Motion of a classical charged particle with spin in the external field of a plane electromagnetic wave

We obtain the solution to the equations of motion for a classical particle with spin, electric and magnetic charges, and electric and magnetic normal and anomalous moments, in the field of a plane electromagnetic wave. An explicit form of the solution is given for linearly polarized waves and monochromatic circularly polarized waves. The possibility is noted that due to the presence of the moments, the particle can be accelerated to speeds arbitrarily close to the speed of light.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 11, pp. 71–74, November, 1981.     

Dynamo-optical effects in a plasma

The propagation of electromagnetic waves in a nonuniformally moving cold electron plasma with no external magnetic field and collisions is considered. The motion is assumed to be stationary. It is shown that in the case of smooth variation of the parameters of the medium the trajectories of the rays in the zero approximation of geometric-optics are determined by the concentration distribution, while the motion leads to rotation of the polarization plane in the wave. For plane-stratified flow with a constant velocity gradient an exact solution of the equations is determined which constitutes the superposition of two independent waves that are elliptically polarized in opposite directions. The refraction law of these waves is found, and the corresponding reflection and penetration coefficients are calculated in the case of a layer having a finite thickness.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 2, pp. 183–190, February, 1972.     

Colliding Plane Waves in Einstein–Maxwell Theory

Recently, a simple solution of the vacuum Einstein–Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein–Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose–Khan solution and a solution obtained by Griffiths as separate limiting cases.     

Motion and radiation of a charge in a plane wave and a magnetic field

The motion and radiation of an electron moving in the field of a plane wave of elliptical polarization and a magnetic field is considered. By the methods of classical and quantum theory, the effect of the plane-wave polarization on the characteristics of the particle motion and radiation is investigated. Some particular cases are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedeniis Fizika, No. 10, pp. 70–74, October, 1978.     

Effect of a longitudinal wave on the self-resonant motion of electrons

The effect of the longitudinal component of an electromagnetic wave on the self-resonant motion of electrons in waveguides is considered. The equation of motion for electrons in a plane, longitudinal-transverse, circularly polarized wave has been solved by the method of successive approximations with allowance for the longitudinal integral of motion present in such a wave. The expansion parameter is the ratio of the amplitudes of the longitudinal and transverse components of the wave. For the case n < 1 the longitudinal field of the wave does not change the nature of the electron motion, but only induces weak oscillations about a solution that does not include the longitudinal field. For n > 1 with spontaneous phasing of the electrons a criterion is obtained for neglecting the effect of the longitudinal field, and numerical estimates are given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 66–71, September, 1978.     

Elastic scattering amplitude of a polarized electron in an arbitrary plane wave field

The elastic scattering amplitude of a polarized electron in an arbitrary plane wave electromagnetic field is obtained by using the method of dispersion relations. Superposition of a constant crossed field and a plane monochromatic wave of elliptic polarization is considered a particular case of giving the field. An anomalous magnetic moment is obtained for the electron in the mentioned field as are also relative contributions to the anomalous magnetic moment due to the transition into the intermediate state with and without spin turnover.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 69–75, October, 1990.     

Nonlinear analysis of interaction between multispiral electron fluxes and electromagnetic wave

The interaction of a circularly polarized plane electromagnetic wave with a multispiral electron flux in the presence of an external magnetic field is considered. It is shown that under certain conditions it is possible to transform the electron-flux energy into wavefield energy as a result of the dependence between the rotational and translational motion of the particles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 87–91, October, 1978.     

Motion and radiation of an electron exhibiting a vacuum magnetic moment in the field of a plane electromagnetic wave

A study is made of the motion of an electron exhibiting an anomalous magnetic moment and moving in the field of a plane circularly polarized electromagnetic wave. An exact solution is found to the generalized Dirac equation and is utilized to study the emission of electromagnetic radiation from the electron (the Compton effect). It is shown that allowance for the anomalous magnetic moment of the electron leads to: a frequency shift, a change in the total radiated power, polarization of the radiation, and to spin effects.     

Dynamics of a charged particle in the presence of both a quasimonochromatic wave and a strong magnetic field

A multiple-frequency system of equations is averaged to obtain the relativistic equations of motion for a charged particle in the field of a quasimonochromatic wave propagating along a strong magnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 70–72, December, 1976.We wish to thank L. M. Gorbunov for valuable discussions.     

