Real-time Tomography-based Bayesian Inference from TCV Bolometry Data

Abstract

Radiated power information is crucial to diagnose and optimize the performance of fusion plasmas. Traditionally, at the TCV tokamak, radiated power analysis has only ever been possible following plasma discharge termination. However, recently, TCV bolometer data have become available in real-time. This offers the opportunity of integrating the radiated power information into the TCV plasma control system. In this work, we propose a novel real-time tomography-based Bayesian technique allowing estimation of the power radiated from user-defined regions of interest in the plasma. The real-time estimates are obtained as computationally cheap linear combinations of bolometer measurements, using pre-computed coefficients that are optimized for the specific discharge planned. This method is not, thus, trained on a set of synthetic or tomographically reconstructed emissivity profiles. We detail the derivation of the technique and show its equivalence to traditional tomographic estimates under suitable conditions. We then demonstrate that this technique enables accurate real-time estimation of the total, core, divertor and main chamber radiated power, by its application to a representative and heterogeneous set of TCV discharges. Finally, we discuss the robustness of the technique to faulty detectors, showing that simple precautions allow safe handling of many common issues. The computational routines implementing the described technique are provided as open-source code.

Figures (7)

• Figure 1: Bolometer diagnostic installed at TCV. On the left, the line of sight configuration (in red) overlaid to a poloidal cross-section of TCV (in black). On the right, the diagnostic coverage in projection space, highlighting the sparse-view nature of the data: each red dot corresponds to a line of sight, parametrized in terms of its steepness $\theta$ and its distance $p$ from the centerpoint of the vessel; the shaded regions represent $(p, \theta)$ combinations corresponding to lines that do not intersect the TCV vessel.
• Figure 2: FBT vs LIUQE magnetic equilibria, for TCV discharge $\#85270$. In red, FBT equilibria, in black, LIUQE equilibria.
• Figure 3: Radiated power estimation: results of application to discharge $\#85270$. In Fig. \ref{['fig_shot_inversions']}, the post-discharge tomographic inversions at 5 reference times; due to the time-varying emissivity levels, two different colormaps and colorbars are used for visualization purposes. In Figs.\ref{['fig_shot_tot_mask']}, \ref{['fig_shot_core_mask']}, \ref{['fig_shot_main_mask']} and \ref{['fig_shot_div_mask']}, the masks used to estimate the total, core, main chamber and divertor radiated power (for $t_{_{FBT}}=1\,\mathrm{s}$). In Figs.\ref{['fig_shot_prad_tot_core']} and \ref{['fig_shot_prad_main_div']}, the radiated powers $\widehat{P}_{rad}^{\,tomo}$ estimated by tomographic reconstruction and the real-time estimates $\widehat{P}_{rad}\pm\sigma$.
• Figure 4: Radiated power estimation: results of application to discharges $\#86839$, $\#86089$, $\#85357$ and $\#85166$, characterized by different magnetic configurations. In Figs. \ref{['usn_config']}-\ref{['ll_config']}, FBT magnetic equilibria at $t\approx1\,\mathrm{s}$ for the four discharges. In Figs. \ref{['usn_prad']}-\ref{['ll_prad']}, results for the estimation of total and core radiated power (same plotting conventions of Figs. \ref{['fig_shot_tot_mask']}-\ref{['fig_shot_prad_tot_core']}). Results for divertor and main chamber radiated power are not shown to avoid redundancy.
• Figure 5: Phantom generation procedure: each phantom $\mathbf{x}$ is obtained as a linear combination of the five shown elements. Elements $\mathbf{x}_{_A}$, $\mathbf{x}_{_B}$, $\mathbf{x}_{_C}$ are obtained from a SOLPS phantom, by isolating its inner leg, outer leg and remaining radiation contributions, respectively; elements $\mathbf{x}_{_D}$ and $\mathbf{x}_{_E}$ are added to model X-point radiator and core radiation features, respectively.