Talk
Recent results on the quasi-neutral limit for the ionic Vlasov-Poisson system
Talk by Dr. Megan Griffin-Pickering
Date: 27.10.22 Time: 16.00 - 18.00 Room: KOL G209
Vlasov-Poisson type systems are well known as kinetic models for plasma. The precise structure of the model differs according to which species of particle it describes, with the `classical’ version of the system describing the electrons in a plasma. The model for ions, however, includes an additional exponential nonlinearity in the equation for the electrostatic potential, which creates several mathematical difficulties. For this reason, the theory of the ionic system has so far not been as fully explored as the theory for the electron equation. A plasma has a characteristic scale, the Debye length, which describes the scale of electrostatic interaction within the plasma. In real plasmas this length is typically very small, and in physics applications frequently assumed to be very close to zero. This motivates the study of the limiting behaviour of Vlasov-Poisson type systems as the Debye length tends to zero relative to the observation scale—known as the ‘quasi-neutral’ limit. In the case of the ionic model, the formal limit is the kinetic isothermal Euler system; however, this limit is highly non-trivial to justify rigorously and known to be false in general without very strong regularity conditions and/or structural conditions. I will present a recent work, carried out in collaboration with Mikaela Iacobelli, in which we prove the quasi-neutral limit for the ionic Vlasov-Poisson system for a class of rough (L^\infty) data: that is, data that may be expressed as perturbations of an analytic function, small in the sense of Monge-Kantorovich distances. The smallness of the perturbation that we require is much less restrictive than in the previously known results.