On the theory of the radiation of an electron moving in the field of two plane waves and a magnetic field

The motion and radiation of electrons in a homogeneous magnetic field and the field of two plane waves propagating along the vector of the magnetic field intensity are considered. The law of motion and expressions for the total power, frequencies, and angular spectral distribution of the electron radiation intensity are obtained. An analysis is carried out of the results obtained in the case of small intensities of the plane waves. It is shown that the presence of the plane waves has a considerable effect on the characteristics of synchroton radiation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 105–110, August, 1977.     

Motion of a particle in a static magnetic field and in the field of a electromagnetic plane wave

The solutions of the equations of motion of a charged particle in an external electromagnetic field consisting of a superposition of a constant uniform magnetic field and the field of a circularly polarized electromagnetic plane wave are presented as solutions of the Cauchy problem. The resonance case is studied. Zh. Tekh. Fiz. 67, 94–99 (February 1997)     

The Aharonov-Bohm effect for nonstationary quasiclassical trajectory-coherent states in a uniform magnetic field

Approximate (as h 0) dynamic states in the form of nondiffusing wave packets, localized in the vicinity of a classical trajectory (nonintersecting the solenoid), quasiclassical nonstationary trajectory-coherent states, are constructed for nonrelativistic electron motion in a uniform magnetic field in the presence of an infinitely thin and long solenoid. The occurrence of the Aharonov-Bohm effect in such states is investigated. Special cases of electron motion — in a uniform magnetic field and in the solenoid field — are considered.Moscow Institute of Electronic Machinery. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 83–90, October, 1992.     

Equilibrium state of charged particles in a wave propagating along the magnetic field

This investigation examines the adiabatic motion of a charged particle near the equilibrium state in a field of a plane, circularly polarized, electromagnetic wave which is propagating with a changing velocity phase along the magnetic field. Approximate equations are found which describe the behavior of the equilibrium state parameters when the wave leaves the medium and enters a vacuum. It is shown that compared to the equilibrium value in this situation under the adiabatic approximation there is a decrease in amplitude of the particle energy fluctuation; this establishes the possibility of a prolonged acceleration of the particle to high energies. It is further demonstrated that a particle moving close to equilibrium state can appear to be in the autoresonance regime when the wave enters vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 117–122, October, 1976.     

Green’s function for an electron model with a plane wave

The Green function for a Dirac particle subject to a plane wave field is constructed according to the path integral approach and the Barut’s electron model. Then it is exactly determined after having fixed a matrix U chosen so that the equations of motion are those of a free particle, and by using the properties of the plane wave and also with some shifts.      

Canonical form of the averaged equations of motion of a charged particle upon superposition of an electromagnetic wave field on a weakly inhomogeneous magnetic field

The Hamiltonian function of a charged particle in a weakly inhomogeneous magnetic field perturbed by a plane wave is determined correct to terms of the order of the small parameter inclusive. The canonical motion equations averaged over the fast phase for motion in the vicinity of the resonance are derived.     

Exact solutions of the equations of motions of quarks in a non-Abelian field of a flat color wave

Exact solutions of the equations of motion of quarks in a non-Abelian field of a flat color wave of a spectral configuration are obtained. The gauge field of the wave takes values from the SU(2) group and is an exact solution of the Yang-Mills equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 76–78, December, 1986.     

Motion of a particle in a static magnetic field and the field of a monochromatic electromagnetic plane wave

A solution of the equation of motion of a charged particle in an external electromagnetic field comprising a superposition of a uniform static magnetic field and the field of a monochromatic, elliptically polarized electromagnetic plane wave is obtained as the solution of a Cauchy problem. The resonance case is investigated. An analysis of the resulting solution is given. Zh. Tekh. Fiz. 69, 106–110 (May 1999)     

Integrals of the motion for an electron in a quantized plane electromagnetic wave

The structure of the integrals of motion of an electron moving in a plane quantized electromagnetic wave is discussed, using the general solution of the integrals of motion of a system whose Hamiltonian is a quadratic form of creation and annihilation operators with constant coefficients.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 116–121, February, 1977.     

Wave Packets in a Magnetic Field

A Gaussian wave packet confined to move on a plane perpendicular to a magnetic field remains a Gaussian wave packet in its time evolution. The average position and momentum follow the Ehrenfest equations which are identical to the classical Hamilton equations. A set of nonlinear equations decoupled from the Ehrenfest equation is derived for the parameters describing the time evolution of the density distribution and phases of a wave packet. Explicit solutions are then obtained when the "internal" angular momentum of the wave packet vanishes. In this case it is shown that the motion of the wave packet is a superposition of a translational motion, a rotation and a vibration.