Neural network surrogates of Bayesian diagnostic models for fast inference of plasma parameters.

We present a framework for training artificial neural networks (ANNs) as surrogate Bayesian models for the inference of plasma parameters from diagnostic data collected at nuclear fusion experiments, with the purpose of providing a fast approximation of conventional Bayesian inference. Because of the complexity of the models involved, conventional Bayesian inference can require tens of minutes for analyzing one single measurement, while hundreds of thousands can be collected during a single plasma discharge. The ANN surrogates can reduce the analysis time down to tens/hundreds of microseconds per single measurement. The core idea is to generate the training data by sampling them from the joint probability distribution of the parameters and observations of the original Bayesian model. The network can be trained to learn the reconstruction of plasma parameters from observations and the model joint probability distribution from plasma parameters and observations. Previous work has validated the application of such a framework to the former case at the Wendelstein 7-X and Joint European Torus experiments. Here, we first give a description of the general methodological principles allowing us to generate the training data, and then we show an example application of the reconstruction of the joint probability distribution of an effective ion charge Zeff-bremsstrahlung model from data collected at the latest W7-X experimental campaign. One key feature of such an approach is that the network is trained exclusively on data generated with the Bayesian model, requiring no experimental data. This allows us to replicate the training scheme and generate fast, surrogate ANNs for any validated Bayesian diagnostic model.

Bayesian inference of spatially resolved Zeff profiles from line integrated bremsstrahlung spectra.

In nuclear fusion research, the effective ion charge Zeff, which characterizes the overall content of impurities, can be experimentally derived from the plasma electron-ion bremsstrahlung, given the electron density ne and temperature Te. At Wendelstein 7-X, a multichannel near-infrared spectrometer is installed to collect the plasma bremsstrahlung along 27 lines of sight covering more than half the plasma cross section, which provides information on Zeff over the entire plasma radius. To infer spatially resolved Zeff profiles, a Bayesian model is developed in the Minerva framework. Zeff, ne, and Te profiles are modeled as Gaussian processes, whose smoothness is determined by hyperparameters. These profiles are transformed to fields in Cartesian coordinates, given the poloidal magnetic flux surfaces calculated by the variational moments equilibrium code. Given all these physical quantities, the model predicts line-of-sight integrals of near-infrared bremsstrahlung spectra. The model includes the predictive (forward) models of the interferometer, Thomson scattering system, and visible and near-infrared spectrometers. Given the observations of all these diagnostics, the posterior probability distribution of Zeff profiles is calculated and shown as an inference solution. The smoothness (gradient) of the profiles is optimally chosen by Bayesian Occam's razor. Furthermore, wall reflections can significantly pollute the measurements of the plasma bremsstrahlung, which leads to over-estimation of Zeff values in the edge region. In the first results presented in this work, this problem does not appear, and the posterior samples of Zeff profiles are overall plausible and consistent with Zeff values inferred, given the data from the single-channel visible spectrometer.

First results from the implementation of the ITER diagnostic residual gas analyzer prototype at Wendelstein 7-X.

Fusion reactors and long pulse fusion experiments heavily depend on a continuous fuel cycle, which requires detailed monitoring of exhaust gases. We have used a diagnostic residual gas analyzer (DRGA) built as a prototype for ITER and integrated it on the most advanced stellarator fusion experiment, Wendelstein 7-X (W7-X). The DRGA was equipped with a sampling tube and assessed for gas time of flight sample response, effects of magnetic field on gas detection and practical aspects of use in a state of the art fusion environment. The setup was successfully commissioned and operated and was used to observe the gas composition of W7-X exhaust gases. The measured time of flight gas response was found to be in the order of a second for a 7 m sample tube. High values of magnetic field were found to affect the partial pressure readings of the DRGA and suggest that additional shielding is necessary in future experimental campaigns.

Spectroscopic imaging of limiter heat and particle fluxes and the resulting impurity sources during Wendelstein 7-X startup plasmas.

