Lorentz Abraham Dirac Research Articles

CGHS Black Hole Analog Moving Mirror and Its Relativistic Quantum Information as Radiation Reaction.

The Callan–Giddings–Harvey–Strominger black hole has a spectrum and temperature that correspond to an accelerated reflecting boundary condition in flat spacetime. The beta coefficients are identical to a moving mirror model, where the acceleration is exponential in laboratory time. The center of the black hole is modeled by the perfectly reflecting regularity condition that red-shifts the field modes, which is the source of the particle creation. In addition to computing the energy flux, we find the corresponding moving mirror parameter associated with the black hole mass and the cosmological constant in the gravitational analog system. Generalized to any mirror trajectory, we derive the self-force (Lorentz–Abraham–Dirac), consistently, expressing it and the Larmor power in connection with entanglement entropy, inviting an interpretation of acceleration radiation in terms of information flow. The mirror self-force and radiative power are applied to the particular CGHS black hole analog moving mirror, which reveals the physics of information at the horizon during asymptotic approach to thermal equilibrium.

Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam

Beginning with a critical examination of the Lorentz-Abraham (LA) classical equation of motion for an extended charge and the closely related Lorentz-Abraham-Dirac (LAD) equation of motion for a mass-renormalized point-charge, the Landau-Lifshitz (LL) approximate solution to the LAD equation of motion is determined for an electron subject to a counterpropagating linearly or circularly polarized plane-wave pulse with an arbitrarily shaped envelope. A convenient three-vector formulation of the LL equation is used to derive closed-form expressions for the velocities and associated powers of the electron directly in terms of the time in the laboratory frame. The three-vector formulation also reveals definitive criteria for the LL solution to be an accurate approximation to the LAD equation of motion and for the LL solution to reduce to the solution of the Lorentz force equation of motion that ignores radiation reaction. Semiclassical analyses are used to obtain simple conditions for determining the regimes where the quantum effects of either Compton electron scattering by the incident photons or electron recoil produced by the emitted photons is significant. It is proven that the LL approximation becomes an inaccurate solution to the LAD equation of motion only for large enough electron velocities and plane-wave intensities that quantum recoil effects on the electron can greatly alter the classical solution. Comparisons are made with previously published analytical and numerical solutions to the LL equation of motion for the velocity of an electron in a counterpropagating plane wave.10 MoreReceived 18 August 2021Accepted 1 November 2021DOI:https://doi.org/10.1103/PhysRevAccelBeams.24.114002Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectromagnetismElectron beams & opticsLaser driven electron accelerationQuantum theorySingle-particle dynamicsAccelerators & BeamsGeneral PhysicsParticles & FieldsNonlinear DynamicsCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Laser-driven radiation-reaction effect and polarized particle acceleration

