Abstract
Velocity-space tomography has been used to infer 2D fast-ion velocity distribution functions. Here we compare the performance of five different tomographic inversion methods: truncated singular value decomposition, maximum entropy, minimum Fisher information and zeroth- and first-order Tikhonov regularization. The inversion methods are applied to fast-ion measurements taken just before and just after a sawtooth crash in the ASDEX Upgrade tokamak as well as to synthetic measurements from different test distributions. We find that the methods regularizing by penalizing steep gradients or maximizing entropy perform best. We assess the uncertainty of the calculated inversions taking into account photon noise, uncertainties in the forward model as well as uncertainties introduced by the regularization which allows us to distinguish regions of high and low confidence in the tomographies. In high confidence regions, all methods agree that ions with pitch values close to zero, as well as ions with large pitch values, are ejected from the plasma center by the sawtooth crash, and that this ejection depletes the ion population with large pitch values more strongly.
Highlights
Traditional fast-ion diagnostics and analysis procedures provide only incomplete information about the 2D fast-ion velocity distribution function
Using velocity-space tomography it is possible to combine data from several such measurements to infer the 2D fast-ion velocity distribution function [3,4,5,6,7,8,9,10]. With this approach it should even be possible to combine measurements from different diagnostics which is beneficial as they are sensitive to different regions of velocity-space [6]. This velocity-space sensitivity is quantified by velocity-space sensitivity functions, called weight functions, which have been developed for FIDA [11, 12], collective Thomson scattering (CTS) [4], fast-ion loss detectors (FILD) [13], neutron emission spectrometry (NES) [14, 15] and gamma-ray spectroscopy (GRS) [16]
In order to estimate the confidence in the presented analysis, uncertainties of the tomographies are defined and calculated taking into account the photon noise, uncertainties in the forward model as well as uncertainty introduced by the inversion methods themselves
Summary
Traditional fast-ion diagnostics and analysis procedures provide only incomplete information about the 2D fast-ion velocity distribution function. Using velocity-space tomography it is possible to combine data from several such measurements to infer the 2D fast-ion velocity distribution function [3,4,5,6,7,8,9,10] With this approach it should even be possible to combine measurements from different diagnostics which is beneficial as they are sensitive to different regions of velocity-space [6]. This velocity-space sensitivity is quantified by velocity-space sensitivity functions, called weight functions, which have been developed for FIDA [11, 12], collective Thomson scattering (CTS) [4], fast-ion loss detectors (FILD) [13], neutron emission spectrometry (NES) [14, 15] and gamma-ray spectroscopy (GRS) [16]. The weight functions, w(x1, x2, φ, E, p), relate a measurement, s(x1, x2, φ), to the fast-ion velocity distribution function, f (E, p), where x1 and x2 define a range in the specific measurement variable, φ is the angle between the projection direction and the magnetic field, E is the fast-ion energy and p is the pitch defined as p
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