Inference of field reversed configuration topology and dynamics during Alfvenic transients

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. We present a spectral decomposition method that allows for corrections to line positions and bound-bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

GS-DeepNet: mastering tokamak plasma equilibria with deep neural networks and the Grad-Shafranov equation

The force-balanced state of magnetically confined plasmas heated up to 100 million degrees Celsius must be sustained long enough to achieve a burning-plasma state, such as in the case of ITER, a fusion reactor that promises a net energy gain. This force balance between the Lorentz force and the pressure gradient force, known as a plasma equilibrium, can be theoretically portrayed together with Maxwell's equations as plasmas are collections of charged particles. Nevertheless, identifying the plasma equilibrium in real time is challenging owing to its free-boundary and ill-posed conditions, which conventionally involves iterative numerical approach with a certain degree of subjective human decisions such as including or excluding certain magnetic measurements to achieve numerical convergence on the solution as well as to avoid unphysical solutions. Here, we introduce GS-DeepNet, which learns plasma equilibria through solely unsupervised learning, without using traditional numerical algorithms. GS-DeepNet includes two neural networks and teaches itself. One neural network generates a possible candidate of an equilibrium following Maxwell's equations and is taught by the other network satisfying the force balance under the equilibrium. Measurements constrain both networks. Our GS-DeepNet achieves reliable equilibria with uncertainties in contrast with existing methods, leading to possible better control of fusion-grade plasmas.

High-fidelity inference of local impurity profiles in C-2W using Bayesian tomography

In C-2W (also called "Norman") [1], beam-driven field reversed configuration plasmas embedded in a magnetic mirror are produced and sustained in a steady state. A multi-chord passive Doppler spectroscopy diagnostic provides line-integrated impurity emission measurements near the center plane of the confinement vessel with fast time resolution. The high degree of plasma non-uniformity across optical sightlines can preclude direct fitting of the measured line-integrated spectra. To overcome this challenge, local impurity profiles are inferred using Bayesian tomography, a superior analysis technique based on a complete forward model of the diagnostic. The measured emission of O⁴⁺ triplet lines near 278.4 nm is modeled assuming two independent populations: thermal and beam ions. Gaussian processes are used to generate and infer local profiles. The inference incorporates details of the geometrical arrangement of the diagnostic, instrument function, intensity calibration, and a noise model. Markov chain Monte Carlo (MCMC) sampling of the posterior distribution of solutions provides high-fidelity uncertainty estimates. The reconstructed O⁴⁺ impurity profiles are consistent with data from other diagnostics and show good agreement with expected physics based on previously developed models of biasing circuit and impurity transport.

Bayesian inference and calibration of magnetic diagnostics

The magnetic diagnostics across TAE Technologies' compact toroid fusion device include 28 internal and 45 external flux loops that measure poloidal flux and axial field strength, 64 three-axis (radial, toroidal, and axial) Mirnov probes, and 22 internal and external, axial-only Mirnov probes. Imperfect construction, installation, and physical constraints required a Bayesian approach for the calibration process to best account for errors in signals. These errors included flux loops not fitted to a perfect circle due to spatial constraints, Mirnov probes not perfectly aligned against their respective axes, and flux pickup that occurred within the insert (feedthrough) of the Mirnov probes. Our model-based calibration is derived from magnetostatic theory and the circuitry of the sensors. These models predicted outputs that were compared against experimental data. Using a simple least-squares optimization, we were able to predict flux loop data within 1% of relative error. For the Mirnov probes, we utilized Bayesian inference to determine three rotation angles and three amplifier gains. The results of this work not only gave our diagnostic measurements physical meaning, but also act as a safeguard to spot when instruments have malfunctioned, or when there is an error in database maintenance. This paper will go into the details of our calibration procedure, our Bayesian modeling, and the accuracy of our results compared to experimental data.

The integrated diagnostic suite of the C-2W experimental field-reversed configuration device and its applications

In the current experimental device of TAE Technologies, C-2W (also called "Norman"), record breaking advanced beam-driven field-reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams (15-40 keV, total power up to 20 MW), advanced divertors, bias electrodes, and an active plasma control system. This fully operational experiment is coupled with a fully operational suite of advanced diagnostic systems. The suite consists of 60+ individual systems spanning 20 categories, including magnetic sensors, Thomson scattering, interferometry/polarimetry, spectroscopy, fast imaging, bolometry, reflectometry, charged and neutral particle analysis, fusion product detection, and electric probes. Recently, measurements of main ion temperatures via a diagnostic neutral beam, axial profiles of energy flux from an array of bolometers, and divertor and edge plasma parameters via an extensive set of electric probes, interferometers, and spectrometers have all been made available. All the diagnostics work together to provide a complete picture of the FRC, fast-ion inventory, and edge plasma details enabling tomographic reconstruction of plasma parameter profiles and real-time plasma control.

Magnetic diagnostic suite of the C-2W field-reversed configuration experiment

A fundamental component of any magnetically confined fusion experiment is a firm understanding of the magnetic field. The increased complexity of the C-2W machine warrants an equally enhanced diagnostic capability. C-2W is outfitted with over 700 magnetic field probes of various types. They are both internal and external to the vacuum vessel. Inside, a linear array of innovative in-vacuum annular flux loop/B-dot combination probes provide information about plasma shape, size, pressure, energy, temperature, and trapped flux when coupled with established theoretical interpretations. A linear array of B-dot probes complement the azimuthally averaged measurements. A Mirnov array of 64 3D probes, with both low and high frequency resolution, detail plasma motion and MHD modal content via singular value decomposition analysis. Internal Rogowski probes measure axial currents flowing in the plasma jet. Outside, every feed-through for an internal probe has an external axial field probe. There are many external loops that measure the plasma formation dynamics and the total external magnetic flux. The external measurements are primarily used to characterize eddy currents in the vessel during a plasma shot. Details of these probes and the data derived from their signals are described.