Comparison of unfolding methods for the inference of runaway electron energy distribution from γ-ray spectroscopic measurements

Abstract

Unfolding techniques are employed to reconstruct the 1D energy distribution of runaway electrons from Bremsstrahlung hard X-ray spectrum emitted during plasma disruptions in tokamaks. Here we compare four inversion methods: truncated singular value decomposition, which is a linear algebra technique, maximum likelihood expectation maximization, which is an iterative method, and Tikhonov regularization applied to χ 2 and Poisson statistics, which are two minimization approaches. The reconstruction fidelity and the capability of estimating cumulative statistics, such as the mean and maximum energy, have been assessed on both synthetic and experimental spectra. The effect of measurements limitations, such as the low energy cut and few number of counts, on the final reconstruction has also been studied. We find that the iterative method performs best as it better describes the statistics of the experimental data and is more robust to noise in the recorded spectrum.

A new hard x-ray spectrometer for runaway electron measurements in tokamaks

“…A common technique to address this problem is to use deconvolution algorithms such as Tikhonov regularization, single value decomposition or Richardson-Lucy deconvolution to guide the selection of the solution with some prior knowledge of its features, such as smoothness or non-negativity. For a detailed analysis of the performance of these algorithms on this specific problem see [9].…”

“…These relativistic particles interact with the post-disruption plasma and emit hard x-rays (HXR) from bremsstrahlung radiation up to several MeVs. Information on the runaway electron energy distribution function can be extracted measuring this hard xray emission [9]. In particular, the study of the RE energy distribution is crucial to understand runaway electron formation, to validate first-principle models and to evaluate the effectiveness of different runaway electron mitigation techniques such as massive gas injection (MGI) [6,10], shattered pellet injection [5] and magnetic resonant perturbation [11,12].…”

Runaway electron velocity-space observation regions of bremsstrahlung hard X-ray spectroscopy

“…For example, in Refs. [4,2,3] the unfolding of the RE 1D energy distribution has been conducted supposing that all REs have p = −1. KM6T is not very sensitive to those particles and, in order to maximise the sensitivity of a tangential LOS to the RE emission, it should have an orientation opposite to the one of KM6T.…”

“…The study of runaway electrons (REs) in magnetically confined fusion plasmas focus on the development of suppression or at least mitigation techniques for safeguarding the structural integrity of future large devices such as ITER [1]. The effects of such techniques on the dynamics of the RE phase-space distribution can be studied using unfolding algorithms that reconstruct the RE distribution from experimental measurements: in particular the 1D energy distribution can be retrieved from the measurements of the bremsstrahlung photons emitted in the Hard X-Ray (HXR) energy region during collisions between REs and ions in the background plasma [2,3,4,5]. Such an analysis is made possible on the Joint European Torus (JET) thanks to three sets of HXR diagnostics which observe the plasma on different lines of sight (LOS).…”

Reconstruction algorithm for the runaway electron energy distribution function of the ITER hard x-ray monitor

“…Instead, methods such as linear regularization [4], Singular-value decomposition (SVD) [20], Maximumlikelihood fitting by Expectation-Maximization (ML-EM) [5,7,21,22] could be used for the reconstruction process. It was shown in [4,23] that the iterative ML-EM method provided the most accurate reconstruction for gamma-ray spectrum reconstruction. The iterative reconstruction algorithm for equation (5) can be written as [5, 24]: ( )…”