Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. II. Energetic Analysis of Certain Types of Monoenergetic Beam-Plasma Interactions Based on the Čerenkov Resonance Condition

The energy and momentum balance equations for a potential wave in a monoenergetic electron beam-plasma system are considered in the linear approximation, when the wave is in ?erenkov resonance with the beam particles. An energetic analysis of certain types of beam-plasma instabilities is given. It is shown that the energy and momentum balance equations are consistent with the dispersion relation for all unstable waves. From this fact follows that the energy and momentum densities of all linear unstable waves in reactive beam-plasma systems are equal to zero. An interpretation and a possible classification of beam-plasma instabilities are given.     

On the electromagnetic energy density and energy transfer rate in a medium with dispersion due to conduction

The simplest dispersion relation determined by dissipation due to conduction is considered; the electromagnetic energy density in a plane monochromatic wave and its (phase and group) velocity are determined, as well as the energy and momentum transfer rates. It is shown that the energy density at low frequencies in this case has the form of the electrostatic density, in which the permittivity is replaced by its real part, and the energy transfer rate in a plane electromagnetic wave is equal to the phase velocity. The group velocity may exceed the speed of light.     

电磁能量-动量转化和守恒定律四维形式的一种推导

定义了电磁场的四维动量流密度张量,并将电磁能量转化和守恒定律及动量转化和守恒定律写成了四维协变形式,给出了三维电磁能量密度、能流密度、动量密度和动量流密度关于两个惯性系之间的变换关系,还给出了四维动量流密度张量与四维电磁场张量之间的依赖关系。     

Energy–momentum tensor for the electromagnetic field in a dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy–momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Rather than construct a total momentum from the Abraham momentum or the Minkowski momentum, we define a thermodynamically closed system consisting of a propagating electromagnetic field and a negligibly reflecting dielectric and we identify the Gordon momentum as the conserved total momentum by the fact that it is invariant in time. In the formalism of classical continuum electrodynamics, the Gordon momentum is therefore the unique representation of the total momentum in terms of the macroscopic electromagnetic fields and the macroscopic refractive index that characterizes the material. We also construct continuity equations for the energy and the Gordon momentum, noting that a time variable transformation is necessary to write the continuity equations in terms of the densities of conserved quantities. Finally, we use the continuity equations and the time–coordinate transformation to construct an array that has the properties of a traceless, symmetric energy–momentum tensor.     

Division of the energy and of the momentum of electromagnetic waves in linear media into electromagnetic and material parts

We defend a natural division of the energy density, energy flux and momentum density of electromagnetic waves in linear media in electromagnetic and material parts. In this division, the electromagnetic part of these quantities have the same form as in vacuum when written in terms of the macroscopic electric and magnetic fields, the material momentum is calculated directly from the Lorentz force that acts on the charges of the medium, the material energy is the sum of the kinetic and potential energies of the charges of the medium and the material energy flux results from the interaction of the electric field with the magnetized medium. We present reasonable models for linear dispersive non-absorptive dielectric and magnetic media that agree with this division. We also argue that the electromagnetic momentum of our division can be associated with the electromagnetic relativistic momentum, inspired on the recent work of Barnett [Phys. Rev. Lett. 104 (2010) 070401] that showed that the Abraham momentum is associated with the kinetic momentum and the Minkowski momentum is associated with the canonical momentum.     

Mass change of dielectric media induced by propagation of electromagnetic waves

It has been experimentally confirmed that an electromagnetic wave carries momentum and thus exerts forces on dielectrics. Combining wave-particle duality with the theory of relativity, it was shown in the present work that the electromagnetic wave also increases the mass of the dielectric medium through which the incident wave propagates. The change in the mass density of the medium, or the mass density of the electromagnetic wave in the medium, was found to be proportional to the energy density of the incident wave. At an absolute temperature T, the mass density of the black body radiation was shown to be proportional to T⁴. “Weighing” the light wave in a glass fiber provides a novel technique to study the particle nature of electromagnetic waves in dielectric media.     

