Investigation of MHD instabilities in tokamak plasmas Using biorthogonal decomposition of Mirnov coil data
الموضوعات : Journal of Theoretical and Applied Physics
Habib Mehrniya
1
(
Plasma Physics Research Center , Science and Research Branch , Islamic Azad University, Tehran ,Iran.
)
Mohammad Kazem Salem
2
(
Plasma Physics Research Center , Science and Research Branch , Islamic Azad University, Tehran ,Iran.
)
Ahmad Salar Elahi
3
(
Plasma Physics Research Center , Science and Research Branch , Islamic Azad University, Tehran ,Iran.
)
الکلمات المفتاحية: Principal axes, Biorthogonal decomposition, instability indicators, Singular values entropy,
ملخص المقالة :
Spatiotemporal signal analysis is essential in investigating magnetic fluctuations of tokamak plasmas. Signal analysis of Mirnov coils through biorthogonal decomposition (BD) can reveal the spatial structure and time evolution of magnetohydrodynamic (MHD) instabilities in a tokamak. This technique is comparable to singular value decomposition in terms of formulation. The present study calculates the probability of instability modes' presence and identifies the dominant modes using the method above. Moreover, the relationship between the singular value entropy as a signal characteristic and magnetic field oscillations of Mirnov coils in the IR-T1 tokamak is investigated. This study evaluated the presence of active modes with and without applying a resonant helical field. The results indicate that when L=2 and L=3 are applied independently, the probability of m=2 & 3 active modes is greater than when the resonant helical field is absent. In contrast, by combining these two, the likelihood of the presence of these modes is reduced.
Investigation of MHD Instabilities in Tokamak Plasmas Using Biorthogonal Decomposition of Mirnov Coil Data
H. Mehrniya1, M.K. Salem1* ,*, A. Salar Elahi
Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, Tehran, Iran
*Corresponding author:
M.K. Salem
Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, Tehran, Iran
E-mail: mkssalem@gmail.com
Abstract
Spatiotemporal signal analysis is essential in investigating magnetic fluctuations of tokamak plasmas. Signal analysis of Mirnov coils usingthrough biorthogonal decomposition (BD) can reveal the spatial structure and time evolution of magnetohydrodynamic (MHD) instabilities in a tokamak. In terms of formulation, thisThis technique is comparable to singular value decomposition. in terms of formulation. The present articlestudy calculates the probability of instability modes' presence and identifies the dominant modes using the method above. Moreover, the relationship between the singular value entropy as a signal characteristic and magnetic field oscillations of Mirnov coils in the IR-T1 tokamak is investigated. In the conducted research, the possibility ofThis study evaluated the presence of active modes with and without the application of theapplying a resonant helical field was evaluated.. The results showindicate that when L=2 and L=3 isare applied separatelyindependently, the probability of the presence of m=2 & 3 active modes increases compared to the case whereis greater than when the resonant helical field is not applied, butabsent. In contrast, by applying the combination ofcombining these two, the probabilitylikelihood of the presence of these modes decreases. is reduced.
Keywords: Biorthogonal decomposition, instability indicators ,, Mirnov coils, Principalprincipal axes, , Singularsingular values entropy
1. Introduction
Nuclear fusion is a significant energy source that researchers areis actively pursuing. The pursued by scientists. For stable operation, the plasma required plasma for fusion in the tokamak machine must reach temperatures of over 150 50 million Kelvin for stable performance [1]. However, the increase in plasma density and current results in a series of instabilities that lead to plasma losses. When the increase in the tokamak plasma current exceeds the critical limit, perturbation instability occursdevelops in the tokamak plasma. As a result, the plasma expands, collides with the tokamak's wall, and eventually cools down. The underlying cause of such perturbations is nonlinear growth in tearing modes [2]. The perturbations give rise to thecause plasma radius expansion and reduced plasma confinement time [3].
