TOPOLOGY OF RELATIVISTIC REFRACTIVE-INDEX SURFACES FOR ELECTRON-CYCLOTRON WAVES

The dispersion of electron cyclotron waves in a weakly relativistic Ma xwellian plasma is investigated. It is shown that the apparently very complicated picture of the coupling of the extraordinary (X) mode to B ernstein waves can be accounted for in a simple way by considering the refractive indices as Riemann-like surfaces in the Clemmow-Mullaly-Al lis (CMA) parameter space, (omega(p)2/omega2, omega(c)/omega), and by introducing a few topological concepts from the analysis of complex fu nctions. A detailed study is made of the surface representing the X mo de for perpendicular propagation, with special attention given to the connection between this mode and Gross-Bernstein modes. For perpendicu lar propagation non-transcendental approximations to the relativistic refractive indices for X and O modes can be given. We show that these approximations are good up to approximately 25 keV and, at frequencies up to the second harmonic of the electron cyclotron frequency, the X mode approximation also accounts correctly for the connection of the X mode to Bernstein modes. The accuracy and the numerical efficiency of the approximations make them well suited for routine calculations for millimetre wave applications in fusion plasmas, including the analysi s of X mode and O mode reflectometry.