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

• Published in: Europhysics letters Vol. 103; no. 2; pp. 28004 - 28008
• Main Authors: André, Frédéric, Bernardi, Pierre, Ryskin, Nikita M., Doveil, Fabrice, Elskens, Yves
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences, IOP Publishing and Società Italiana di Fisica 01.07.2013; IOP Publishing; European Physical Society / EDP Sciences / Società Italiana di Fisica / IOP Publishing
• Subjects: 52.35.Fp; 52.40.Mj; 84.40.Fe; Chaotic Dynamics; Classical Physics; Electromagnetism; Engineering Sciences; Nonlinear Sciences; Physics; Floquet boundary condition; wave-particle interaction; traveling wave tube; beta$-transform
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/103/28004

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.