Port-based modeling of magnetohydrodynamics equations for Tokamaks

This paper shows the port-representation of the magnetohydrodynamics of Tokamaks. The port-representation consists of coupled two physical systems, i.e. Maxwell equations and the equations of ideal compressible isentropic fluids. The coupling term is the product of the free current density and the magnetic field induction. Port-Hamiltonian systems is a control system representation based on passivity. Port-Hamiltonian systems can express connected multi-physical systems (e.g., electric systems, mechanical systems, fluid systems, dissipative systems and controllers). The port-Hamiltonian system has been extended as a distributed system by introducing a Stokes-Dirac structure. The Stokes-Dirac structure directly relates to boundary integrability of the Stokes theorem. Therefore, the Stokes-Dirac structure can express boundary energy control problems, because we can observe boundary integrable energies distributed in internal domains from boundaries. Our present interest is to clarify the counter part of the distributed port-Hamiltonian system representation in the Lagrangian side. The representation will provide us a more general control framework based on variational structures.