Port-Hamiltonian formulation for systems of conservation laws: application to plasma dynamics in Tokamak reactors

A port-Hamiltonian model is derived for the thermo-magneto-hydro dynamics of plasma in tokamaks. Magnetohydrodynamic and energy balance equations are expressed in their covariant form and written in the port-Hamiltonian formalism using Dirac structures. This Dirac structure is established as the interconnection of Stokes-Dirac structures with a specific interconnection structure representing the magneto-hydrodynamical coupling. Finally the problem of current density profile control is defined and potential approaches are discussed.