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Modélisation hamiltonienne N-corps de l’échange de moment dans l’interaction onde-particule non-linéaire

Abstract : We investigate the wave-particle dynamics using an $N$-body description (often deemed impossible due to the number of degrees of freedom involved). The evolution of our system rests on a hamiltonian composed of an electromagnetic part $\int_V (\epsilon_0 |{\bf E}|^2 + \mu_0 |{\bf H}|^2)/2 \, {\rm d} V$, a particle part $|{\bf p} -e {\bf A}|^2/(2m)$ and a space charge part. For periodic waveguides, we use a model reduction, called the ``discrete model'', to drastically reduce the number of degrees of freedom. This model decomposes electromagnetic fields ${\bf E}({\bf r},t) = \sum_n V_n (t) {\bf E}_n ({\bf r})$ and ${\bf H}({\bf r},t) = \sum_n I_n (t) {\bf H}_n ({\bf r})$ with time amplitudes and field shapes depending on the geometry. This technique enables us to obtain smooth coupling terms, enabling the use of macro-particles. Our hamiltonian is reformulated with the discrete model to obtain a one-dimensional $N$-body self-consistent theory able to describe non-linear effects (oscillations, trapping and chaos) of the wave-particle interaction in time domain. Applying Noether's theorem, we investigate the canonical momentum exchange at the origin of the interaction. A reformulation of the electromagnetic power in time domain is proposed using the discrete model's representation. Moreover, our theory is validated analytically against a robust equivalent circuit model. We also investigate a tridimensional version of our theory resting on the helix geometry. Our hamiltonian provides the basis to build a numerical symplectic integrator. This algorithm is used to simulate several traveling-wave tube geometries (for MHz to sub-THz, with helix and folded waveguide tubes, from centimeters to meters long). Our algorithm is benchmarked against experimental measurements. It also allows the investigation of nonlinear effects in tubes as well as the analysis of the distortion of telecommunication signals. Finally, we demonstrate that, when the phase velocity of an electromagnetic field is not equal to the speed of light in vacuum, then this field has distinct kinematic and canonical momenta. This phenomenon, at the heart of the Abraham-Minkowski controversy, was only observed in dielectric materials so far. We extend its scope to vacuum waveguides and to plasmas, and we suggest its universality.
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Damien F. G. Minenna. Modélisation hamiltonienne N-corps de l’échange de moment dans l’interaction onde-particule non-linéaire. Physique des plasmas [physics.plasm-ph]. Aix Marseille Université, 2019. Français. ⟨tel-02479923⟩

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