At the plasma/vacuum interface, the electromagnetic modes supported invacuum connect to their finite-density counterparts as well as tosupplementary finite-temperature modes supported by the plasma. To find themost general solution for a given plasma model containing M independentsolutions inside the plasma, M boundary conditions have to be imposed. Ateach interface, two boundary conditions directly follow from Maxwell'sequations. They require that the two components of the electric fieldtangential to the interface are continuous at the edge. The present paperproposes a method for finding the appropriate supplementary boundaryconditions. Although the boundary conditions are derived to interface theTOMCAT wave code (Van Eester D and Koch R 1998 Plasma Phys. Control.Fusion40 1949) with antenna coupling codes via the surfaceimpedance matrix, the adopted philosophy can easily be extended to wavemodels other than the one used here. It is shown that, when formulating theproblem in variational form (anticipating subsequent exploitation of thefinite-element method), it suffices to impose the continuity of the surfaceterms (corresponding to the total flux) at the plasma/vacuum interface.When the test function in the variational is substituted for the electricfield, the wave equation reduces to the power balance equation. Thecontinuity of the surface terms guarantees that no power is lost at theinterface where the vacuum modes (which carry their energyelectromagnetically via the Poynting flux) pass on their energy to theplasma modes (which carry their energy both electromagnetically and viaparticles in coherent motion with the wave, i.e. as kinetic flux).
Theory of waveguide antennas for plasma heating and current drive