<sec>Laser-plasma interaction at intensities beyond 10<sup>22</sup> W/cm<sup>2</sup> enters a new regime where gamma-photon emission and the induced radiation-reaction effect dominate. In extreme laser fields, high energy electrons emit gamma-photons efficiently, which take considerable portion of energy away and impose strong reaction forces on radiating electrons. When the radiation power is comparable to the electron energy gained in a certain period of time, the radiation-reaction (RR) effect becomes significant, which fundamentally changes the picture of laser-plasma interaction. In this review article, we introduce the physics of radiation-reaction force, including both classical description and quantum description. The effects of stochastic emission and particle spins in the quantum-electrodynamics (QED) RR process are discussed. We summarize the RR-induced phenomena in laser-plasma interaction and some proposed measurements of RR. As a supplement, we also introduce the latest progress of producing spin polarized particles based on laser-plasma accelerations, which provides polarized beam sources for verifying the QED-RR effects.</sec><sec>In the classical picture, the RR force can be described by the Landau-Lifshitz (LL) equation, which eliminates the non-physical run-away solution from the Lorentz-Abraham-Dirac (LAD) equation. The damping force could induce the electron trajectories to instantaneously reverse, electrons to cool and even high energy electrons to be reflected by laser pulses. The latter leads to a “potential barrier” at a certain threshold that prevents the electrons of arbitrarily high energy from penetrating the laser field. In general, classical LL equation overestimates the RR effect, thus calling for more accurate quantum description.</sec><sec>When the emitted photon energy is close to the electron energy, radiation becomes discrete. Quantum effects arise such that the process, also known as nonlinear multi-photon Compton Scattering, must be considered in the strong-field QED picture. This is resolved in the Furry picture by using the laser-dressed Volkov state in the local constant cross-field approximation (LCFA). The QED model is applied to particle dynamics via Monte-Carlo (MC) sampling. We introduce the prominent feature of quantum RR-stochastic photon emission. It allows the processes forbidden in classical picture to emerge, such as quantum ‘quenching’, quantum ‘reflection’, etc. These observables validate the strong-field QED theory. Recently, there has been a rising interest in identifying the spin effect in the QED-RR force. We summarize the latest progress of this topic, showing that when spins are coupled with photon emission the electrons of different spin states undergo distinctive RR force. </sec><sec>The RR force has a significant effect on laser-plasma interaction. The review paper introduces recent QED-MC based PIC simulation results. Some key features include electron cooling in laser-driven radiation pressure acceleration and the radiation-reaction trapping (RRT) mechanism. In the RRT regime the laser pulse conveys over 10% of its energy to gamma-photons, facilitating the creation of a highly efficient gamma-ray source and electron-positron pair. In addition, the paper mentions the major efforts to measure the RR effect in recent years. It relies on high energy electrons either colliding with ultra-intense laser pulses or traversing crystals. Primitive observations indicate that existing theories do not match experimental results. Further investigation is required in both SF-QED theory and experiment.</sec><sec>Finally, the review paper discusses the idea of laser-driven polarized particle acceleration as a supplement. The all-optical approach integrates pre-polarized gas target into laser wakefield acceleration, offering a compact all-optical polarized particle source, which is highly favorable for strong-field QED studies, high-energy colliders and material science.</sec>

Stationary solutions of equations of motion for a radiating charged particle including a radiation reaction effect.

For a radiating charged particle, the radiation reaction force plays an important role in determining its motion. Several formulas have been proposed to describe the radiation reaction force. Stationary solutions of the Lorentz-Abraham-Dirac (LAD), Mo-Papas, Landau-Lifshitz, and Ford-O'Connell equations are obtained and compared for a charged particle under a static magnetic and a rotating electric field. The behaviors of the obtained solutions look quite similar. The relative differences of the Lorentz factor, calculating the values using the LAD equation compared to the other equations, are evaluated; these values are shown to be less than 10^{-6} in the regime where classical radiation reactions are applicable.

On the Schott Term in the Lorentz-Abraham-Dirac Equation

The equation of motion for a radiating charged particle is known as the Lorentz–Abraham–Dirac (LAD) equation. The radiation reaction force in the LAD equation contains a third time-derivative term, called the Schott term, which leads to a runaway solution and a pre-acceleration solution. Since the Schott energy is the field energy confined to an area close to the particle and reversibly exchanged between particle and fields, the question of how it affects particle motion is of interest. In here we have obtained solutions for the LAD equation with and without the Schott term, and have compared them quantitatively. We have shown that the relative difference between the two solutions is quite small in the classical radiation reaction dominated regime.

A comparison of the bremsstrahlung cross section in two frameworks: classical Lorentz–Abraham–Dirac dynamics and quantum field theory

