Modelling of the continuum x-ray spectra produced by anisotropic electron distributions in tokamak plasmas under LHCD conditions

The continuum X-ray spectrum resolved in angle due to the axisymmetric anisotropic electron velocity distribution F(v) produced during lower hybrid current drive (LHCD) in tokamak plasmas is modelled. The radiative processes considered are the electron-ion (e-i) and electron-electron (e-e) bremsstrahlung, and the direct radiative recombination (DRR) averaged over the velocity distribution F(v) predicted by the one-dimensional Fokker-Planck model. The relativistic cross sections for the e-i and e-e bremsstrahlung in the Born approximation and corrected by the respective Elwert factors are used in the computation. Since the DRR becomes negligible relative to the bremsstrahlung in the relativistic domain under LHCD conditions, the non-relativistic cross section for DRR in the dipole approximation is used for simplicity and analytical expressions cast into real form are given to evaluate the hypergeometric series solution of the form function for all shells and levels nl. The mathematical expressions are also given to obtain the total number of photons in a detector looking through a plasma column for a two-aperture system and sample calculations for LHCD conditions on the Tokamak de Varennes, are presented. (Author)