QED corrections to the electromagnetic Abraham force

Tiggelen, B. A. van; Kawka, Sébastien; Rikken, G. L. J. A.

doi:10.1140/epjd/e2012-30118-1

Cited by 14 publications

(22 citation statements)

References 27 publications

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“…For instance, in the limit where the electron radiates a large number of photons, each of them having a small energy compared with its kinetic energy, which is the case for the aforementioned devices, one could expect that averaging the quantum theory over a large number of emitted photons would provide a consistent classical limit. But such a theory, free of the above problems, remains to be found [9,16,20,21].To progress in this direction, we undertake the construction of a Hamiltonian in situations where the boundary conditions are periodic in one or more dimensions, and we focus on the radiated field modes interacting with the electrons. Our method applies both to traveling wave tubes, meant to amplify "slow" modes in the periodic structure, and to free electron lasers where the electrons couple to "fast" modes.…”

mentioning

confidence: 99%

Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure

André¹,

Bernardi²,

Ryskin³

et al. 2013

EPL

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Conservation of energy and momentum in the classical theory of radiating electrons has been a challenging problem since its inception. We propose a formulation of classical electrodynamics in Hamiltonian form that satisfies the Maxwell equations and the Lorentz force. The radiated field is represented with eigenfunctions using the Gel'fand β-transform. The electron Hamiltonian is the standard one coupling the particles with the propagating fields. The dynamics conserves energy and excludes self-acceleration. A complete Hamiltonian formulation results from adding electrostatic action-at-a-distance coupling between electrons. PACS numbers: 84.40.Fe (microwave tubes) 52.35.Fp (Plasma: electrostatic waves and oscillations) 52.40.Mj (particle beam interaction in plasmas) 52.20.Dq (particle orbits) Keywords : wave-particle interaction, traveling wave tube, β-transform, Floquet boundary conditionTo model consistently the interaction between electrons and waves in devices such as traveling wave tubes, free electron lasers or synchrotrons, we are presently left with two options. The first [6,11,17] is to consider the flow of electrons as a distributed charge and current density coupled with the field through the Maxwell equations. Since it generates diverging singularities, the particle nature of electrons is intentionally overlooked until the question of determining the trajectories of the flow is raised. For the latter, the only possibility is to return to a particle description in which the Lorentz force applies. This change of model for the flow precludes the description of the wave-electron system in Hamiltonian form. One reason is that a procedure is needed to distribute the electron charge and current into a finite volume. This procedure, usually based on meshing space, can only be arbitrary. The second option [8,10,13] is to consistently consider electrons as particles and to determine the field they radiate starting from the Liénard-Wiechert potentials. Dirac's [4] sharp analysis indeed provides an accurate determination of the reaction from the radiated field in the limit of a point electron, yet this approach leads to serious difficulties [4,10,13,16,18]; among these an infinite rest mass of the electron, self-acceleration and acausality, also appear incompatible with the existence of a well-posed Hamiltonian.Hamiltonians are essential to consistently define energy and momentum. They also have great practical usefulness to find approximate solutions in complex systems or to control errors in numerical integration schemes [7]. So their absence in the case of the classical wave-electron interaction is both theoretically and practically unsatisfactory. While the final solution to these problems may involve (upgraded, regular) quantum electrodynamics, one could at least hope for a consistent classical approximation, which would be the classical limit of its quantum counterpart. For instance, in the limit where the electron radiates a large number of photons, each of them having a small energy compared with its kin...

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confidence: 99%

Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure

André¹,

Bernardi²,

Ryskin³

et al. 2013

EPL

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“…The radiation reaction induces a non-causal and large "run-away" pole ω ≈ i/τ R in the upper complex plane [22] that is often avoided by putting iτ R ω 3 → iAω and by identifying the radiation life time A = τ R ω 2 0 . We can compare this outcome to scattering theory, according to which the Helmholtz Green function (7) is related to the T -matrix of the dielectric object according to,…”

Section: Single Electric Dipolementioning

confidence: 99%

“…For macroscopic objects both suffer often from power-law divergencies at high photon energies. Some are nonphysical or not observable and removed by dimensional regularization [5], others require QED mass renormalization [7,8]. The classical electromagnetic "Abraham" momentum was observed first by Walker etal.…”

Section: Introductionmentioning

confidence: 99%

Longitudinal Angular Momentum in Magneto-Mie Scattering: Quantum Vacuum Correction to the Einstein-De Haas effect

van Tiggelen

2021

Preprint

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This work investigates the angular momentum of the electromagnetic quantum vacuum residing in a dielectric Mie sphere subject to the Faraday effect. Longitudinal electric modes are excited on its surface and are also created inside the sphere by the Faraday effect. The electromagnetic quantum vacuum creates a vortex of the Poynting vector that varies as 1/r to the center of the sphere and is associated with longitudinal angular momentum, connected to the vector potential A(r, t). It emerges as a non-negligible quantum vacuum correction to the classical (diamagnetic) Einstein-De Haas effect in which an applied external magnetic field -via its action on microscopic magnetism -enforces macroscopic rotation.

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“…Besides, it was found in Ref. [18] that, still in the electric dipole approximation, in addition to the conservative vdW forces nonconservative forces may arise from the time variation of the EM longitudinal momentum [19][20][21][22][23][24]. Since the interaction between two atoms becomes time-dependent when one of them is excited nonadiabatically, so does the EM longitudinal momentum of the system.…”

Section: Introductionmentioning

confidence: 99%

Nonconservative dipole forces in a two-atom system with one atom excited

Sánchez-Cánovas¹,

Donaire²

2021

Preprint

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We compute the nonconservative electric dipole forces between two atoms, one of which is initially excited. These forces derive from the time variation of the longitudinal electromagnetic momentum. In contrast to the conservative van-der-Waals forces, the nonconservative forces posses components orthogonal to the interatomic axis. Thus, despite being several orders of magnitude smaller than vander-Waals', they might be accessible experimentally for the case of two identical atoms. In addition, as with the van-der-Waals forces, the nonconservative forces present nonreciprocal constituents which result in a net force on the two-atom system. We offer an estimate of the spatial displacement caused by the nonconservative forces on a binary system of Hydrogen atoms.

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QED corrections to the electromagnetic Abraham force

Cited by 14 publications

References 27 publications

Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure

Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure

Longitudinal Angular Momentum in Magneto-Mie Scattering: Quantum Vacuum Correction to the Einstein-De Haas effect

Nonconservative dipole forces in a two-atom system with one atom excited

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