In classical electromagnetic theory, the Lorentz–Abraham–Dirac (LAD) equation describes the dynamics of a charged particle, including radiation reaction. Though the LAD equation is derived from Maxwell’s equations, consistent with the conservation of energy and momentum, it admits unphysical solutions for point-like charged particles. By assuming small radiative effects, Landau and Lifshitz (LL) develop an approximation of the LAD equation that has no pathological solutions. Though the LL approximation is dynamically sound, it is the LAD equation that has firm theoretical underpinning. As such, the difficulties encountered in LAD dynamics suggest, in part, that an electrodynamic treatment of point-like particles lies outside the classical domain. Herein, we compute the cross section of a charged particle scattered by an attractive Coulombic potential using classical LAD and LL dynamics. We then compare this with the analogous cross section in quantum field theory (QFT). In particular, we compute the cross section for a charged scalar particle incident upon another extremely massive charged scalar with a single photon in the final state. We include the following -radiative corrections: scalar-photon vertex correction, infrared photon emission, vacuum polarization, and two-photon exchange. We find that the classical and quantum frameworks do not produce similar cross sections. Relative to the elastic cross section, the classical bremsstrahlung cross section vastly overestimates the relative QFT cross section; this is, in part, due to the fact that the additional radiative corrections in QFT do not have a classical analog in either the LAD or LL framework.

Radiation reaction of classical hyperbolic oscillator: Experimental signatures

When accelerated by a constant force in the lab frame, a classical charge experiences no self force. In this case, the particle radiates without dissipating its kinetic and potential energy. But what happens when the particle enters another region with equal and opposite acceleration? Does the oscillating charge lose its mechanical energy similar to a radiating dipole, even though it seems to lose no mechanical energy within each region of constant acceleration? In this paper, I will show how mechanical energy is transferred to radiation energy via the Schott energy when the particle crosses the boundary between the two regions. In particular, I will show how preacceleration, which is usually regarded as an unphysical effect of the Lorentz–Abraham–Dirac self force, is essential for the energy transfer. Moreover, I will show that the commonly adopted Landau–Lifshitz approximation, which removes preacceleration, introduces second-order secular energy error. On a more fundamental level, the validity of classical electrodynamics is in fact questionable because quantum effects are likely important. The classical prediction can be tested experimentally by observing frequency chirping of radiation, whereby micro physics leaves signatures on macroscopic scales. The required experimental accuracy is estimated. Trap experiments of this type is complementary to collider experiments that endeavor to observe radiation reaction for elementary particles.

Erratum to: “Renormalization of the Lorentz–Abraham–Dirac equation for radiation reaction force in classical electrodynamics”

Erratum to: “Renormalization of the Lorentz–Abraham–Dirac equation for radiation reaction force in classical electrodynamics”

Critical remarks on Sokolov's equation of the dynamics of a radiating electron

In the article by Sokolov [J. Exp. Theor. Phys. 109(2), 207 (2009)], the so-called renormalization of the Lorentz-Abraham-Dirac (LAD) equation was proposed. The latter describes the motion of an electron in the electromagnetic field in consideration of the radiation reaction. In many articles of Sokolov and his colleagues, this model is promoted as more appropriate one when an electron is under the effect of a super-strong laser field. In this article, it is shown that such assertions are baseless and the physical importance of this model is vastly overestimated. Sokolov's equation suffers from numerous drawbacks arising from the fact that it represents not modified but distorted LAD. In particular, superluminal paradoxes arise in the framework of this model.

Explicit mass renormalization and consistent derivation of radiative response of classical electron

The radiative response of the classical electron is commonly described by the Lorentz–Abraham–Dirac (LAD) equation. Dirac’s derivation of this equation is based on energy and momentum conservation laws and on regularization of the field singularities and infinite energies of the point charge by subtraction of certain quantities: “We... shall try to get over difficulties associated with the infinite energy of the process by a process of direct omission or subtraction of unwanted terms”. To substantiate Dirac’s approach and clarify the mass renormalization, we introduce the point charge as a limit of extended charges contracting to a point; the fulfillment of conservation laws follows from the relativistic covariant Lagrangian formulation of the problem. We derive the relativistic point charge dynamics described by the LAD equation from the extended charge dynamics in a localization limit by a method which can be viewed as a refinement of Dirac’s approach in the spirit of Ehrenfest theorem. The model exhibits the mass renormalization as the cancellation of Coulomb energy with the Poincaré cohesive energy. The value of the renormalized mass is not postulated as an arbitrary constant, but is explicitly calculated. The analysis demonstrates that the local energy–momentum conservation laws yield dynamics of a point charge which involves three constants: mass, charge and radiative response coefficient θ. The value of θ depends on the composition of the adjacent potential which generates Poincaré forces. The classical value of the radiative response coefficient is singled out by the global requirement that the adjacent potential does not affect the radiated energy balance and affects only the local energy balance involved in the renormalization.

