Lawson Criterion for Different Scenarios of Using D-3 He Fuel in Fusion Reactors

Abstract

The paper is devoted to refining the Lawson criterion for three scenarios of using D-3He fuel in fusion reactors (fully catalyzed and non-catalysed D-D cycles and a D-3He cycle with 3He self-supply). To this end, a new parameterization of the D + 3He → p + 4He fusion reaction cross-section and astrophysical factor has been developed based on the effective radius approximation (Landau-Smorodinsky-Bethe approximation), which is a model-free theoretical approach to investigating near-threshold nuclear reactions, including resonant reactions. In the framework of this approximation, experimental data from studies in the NACRE II and EXFOR libraries, believed to provide the most reliable results to date, have been described within the accuracy declared in the studies in question in the energy range of 0 to 1000 keV, and the fusion reactivity averaged over the Maxwell distribution has been calculated. The results obtained are in good agreement with the calculations based on the R-matrix theory and the NACRE II fusion reactivity data. For the fully catalyzed D-D cycle and the cycle with 3He self-supply, the Lawson criterion and the triple Lawson criterion have been calculated based on solving the equations of the stationary process kinetics in a fusion reactor for three fuel ions (D, 3He, and T) taking into account the potential for external supply of 3He and p and 4He impurity ions removed from the reaction zone. The parameters of the triple Lawson criterion found are as follows: nτT = 6.42∙1016 cm-3∙s∙keV (T = 54 keV) for the fully catalyzed D-D cycle, nτT = 1.03∙1017 cm-3∙s∙keV (T = 45 keV) for the cycle with 3He self-supply, and nτT = 4.89∙1016 cm-3∙s∙keV (T = 67 keV) for the non-catalyzed D-D cycle with equimolar D-3He fuel.