Abstract This work reviews the current state of research on the three main components of the turbulence spectrum observed in modern tokamaks. These components differ in frequency range and correlation properties, have relatively wide frequency intervals, and sizes larger than the ion Larmor radius. These are broadband (BB), quasi-coherent (QC), and stochastic low-frequency (SLF) fluctuations. BB fluctuations have the broadest frequency range, from 0 to 200–400 kHz, and make the main contribution to the total amplitude of density fluctuations. The characteristic BB sizes are close to those predicted by theory for the ion temperature gradient (ITG) and trapped electron mode (TEM) instabilities. BB are the least correlated fluctuations; in the T-10 tokamak plasma (R/a = 1.5/0.3 m), their typical radial and poloidal correlation lengths are approximately 1 and 2 cm, respectively, while the correlation length along the magnetic field line is less than 2.5 m. Quasi-coherent fluctuations (QC) are manifested as local maxima in the frequency spectra of density oscillations; however, they are most clearly visible in the coherence spectra, since they have radial and poloidal correlation lengths significantly longer than BB. In the T-10 tokamak plasma, correlations along the magnetic field line over a length of up to 10 m were observed for QC modes. Two types of such fluctuations were observed at T-10: low-frequency (LFQC) and high-frequency (HFQC). The characteristic poloidal sizes and dependences on discharge parameters in the T-10 experiments show that the properties of LFQC and HFQC are close to those of ITG and TEM, respectively. The poloidal rotation of QC coincides with the drift [E × B] rotation in magnitude and direction. A relation between the characteristics of these modes and the discharge parameters is demonstrated with a change in density. The magnetic component in QC was demonstrated at T-10 and DIII-D. Gyrokinetic simulation of these experiments showed that the properties of QC are close to the micro-tearing mode (MTM). Additional evidence for the MTM nature of QC is the strong dependence of their spectra on the current profile, the discrete mode structure, and the absence of QC in stellarator plasma. Stochastic low-frequency fluctuations (SLF), excited in the range from 0 to 70 kHz, are the least studied. In the T-10 tokamak, plasma on the side of a low magnetic field, these fluctuations can rotate in the direction opposite to QC. SLFs are uncorrelated along the magnetic field line at the LFS, but correlated at the HFS. SLF fluctuations have a magnetic component. Density and potential fluctuations have different radial and poloidal sizes and are uncorrelated with each other. This suggests the existence of two independent types of fluctuations in the SLF frequency domain. Experiments at DIII-D, by comparing spectra in the L, I, and H modes, showed that fluctuations in the SLF region (up to 70 kHz) can be associated with particle transport, while high-frequency fluctuations, such as QCM and BB, can be associated with heat transport.

Study of the Main Components of Tokamak Plasma Turbulence

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发表日期：

2025年10月1日

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V. A. Vershkov,
A. V. Melnikov,
L. G. Eliseev

摘要

Abstract

This work reviews the current state of research on the three main components of the turbulence spectrum observed in modern tokamaks. These components differ in frequency range and correlation properties, have relatively wide frequency intervals, and sizes larger than the ion Larmor radius. These are broadband (BB), quasi-coherent (QC), and stochastic low-frequency (SLF) fluctuations. BB fluctuations have the broadest frequency range, from 0 to 200–400 kHz, and make the main contribution to the total amplitude of density fluctuations. The characteristic BB sizes are close to those predicted by theory for the ion temperature gradient (ITG) and trapped electron mode (TEM) instabilities. BB are the least correlated fluctuations; in the T-10 tokamak plasma (R/a = 1.5/0.3 m), their typical radial and poloidal correlation lengths are approximately 1 and 2 cm, respectively, while the correlation length along the magnetic field line is less than 2.5 m. Quasi-coherent fluctuations (QC) are manifested as local maxima in the frequency spectra of density oscillations; however, they are most clearly visible in the coherence spectra, since they have radial and poloidal correlation lengths significantly longer than BB. In the T-10 tokamak plasma, correlations along the magnetic field line over a length of up to 10 m were observed for QC modes. Two types of such fluctuations were observed at T-10: low-frequency (LFQC) and high-frequency (HFQC). The characteristic poloidal sizes and dependences on discharge parameters in the T-10 experiments show that the properties of LFQC and HFQC are close to those of ITG and TEM, respectively. The poloidal rotation of QC coincides with the drift [E × B] rotation in magnitude and direction. A relation between the characteristics of these modes and the discharge parameters is demonstrated with a change in density. The magnetic component in QC was demonstrated at T-10 and DIII-D. Gyrokinetic simulation of these experiments showed that the properties of QC are close to the micro-tearing mode (MTM). Additional evidence for the MTM nature of QC is the strong dependence of their spectra on the current profile, the discrete mode structure, and the absence of QC in stellarator plasma. Stochastic low-frequency fluctuations (SLF), excited in the range from 0 to 70 kHz, are the least studied. In the T-10 tokamak, plasma on the side of a low magnetic field, these fluctuations can rotate in the direction opposite to QC. SLFs are uncorrelated along the magnetic field line at the LFS, but correlated at the HFS. SLF fluctuations have a magnetic component. Density and potential fluctuations have different radial and poloidal sizes and are uncorrelated with each other. This suggests the existence of two independent types of fluctuations in the SLF frequency domain. Experiments at DIII-D, by comparing spectra in the L, I, and H modes, showed that fluctuations in the SLF region (up to 70 kHz) can be associated with particle transport, while high-frequency fluctuations, such as QCM and BB, can be associated with heat transport.