Diagnostic weight functions in constants-of-motion phase-space

The fast-ion phase-space distribution function in axisymmetric tokamak plasmas is completely described by the three constants of motion: energy, magnetic moment and toroidal canonical angular momentum. In this work, the observable regions of constants-of-motion phase-space, given a diagnostic setup, are identified and explained using projected velocities of the fast ions along the diagnostic lines-of-sight as a proxy for several fast-ion diagnostics, such as fast-ion $\text{D}_{\alpha}$ spectroscopy, collective Thomson scattering, neutron emission spectroscopy and gamma-ray spectroscopy. The observable region in constants-of-motion space is given by a position condition and a velocity condition, and the diagnostic sensitivity is given by a gyro-orbit and a drift-orbit weighting. As a practical example, 3D orbit weight functions quantifying the diagnostic sensitivity to each point in phase-space are computed and investigated for the future COMPASS-Upgrade and MAST-Upgrade tokamaks.