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Multiple low-frequency beta-induced Alfvén eigenmodes (BAEs, 10 - 20 kHz) and a high-frequency toroidal Alfvén eigenmode (TAE, 120 - 145 kHz) driven by runaway electrons are simultaneously observed in the EAST low-density Ohmic discharges. A new high-frequency mode (HFM, 100 - 170 kHz), generated by nonlinear coupling between BAEs and TAE, are conclusively identified.
The experiments were performed on the EAST tokamak in ohmic plasmas. As the electron density decreases to approximately 0.41019 m–3, a large population of REs are generated. Multiple low-frequency BAEs and a high-frequency TAE are simultaneously driven by REs [1,2]. All these modes are measured with the same toroidal mode number of n = 1 and propagate in the electron diamagnetic drift direction. An HFM is additionally identified, of which the frequency and temporal evolution are closely correlated with those of the TAE. Triplets of modes are identified whose frequencies and mode numbers, respectively, satisfy energy and momentum conservation laws, suggesting that three-wave coupling occurs [3]. This is confirmed through bicoherence analysis, which establishes unambiguously that the coupled modes have the requisite fixed phase relationships.
Further analysis reveals that the dominant HFM number from mode coupling depends on the BAE's position relative to the TAE: it is n = 0 when the BAE is outside, and n = 2 when it is inside. The nonlinear coupling equation can be derived from the vorticity equation and the quasi-neutrality condition. The Reynolds stresses, which are additive in this framework, contribute to the excitation of the HFM.
Reference:
1 Luo C. et al 2025 Nucl. Fusion 65 076020
[2] Zhu X. et al 2024 Nucl. Fusion 64 126023
[3] Zhu X. et al 2022 Phys. Plasmas 29 062504