Reconstruction of Zeff profiles at TEXTOR through Bayasian source separation

The understanding of the behaviour of impurities is a critical issue in tokamak physics. The ion effective charge Zeff provides a measure for impurity concentration. On the TEXTOR tokamak (Julich, Germany), we run a diagnostic to determine Zeff from the bremsstrahlung emissivity E. From radial profiles of E, electron density ne and temperature Te, profiles for Zeff can be reconstructed. However, their interpretation is difficult outside the plasma centre, because of various uncertainties in E, ne and Te at the edge, which render the radial matching of the different profiles problematic. Conversely, if it were possible to obtain a set of line-integrated values for Zeff directly from the line-integrated measurements of E, ne and Te, then these problems would be avoided. Now, recent advances in the field of statistical signal processing allow the extraction of an unknown signal from a signal mixture. In particular, we describe a procedure for the single-channel Bayesian source separation of a line-integrated Zeff signal from a line-integrated emissivity source, using as a forward model a linearized version of the known functional dependence of Zeff on E, ne and Te. Here, a line-integral over a traditionally obtained Zeff profile may serve as a prior for the line-integrated Zeff signal. In this way, precise information on the electron density and temperature may even become superfluous for the determination of Zeff.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Investigation of a 1-D Fluid Probe Model for Mach Probe Measurements

In this paper we show how a two dimensional fluid model can be used to interpret data obtained from an inclined Mach-probe or a Gundestrup probe. We use an analytical approximation of the solution of the differential equations describing the relation between the plasma flow and the measured ion saturation currents at the probe's surface. The parameters of this analytical solution are determined by comparison with the exact numerical solution of the equations. In this way we are able to measure the parallel as well as the perpendicular Mach numbers over the whole parameter range with a minimum accuracy of 90%.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Visualization of tokamak operational spaces through the projection of data probability distributions

Information visualization is becoming an increasingly important tool for making inferences from large and complex data sets describing tokamak operational spaces. Landmark MDS, a computationally efficient information visualization tool, well suited to the properties of fusion data, along with a comprehensive probabilistic data representation framework, is shown to provide a structured visual map of plasma confinement regimes, plasma disruption regions and plasma trajectories. This is aimed at contributing to the understanding of underlying physics of various plasma phenomena, while providing an intuitive tool for plasma monitoring

Advanced learning in massive fusion databases : nonlinear regression, clustering, dimensionality reduction and information retrieval

The use of advanced data mining techniques in fusion experiments can help both in the progress of physical insight as well as in solving current engineering challenges in a fast track approach to the realization of fusion power. We present a research program concerning several important operations that are useful for detecting structures of interest in massive fusion databases. We consider measurement uncertainty through a probabilistic approach and we exploit useful information residing in the temporal structure of signals (e.g. the $D_\alpha$ signal for plasma regime identification), explicitly taking into account nonstationarity and transient behavior. Therefore we adopt a multiscale wavelet representation, modeling the wavelet coefficients through appropriate probability distributions. We integrate data from multiple diagnostics, optionally capturing signal dependencies by multivariate distributions. Our framework is concerned with the following tasks: for learning an in general nonlinear relation between physical variables and for extrapolation toward reactor-relevant conditions (e.g. confinement prediction); of objects (e.g. discharges) into physically meaningful groups; to uncover the fundamental degrees of freedom driving certain aspects of plasma behavior. In addition, this scheme is useful for data visualization and as a preprocessing step for various machine learning algorithms, in order to mitigate issues related to a high data dimensionality; by searching in a database for plasma conditions or phenomena that are similar to a given query. In order to accomplish our program, we employ the powerful language of information geometry, i.e. the study of probabilistic manifolds using differential geometry. In this work, we present the details of our mathematical framework and we show results of an example clustering application for plasma regime identification

Comparison between Theoretical and Experimental Radial Electron Temperature Profiles in a Low Density Weakly Ionized Plasma

Experimental and theoretical studies of the radial distribution function of the electron temperature (RDFT) in a low-density plasma and weakly ionized gas for the abnormal glow region are presented. Experimentally, the electron temperatures and densities are measured by a Langmuir probe moved radially from the center to the edge of the cathode electrode for helium gas at different pressures in the low-pressure glow discharge. The comparison of the final experimental data for the radial distribution of electron temperatures and densities for different low pressures ranging from 0.2 to 1.2 torr, with the final proved equation of RDFT confirms that the electron temperatures decrease with increasing product of radial distance and gas pressures, showing a radial decrement dependence of the electron temperature from the center to the edge of the electrode. This is attributed to the increase of the number of electron-atom collisions at higher gas pressures and consequently of the rate of ionization. For the axial distance (L) from the tip of the probe to cathode electrode and the cathode electrode radius (R), a theoretical and experimental comparison for the two conditions L R, for both cases the produced plasma temperatures decrease and densities increase. It is concluded that the RDFT accurately shows a dramatic decrease for L R similar as for conditions of magnetized and unmagnetized effect for DC plasma. This means that the rate of plasma loss by diffusion decreased for L < R, agrees well with the applied of magneti