Radiation reaction in strong field QED

We derive radiation reaction from QED in a strong background field. We identify, in general, the diagrams and processes contributing to recoil effects in the average momentum of a scattered electron, using perturbation theory in the Furry picture: we work to lowest nontrivial order in α. For the explicit example of scattering in a plane wave background, we compare QED with classical electrodynamics in the limit ℏ→0, finding agreement with the Lorentz–Abraham–Dirac and Landau–Lifshitz equations, and with Larmorʼs formula. The first quantum corrections are also presented.

Radiation reaction in ultrarelativistic laser-spinning electron interactions

The intensity of ultra-short pulse lasers has reached 10 W/cm owing to the advancements in laser technology. The large radiation from the electron behaves something like resistance in this ultrarelativistic laser–electron interaction. This effect is called the “radiation reaction”. The equation of motion with the radiation reaction is known as the Lorentz–Abraham–Dirac equation; however, this equation does not incorporate the spin property. In laser plasmas, classical physics descriptions are preferred for simulations. This paper discusses how to describe the radiation reaction of a spinning relativistic electron in classical dynamics. Subject Index A00, A01, G03, J25

Theoretical Study of Ultra-Relativistic Laser Electron Interaction with Radiation Reaction by Quantum Description

In the near future, the intensity of the ultra-short pulse laser will reach to 1022 W/cm2. When an electron is irradiated by this laser, the electron's behavior is relativistic with significant bremsstrahlung. This radiation from the electron is regarded as the energy loss of electron. Therefore, the electron's motion changes because of the kinetic energy changing. This radiation effect on the charged particle is the self-interaction, called the “radiation reaction” or the “radiation damping”. For this reason, the radiation reaction appears in laser electron interactions with an ultra-short pulse laser whose intensity becomes larger than 1022 W/cm2. In the classical theory, it is described by the Lorentz-Abraham-Dirac (LAD) equation. But, this equation has a mathematical difficulty, which we call the “run-away”. Therefore, there are many methods for avoiding this problem. However, Dirac's viewpoint is brilliant, based on the idea of quantum electrodynamics. We propose a new equation of motion in the quantum theory with radiation reaction in this paper.

Equation of motion with radiation reaction in ultrarelativistic laser-electron interactions

The intensity of the ultra-short pulse lasers has reached 1022 W/cm2 owing to the advancements of laser technology. When the motion of an electron becomes relativistic, bremsstrahlung accompanies it. The energy from this bremsstrahlung corresponds to the energy loss of the electron; therefore, the motion of the electron deviates from the case without radiation. The radiation behaves something like resistance. This effect called “radiation reaction” or “radiation damping” and the force converted from the radiation is named the “radiation reaction force” or the “damping force”. The equation of motion with the reaction force is known as the Lorentz-Abraham-Dirac (LAD) equation, but the solution of this equation is not physical due to the fact that it has a “run-away” solution. As one solution of this problem, we have derived a new equation which takes the place of the Lorentz-Abraham-Dirac equation. We will show the validity of this equation with a simple theoretical analysis.

The significance of the Schott energy for energy-momentum conservation of a radiating charge obeying the Lorentz–Abraham–Dirac equation

It is shown that energy and momentum are conserved during the runaway motion of a radiating charge and during free fall of a charge in a gravitational field. The runaway motion demonstrates the consistency of classical electrodynamics and the Lorentz–Abraham–Dirac equation. The important role of the Schott (acceleration) energy in this connection is made clear, and it is shown that the Schott energy is the part of the electromagnetic field energy that is proportional to (minus) the scalar product of the velocity and acceleration of a moving accelerated charged particle. The Schott energy is negative if the acceleration is in the same direction as the velocity and positive if it is opposite. During runaway motion, the Schott energy becomes more and more negative, and for a charged particle, it is localized at the particle. It is also shown that a proton and a neutron fall with the same acceleration in a uniform gravitational field, although the proton radiates and the neutron does not. The radiation energy comes from the Schott energy.

