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.

Stellarators Resist Turbulent Transport on the Electron Larmor Scale.

Electron temperature gradient (ETG)-driven turbulence, despite its ultrafine scale, is thought to drive significant thermal losses in magnetic fusion devices-but what role does it play in stellarators? The first numerical simulations of ETG turbulence for the Wendelstein 7-X stellarator, together with power balance analysis from its initial experimental operation phase, suggest that the associated transport should be negligible compared to other channels. The effect, we argue, originates essentially from the geometric constraint of multiple field periods, a generic feature of stellarators.

Collective Thomson scattering diagnostic at Wendelstein 7-X.

A Collective Thomson Scattering (CTS) diagnostic is installed at Wendelstein 7-X for ion temperature measurements in the plasma core. The diagnostic utilizes 140 GHz gyrotrons usually used for electron cyclotron resonance heating (ECRH) as a source of probing radiation. The CTS diagnostic uses a quasi-optical transmission line covering a distance of over 40 m. The transmission line is shared between the ECRH system and the CTS diagnostic. Here we elaborate on the design, installation, and alignment of the CTS diagnostic and present the first measurements at Wendelstein 7-X.

Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7-X.

We make use of a Bayesian description of the neural network (NN) training for the calculation of the uncertainties in the NN prediction. Having uncertainties on the NN prediction allows having a quantitative measure for trusting the NN outcome and comparing it with other methods. Within the Bayesian framework, the uncertainties can be calculated under different approximations. The NN has been trained with the purpose of inferring ion and electron temperature profile from measurements of a X-ray imaging diagnostic at W7-X. The NN has been trained in such a way that it constitutes an approximation of a full Bayesian model of the diagnostic, implemented within the Minerva framework. The network has been evaluated using measured data and the uncertainties calculated under different approximations have been compared with each other, finding that neglecting the noise on the NN input can lead to an underestimation of the error bar magnitude in the range of 10%-30%.