Analytical approximation of cross-section effects on charge exchange spectra observed in hot fusion plasmas

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Abstract
An analytical procedure is presented which enables a fast estimate of collision-energy-dependent cross-section effects on thermal charge exchange spectra. The model is based both on experimental evidence and numerical simulations showing that the observed charge exchange (CX) spectra are essentially Gaussian in their shape. The collision-energy-dependent emission rate leads effectively to a lineshift (apparent velocity), usually to a reduction in linewidth (apparent temperature), and to a change in the effective emission rate averaged over the entire thermal velocity distribution function. It is demonstrated that the cross-section effect can be treated analytically introducing an approximated emission rate factor which retains the characteristics of a Maxwellian velocity distribution function using an exponential expression with only linear and quadratic velocity terms in its exponent. An algebraic deconvolution procedure is described, which enables the reconstruction of true temperature, velocity and intensities from measured CX spectra. Examples taken from a recent JET experimental campaign are used to illustrate the cross-section effects on low-Z impurity CX spectra for a comprehensive variety of neutral beams (deuterium, tritium or helium), target densities, temperatures and toroidal rotation speeds. An overview is given of representative correction factors established for high-power, high-temperature plasmas, as well as for plasmas with combined neutral beam and radiofrequency heating, and for the case of locked modes.