On the value of geometric algebra for spacetime analyses using an investigation of the form of the self-force on an accelerating charged particle as a case study

The ability to treat vectors in classical mechanics and classical electromagnetism as single geometric objects rather than as a set of components facilitates physical understanding and theoretical analysis. To do the same in four-dimensional spacetime calculations requires a generalization of the vector cross product. Geometric algebra provides such a generalization and is much less abstract than exterior forms. It is shown that many results from geometric algebra are useful for spacetime calculations and can be presented as simple extensions of conventional vector algebra. As an example, it is shown that geometric algebra tightly constrains the possible forms of the self-force that an accelerating charged particle experiences and predicts the Lorentz–Abraham–Dirac equation of motion up to a constant of proportionality. Geometric algebra also makes the important physical content of the Lorentz–Abraham–Dirac equation more transparent than does the standard tensor form of this equation, thus allowing a proposed modification to this equation free from the problems of preacceleration and runaway motion to be easily predicted.

Dynamics of emitting electrons in strong laser fields

A new derivation of the motion of a radiating electron is given, leading to a formulation that differs from the Lorentz–Abraham–Dirac equation and its published modifications. It satisfies the proper conservation laws. Particularly, it conserves the generalized momentum, eliminating the symmetry-breaking runaway solution. The equation allows a consistent calculation of the electron current, the radiation effect on the electron momentum, and the radiation itself, for a single electron or plasma electrons in strong electromagnetic fields. The equation is then applied to a simulation of a strong laser pulse interaction with a plasma target. Some analytical solutions are also provided.

Exact Solution of the Landau-Lifshitz Equation in a Plane Wave

The Landau–Lifshitz (The Classical Theory of Fields. Elsevier, Oxford 1975) form of the Lorentz–Abraham–Dirac equation in the presence of a plane wave of arbitrary shape and polarization is solved exactly and in closed form. The explicit solution is presented in the particular, paradigmatic cases of a constant crossed field and of a monochromatic wave with circular and with linear polarization.

Maxwell–Faraday stresses in electromagnetic fields and the self-force on a uniformly accelerating point charge

The physical analysis of a uniformly accelerating point charge provides a rich problem to explore in advanced courses in electrodynamics and relativity since it brings together fundamental concepts in relation to electromagnetic radiation, Einstein's equivalence principle and the inertial mass of field energy in ways that reveal subtleties in each of these concepts. By first exploring the heuristic value of Maxwell's and Faraday's idea that the electromagnetic field is like a stressed material medium, it is shown in this paper that the problem also provides an interesting application of the electromagnetic stress–energy–momentum tensor and that an analysis using this tensor provides clear physical insight into this highly subtle and contentious problem and the so-called ‘4/3 problem’ of classical electromagnetic theory. In particular, it is shown that the stress force on a uniformly accelerating, uniformly charged spherical shell due to its own field is simply the (relativistic) inertial mass of the charge's electrostatic field times the acceleration. Since the inertial mass of the electromagnetic field forms part of the observed rest mass of a charged particle, it is argued that the results are therefore consistent with the Lorentz–Abraham–Dirac equation of motion for an accelerating point charge, which implies that for uniform acceleration, the work done by the force acting on the charge only goes into increasing the kinetic energy of the charge, none goes into the creation of radiation.

Dynamics of a classical quasi-point charge

Abstract The correct equation for the dynamics of a classical charged particle (when its structure is neglected) has been derived previously, replacing the Lorentz–Abraham–Dirac (LAD) equation. The present Letter completes that dynamics by providing essential conditions necessary for its internal consistency. These are closely related to the limitations of classical physics imposed by quantum mechanics: a point limit is not allowed in a classical theory . The result is a classical dynamics of quasi-point charges.