Generalization of the Larmor radiation formula

The Larmor radiation formula relates the momentum radiated toward infinity along a light cone from a single point charge to the velocity and acceleration of the particle. The formula applies only to a light cone whose apex is on the world line of the particle. This paper generalizes the Larmor formula to an arbitrary light cone. An example involving circular motion is worked.     

Comment on “Exact Expression for Radiation of an Accelerated Charge in Classical Electrodynamics”

It is shown that a newly derived “exact expression” for radiation of an accelerated charge in the recent literature is simply incorrect, having arisen because of a wrong relativistic transformation of the distance parameter. The ensuing claim that the newly derived expression alone satisfies the energy conservation for the electromagnetic radiation, is based on a wrong reasoning where a proper distinction between the time during which the radiation is received and the time for emission (retarded time of the charge) was not maintained.     

Self-force of a charge in a real current

The analysis of the EM radiation from a single charge shows that the radiated power depends on the retarded acceleration of the charge. Therefore for consistency, an accelerated charge, free from the influence of external forces, should gradually lose its acceleration, until its total energy is radiated. Calculations show that the self force of a charge, which compensates for its radiation, is proportional to the derivative of the acceleration. However, when using this self force in the equation of motion of the charge, one gets a diverging solution, for which the acceleration runs away to infinity. This means that there is an inconsistency in the solution of the single charge problem. However, in the construction of the conserved Maxwell charge density, there is implicitly an integral over the corresponding world line which corresponds to a collection of charged spacetime events. One may therefore consistently think of the “self force” as the force on a charge due to another charge at the retarded position. From this point of view, the energy is evidently conserved and the radiation process appears as an absorbing resistance to the feeding source. The purpose of this work is to learn about the behavior of single charges from the behavior of a real current, corresponding to the set of charges moving on a world line, and to study the analog of the self force of a charge associated with the radiation resistance of a continuum of charges.     

Characteristic Length in a Linear Acceleration

The role of the characteristic length that characterizes linear acceleration is studied, in order to find how does this length determine the characteristic wavelength of the radiation created by the accelerated charge. Unruh equation for the temperature observed by a detector accelerated relative to the vacuum is used to determine the wavelength distribution of the radiation emitted by a linearly accelerated charge, and it is found that this distribution is peaked close to the characteristic length that characterizes the linear acceleration, which is the radius of curvature of the curved electric field created by the acelerated charge. PACS numbers: 11.10; 41.60.m.     

Equation of Motion of an Electric Charge

The appearance of the time derivative of the acceleration in the equation of motion (EOM) of an electric charge is studied. It is shown that when an electric charge is accelerated, a stress force exists in the curved electric field of the accelerated charge, and in the case of a constant linear acceleration, this force is proportional to the acceleration. This stress force acts as a reaction force which is responsible for the creation of the radiation (instead of the radiation reaction force that actually does not exist at low velocities). Thus the initial acceleration should be supplied as an initial condition for the solution of the EOM of an electric charge.     

Quantum Vacuum Radiation and Detection Proposals

We first review the 20-year-old results of Letaw on stationary vacuum radiation patterns originating from world lines defined as Frenet–Serret curves. The corresponding body of literature as well as the experimental proposals that have been suggested to detect quantum vacuum field radiation patterns, are shortly presented and some related topics, such as the anomalous Doppler effect and the decay of accelerated protons are also included.     

Electromagnetic Fields of Non-Equilibrium Plasmas

A statistical treatment of the electromagnetic fields of a fully ionized plasma shows that there are two types of radiation. One of the radiation fields is determined by the time change of the distribution function and is characteristic of such plasmas. When the time change is due to the many-body couplings of the charges in the plasma, the radiation can be related to the nonequilibrium stress tensor. In particular, for large distances the radiation is determined by the total internal pressure in a way similar to the classical Larmor formula for a point charge.     

Correlation phenomena in the Cherenkov radiation of accelerated multiply charged ions

Correlation phenomena occurring in Cherenkov radiation are considered which are related to fluctuations of the charge states of multiply charged accelerated ions in a medium. The additional correlation contribution to the radiation is determined by the root-mean-square deviation of the ion charge from its equilibrium value and is responsible for the nonzero radiation yield in the event that the threshold condition is not fulfilled. Numerical estimates of the radiation yield of heavy ions in the optical and X-ray frequency ranges are given. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 41–46, January, 2009.     

