Discrete action principle and hamiltonian formalism for the Vlasov-Maxwell equations

Eric Sonnendrücker
Date and time
Workshop - Multiscale numerical methods for differential equations

Many models in plasma physics kinetic as well as fluid are based on an principle and can be written with a Poisson bracket. This is true in particular
for the Vlasov-Maxwell equations, but also for different reduced models like the gyrokinetic model widely used in magnetic fusion applications and several MHD models. These provided many conservation laws that should be enforced as well as possible in discrete approximations. We will show in this talk how the Particle In Cell Finite Element approximation of the Vlasov-Maxwell equations provides in a natural way a discrete action principle and Poisson bracket in the discrete unknown which are the particles phase-space positions and the Finite Elements degrees of freedom.