General Proof of Symmetry Relations in Mode Conversion With Application to Excitation of, and Emission From, Electron Bernstein Waves

From general principles of wave energy flow conservation and wave energy flow in the time reversed system, we derive symmetry properties that must be satisfied by the coupling of waves in dissipation-free mode conversion regions of an inhomogeneous plasma confined by a magnetic field. The results are valid for any kinetic (Vlasov-Maxwell) full-wave description of a plasma in a magnetic field with an equilibrium distribution function symmetric in momentum parallel to the magnetic field. Thus, without solving the full-wave equations, we obtain the symmetries in transmission, reflection, and mode conversion excitation and emission. The important physical and practical consequences of the various symmetries are illustrated for O and X modes coupling to electron Bernstein waves in the vicinity of the upper-hybrid resonance, with adjoining cutoffs, relevant to plasma heating and current drive, and emission from high-β spherical tori (ST) plasmas.