Magnetohydrodynamic (MHD) fluid modeling is commonly used to characterize the most severe instabilities. Changes, in which changes in the magnetic topological configuration at surfaces with a rational safety factor cause MHD instabilities in the tokamak plasma. InMagnetic field lines break in rational surfaces, magnetic field lines break, and their reconstructions produce magnetic islands with resistance instabilities such as tearing modes.
The ultimate effects of tearing modes consist ofcomprise both large and small perturbations. Small perturbations destabilize the plasma and diminish particle confinement, whereas large perturbations are highly dangerous and terminate plasma discharge [4, 5]. In tokamaks with circular cross-sections and high aspect ratios, these modes oscillate per equation , where m denotes the number of poloidal modes, and n represents the toroidal mode number [6].
A crucialAn effective tool for detecting MHD modes is utilizing data from the magnetic fluctuations in Mirnov coils. Data processing techniques are often used to analyze the oscillations associated with the tokamak's tearing mode instabilities, such as Mirnov oscillations [7- 11].
Modes must be detected using spatiotemporal signal processing to analyze MHD instabilities in plasmas. Consequently, it is vital to determine the spatial structure and temporal evolution of MHD instabilities in a tokamak machine so that the required measures can be implemented to ensure the stable performance of the tokamak plasma [9-13].
Various techniques are utilized for signal processing and mode detection. The present study examinesuses biorthogonal decomposition (BD), essentially an expansion ofexpanding definite functions in time and space. To this end, the present paper describesutilizes the BD technique for Mirnov coils in the IR-T1 tokamak machine to obtain mode structure indices and presence probability.
The BD method originated in nonlinear dynamics, where it was used to examine wave propagation in turbulent systems [14, 15]. In terms of formulation, this method is comparable to SVD ( singular value decomposition ) . InThe authors of [16 & ] and [17], BD is] applied BD to the FTU and IR-T1 tokamaks respectively,, extracted instability indices are extracted, and determined the instabilities' onset time is determined.. The technique iswas also employed by [18] and [19] to analyze the JET tokamak, and the SUPRE TORE Mirnov coil, respectively. The authors ofRefs. [20] and [21] comprehensively analyzeanalyzed Mirnov coils in the ASDX tokamak using BD to detectidentify paired modes. The results of [21] are strikingly similarvirtually identical to those presented in this article. Studies [23] and [24] utilizeutilized a combination of diagnostic detectors (Mirnov probes and soft X-ray [SXR]) and electron cyclotron emission (ECE) detectors to determine mode behavior.
The present article appliescurrent study employs the BD technique to detectdetermine the dominant modes by processinganalyzing the signals from magnetic field fluctuations in Mirnov coils. The articlepaper is structured as follows: The IR-T1 tokamak's structural characteristics are described in Section 2. Biorthogonal decomposition (BD)BD and singular value decomposition (SVD) are discussed in Section 3. The results from experimental data of Mirnov coils in the IR-T1 tokamak are provided in Section 4. Section 5 summarizes the paper with a conclusion and provides additional remarks.
2. Experimental setup
TheA small research tokamak (, IR-T1), was constructed of stainless steel and lacked a first wall. The device was installed at the Plasma Physics Research Center of the Science and Research Branch of Islamic Azad University and operated under a hydrogen atmosphere. The applied tokamak, which had a circular cross-section and a high aspect ratio, comprised of an inner radius of 12.5 cm, a minor radius of a=12.5 cm, and a major radius of R=45 cm. The IR-T1Furthermore, it was outfitted with a poloidal array of 12 discrete Mirnov coils separated by the same distance from the poloid. The characteristics of IR-T1 are summarized in Table 1.
Table 1. IR-T1 Tokamaktokamak parameters
Parameters | Value |
Toroidal field | <0.9 T |
Plasma current | <40 KA |
Discharge time | <35 ms |
Electron density | 0.7-1.5× |
Electron temperature | 150 – 230 eV |
Pressure before discharge | 2.5-2.9 Torr |