Confinement of an Electron in an Image Potential and an External Electrostatic Field

The quasi-classical approximation is used to determine the positions of the classical turning points upon motion of an electron that is bound by an image field and a constant homogeneous electric field of the same direction. Power expansions of the coordinates of the turning points in a wide range of electron energies and field strengths are obtained. The mechanism of one-dimensional confinement of an electron, which determines a completely discrete spectrum of states, is described. The dependence of the spatial width of the confinement region on the field strength and electron energy is determined. The dependences of the electron energy in different states on the external field strength are calculated numerically. Quasi-classical quantization is performed, and the dependence of the electron energy on the width of the confinement region is determined. The energy interval of a maximum density of electron states is found, which is determined by the dependence of the width of the confinement region on the electric field strength.     

Radiation of an electron in an electric field

By the methods of classical theory, the motion of an electron in the field of a longitudinal electric wave is analyzed. This field may be taken as a model of the accelerating field at the axis of a linear accelerator. It was shown that the radiation of electrons in this field is analogous to the radiation in a constant homogeneous electric field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 96–99, May, 1976.The authors are sincerely grateful to Prof. V. A. Bagrov for formulating the problem and for his constant interest in the work.     

Bubbles in an acoustic field: an overview

Acoustic cavitation is the fundamental process responsible for the initiation of most of the sonochemical reactions in liquids. Acoustic cavitation originates from the interaction between sound waves and bubbles. In an acoustic field, bubbles can undergo growth by rectified diffusion, bubble-bubble coalescence, bubble dissolution or bubble collapse leading to the generation of primary radicals and other secondary chemical reactions. Surface active solutes have been used in association with a number of experimental techniques in order to isolate and understand these activities. A strobe technique has been used for monitoring the growth of a single bubble by rectified diffusion. Multibubble sonoluminescence has been used for monitoring the growth of the bubbles as well as coalescence between bubbles. The extent of bubble coalescence has also been monitored using a newly developed capillary technique. An overview of the various experimental results has been presented in order to highlight the complexities involved in acoustic cavitation processes, which on the other hand arise from a simple, mechanical interaction between sound waves and bubbles.     

Wrapping an adhesive sphere with an elastic sheet

We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss's Theorema Egregium shows that this operation necessarily generates metric distortions (i.e., stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two nondimensional parameters comparing, respectively, bending and stretching energies to adhesion. A complete configuration diagram is finally proposed.     

Diffraction of an ultrashort pulse by an aperture

The scalar problem of diffraction of an infinitely short pulse by a plane screen is solved within Kirchhoff’s approximation. The response of an infinitely small aperture is calculated, and the explicit solution is found for the case of a circular aperture.     

Diffraction of an electromagnetic wave from an infinitely long slit in an infinite metallic sheet

The diffraction of anE-polarized and anH-polarized wave by an imperfectly conducting slit (on which impedance boundary conditions are imposed) in an infinite metallic plane is investigated. The two independent problems are solved by using integral transforms, the Wiener-Hopf technique and asymptotic approximations. It is found that the diffracted field consists of the sum of fields produced by the two edges of the planes formed by the slit and a field due to the interaction of the two edges.     

Splitting of an edge dislocation by an optical vortex

In a linear medium an optical vortex induces the splitting of an edge dislocation into vortices of both topological charges. Their positions and number depend on which of the phase dislocations is shifted from the center of the host beam. Violations of the charge conservation law are discussed.     

Flow of an elastico-viscous fluid past an oscillating plate

An exact solution for the flow of an elastico-viscous fluid (Walters' liquid B') due to an oscillating infinite plate has been derived. It has been observed that forgwt=0, ( — frequency,t — time) the flow near the plate may become unstable with increasing whereas fort>0, the velocity increases with increasing. The shearing stress decreases with increasing.I wish to thank the referee for his useful comments which led to the improvement of this paper.     

Breakup of an uncharged droplet in an electrostatic field

The breakup of an uncharged electrically conducting liquid dropet placed in a uniform electrostatic field into two daughter droplets caused by strong nonspheroidal deformation is qualitatively analyzed by applying the principle of minimum potential energy under spontaneous virtual variations of the droplet’s state. It is shown that the breakup mechanism involves asymmetric mass distribution among the daughter droplets, which are found to be stable with respect to their respective intrinsic charges.     

Response of an ideal gas in an external potential

We construct the exact solution for the time evolution of the local mass density in an ideal gas in which an external short-ranged separable potential is switched on at time t = 0. The redistribution of matter in strong potentials causing bound states or resonances is studied in great numerical detail.     

Effective mass of an electron in an electromagnetic field

The effective-mass formalism is shown capable to describe the fully relativistic motion of an electron in a strong, locally plane, electromagnetic wave, determining the drift caused by the wave inhomogeneity and by additional weaker fields. The limits of this approach are discussed, in connection with the occurrence of resonances.     

Backscattering of an intense laser beam by an electron

We present a novel, simple asymptotic expansion for the spectrum of radiation that is backscattered from a laser by a counterpropagating (or copropagating) electron. The solutions are presented in such a way that they explicitly show the relative merit of using an intense laser and of an energetic electron beam in x-ray production in the single particle regime. Simple scaling laws are given.     

Quasilinear response of an atom to an external disturbance

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 50, No. 4, pp. 560–565, April, 1989.     

Dynamics of an ion flow in an electron layer

We study the acceleration of an ion flow in the electron layer formed by an electron flow moving in a transverse electric field and confined by the intrinsic magnetic field. The possibility of extraction of heavy ions with velocities lower than the ion sound velocity from the plasma, and the feasibility of their further acceleration by an external field is demonstrated.