Orbit tomography in constants-of-motion phase-space

Abstract Tomographic reconstructions of a 3D fast-ion constants-of-motion phase-space distribution function are computed by inverting synthetic signals based on projected velocities of the fast ions along the diagnostic lines of sight. The fast-ion distribution functions are parameterised by three constants of motion, the kinetic energy, the magnetic moment and the toroidal canonical angular momentum. The reconstructions are computed using both zeroth-order and firstorder Tikhonov regularisation expressed in terms of Bayesian inference to allow uncertainty quantification. In addition to this, a discontinuity appears to be present in the solution across the trapped passing boundary surface in the three-dimensional phase space due to a singularity in the Jacobian of the transformation from position and velocity space to phase space. A method to allow for this apparent discontinuity while simultaneously penalising large gradients in the solution is demonstrated. Finally, we use our new methods to optimise the diagnostic performance of a set of six fans of sightlines by finding where the detectors contribute most complementary diagnostic information for the future COMPASS-Upgrade tokamak.