Evaluation of Tokamak MHD Instabilities by Instability Indices Investigating Such as Entropy

Abstract

To investigate the fluctuations of the Mirnov coils magnetic field in tokamak plasma, it is required to assess the spatiotemporal signals. Spatial structure and time evolution related to MHD instabilities in a tokamak can be shown by analyzing the signals from an array of Mirnov coils using the biorthogonal decomposition (BD) method. In this paper by Using this method, the presence of instability modes indices in tokamak IR-T1 namely, singular values entropy and the relative squared magnitude of the first two pairs of the principal axes were calculated and studied. Also, the behavior of indices was also evaluated with and without resonance helical magnetic field (RHF). In this research, the effect of the L = 3/n = 1 and L = 2/n = 1 RHF was examined on the amplification and suppression of MHD activities along with the modification of MHD modes number and the behavior of singular values entropy extraction from BD. We show that, MHD activities mode numbers altered due to the application of RHF or even some MHD modes may be suppressed or amplified. The behavior of P1 and P2 and their temporal dependence and their rate of change will also be investigated under the RHF field. The calculation of singular values entropy of the extraction energy using the BD biorthogonal decomposition method is an important index since the MHD activities in most tokamaks have several MHD modes. The result show that, the entropy of the system increases during MHD activities. The entropy value in IR-T1 tokamak plasma depends on the number of the non-zero singular values extracted from Mirnov fluctuations analysis by biorthogonal decomposition. The results indicate that the very lower number of non-zero eigenvalues will lead to a lower entropy compared to the condition that the number of non-zero eigenvalues is more. It is also expected to identify the MHD activities and mode number and their frequency with other diagnostic tools by observing the changes of entropy. Observing the entropy behavior depends on the tokamak aspects and tokamak plasma parameters. It demonstrates the existence of MHD activities with different frequencies and wavelengths.