Gamma-ray emission spectrum from thermonuclear fusion reactions without intrinsic broadening

First principle calculations of the gamma-ray energy spectrum arising from thermonuclear reactions without intrinsic broadening in fusion plasmas are presented, extending the theoretical framework needed to interpret measurements up to the accuracy level enabled by modern high resolution instruments. An analytical formula for the spectrum from Maxwellian plasmas, which extends to higher temperatures than the results previously available in the literature, has been derived and used to discuss the assumptions and limitations of earlier models. In case of radio-frequency injection, numerical results based on a Monte Carlo method are provided, focusing in particular on improved relations between the peak shift and width from the reaction and the temperature of protons accelerated by radio-frequency heating.The results presented in this paper significantly improve the accuracy of diagnostic information that can be extracted from the gamma-ray emission spectrum of fusion reactions without intrinsic broadening and are of relevance for applications to high performance plasmas of present and next generation devices.