Nonlinear oscillations of electron layers

📅 martes 24 de marzo — 11:00

📍 Aula A16, Facultad de Ciencias

👤Conferenciante: Émeric Roulley (Università degli Studi di Milano)

📖 Título: Nonlinear oscillations of electron layers

📄 Resumen: We consider the one-dimensional space periodic Vlasov-Poisson equation. A particular class of solutions, called electron layers, arises when the electron density is given by the characteristic function of a strip in phase space. The evolution of such configurations is governed by a Hamiltonian system consisting of coupled transport equations. We construct, near stationary flat velocity layers, both periodic traveling and quasi-periodic traveling solutions. The periodic traveling solutions are obtained via bifurcation theory, and their phase portrait exhibits a hyperbolic structure. We will also briefly discuss some extensions to the two-component system where the ions are also allowed to have inertia. The construction of quasi-periodic traveling solutions is considerably more delicate and requires a combination of KAM theory, Nash–Moser iteration, and pseudo-differential calculus. In order to exclude resonances and make the KAM scheme applicable, the strip width must be chosen from a suitable set of parameters of almost full measure.