In magnetically confined fusion plasmas it is possible to distinguish between low confinement (L-mode) and high confinement (H-mode). At the transition from L-mode to H-mode and vice versa a phase with intermediate confinement exists, which is also called I-phase. During this intermediate state limit-cycle oscillations (LCO) with a frequency in the low kilohertz range occur, corresponding to fluctuations in the plasma temperature, density and other key parameters.
This work investigates the spatial distribution of these LCOs within the plasma by diode bolometry. The 2D spatial structure of the Iphase as it appears in the diode bolometers is resolved using correlation and coherence techniques between bolometer channels. It is found that limit-cycle oscillations are localized in the region of the magnetic X-point and it is indicated that they are not stationary but poloidal moving along the separatrix during the I-phase.
Table of Contents
1 Introduction
2 Experimental setup
2.1 ASDEX Upgrade
2.1.1 Setup
2.1.2 Magnetic field
2.1.3 Divertors
2.2 Diagnostics
2.2.1 Mirnov coils
2.2.2 Bolometry
2.2.2.1 Functionality
2.2.2.2 Setup and spatial resolution
3 Theoretical background
3.1 Plasma confinement
3.1.1 Energy confinement time and Lawson criterion
3.1.2 L-mode
3.1.3 H-mode
3.1.4 I-phase and limit-cycle oscillations
3.2 Data analysis
3.2.1 Fourier-based analysis
3.2.1.1 Fast Fourier transform
3.2.1.2 Power Spectral Density
3.2.1.3 Spectrogram
3.2.1.4 Example
3.2.2 Dual channel analysis
3.2.2.1 Correlation
3.2.2.2 Coherence
4 I-phase investigation
4.1 Experimental data
4.2 Identifying limit-cycle oscillations
4.2.1 Power Spectral Density
4.2.2 Spectrogram
4.3 2D-analysis of LCOs with bolometer
4.3.1 Cross-correlation
4.3.1.1 Propagation of I-phase
4.3.1.2 Spatial structure
4.3.2 Coherence
4.3.2.1 Cross Power Spectrum and Phase
4.3.2.2 Spatial structure
4.3.2.3 Comparsion with upper single null discharge
4.3.2.4 Movement
5 Conclusion
Research Objectives and Themes
The primary objective of this thesis is to investigate the spatial structure and dynamics of limit-cycle oscillations (LCO) during the I-phase transition in magnetically confined fusion plasmas. By utilizing diode bolometer data from the ASDEX Upgrade tokamak, the research aims to localize these oscillations within the plasma vessel and determine whether they exhibit poloidal movement along the separatrix.
- Analysis of plasma confinement modes (L-mode, H-mode, and I-phase).
- Development and application of correlation and coherence techniques for bolometric data analysis.
- Experimental identification and localization of LCOs relative to the magnetic X-point.
- Validation of results through comparison with magnetic diagnostics and alternative magnetic configurations.
Excerpt from the Book
3.2.2.1 Correlation
The correlation function tells how similar two signals are as a function of the time displacement τ between both signals. The value is always between -1 (total anti-correlated) and 1 (total correlated) if the correlation is normalized to the standard deviation of the input signals.
The correlation between two standardized functions ˆx = x/σx and ˆy = y/σy is defined as Rxy(τ) = ∫[−∞,∞] ˆx∗(t) · ˆy(t + τ)dt. The larger Rxy becomes the higher the correlation is. The position of the maximum of Rxy provides the time shift τ between both signals. Usually, the cross-correlation is calculated for two different functions x and y. If they are the same function this is also known as the auto-correlation. The Fourier transform of the auto-correlation Sxx(ω) = F(Rxx)(ω) = 1/√2π ∫[−∞,∞] Rxx(t) · e[−iωt]dt results in the PSD (eq. 3.7) after averaging (Sxx=
Chapter Summaries
1 Introduction: Provides an overview of nuclear fusion, the concepts of plasma confinement, and the motivation for studying LCOs in the ASDEX Upgrade tokamak.
2 Experimental setup: Describes the ASDEX Upgrade tokamak, its magnetic field configuration, divertors, and the diagnostic systems, specifically focusing on Mirnov coils and diode bolometers.
3 Theoretical background: Covers the physics of plasma confinement, the definition of the I-phase, and the mathematical foundations for signal analysis, including Fourier transforms, PSD, correlation, and coherence.
4 I-phase investigation: Presents the application of the developed analytical methods to experimental discharge data, identifying LCOs and resolving their 2D spatial structure near the magnetic X-point.
5 Conclusion: Summarizes the findings regarding the V-shaped localization of LCOs near the X-point and the separatrix, while suggesting directions for future research.
Keywords
Nuclear fusion, ASDEX Upgrade, Tokamak, Plasma confinement, I-phase, Limit-cycle oscillations, LCO, Diode bolometry, Correlation analysis, Coherence, Fourier transform, Magnetic X-point, Separatrix, Plasma diagnostics
Frequently Asked Questions
What is the core subject of this thesis?
The thesis explores the spatial characteristics and physical behavior of limit-cycle oscillations (LCO) that occur during the intermediate phase (I-phase) between low and high confinement modes in fusion plasmas.
Which central themes are examined?
Key themes include plasma confinement regimes, the use of diode bolometers for 2D spatial resolution in tokamaks, and the implementation of signal processing techniques like cross-correlation and coherence to identify localized plasma phenomena.
What is the primary research question?
The research seeks to identify the exact spatial location of LCOs within the plasma vessel and determine if these oscillations are stationary or if they propagate poloidally along the separatrix.
Which scientific methods are utilized?
The study relies on Fourier-based analysis (Fast Fourier Transform, Power Spectral Density, Spectrograms) and dual-channel analysis using cross-correlation and coherence functions to evaluate the similarity and phase relationships of bolometer signals.
What does the main body address?
The main body detailes the experimental setup, introduces the theoretical background for the analytical tools, and conducts an investigation into LCOs, concluding with a spatial mapping of these oscillations in the 2D cross-section of the plasma.
What are the characterizing keywords of the work?
The work is characterized by terms such as Plasma confinement, I-phase, Limit-cycle oscillations, Bolometry, Coherence, and Magnetic X-point.
How are the diode bolometer channels used in this research?
The channels provide line-of-sight measurements of radiated energy; by calculating the intersection points of these lines, the author achieves a 2D spatial resolution of the plasma activity.
How does the author validate the findings?
The findings are validated by comparing results with data from Mirnov coils and by examining an inverted magnetic field configuration (Upper Single Null) to see if the LCOs shift position accordingly.
- Arbeit zitieren
- Bernd Kohler (Autor:in), 2016, Spatial Structure of Limit-Cycle Oscillations, München, GRIN Verlag, https://www.grin.com/document/342545
