Doppler spectral line shapes and apparent velocity distribution in plasmas affected by low-frequency turbulence

Starting from first principles, we derive for the first time a comprehensive formalism allowing to calculate Doppler spectral line shapes emitted in plasmas affected by low-frequency turbulence. The apparent velocity distribution function (VDF) of the emitters in a turbulent plasma, deduced from spectral line analysis, is expressed in terms of the joint probability density function (PDF) of the fluctuating plasma fields. In the case where temperature fluctuations are dominant, we use analytic expressions for the PDF, allowing theoretical predictions for the apparent VDF. We show that temperature PDFs behaving asymptotically as a power law lead to a similar behaviour for the Doppler line wings