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

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 represent...

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Published inEurophysics letters Vol. 103; no. 2; pp. 28004 - 28008
Main Authors André, Frédéric, Bernardi, Pierre, Ryskin, Nikita M., Doveil, Fabrice, Elskens, Yves
Format Journal Article
LanguageEnglish
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
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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 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.
AbstractList 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.
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.
Author Bernardi, Pierre
Ryskin, Nikita M.
André, Frédéric
Doveil, Fabrice
Elskens, Yves
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Issue 2
Keywords Floquet boundary condition
wave-particle interaction
traveling wave tube
beta$-transform
Language English
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SubjectTerms 52.35.Fp
52.40.Mj
84.40.Fe
Chaotic Dynamics
Classical Physics
Electromagnetism
Engineering Sciences
Nonlinear Sciences
Physics
Title Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure
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