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Register a new userTime simulation of the nonlinear wave-particle interaction in meters long traveling-wave tubes
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We propose a multi-particle self-consistent Hamiltonian (derived from an N-body description) that is applicable for periodic structures such as traveling-wave tubes (TWTs), gyrotrons, free-electron lasers, or particle accelerators. We build a 1D symplectic multi-particle algorithm to simulate the nonlinear wave-particle interaction in the time domain occurring in an experimental 3-meters long helix TWT. Our algorithm is efficient thanks to a drastic reduction model. A 3D helix version of our reduction model is provided. Finally, we establish an explicit expression of the electromagnetic power in the time domain and in non-monochromatic (non-continuous waveform) regime.
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We discuss the envelope modulation assumption of frequency-domain models of traveling wave tubes (TWTs) and test its consistency with the Maxwell equations. We compare the predictions of usual frequency-domain models with those of a new time domain model of the TWT.
We investigate the interaction of electromagnetic waves and electron beams in a 4 meters long traveling wave tube (TWT). The device is specially designed to simulate beam-plasma experiments without appreciable noise. This TWT presents an upgraded slow wave structure (SWS) that results in more precise measurements and makes new experiments possible. We introduce a theoretical model describing wave propagation through the SWS and validated by the experimental dispersion relation, impedance, phase and group velocities. We analyze nonlinear effects arising from the beam-wave interaction, such as the modulation of the electron beam and the wave growth and saturation process. When the beam current is low, the wave growth coefficient and saturation amplitude follow the linear theory predictions. However, for high values of current, nonlinear space charge effects become important and these parameters deviate from the linear predictions, tending to a constant value. After saturation, we also observe trapping of the beam electrons, which alters the wave amplitude along the TWT.
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 Maxwells 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.
The interaction between a linear electron beam and a guided electromagnetic wave is studied in the contest of exceptional points of degeneracy (EPD) supported by such an interactive system. The study focuses on the case of a linear beam traveling wave tube (TWT) with a realistic helix waveguide slow-wave structure (SWS). The interaction is formulated by an analytical model that is a generalization of the Pierce model, assuming a one-dimensional electron flow along a dispersive single-mode guiding SWS and taking into account space-charge effects in the system. The augmented model using phase velocity and characteristic impedance obtained via full-wave simulations is validated by calculating gain versus frequency and comparing it with that from more complex electron beam simulators. This comparison also shows the accuracy of our new model compared with respect to the non-dispersive Pierce model. EPDs are then investigated using the augmented model, observing the coalescence of complex-valued wavenumbers and the systems eigenvectors. The point in the complex dispersion diagram at which the TWT-system starts/ceases to exhibit a convection instability, i.e., a mode starts/ceases to grow exponentially along the TWT, is the EPD. We also demonstrate the EPD existence by showing that the Puiseux fractional power series expansion well approximates the bifurcation of the dispersion diagram at the EPD. This latter concept also explains the exceptional sensitivity of the TWT-system to changes in the beams electron velocity when operating near an EPD.
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and constant segments, glued together at points where at least one one-sided derivative is unbounded. Applying the method of proof to the Camassa--Holm equation, we recover some well-known results on its traveling wave solutions.
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