Nonlinear dynamics of charged particles in an oblique electromagnetic wave

We study dynamics of a charged particle under action of an electromagnetic wave that propagates obliquely to a background uniform magnetic field. The dynamics is described by a slow-fast Hamiltonian system. We show that long-term dynamics is dominated by phenomena of capture of particle into resonance with the wave and escape from this resonance, as well as of scattering on resonance. We find that the variation of the particle?s kinetic energy on the time interval between capture and escape is bounded and accumulated in the motion along the background field. We discuss possible applications of the obtained results.     

梯度磁场中静电波引起的粒子随机运动

本文讨论了一般非均匀梯度磁场下任意方向传播的静电波引起粒子随机运动的非线性效应。用正则久期扰动理论给出包含粒子周期运动和波振荡之间非线性共振的哈密顿量。根据Chirikov岛重叠条件给出一般梯度磁场下粒子进入随机态的临界波幅值。分析表明,相对均匀磁场,在弱非均匀情形下,该临界值降低,意味着粒子更易进入随机态。 关键词：     

Scalar particle with polarizability in the field of a plane electromagnetic wave and in an electric field

Exact solutions are obtained for the wave equations for a scalar particle that possesses polarizability in the field of a plane electromagnetic wave of arbitrary polarization and in a constant electric field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 40–43, February, 1991.     

Chaotic dynamics of charged particles in the field of two monochromatic waves in a magnetized plasma

We study the dynamics of charged particles in the presence of two electrostatic waves propagating obliquely to an ambient magnetic field. The presence of a second wave makes the problem a two-dimensional and time-dependent one with a complicated phase space behavior. We derive a set of difference equations (maps) for the nonrelativistic particle motion limit and numerically study them to elucidate the various aspects of the phase space dynamics. For the general case of oblique propagation, we observe synergistic effects leading to the lowering of the stochasticity threshold and the concomitant reduction in electric field amplitudes for particle heating applications. These results can be understood in terms of the resonance structures associated with the two waves and we obtain approximate analytic expressions for the thresholds. For the degenerate case of omega(1)=nOmega,omega(2)=mOmega (where omega(1),omega(2) are the frequencies of the two waves, Omega is the cyclotron frequency and n,m are integers) and strictly perpendicular propagation, the problem simplifies to a one-and-one-half-dimensional one. We observe the presence of stochastic webs in this situation. (c) 1996 American Institute of Physics.     

Autoresonance interaction of a charged particle with an electromagnetic wave in the presence of static electric and gravitational fields

The maintenance of resonance between a particle and a nonuniform, circularly polarized wave in a vacuum by a longitudinal electrostatic field is analyzed on the basis of the concept of an autoresonance regime as the motion of a charged particle along the autoresonance separatrix; the possibility in principle of autoresonance motion of a particle in a space with nonzero curvature is established: the conditions for autoresonance in a strong static gravitational field are obtained and discussed. Taganrog State Radio-Engineering University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 29–34, February, 1997.     

Elastic scattering amplitude of a scalar particle in a plane wave field

The elastic scattering amplitude of a scalar particle in an arbitrary plane wave electromagnetic field is obtained in the form of a double integral by the method of dispersion relations. Particular cases of giving the plane wave field are investigated. It is shown that the existence of scalar particle radiation in an arbitrary plane wave electromagnetic field results in elastic scattering, whose amplitude determines the change in particle mass in this field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 32–37, May, 1990.     

Embedding of Particle Waves in a Schwarzschild Metric Background

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a particle wave, which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity.     

Confinement of charged particles by an electromagnetic wave leaving the region of a strong gravitational field

The interaction of a charged particle in vacuum with a circularly polarized wave leaving the region of a strong static gravitational field in the direction of a magnetostatic field is considered. It turns out that this combination of fields forms, generally speaking, two capture regions (CR₁ and CR₂) on the phase cylinder of the particle. The evolution of these regions is determined by the gravitational field. The influence of the gravitational field on the rigidity of confinement of the particle in one of these regions (CR₁) is investigated. It is shown that the rigidity of confinement of particles with relatively high energies may increase toward the periphery of the gravitational field. The possibility of particle escape by the wave is demonstrated for particles whose initial energy is insufficient to leave the gravitational field region in the absence of the wave. In this case, the particle is trapped by the wave in CR₁ and subsequently confined. The mechanism of trapping the particle is discussed. Taganrog State Radio-Engineering University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–10, June, 2000.     

Operator representation of the wave function for a charged particle in an external field and its applications

A consistent derivation of the operator form for the solution of the wave equation for a charged particle in an arbitrary external electromagnetic field is presented. The expressions obtained can be used for solving any problems in quantum electrodynamics in external fields in the framework of the semiclassical operator method. The peculiarities of the application of this method are demonstrated for the small-angle elastic scattering of a high-energy photon in an arbitrary localized electric field. The problem is solved for the first time without presuming the central symmetry of the external field potential.     

Ponderomotive nongradient force acting on a relativistic particle crossing an inhomogeneous electromagnetic wave

The ponderomotive force acting on a relativistic charged particle crossing an inhomogeneous electromagnetic wave is investigated numerically and analytically. The initial velocity of the particle is perpendicular to the electric field vector of the wave and to the direction of its propagation. The wave has zero gradient in the direction of propagation and is inhomogeneous in both transverse directions. It is shown that the ponderomotive force acting on the particle is parallel to the wave vector. The magnitude of the force is determined not only by the extent of wave inhomogeneity in the direction of the translational motion of particle, but also by its inhomogeneity in the transverse direction. It is found that the trajectory of a particle is determined by the action of ponderomotive forces as well as by its drift in a nonuniform field.     

