Orbit-space sensitivity of two-step reaction gamma-ray spectroscopy

We calculate the orbit-space sensitivity of two-step reaction gamma-ray spectroscopy diagnostics in toroidally symmetric magnetic equilibria, using the reaction between alpha particles and beryllium-9 as an example. To reduce the computational cost, we use analytical solutions obtained by neglecting the velocity of the thermal beryllium. The sensitivity is quantified by weight functions, which we calculate in the alpha-particle orbit space of energy, maximum major radius and pitch at that maximum major radius. Each alpha-particle guiding-center orbit leads to a characteristic gamma-ray spectrum depending on the line-of-sight geometry. We highlight the geometry dependence by repeating the calculation for three different cases, observing significant changes in the sensitivity patterns. Weight functions also allow one to quickly compute forward model problems if spectra from many distribution functions are to be calculated and compared with experimental measurements.