Control of the Reflections at the Terminations of a Slow Wave Structure in the Nonstationary Discrete Theory of Excitation of a Periodic Waveguide

Bernardi, Pierre; André, Frédéric; David, Jean-François; Clair, A. Le; Doveil, Fabrice

doi:10.1109/ted.2011.2163410

Cited by 6 publications

(4 citation statements)

References 3 publications

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“…In contrast, in the present work all periods are coupled with each other. With this model, we can compute the time-dependent behavior of a helix traveling-wave tube, much faster than industrial PIC codes [3]. The reason is that the number of degrees of freedom to describe the propagating wave with sufficient accuracy in finite-difference time-domain or finite element techniques amounts to tens of thousands per pitch [1].…”

Section: πǫ0mentioning

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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Section: πǫ0mentioning

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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“…This work was revisited from 2007 on at Saratov University [15,17], to model coupled cavity traveling wave tubes in frequency domain. This decomposition was then adapted to simulate helix traveling wave tubes by a collaboration [27,28] between Thales Electron Devices at Vélizy, and Aix-Marseille University, as an alternative to equivalent circuit approaches [29]. Finally renamed discrete model, Kuznetsov's decomposition has been extended [16,18,19,30] to express a self-consistent hamiltonian in a periodic structure with conjugate variables representing electric and magnetic fields.…”

Section: Discrete Modelmentioning

confidence: 99%

Recent discrete model for small-signal analysis of traveling-wave tubes

et al. 2019

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equipe turbulence plasma, case 322 campus Saint Jérôme, av. esc. Normandie-Niemen, To perform accurate numerical simulations of the wave-particle interaction as it occurs in particular in traveling wave tubes, a new approach using field decomposition with large reduction of degrees of freedom has been proposed : the discrete model. To assess its validity, we compare it with the well-established Pierce equivalent circuit model in small signal regime.Before the comparison, the beam-wave interaction in both models is reformulated using a new pedagogical approach, dealing with associated beam, circuit-beam, and circuit impedances.We show analytically and with a numerical example that the newly developed reduced model is very close to the Pierce model. Interestingly, small deviations do exist at the edges of the amplification band, for which the reduced model offers a physical interpretation. PACS numbers: 84.40.Fe (Microwave tubes), 52.40.Mj (Particle beam interaction in plasmas)

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“…Our algorithm dimoha is based on the Kuznetsov discrete model [12,13,[17][18][19][20][21][22][23] which uses an exact field decomposition for periodic structures for large-signal regimes. The SWS is directed along the z-axis with pitch d and cell index n ∈ Z.…”

Section: B the Discrete Modelmentioning

confidence: 99%

DIMOHA: A Time-Domain Algorithm for Traveling-Wave Tube Simulations

Minenna

Elskens

André

et al. 2019

IEEE Trans. Electron Devices

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To simulate traveling-wave tubes (TWTs) in time domain and more generally the wave-particle interaction in vacuum devices, we developed the DIscrete MOdel with HAmiltonian approach (dimoha) as an alternative to current particle-in-cell (PIC) and frequency approaches. Indeed, it is based on a longitudinal N -body Hamiltonian approach satisfying Maxwell's equations. Advantages of dimoha comprise: (i) it allows arbitrary waveform (not just field envelope), including continuous waveform (CW), multiple carriers or digital modulations (shift keying); (ii) the algorithm is much faster than PIC codes thanks to a field discretization allowing a drastic degree-of-freedom reduction, along with a robust symplectic integrator; (iii) it supports any periodic slow-wave structure design such as helix or folded waveguides; (iv) it reproduces harmonic generation, reflection, oscillation and distortion phenomena; (v) it handles nonlinear dynamics, including intermodulations, trapping and chaos. dimoha accuracy is assessed by comparing it against measurements from a commercial Ku-band tapered helix TWT and against simulations from a sub-THz folded waveguide TWT with a staggered double-grating slow-wave structure. The algorithm is also tested for multiple-carriers simulations with success. PACS numbers: 45.20.Jj (Lagrangian and hamiltonian mechanics), 52.40.Mj (Particle beam interaction in plasmas), 84.40.Fe (Microwave tubes)

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Control of the Reflections at the Terminations of a Slow Wave Structure in the Nonstationary Discrete Theory of Excitation of a Periodic Waveguide

Cited by 6 publications

References 3 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

Recent discrete model for small-signal analysis of traveling-wave tubes

DIMOHA: A Time-Domain Algorithm for Traveling-Wave Tube Simulations

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