Volume 103, Number 2, July 2013
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||12 August 2013|
Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure
1 Thales Electron Devices - rue Latécoère, 2, 78140 Vélizy, France, EU
2 UMR 7345 CNRS–Aix-Marseille- Université, campus Saint-Jérôme - case 321, av. esc. Normandie-Niemen, 13397 Marseille cedex 20, France, EU
3 Saratov State University - Saratov 410012, Russia
Received: 5 April 2013
Accepted: 23 July 2013
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: 84.40.Fe – Microwave tubes (e.g., klystrons, magnetrons, traveling-wave, backward-wave tubes, etc.) / 52.35.Fp – Electrostatic waves and oscillations (e.g., ion-acoustic waves) / 52.40.Mj – Particle beam interactions in plasmas
© EPLA, 2013
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