A combined IR and visible camera system [G. A. Wurden et al., "A high resolution IR/visible imaging system for the W7-X limiter," Rev. Sci. Instrum. (these proceedings)] and a filterscope system [R. J. Colchin et al., Rev. Sci. Instrum. 74, 2068 (2003)] were implemented together to obtain spectroscopic data of limiter and first wall recycling and impurity sources during Wendelstein 7-X startup plasmas. Both systems together provided excellent temporal and spatial spectroscopic resolution of limiter 3. Narrowband interference filters in front of the camera yielded C-III and Hα photon flux, and the filterscope system provided Hα, Hß, He-I, He-II, C-II, and visible bremsstrahlung data. The filterscopes made additional measurements of several points on the W7-X vacuum vessel to yield wall recycling fluxes. The resulting photon flux from both the visible camera and filterscopes can then be compared to an EMC3-EIRENE synthetic diagnostic [H. Frerichs et al., "Synthetic plasma edge diagnostics for EMC3-EIRENE, highlighted for Wendelstein 7-X," Rev. Sci. Instrum. (these proceedings)] to infer both a limiter particle flux and wall particle flux, both of which will ultimately be used to infer the complete particle balance and particle confinement time τP.

Overview of diagnostic performance and results for the first operation phase in Wendelstein 7-X (invited).

Wendelstein 7-X, a superconducting optimized stellarator built in Greifswald/Germany, started its first plasmas with the last closed flux surface (LCFS) defined by 5 uncooled graphite limiters in December 2015. At the end of the 10 weeks long experimental campaign (OP1.1) more than 20 independent diagnostic systems were in operation, allowing detailed studies of many interesting plasma phenomena. For example, fast neutral gas manometers supported by video cameras (including one fast-frame camera with frame rates of tens of kHz) as well as visible cameras with different interference filters, with field of views covering all ten half-modules of the stellarator, discovered a MARFE-like radiation zone on the inboard side of machine module 4. This structure is presumably triggered by an inadvertent plasma-wall interaction in module 4 resulting in a high impurity influx that terminates some discharges by radiation cooling. The main plasma parameters achieved in OP1.1 exceeded predicted values in discharges of a length reaching 6 s. Although OP1.1 is characterized by short pulses, many of the diagnostics are already designed for quasi-steady state operation of 30 min discharges heated at 10 MW of ECRH. An overview of diagnostic performance for OP1.1 is given, including some highlights from the physics campaigns.

Status of the diagnostics development for the first operation phase of the stellarator Wendelstein 7-X.

An overview of the diagnostics which are essential for the first operational phase of Wendelstein 7-X and the set of diagnostics expected to be ready for operation at this time are presented. The ongoing investigations of how to cope with high levels of stray Electron Cyclotron Resonance Heating (ECRH) radiation in the ultraviolet (UV)/visible/infrared (IR) optical diagnostics are described.

Bayesian experimental design of a multichannel interferometer for Wendelstein 7-X.

Bayesian experimental design (BED) is a framework for the optimization of diagnostics basing on probability theory. In this work it is applied to the design of a multichannel interferometer at the Wendelstein 7-X stellarator experiment. BED offers the possibility to compare diverse designs quantitatively, which will be shown for beam-line designs resulting from different plasma configurations. The applicability of this method is discussed with respect to its computational effort.

Diagnostic developments for quasicontinuous operation of the Wendelstein 7-X stellarator.

The stellarator Wendelstein 7-X will allow for quasicontinuous operation with the duration only being limited to two 30 min discharges per day, at a continuous heating power of 10 MW electron cyclotron resonance heating (ECRH) at 140 GHz, by the capacity of the cooling water reservoir. This will result in high thermal loads on all plasma facing components of 50-100 kW/m(2) from radiation alone and of up to about 500 kW/m(2) on components additionally exposed to convective loads. In high density scenarios toroidally varying ECRH stray radiation levels of 50-200 kW/m(2) need to be coped with, requiring careful material selection and different shielding and hardening techniques. Furthermore, a gradual buildup of coatings on plasma facing optical components, which without any measures being taken, would lead to high transmission losses already within a few days of long pulse operation (equivalent to about 1 year of operation in pulsed devices like JET or ASDEX-upgrade) and therefore needs to be prevented as much as possible. In addition in situ cleaning as well as absolute calibration techniques need to be developed for all plasma facing optical systems. Here we report about some of our efforts to find, for various types of diagnostics, ways to cope with these adverse effects. Moreover, we give a few examples for individual diagnostic specific issues with respect to quasicontinuous operation, such as the development of a special integrator for the magnetic diagnostics as well as special interferometer types which can cope with unavoidable vibrations and slow path length changes due to, e.g., thermal expansion of the plasma vessel.