A second order yield-temperature relation for accurate inference of burn-averaged quantities in multi-species plasmas

Measured yields and ion temperatures inferred from the fusion product energy spectra can be used as metrics for the performance of an ICF implosion. This can be to infer species separation, thermal decoupling, flows or other effects that can cause the inferred ion temperatures to deviate from the true underlying thermal temperature and the yield ratio to deviate from the expected value. Direct inference of the impact of these effects on observed temperatures and yields can be difficult to uncover due to underlying dependence on the shape and time evolution of the temperature and density proles of the fusing plasma. Due to differences in the temperature dependence of the reactivities, different fusion products are emitted from different regions and times within the implosion. In order to properly account for this, a second order analytic expression relating the apparent temperatures and yield ratios is developed. This expression can be coupled to models of yield and/or temperature altering effects to infer their burn-averaged impact on an implosion. The second order expression shows significant improvement over lower order expressions in synthetic data studies. Demonstrations of its applications to synthetic data coupled with models of ion thermal decoupling and radial flows are presented. In the case of thermal decoupling both first and second order expressions show reasonable levels of accuracy. To consistently infer the amplitude of radial flow with <10% error the second order equation is required.