field E ₀. It is shown that they depend both on the magnitude of E ₀ and on the properties of the liquid, as well as on the gas pressure in the bubble. In a linear approximation with respect to the square of the eccentricity of an equilibrium spheroidal form, the equilibrium eccentricity of the bubble exceeds the equilibrium eccentricity of a drop in the field E ₀. The gas pressure in the bubble lowers the critical electric field E ₀ for development of an instability in the bubble. Zh. Tekh. Fiz. 69, 43–48 (August 1999)     

On the possibility of corona initiation near a conducting drop nonlinearly vibrating in an external electrostatic field

An analytical asymptotic expression for the field strength near an ideal incompressible electrically conducting liquid drop nonlinearly vibrating in external electrostatic field E ₀ is found in an order of 5/2 in a small parameter. The small parameter here is the amplitude of deformation of the spherical shape of the drop. It is found that the strength of the electric field resulting at the tops of the drop exceeds the corona-initiating field even if E ₀ is one order of magnitude lower than the value at which the drop becomes unstable against the induced charge (that is, at such values of E ₀ as are observed in storm clouds in full-scale experiments).     

Instability of a bubble in a liquid dielectric in an external electrostatic field

The sizes, charges, and number of daughter bubbles emitted during the development of instability with respect to the polarization charge in a uniform electrostatic field of a gas bubble in a liquid dielectric are found on the basis of the Onsager principle of minimum energy dissipation for nonequilibrium processes. Zh. Tekh. Fiz. 69, 10–13 (November 1999)     

Cerenkov radiation of a spatially extended charged bunch moving along the axis of a cylindrical channel in a transparent medium

Relations are obtained which determine the electromagnetic field produced by an axially symmetric bunch of charged particles moving along the axis of a cylindrical channel in a transparent medium. The problem of the Cerenkov radiation of such a bunch is investigated and relations are obtained for the intensity of this radiation.In conclusion the author thanks Professor A. A. Sokolov for discussing the results.     

Stability of a liquid-dielectric jet in a longitudinal electrostatic field

Conclusions A longitudinal electrostatic field tends to stabilize a jet of liquid dielectric.     

Behavior of electron spin in an external axisymmetric electrostatic field

The self-orientation of the spin of an ultrarelativistic electron in an external axisymmetric focusing electrostatic field is investigated qualitatively. The conditions under which a collective phenomenon of this kind occurs and its nature are clarifiedTranslated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 14–17, February, 1991.     

Radiation of electromagnetic waves by a dipole in an external uniform electrostatic field

Exact solution for the electromagnetic field densities E and H of a dipole of uniformly accelerated point-charges with identical masses is discussed. It is shown that, for any fixed time t and a large distance R between the center of the dipole and the fieldpoint, |E| ~ R ^?4, |H| ~ R ^?5, while for large c|t| ~ R, |E| ~ |H| ~1/R as in spherical electromagnetic waves. Nevertheless, any irreversible radiation of electromagnetic waves is absent since the wave zone does not exist.     

Electromagnetic radiation of a neutral fermi particle moving in an external field

The neutral particle has an anomalous magnetic moment; the motion in constant and homogeneous electric and magnetic fields is discussed. Photons can be emitted; the polarization is examined. It is shown that the emission is related to spin rotation.     

Nonlinear oscillations of an uncharged conducting drop in an external uniform electrostatic field

The problem of nonlinear oscillations of the finite amplitude of an uncharged drop of an ideal incompressible conducting liquid in an external uniform electrostatic field is solved for the first time by analytical asymptotic methods. The problem is solved in an approximation quadratic in amplitude of the initial deformation of the equilibrium shape of the drop and in eccentricity of its equilibrium spheroidal deformation. Compared with the case of nonlinear oscillations of charged drops in the absence of the field, the curvature of the vertices of uncharged drops nonlinearly oscillating in the field is noticeably higher, whereas the number of resonant situations (in the sense of internal resonant interaction of modes) is much smaller.     

Equation of motion of a particle in an external electromagnetic field in cylindrical coordinates

Translated from Isvetiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 4, p. 435, April, 1991.     

在柱坐标系中求解轴对称的静电场

提出了求解轴对称静电场的柱函数展开法,推导出用对称轴上的电势分布表示空间电势分布的级数展开式,并给出了求解轴对称静电场的例子.