On the momentum of quasi-monochromatic waves in a plasma

The formulae for the momentum of quasi-monochromatic wave packets of transverse and longitudinal waves in a plasma without a magnetic field are derived including the terms of the second order in the amplitude of the electromagnetic field. The well-known increase of the momentum of the transverse wave penetrating into the plasma is given by the momentum (transported with the group velocity of the wave) of the averaged motion of the plasma. The laws of energy and momentum conservation lead simply to some results of the theory of the wave decay.Nademlýnská 600, Praha 9, Czechoslovakia.The authors thank K. Jungwirth for valuable discussions.     

Geometrical phase shift of the extrinsic orbital angular momentum density of light propagating in a helically wound optical fiber

We calculate the intrinsic spin and extrinsic orbital angular momentum densities of an electromagnetic plane wave propagating in a helically wound optical fiber. The geometrical phase shift of the extrinsic angular momentum density of light traveling in such a fiber is derived analytically and discussed in comparison with that of the intrinsic angular momentum density.     

Energy and angular momentum transfers from an electromagnetic wave to a copper ring in the UHF band

Electromagnetic waves could carry orbital angular momentum. Such momentum can be transferred to macroscopic objects and can make them rotate under a constant torque. Based on experimental observations, we investigate the origin of orbital angular momentum and energy transfer. Due to angular momentum and energy conservation, we show that angular momentum transfer is due to the change in the sign of angular momentum upon reflection. This leads to a rotational Doppler shift of the electromagnetic wave frequency, ensuring energy conservation.     

Decomposition of the total momentum in a linear dielectric into field and matter components

The long-standing resolution of the Abraham–Minkowski electromagnetic momentum controversy is predicated on a decomposition of the total momentum of a closed continuum electrodynamic system into separate field and matter components. Using a microscopic model of a simple linear dielectric, we derive Lagrangian equations of motion for the electric dipoles and show that the dielectric can be treated as a collection of stationary simple harmonic oscillators that are driven by the electric field and produce a polarization field in response. The macroscopic energy and momentum are defined in terms of the electric, magnetic, and polarization fields that travel through the dielectric together as a pulse of electromagnetic radiation. We conclude that both the macroscopic total energy and the macroscopic total momentum are entirely electromagnetic in nature for a simple linear dielectric in the absence of significant reflections.     

Exact equations for radiative transfer of energy and momentum in free electromagnetic fields

In a recent paper a new theory of radiative energy transfer in free electromagnetic fields was formulated. The basic quantities in this theory are the so-called angular components of the average electromagnetic energy density and of the average Poynting vector. In the present paper it is shown that these angular components obey differential equations that may be considered to be rigorous equations for the radiative transfer of energy and of momentum in free electromagnetic fields.     

Electromagnetic energy, momentum, and angular momentum in an inhomogeneous linear dielectric

In a previous work, Optics Communications 284 (2011) 2460-2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy-momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy-momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.     

时空非均匀等离子体鞘套中太赫兹波的传播特性

高超声速飞行器再入地面的过程中,其周围等离子体的电子密度是非均匀且随时间变化的.对于不同的再入高度,飞行器周围的温度和压强也会发生改变.因此,研究电磁波在时空非均匀等离子体鞘套中的传播特性意义重大.首先建立了时变非均匀的等离子体鞘套模型,然后通过经验公式得到温度、压强与碰撞频率三者的关系.采用时域有限差分方法计算了太赫兹波段中不同电子密度弛豫时间、温度、压强时的反射系数、透射系数和吸收率.研究结果表明:在太赫兹波段中,电子密度的弛豫时间越长,温度越高,压强越大,电磁波越容易穿透等离子体;弛豫时间越短,温度越低,压强越小,等离子体对电磁波吸收率的变化越明显.这些结果为解决"黑障"问题提供了理论依据.     

