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

Abstract

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 $\beta$-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.

arXiv comment5 pages

References in corpus (4)

• Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation
• Comment on "Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation"
• Comment on "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"
• QED Corrections to the Electromagnetic Abraham Force. Casimir Momentum of the Hydrogen atom?

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• On frequency and time domain models of traveling wave tubes
• Comparison Between Pierce Equivalent Circuit and Recent Discrete Model for Traveling-Wave Tubes