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)     

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.     

On the theory of the relativistic motion of a charged particle in the field of intense electromagnetic radiation

Averaged relativistic equations of motion of a charged particle in the field of intense electromagnetic radiation have been obtained in the geometrical optics approximation using the Bogoliubov method. Constraints are determined under which these equations are valid. Oscillating additions to the smoothed dynamical variables of the particle have been found; they are reduced to known expressions in the case of the circularly and linearly polarized plane waves. It has been shown that the expressions for the averaged relativistic force in both cases contain new additional small terms weakening its action. The known difference between the expressions for the ponderomotive force in the cases of circularly and linearly polarized waves has been confirmed.     

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     

Cartesian Ovals as Phase Trajectories of Relativistic Charged Particles

For a relativistic charged particle interacting with a circularly polarized stationary electromagnetic wave running along a uniform magnetostatic field, it is shown that the plane on which the set of trajectories of the particle coincides with a set of Cartesian ovals can serve as a phase space, provided that certain conditions are fulfilled. The cases of both decelerated and accelerated waves are investigated, and the results obtained confirm the statement that the mentioned plane is the most natural phase surface for a particle in the system of fields under consideration.     

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.     

The exact solution of the relativistic equation of motion of acharged particle driven by an elliptically polarized electromagneticwave

An exact solution of the relativistic equation of motion of a charged particle driven by an elliptically polarized electromagnetic wave is obtained. The method used for this purpose is simple, and the results of earlier authors for the linearly and circularly polarized waves can be recovered as special cases of the solution     

Asymptotic analysis of ultra-relativistic charge

This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneous linear equations for the self-consistent Maxwell field, charge current and time-like velocity field of the charged fluid and is defined as an ultra-relativistic configuration. To facilitate comparisons with existing accounts of beam dynamics an appendix translates the tensor formulation of the perturbation scheme into the language involving electric and magnetic fields observed in a laboratory (inertial) frame.     

Particle Creation in the Effective Action Method

The effect of particle creation by nonstationary external fields is considered as a radiation effect in the expectation-value spacetime. The energy of created massless particles is calculated as the vacuum contribution in the energy-momentum tensor of the expectation value of the metric. The calculation is carried out for an arbitrary quantum field coupled to all external fields entering the general second-order equation. The result is obtained as a functional of the external fields. The paper gives a systematic derivation of this result on the basis of the nonlocal effective action. Although the derivation is quite involved and touches on many aspects of the theory, the result itself is remarkably simple. It brings the quantum problem of particle creation to the level of complexity of the classical radiation problem. For external fields like the electromagnetic or gravitational field there appears a quantity, the radiation moment, that governs both the classical radiation of waves and the quantum particle production. The vacuum radiation of an electrically charged source is considered as an example. The research is aimed at the problem of backreaction of the vacuum radiation.     

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.     

Phase structure of the Nambu-Jona-Lasinio model in a constant electromagnetic field in d-dimensional curved spacetime

Dynamical symmetry breaking in the Nambu-Jona-Lasinio model in a constant external electromagnetic field is studied in curved spacetime of arbitrary dimension. The effective potential of composite bifermion fields is calculated in the proper-time formalism to terms linear in curvature. Curvature-and electromagnetic-field-induced phase transitions are analyzed.     

Amplitude characteristic of cyclotron resonance

The motion of a charged particle under the combined action of a magnetostatic field and a circularly polarized electromagnetic wave of phase velocity u higher than c, the wave being aligned with the field, is studied theoretically. A nonlinear resonance curve is found. Certain integrals of motion are derived.     

About the linewidth of cyclotron resonance in band-gap graphene

The critical amplitude of circularly polarized electromagnetic wave when the hysteresis of cyclotron absorption takes place, was found for band-gap graphene. The dependence of critical amplitude on the gap value and on the relaxation time was investigated. The conditions of applicability of linear theory describing the electromagnetic response of band-gap graphene in a non-zero magnetic field were found. The power of the circularly polarized electromagnetic radiation absorbed by band-gap graphene in the presence of a magnetic field was calculated. The linewidth of cyclotron absorption was shown to be not zero even for pure band-gap graphene.     

