Impact of Grid Discretization on Reconstruction Accuracy in Fast-Ion Velocity-Space Tomography

Fast-ion velocity-space tomography is used to infer the fast-ion velocity-space distribution function from measured fast-ion data, revealing details about plasma interactions and energy dynamics. Central to this technique is a fundamental decision in computational physics: selecting the appropriate discretization strategy for numerically solving mathematical equations. For the specific model of projected velocities, applicable to all spectroscopic fast-ion diagnostics such as collective Thomson scattering and fast-ion D-alpha spectroscopy[1, 2], using a grid resolution above 2 · 10⁵ m/s in v_‖ leads to a lack of detail in the physical model, affecting sensitivity in v_⊥. This insufficiency leads to large reconstruction errors and significant inaccuracies in the reconstructed velocity distributions when computed using Tikhonov regularization. Perturbation analysis shows that discrepancies between the discretized (A^TA) and continuous (A_cont^T A_cont) Gram matrices account for the differences in the reconstructions, where A is the discretized system matrix and A_cont the continuous analog.

[1] Salewski M et al 2014 Plasma Phys. Control. Fusion 56 105005

[2] Salewski M et al 2014 Nucl. Fusion 53 063019