Hamiltonian systems, from topology to applications through analysis I October 08, 2018 - October 12, 2018
Location: MSRI: Simons Auditorium
infinite-dimensional Hamiltonian systems
slow manifold reduction
Fully ionized plasmas emit both incoherent light and coherent light. Incoherent emission occurs whenever plasma particles suffer Coulomb collisions, and is therefore ubiquitous. On the other hand, coherent emission involves macroscopic collections of particles moving in concert. This incoherent emission is well described by the Vlasov-Maxwell system of equations. In this talk I will argue for the existence of plasmas that are "dark" in the sense that their coherent emission is extremely weak. The dark plasma motions will be identified with a slow manifold in the Vlasov-Maxwell phase space. In the case where collisions are extremely rare, I will give a complete description of the Hamiltonian formulation of dynamics on the slow manifold. In the leading-order approximation, the dark motions are modeled by the Vlasov-Poisson system of equations. At the next order, which accounts for magnetostatic effects, the model also has a name: the Vlasov-Darwin system. Higher-order approximations account for non-radiative electromagnetic fields generated by collective acceleration of plasma particles. The dark motions may be modeled with any desired order of accuracy without sacrificing the problem's underlying Hamiltonian structure.