A Coaccelerated Observer

We analyze the situation of an observer coaccelerated relative to a linearly accelerated charge, in order to find whether he can observe the radiation emitted from the accelerated charge. It is found that the seemingly special situation of the coaccelerated observer relative to any other observer, is deduced from a wrong use of the retarded coordinate system, when such a system is inadmissible. It is also found that the coaccelerated observer has no special position other than any other observer, and hence, he can observe any physical events as any other observer.     

Electrodynamics of hyperbolically accelerated charges V. The field of a charge in the Rindler space and the Milne space

We describe the electromagnetic field of a uniformly accelerated charge in its co-moving Rindler frame. It is shown that the electrical field lines coincide with the trajectories of photons. The self force of a charged particle at rest in Rindler space, and the increase of its weight due to its charge, is calculated. The general case of an accelerated charge in Rindler space is also considered. It is shown that the electrical field inside a uniformly charged spherical shell can be used as a measure of it 4-acceleration. A result that has earlier been deduced in a different way by Fugmann and Kretzschmar is confirmed, namely that the intensity of radiation from a point charge instantaneously at rest in an accelerated frame is proportional to the square of the relative acceleration of the charge and the observer. In particular it is shown that a freely falling charge in Rindler space radiates in accordance with Larmor’s formula. In this case the radiation energy is taken from the Schott energy. The energy of the electromagnetic field is analysed from the point of view of the Hirayama-separation, which generalizes the Teitelboim-separation to non-inertial frames, of the field in a bound part and an unbound part. A detailed account, with reference to the Rindler frame, of the field energy and particle energy is given for the case of a charge entering and leaving a region with hyperbolic motion. We also consider the electromagnetic field of a uniformly accelerated charge with reference to the Milne frame, which covers a different part of spacetime than the Rindler frame. The radiating part of the electromagnetic field is found in the Milne sector of spacetime.     

Electrodynamics in accelerated frames revisited

Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space‐time. We assume the existence of a general distribution of charges and currents in an inertial frame. Tetrad fields are used to project the electromagnetic fields and sources on accelerated frames. The purpose is to study several configurations of fields and observers that in the literature are understood as paradoxes. For instance, are the two situations, (i) an accelerated charge in an inertial frame, and (ii) a charge at rest in an inertial frame described from the perspective of an accelerated frame, physically equivalent? Is the electromagnetic radiation the same in both frames? Normally in the analysis of these paradoxes the electromagnetic fields are transformed to (uniformly) accelerated frames by means of a coordinate transformation of the Faraday tensor. In the present approach coordinate and frame transformations are disentangled, and the electromagnetic field in the accelerated frame is obtained through a frame (local Lorentz) transformation. Consequently the fields in the inertial and accelerated frames are described in the same coordinate system. This feature allows the investigation of paradoxes such as the one mentioned above.     

On the Energy Radiation from an Accelerated Charge

In the framework of classical electromagnetism, a charge however accelerated with respect to an inertial frame radiates energy, in any circumstance. Regarding the energy as made of photons, the hypothesis is here introduced that the emission of a photon is only possible as a result of a change of the energy of the charge, which requires an energy-work exchange with the accelerating field. On such an hypothesis an elementary impulsive-dissipative model for the photon emission is constructed, in the framework of special relativity, in which no energy radiation is emitted from a charge in a central Coulomb field uniformly describing a circular orbit.     

Improved calculation of the radiation power of a charged particle undergoing hyperbolic motion

Within classical electrodynamics, exact formulas for calculating the radiation loss of the energy of a point charge undergoing hyperbolic motion, including the relativistic region, are proposed. For an ultrarelativistic particle, the improved radiation loss factor \(\frac{4}{5}\) γ ² · e ² · a ² was obtained instead of the commonly used Larmor quantity \(\frac{2}{3}\) γ ² · e ² · a ².     

Force approach to radiation reaction

The difficulty of the usual approach to deal with the radiation reaction is pointed out, and under the condition that the radiation force must be a function of the external force and is zero whenever the external force be zero, a new and straightforward approach to radiation reaction force and damping is proposed. Starting from the Larmor formula for the power radiated by an accelerated charged particle, written in terms of the applied force instead of the acceleration, an expression for the radiation force is established in general, and applied to the examples for the linear and circular motion of a charged particle. This expression is quadratic in the magnitude of the applied force, inversely proportional to the speed of the charged particle, and directed opposite to the velocity vector. This force approach may contribute to the solution of the very old problem of incorporating the radiation reaction to the motion of the charged particles, and future experiments may tell us whether or not this approach point is in the right direction.     

Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect

We present a stochastic theory for the nonequilibriurn dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We summarize (1) the steps leading to a derivation of a modified Abraham-Lorentz-Dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre-acceleration patholigies, and (2) the transformation to a stochastic effective action, which generates Abraham-Lorentz-Dirac-Langevin equations depicting the fluctuations of a particle’s worldline around its semiclassical trajectory. We point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations, and discuss how, in the framework that we have developed, an array of phenomena, from classical radiation and radiation reaction to the Unruh effect, are interrelated to each other as manifestations at the classical, stochastic and quantum levels. Using this method we give a derivation of the Unruh effect for the spacetime worldline coordinates of an accelerating charge. Our stochastic particle-field model, which was inspired by earlier work in cosmological backreaction, can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon.     

Acceleration and classical electromagnetic radiation

Classical radiation from an accelerated charge is reviewed along with the reciprocal topic of accelerated observers detecting radiation from a static charge. This review commemerates Bahram Mashhoon’s 60th birthday.     

<Emphasis Type="Italic">SO</Emphasis>(3,1)-Invariant Approach to Dipole Radiation

The aim of the present work is to revisit the theory of the dipole radiation, within an SO(3,1)-gauge invariant formulation, by solving the Maxwell equations. Thus, we obtain the two interconnected components, A _B , B=1,2, of the vector potential A, in terms of Hankel and Legendre polynomials. Finally, for the pure dipole-like radiation, the observables, regarded as phasors, the Umov–Poynting vector components and the well-known Larmor formula for the effective radiated power are explicitly derived.     

Radiation from electrons in graphene in strong electric field

We study the interaction of electrons in graphene with the quantized electromagnetic field in the presence of an applied uniform electric field using the Dirac model of graphene. Electronic states are represented by exact solutions of the Dirac equation in the electric background, and amplitudes of first-order Feynman diagrams describing the interaction with the photon field are calculated for massive Dirac particles in both valleys. Photon emission probabilities from a single electron and from a many-electron system at the charge neutrality point are derived, including the angular and frequency dependence, and several limiting cases are analyzed. The pattern of photon emission at the Dirac point in a strong field is determined by an interplay between the nonperturbative creation of electron–hole pairs and spontaneous emission, allowing for the possibility of observing the Schwinger effect in measurements of the radiation emitted by pristine graphene under DC voltage.     

金属-氧化物-半导体场效应管辐射效应模型研究

基于氧化层陷阱电荷以及界面陷阱电荷的产生动力学以及辐射应力损伤的微观机理,推导出了金属-氧化物-半导体场效应管(MOSFET)中辐射应力引起的氧化层陷阱电荷、界面陷阱电荷导致的阈值电压漂移量与辐射剂量之间定量关系的模型. 根据模型可以得到:低剂量情况下,氧化层陷阱电荷与界面陷阱电荷导致的阈值电压漂移量与辐射剂量成正比;高剂量情况下,氧化层陷阱电荷导致的阈值电压漂移量发生饱和, 其峰值与辐射剂量无关,界面陷阱电荷导致的阈值电压漂移量与辐射剂量呈指数关系. 另外,模型还表明氧化层陷阱电荷与界面陷阱电荷在不同的辐射剂量点开始产生饱和现象, 其中界面陷阱电荷先于氧化层陷阱电荷产生饱和现象.最后,用实验验证了该模型的正确性. 该模型可以较为准确地预测辐射应力作用下MOSFET的退化情况.     

Radiation from a Uniformly Accelerated Charge

The emission of radiation by a uniformly accelerated charge is analyzed. According to the standard approach, a radiation is observed whenever there is a relative acceleration between the charge and the observer. Analyzing difficulties that arose in the standard approach, we propose that a radiation is created whenever a relative acceleration between the charge and its own electric field exists. The electric field induced by a charge accelerated by an external (nongravitational) force is not accelerated with the charge. Hence the electric field is curved in the instantaneous rest frame of the accelerated charge. This curvature gives rise to a stress force, and the work done to overcome the stress force is the source of the energy carried by the radiation. In this way, the energy balance paradox finds its solution.