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To model momentum exchange in nonlinear wave-particle interaction, as inamplification devices like traveling-wave tubes, we use an $N$-bodyself-consistent hamiltonian description based on Kuznetsov's discrete model,and we provide new formulations for the electromagnetic power and the conservedmomentum. This approach leads to fast and accurate numerical simulations intime domain and in one dimensional space.

Electromagnetic power and momentum in N-body hamiltonian approach to wave-particle dynamics in a periodic structure