Behavior of a spin-1/2 massive charged particle in Schwarzschild immersed in an electromagnetic universe

The Dirac equation is considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic field. Due to the presence of electromagnetic field from the surroundings, the interaction with the spin-1/2 massive charged particle is considered. The equations of the spin-1/2 massive charged particle are separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular equations obtained are similar to the Schwarzschild geometry. For the radial equations we manage to obtain the one dimensional Schrödinger-type wave equations with effective potentials. Finally, we study the behavior of the potentials by plotting them as a function of radial distance and expose the effect of the external parameter, charge and the frequency of the particle on them.     

任意纵向磁场中等离子体-腔漂移通道电磁波的解析解

 从麦克斯韦方程和双成分等离子体粒子在外部轴向磁场的线性化运动方程出发，推导出了任意纵向磁场中等离子体介电张量和等离子体-腔漂移通道的电磁波的解析解。结果表明在一般情形下，在位于外部均匀纵向磁场的等离子体波导中，不存在分离的轴对称E波和H波。在此基础上进一步得到轴对称波的具体解析式。单波近似下的结果和俄罗斯全俄电技术研究所M.A.Zavjalov等的结果一致。     

带电粒子与静电波相互作用单粒子方程的严格解

研究了带电粒子与静电波之间的相互作用, 给出了带电粒子运动方程的严格解, 得出了粒子的速度的解析表达式, 同时推导出了带电粒子被静电波俘获的数学条件, 讨论了粒子与波能量交换的物理过程, 对现有等离子体物理的教材中相关的问题是一个补充. 本文结果对带电粒子加速器、微波管以及基础等离子体问题的研究有一定参考意义.     

Physical forces exerted by microbubbles on a surface in a traveling wave field

The effect of a wave with a varying traveling component on the bubble activity as well as the physical force generated by microbubbles on a surface has been studied. The acoustic emission from a collection of bubbles is measured in a 928 kHz sound field. Particle removal tests on a surface, which actually measures the applied physical force by the bubbles on that surface, indicate a very strong dependence on the angle of incidence. In other words, when the traveling wave component is maximized, the average physical force applied by microbubbles reaches a maximum. Almost complete particle removal for 78 nm silica particles was obtained for a traveling wave, while particle removal efficiency was reduced to only a few percent when a standing wave was applied. This increase in particle removal for a traveling wave is probably caused by a decrease in bubble trapping at nodes and antinodes in a standing wave field.     

An exact solution of the relativistic equation of motion of acharged particle driven by a circularly polarized electromagnetic waveand a constant magnetic field

An exact solution is found for the relativistic equation of motion of a charged particle driven by a circularly polarized electromagnetic wave and a constant magnetic field. The explicit expressions of particle position and velocity are obtained for certain initial conditions. The results are of interest to the interaction of the high-power laser with the magnetized plasma, electromagnetically pumped free-electron laser with a guide magnetic field, propagation of electromagnetic wave signals through a re-entry plasma sheath in the presence of a strong magnetic field, and magnetic confinement plasmas     

On the theory of the relativistic cross-sections for stimulated bremsstrahlung on an arbitrary electrostatic potential in the strong electromagnetic field

On the base of relativistic generalized eikonal approximation wave function the multiphoton cross-sections of a Dirac particle bremsstrahlung on an arbitrary electrostatic potential and strong laser radiation field are presented. In the limit of the Born approximation the ultimate analytical formulas for arbitrary polarization of electromagnetic wave have been obtained and numerically analyzed. Received 5 April 2001 / Received in final form 18 March 2002 Published online 28 June 2002     

Electrodynamics of a Scalar Particle in a Plane Electromagnetic Wave Field

In the present paper, compact expressions are derived for the probability of photon emission by a scalar particle and for the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field. Based on these general expressions, the amplitude of elastic scattering of a scalar particle and the amplitude of elastic scattering of a photon are derived by the method of dispersion relations (in the first-order approximation for the fine-structure constant ₀ = e ²/4). The real components of these amplitudes determine the radiative corrections for particle masses in the examined fields. Some particular cases of the plane wave field are examined. In particular, the above-indicated amplitudes in the external electromagnetic field being a superposition of a constant crossed field and a plane elliptically polarized electromagnetic wave propagating along the direction orthogonal to the magnetic and electric components of the constant crossed field are investigated. The amplitude of elastic scattering of a scalar particle in an arbitrary plane electromagnetic wave field is also obtained by direct calculations of the corresponding mass operator of the scalar particle in this field.     

Motion of a charged fermion with an anomalous magnetic moment in magnetized media

A quantization method based on the use of lowering and raising operators is developed and applied to describing states of Fermi particles that move under extreme external conditions (strong magnetic field and dense matter). The efficiency of this method is demonstrated by applying it to examples of finding exact solutions of quantum equations that describe the motion of charged particles in a magnetic field and dense matter. For the first time, the problem of charged-fermion motion in matter and an external magnetic field is formulated and solved with allowance for the anomalous magnetic moment of the particle. Exact solutions for the wave functions and energy spectrum of the respective modified Dirac equation are obtained. The application of these results to describing fermions and neutrinos is of special interest for astrophysical applications.