7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Theoretic studies of low-frequency shear Alfvén waves in reversed shear
tokamak plasmas

Ruirui Ma1,4, W.W. Heidbrink2, Liu Chen2,3,4, Fulvio Zonca4,3 and Zhiyong Qiu3,4Southwestern Institute of Physics, 2 Department of Physics and Astronomy, University of California,
3Institute for Fusion Theory and Simulation, School of Physics, Zhejiang University, 4 Center for
Nonlinear Plasma Science and C.R. ENEA Frascatie-mail (speaker): rrma@swip.ac.cn
The linear properties of the low-frequency shear Alfvén
waves such as those associated with the beta-induced
Alfvén eigenmodes (BAEs) and the low-frequency
modes observed in reversed-magnetic-shear DIII-D
discharges are theoretically investigated and delineatedbased on the theoretical framework of the general
fishbone-like dispersion relation (GFLDR) [1,2]. By
adopting representative experimental equilibrium
profiles, it is found that, even though both modes arepredominantlyof
Alfvénic
polarization,
thelow-frequency mode is a reactive unstable mode withweak coupling to the energetic particles, while the BAE
involves a dissipative instability due to resonant
excitation by the energetic ions. Thus, the low-frequency
fluctuation is more appropriately called low-frequency
Alfvén mode (LFAM). Moreover, the ascending
frequency spectrum patterns of the experimentallyobserved BAEs and LFAMs can be theoreticallyreproduced by varying the minimum of the safety factor(as shown in Figure 1), and also be well interpreted
based on the GFLDR [3]. The present analysis illustrates
the solid predictive capability of the GFLDR and its
practical usefulness in enhancing the interpretative
capability of both experimental [4] and numericalsimulation results [5].
Acknowledgement:This work has been supported in part by the National key
R&D Program of China under Grant No.
2022YFE03040002, by the National Science Foundationof China under Grant Nos. 12261131622 and 12175053,
the Italian Ministry of Foreign Affairs with Grant No.
CN23GR02, and the Natural Science Foundation ofSichuan under Grant No. 2022NSFSC1814. This work
has also been carried out within the framework of theEUROfusion Consortium, funded by the European
Union via the Euratom Research and Training
Programme (Grant Agreement No. 101052200 -EUROfusion). This work has also been supported by US
Department of Energy awards DE-FC02-04ER54698 andDE-SC0020337.

References:[1] F. Zonca and L. Chen, Phys. Plasmas 21, 072120(2014).
[2] F. Zonca and L. Chen, Phys. Plasmas 21, 072121(2014).
[3] L. Chen and F. Zonca, Rev. Mod. Phys. 88, 015008(2016).
[4] W.W. Heidbrink, M.A. Van Zeeland, M.E. Austln, etal. Nucl. Fusion, 61, 016029 (2021).
[5] R.R. Ma, W.W. Heidbrink, L. Chen, F. Zonca, et al.
Phys. Plasma30, 042105 (2023).

Figure 1. Dependence of mode frequencies (solid curveswith markers) and growth rates (dashed curves withmarkers) on qmin of the KBMs (red curves) and the BAEs
(blue, green, purple and orange curves) for different(m,n). The experimentally observed frequencies are also
shown. For the BAE, since the modes span a range offrequencies, the lines indicate the upper and lower limitsof the unstable bands; for the LFAM, the experimental
frequency variation is < 0.5 kHz. In the abscissa, theexperimentally measured qmin(t) fit shown in Fig. 8 ofRef. 4 is used to convert time to qmin, with an associateduncertainty of qmin ≈ 0.01. In the ordinate, the theoreticallab-frame frequency incorporates a Doppler shift to thecalculated plasma-frame frequency of nfrot, with anassociated uncertainty of ~ 0.5n ~ kHz.