Integrating the finite-temperature wave equation across the plasma/vacuum interface

At the plasma/vacuum interface, the electromagnetic modes supported in vacu um connect to their finite-density counterparts as well as to supplementary finite-temperature modes supported by the plasma. To find the most general solution for a given plasma model containing M independent solutions insid e the plasma, M boundary conditions have to be imposed,. At each interface, two boundary conditions directly follow from Maxwell's equations. They req uire that the two components of the electric field tangential to the interf ace are continuous at the edge. The present paper proposes a method for fin ding the appropriate supplementary boundary conditions. Although the bounda ry conditions are derived to interface the TOMCAT wave code (Van Eester D a nd Koch R 1998 Plasma Phys. Control. Fusion 40 1949) with antenna coupling codes via the surface impedance matrix, the adopted philosophy can easily b e extended to wave models other than the one used here. It is shown that, w hen formulating the problem in variational form (anticipating subsequent ex ploitation of the finite-element method), it suffices to impose the continu ity of the surface terms (corresponding to the total flux) at the plasma/va cuum interface. When the test function in the variational is substituted fo r the electric field, the wave equation reduces to the power balance equati on. The continuity of the surface terms guarantees that no power is lost at the interface where the vacuum modes (which carry their energy electromagn etically via the Poynting flux) pass on their energy to the plasma modes (w hich carry their energy both electromagnetically and via particles in coher ent motion with the wave, i.e. as kinetic flux).