High intensity Compton scattering in a strong plane-wave field of general form

Photon emission by an electron embedded in a strong external field of general form is studied theoretically. The external field considered is a plane-wave electromagnetic field of any number of components, period and polarisation. Exact, Volkov solutions of the Dirac equation with the 4-potential of the general external field are obtained. The photon emission is considered in the usual perturbation theory using the Volkov solutions to represent the electron. An expression for the transition probability of this process is obtained after the usual spin and polarisation sums, trace calculation and phase space integration. The final transition probability in the general case contains a single sum over contributions from external field photons, an integration over one of the phase space components and the Fourier transforms of the Volkov phases. The validity of the general expression is established by considering specific external fields. Known specific analytic forms of the transition probability are obtained after substitution of the 4-potential for a circularly polarised and constant crossed external field. As an example usage of the general result for the transition probability, the case of two circularly polarised external fields separated by a phase difference is studied both analytically and numerically.     

Dynamic Hall effect driven by circularly polarized light in a graphene layer

We report the observation of the circular ac Hall effect where the current is solely driven by the crossed ac electric and magnetic fields of circularly polarized radiation. Illuminating an unbiased monolayer sheet of graphene with circularly polarized terahertz radiation at room temperature generates--under oblique incidence--an electric current perpendicular to the plane of incidence, whose sign is reversed by switching the radiation helicity. Alike the classical dc Hall effect, the voltage is caused by crossed E and B fields which are, however rotating with the light's frequency.     

Superluminal spectral densities of ultra-relativistic electrons in intense electromagnetic wave fields

Superluminal radiation from electrons accelerated in electromagnetic waves is investigated. The radiation field is a Proca field with negative mass-square, minimally coupled to the electron current. The spectrum is continuous in the ultra-relativistic regime, where steepest-descent asymptotics can be used to evaluate the power coefficients. The time averaging of Lissajous orbits in polarized wave fields is discussed, and the tachyonic spectral densities of electrons orbiting in intense laser beams are derived. In the ultra-relativistic limit, realized by high injection energy or high field intensity, the spectral functions are evaluated in closed form in terms of Airy integrals. In contrast to electromagnetic radiation, there is a longitudinal polarization component, and oscillations emerge at high beam intensity in the longitudinal and transversal spectral slopes, generated by the negative mass-square of the tachyonic quanta. The thermal ultra-relativistic electron plasma of two active galactic nuclei is analyzed in this regard, based on TeV spectral maps obtained with imaging air Cherenkov detectors. Specifically, tachyonic cascade fits are performed to γ-ray flares of the TeV blazars RGB J0152+017 and 3C 66A, and the transversal and longitudinal radiation components are disentangled in the spectral maps. The curvature of the spectral slopes is shown to be intrinsic, caused by the Boltzmann factor of the electronic source plasma radiating the tachyonic cascades.     

Interaction of electromagnetic waves with anisotropic collisional plasma half space

Interaction of electromagnetic waves penetrating into anisotropic semi-infinite collisional plasma embedded in a uniform external magnetic field is studied using half range Fourier transforms. General field equations are developed for fractionally accommodating boundary and a particular case of specular reflection is discussed both for right handed as well as left handed circularly polarized modes. Anisotropy effects are found to be more prominent in the continuum mode of field component. Anisotropy as well as collisions make the field to attain a constant value at a shorter distance. Left handed polarized modes are found to be more penetrating than right handed modes. Surface impedance is calculated and effects of collisions as well as anisotropy are discussed.     

Analysis of FEL radiation in pulsed raman regime

Summary A direct numerical analysis, based on the Lienard-Wiechert potentials, is performed in the present paper, aiming to describe the relativistic interaction of the electrons composing a high-intensity beam (in Raman regime) both with each other and with the fields of an FEL structure and of an external resonant travelling electromagnetic wave. The different accelerations, due to the various forces acting on the charged particles, are seen to give different contributions to the total radiation field, which are separately considered here. The angular and frequency distributions of the obtained radiation are compared with the analytic ones deduced in the particular case of a single charge launched along the FEL structure. The interference effect between the fields of many bunches is seen to cause the shrinkage of the resulting radiation beam.     

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.