Momentum, radiation pressure, and other second-order quantities in ideal gas (liquid) in some boundary-value problems

Problems related to such properties of sound waves as momentum, radiation pressure, and sound energy density and flux are investigated on the basis of the solutions of particular problems in the first-and second-order approximations using the Eulerian representation. Specifically, it is shown that a disturbance propagating in a continuous medium may have a nonzero momentum when the average density of the medium in the volume occupied by the wave coincides with the density of the undisturbed medium. In this case, the momentum and the related mass transfer and radiation pressure are caused by variations in the wave profile (envelope). Andreev’s expression for the energy density that differs from the commonly used one is verified, and some other paradoxical consequences of the theory of sound are considered. The correctness of using the quantities averaged over time and space is discussed.     

Ku/K波段双频涡旋电磁阵列天线设计

涡旋电磁波具有携带轨道角动量的特性,利用这一特性,采用涡旋电磁波作为信号的载体,可以实现同一时间、同一频段的多路信号传输,极大地提高系统容量和频带利用率。以同轴馈电的半圆型开槽微带天线为单元,设计出了一种能工作在Ku波段和K波段的涡旋电磁阵列天线。使用三维电磁场仿真软件建模并且优化参数,最终得到在中心频率分别为17.1 GHz和19.7 GHz时,阵列天线产生的电磁波携带有轨道角动量。结论表明:该阵列天线能够产生双频涡旋电磁波。     

Zur Thermodynamik des elektromagnetischen Feldes in der kontinuierlichen Materie

The following questions are discussed. Does the electromagnetic field energy add to the internal energy or to the free energy? What are density of momentum and flow of energy in the presence of an electromagnetic field? How is the electromagnetic force density to be formulated in the best way? With respect to the first question, various thermostatic potentials are considered. The other questions find an answer from a relativistic formulation of the equations of motion. In particular it is shown that the various definitions of the pressure which arise from the manifold of thermostatic potentials and which lead to different expressions for the electromagnetic force density are irrelevant if, instead, one uses the gradients of the unambiguous chemical potential and of the temperature, multiplied by the entropy density, as parts of the total force density.     

Nonlinear Theory of the Plasma Wave Excitation in a Bounded Beam-Plasma System

The excitation of symmetric and antisymmetric plasma waves by a beam layer that moves within a homogeneous plasma enclosed by a metallic wall was dealt with theoretically. Investigations were carried out for the magnetic field free case and for a magnetized electron beam. In the latter case, the beam electrons are assumed to be unable to move in the perpendicular direction. The theoretical model bases upon an extension of the well known single wave theory to a two-dimensional beam-plasma system. Special emphasis should be paid to the fact that the perpendicular wave profile of the excited waves was determined self-consistently. Energy and momentum balance equations are derived for this system. The theoretical method outlined in this paper which is based on a Green's-function technique can be extended easily to three-dimensional systems or to beam-plasma systems with other boundary conditions. The main features of the saturation process of the basic unstable wave types are discussed. Several interesting effects were found in the magnetic field free case: (i) numerical solutions describe an increasing steepening of the wave amplitudes in perpendicular direction near the center of the system for the symmetric potential wave; (ii) for the antisymmetric wave, a smoothing tendency was found in the development of the perpendicular wave potential profile; (iii) spatial separation of the slow and fast beam electrons was observed; (iv) it is shown for the antisymmetric potential wave type that, under certain conditions, a very efficient beam particle retardation mechanism occurs which is connected with a strong reduction of the formation of a fast particle group; (v) generally it was shown that the conversion of the kinetic energy of the beam electrons into the plasma wave energy may be more effective as compared with the case of the magnetized beam.     

Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave

We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.     

Hamiltonian Structure for Dispersive and Dissipative Dynamical Systems

We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary fields, in the universal form of a so-called canonical heat bath. After integrating out the heat bath the original dissipative evolution is exactly reproduced. Furthermore, we show that the dynamics associated to a minimal Hamiltonian are essentially unique, up to a natural class of isomorphisms. Using this formalism, we obtain closed form expressions for the energy density, energy flux, momentum density, and stress tensor involving the auxiliary fields, from which we derive an approximate, “Brillouin-type,” formula for the time averaged energy density and stress tensor associated to an almost mono-chromatic wave.     

Two-Level Atom in a Standing, Electromagnetic Wave

We study a two-level atom interacting with a standing electromagnetic wave, and work out the wave functions, the energy values and the momentum values of the atom.