Radiation temperature of nonequilibrium plasmas

In fusion devices measurements of the radiation temperature Tr(ω,k) near the electron cyclotron frequency ωc and the second harmonic 2ωc in directions nearly perpendicular to the confining magnetic field B (i.e., k≊k⊥ ) serve to map out the electron temperature profiles Te(r,t). For optically thick plasmas at thermodynamic equilibrium Tr=Te. However, there is increasing experimental evidence for the presence of nonequilibrium electron distributions (such as a drifting Maxwellian with appreciable values of the streaming parameter ξ=vd/vt, a bi-Maxwellian, an anisotropic Maxwellian with T⊥≠T∥, etc.) in tokamak plasmas, especially in the presence of radio-frequency heating. Examined here (both nonrelativistically and relativistically), is the dependence of Tr on ξ, T⊥/T∥, Th/Tb, nh/nb, etc., where nb, nh, Tb, and Th are the densities and temperatures, respectively, of the bulk and the hot components of the bi-Maxwellian plasma. The bi-Maxwellian results predict that the ratio Tr/Te is a very sensitive function of the ratios nh/nb and Th/Tb. Further, these relativistic and nonrelativistic results satisfy the well-known ‘‘limit c→∞ correspondence principle,’’ showing that the intensity of the emission and absorption line is independent of the line broadening mechanism. An alternative derivation of the ‘‘Trubnikov O-mode factor’’ is given in the Appendix. A number of side issues relevant to the existing disagreement between the Trubnikov results and those of some authors (in the published literature) for the O-mode processes are raised, and the plausible physical reasons for this disagreement are also pointed out in the Appendix and footnotes.