Udo von Toussaint

Statistical analysis of blister bursts during temperature-programmed desorption of deuterium-implanted polycrystalline tungsten

During temperature-programmed desorption (TPD) of stress-relieved polycrystalline tungsten samples exposed to a deuterium plasma, short, intense bursts of D2 were observed on the low-temperature flank of the main desorption peak. These bursts are attributed to the rupturing of blisters filled with high-pressure D2 gas. A statistical analysis of the size distribution and temporal correlation of the bursts is presented. The influence of different measurement intervals and TPD heating rates on the observed bursts is simulated based on these statistics and compared to the experimental results. The contribution of bursts to the total D inventory in the sample is also estimated.

Relevance of surface roughness to tungsten sputtering and carbon implantation

Tungsten sputtering and carbon layer growth by carbon ion bombardment has been investigated by experiments with thin W layers. Preparation of tungsten layers by magnetron deposition allows one to control the surface roughness by choosing appropriate substrates. The fluence dependent elemental composition of the bombarded surface has been studied in situ with ion beam analysis allowing separate measurements of the areal densities of tungsten and carbon atoms. In contrast to weight-loss measurements, this approach is much less affected by nonuniformities of the incident flux and therefore allows one to determine the dependency of the principal physics processes on input parameters with much higher accuracy. After bombardment, ex situ scanning electron microscopy has been used for the qualitative understanding of the evolution of the surface topography with increasing fluence. The experiments clearly show the influence of surface roughness, leading to increased tungsten sputter yields and strongly reduced ca...

Depth profile determination with confidence intervals from Rutherford backscattering data

A new simulation program for Rutherford backscattering spec- troscopy (RBS) together with an adaptive kernel method in the Bayesian proba- bility theory framework was applied to the analysis of RBS data. Reconstructed depth profiles are free from noise-induced ringing, even for strongly overlapping RBS peaks. This has been achieved by the use of the adaptive kernel method, which generates the least informative depth profile according to the data and in addition allows one to calculate the uncertainty of the obtained depth profiles. The method is applied to erosion measurements of carbon samples.

Fuel removal from tile gaps with oxygen discharges: reactivity of neutrals

Carbon removal in the so-called remote areas, where no energetic species can reach the surface, is investigated with low-temperature glow discharges in pure oxygen. Plasma-deposited amorphous hydrogenated carbon thin films are used as a model system for redeposited films. Erosion measurements are performed on flat substrates as well as on two different three-dimensional (3D) test structures. One design consists of 19 mm deep gaps with widths ranging from 0.5 to 4 mm to simulate ITER tile gaps. A second design consists of a flat box-like structure where particles can enter only through a narrow slit. Measurements are performed for substrate temperatures ranging from 290 to 580 K. Erosion rates follow an Arrhenius-type dependence on substrate temperature with an effective activation energy of 0.25 eV. While at room temperature the surface loss probability of the dominant eroding species is 50% it becomes smaller at elevated temperatures. At elevated temperatures, the films are not only removed faster but simultaneously erosion penetrates deeper into the gaps.

Invariance priors for Bayesian feed-forward neural networks

Neural networks (NN) are famous for their advantageous flexibility for problems when there is insufficient knowledge to set up a proper model. On the other hand, this flexibility can cause overfitting and can hamper the generalization of neural networks. Many approaches to regularizing NN have been suggested but most of them are based on ad hoc arguments. Employing the principle of transformation invariance, we derive a general prior in accordance with the Bayesian probability theory for feed-forward networks. An optimal network is determined by Bayesian model comparison, verifying the applicability of this approach. Additionally the prior presented affords cell pruning.

Tungsten erosion under combined hydrogen/helium high heat flux loading

We investigated the erosion behaviour of tungsten under irradiation with a fusion reactor-relevant H/He mixture of 94%/6% at a power density of 10 MW m−2. The investigated surface temperatures range up to 2000 °C and the range of the applied fluence was up to 7 × 1025 m−2. The erosion yield we observe exceeds the value expected from physical sputtering data by a factor of 2. In addition we observe an Arrhenius-like increase of the erosion yield with temperature with an activation energy of 0.04 eV.

General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression

Based on geometric invariance properties, we derive an explicit prior distribution for the parameters of multivariate linear regression problems in the absence of further prior information. The problem is formulated as a rotationally-invariant distribution of \(L\)-dimensional hyperplanes in \(N\) dimensions, and the associated system of partial differential equations is solved. The derived prior distribution generalizes the already known special cases, e.g., 2D plane in three dimensions.

Global Optimization Employing Gaussian Process-Based Bayesian Surrogates

The simulation of complex physics models may lead to enormous computer running times. Since the simulations are expensive it is necessary to exploit the computational budget in the best possible manner. If for a few input parameter settings an output data set has been acquired, one could be interested in taking these data as a basis for finding an extremum and possibly an input parameter set for further computer simulations to determine it—a task which belongs to the realm of global optimization. Within the Bayesian framework we utilize Gaussian processes for the creation of a surrogate model function adjusted self-consistently via hyperparameters to represent the data. Although the probability distribution of the hyperparameters may be widely spread over phase space, we make the assumption that only the use of their expectation values is sufficient. While this shortcut facilitates a quickly accessible surrogate, it is somewhat justified by the fact that we are not interested in a full representation of the model by the surrogate but to reveal its maximum. To accomplish this the surrogate is fed to a utility function whose extremum determines the new parameter set for the next data point to obtain. Moreover, we propose to alternate between two utility functions—expected improvement and maximum variance—in order to avoid the drawbacks of each. Subsequent data points are drawn from the model function until the procedure either remains in the points found or the surrogate model does not change with the iteration. The procedure is applied to mock data in one and two dimensions in order to demonstrate proof of principle of the proposed approach.

Sequential Batch Design for Gaussian Processes Employing Marginalization

Within the Bayesian framework, we utilize Gaussian processes for parametric studies of long running computer codes. Since the simulations are expensive, it is necessary to exploit the computational budget in the best possible manner. Employing the sum over variances —being indicators for the quality of the fit—as the utility function, we establish an optimized and automated sequential parameter selection procedure. However, it is also often desirable to utilize the parallel running capabilities of present computer technology and abandon the sequential parameter selection for a faster overall turn-around time (wall-clock time). This paper proposes to achieve this by marginalizing over the expected outcomes at optimized test points in order to set up a pool of starting values for batch execution. For a one-dimensional test case, the numerical results are validated with the analytical solution. Eventually, a systematic convergence study demonstrates the advantage of the optimized approach over randomly chosen parameter settings.

Optimizing Nuclear Reaction Analysis (NRA) using Bayesian Experimental Design

Nuclear Reaction Analysis with 3He holds the promise to measure Deuterium depth profiles up to large depths. However, the extraction of the depth profile from the measured data is an ill‐posed inversion problem. Here we demonstrate how Bayesian Experimental Design can be used to optimize the number of measurements as well as the measurement energies to maximize the information gain. Comparison of the inversion properties of the optimized design with standard settings reveals huge possible gains. Application of the posterior sampling method allows to optimize the experimental settings interactively during the measurement process.