Spectroscopic analysis of X-pinch plasma produced on the compact LC-generator of Ecole Polytechnique using artificial neural networks
Introduction
X-pinch plasmas are point like x-ray sources (10–100 μm diameter) which are created by the explosions of two or more fine wires arranged to cross and touch at a single point. Investigation of X-pinch plasmas on large pulse power facilities (1 MA and 100 ns current rise-time generators) showed that these plasmas are hot (Te > 1 keV) and dense (ne∼1019–1024 cm−3) and applicable for x-ray backlighting of dense matter and microscopy for biology [1], [2], [3]. However, the required technology for large pulse power facilities is expensive and complicated. Therefore, there has been some interest in compact and efficient generators and the recent developments showed that, table-top generators have the capability of producing high energy density plasmas which are also applicable to X-ray backlighting, microscopy and spectroscopy [4], [5], [6].
X-ray spectroscopy is widely used to diagnose the astrophysical and laboratory plasmas for the determination of electron temperatures (Te) and densities (ne). The classical process is the following: one obtains the peak intensities of spectral lines, emitted by the plasma in certain regions, by the spectrometers and compares with the synthetic spectra which are produced by complex collisional radiative models at certain plasma electron temperatures and densities [7]. However, these processes can be time and effort consuming, depending on the complexity of the model. To eliminate these difficulties, different approaches of plasma spectral analysis have been proposed, such as artificial neural networks (ANN) and genetic algorithms (GA) [8], [9], [10].
The ANN algorithms have been rapidly considered of high potential interest and they were used over the last couple of decades in many realtime applications and in various areas such as remote sensing, computer vision, pattern recognition and medical diagnosis. The ANN can easily identify and correlate the pattern between some inputs through a training process, and set correlations for the outputs. Especially, their adaptative nature allows solving complex and non-linear problems [11], [12], [13], [14]. ANN started to be used in diagnosing specifically the astrophysical plasmas, the laboratory produced magnetically and inertially confined fusion plasmas: in 1994, Morgan et al. implemented the technique for spectroscopic modeling of Tokomak plasmas [8] and Osterheld et al. estimated the electron temperature and density of laser produced K-shell Al plasma [9]. Meanwhile, Genetic Algorithms (GA) have been successively applied to diagnose K-shell Ar, Al and L-shell Mo in laser and Z-pinch produced plasmas, due to their natural selection mechanism for searching solution and optimization algorithms [10], [15], [16].
In the present work, modeling of particular Molybdenum L-shell spectra is based on ANN training over L-shell Mo collisional radiative model produced spectra in the region of 4.0–5.5 Å [15], [17]. The paper is organized as follows. The second section explains the ANN methodology. In the third section, we describe the experimental data used as experimental reference. The fourth section presents neural network modeling of experimental data and the paper is concluded in the last section.
Section snippets
Artificial neural networks
Neural networks, with massive parallelism in their structure and high computation rates, provide a great alternative to other conventional classifiers and decision making systems. Neural networks are powerful tools that can be trained to perform complex and various functions in computer vision applications, such as preprocessing (boundary extraction, image restoration, image filtering), feature extraction (extract transformed domain features), associative memory (storing and retrieving
Experimental data and interpretation
The x-ray spectrum of Mo (shot XP_601) was produced on the compact LC-generator (40 kV, 250 kA, 200 ns). The 25-μm X-shaped Mo wires were placed in the anode–cathode gap of 9 mm. Spectra in the region of 950–1350 eV band were recorded with two x-ray spectrographs [6].
A wide spectral region was registered with a convex mica crystal (2d = 1.984 Å). With 11.5 mm radius of curvature, 220 mm distance between the x-ray source and the crystal bending axis, it gives an effective dispersion of 25 eV/mm
Neural network modeling of experimental data
The Mo plasma electron density and temperature (shot XP_601) was modeled using previously developed non-LTE collisional radiative model. The energy level structures, spontaneous and collisional rates, collisional and photoionization cross-sections calculations were performed using the Hebrew University–Lawrence Livermore atomic code (HULLAC) [20]. The L-shell Mo model has the total energy levels of 6137 with detailed structure for O-like to Mg-like Mo ions, included singly excited states up to n
Conclusion
An artificial neural network is a good choice as a classifier because it correlates features in synthetic data with features in the measured data, even if there are ambiguities coming from the noise and from the location of the lines. In the present work, back-propagation neural network was applied as a classifier for estimating plasma parameters from typical Molybdenum X-pinch L-shell spectra. The linewidth of 500 eV was selected to aid in characterizing plasma electron temperature and
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