Abstract

In this talk, I will discuss several models for plasma. A plasma is an ionised gas, and can be modelled as a large number of charged particles interacting with each other through their self-generated electric field. When the number of particles is very large, a particle model is impractical and it is common to use a PDE instead. A well-known example is the Vlasov-Poisson equation. Physical plasmas typically have an additional property called `quasi-neutrality’. In this regime, an appropriate model is the kinetic isothermal Euler equation, which can be obtained from the Vlasov-Poisson equation under a suitable scaling. Deriving these PDE models from the associated particle dynamics is an important mathematical problem. I will begin by introducing the kinetic isothermal Euler and Vlasov-Poisson equations and discussing the difficulties involved in relating these models rigorously to the underlying particle dynamics. I will then present some recent results, obtained in collaboration with Mikaela Iacobelli, in which we derive the kinetic isothermal Euler equation from a system of extended charges.