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Mode structures and excitation conditions for the low-frequency modes (LFMs) have been investigated in experimental advanced superconducting tokamak (EAST) plasmas with q min ⩽ 2. Two different stages/categories of the LFM instabilities are observed during the oscillation of annular/central collapse events: (I) the upward sweeping frequency of LFMs; (II) the upward frequency jumpsof LFMs. The annular/central events are triggered by the m/n = 2/1 double tearing modes with different q-profiles, while the LFMs are characterized by higher mode numbers m/n = 4/2, 6/3, …, where m and n are the poloidal and toroidal mode numbers, respectively. The maximum radial coverage of the LFMs is located in the annular region of 1.97 ⩽ R ⩽ 2.07 m with the normalized minor radius 0.2 ⩽ ρ ⩽ 0.4, while the higher-frequency (or upward sweeping frequency) branch is more localized to the radial position of 2 ⩽ R ⩽ 2.02 m (q min). The frequency characteristics of upward sweeps or upward jumps of the LFMs are mainly attributed to the change in the q-profile, e.g. the upward sweeping frequency in stage I is caused by q min decreasing. Accordingly, the linear wave properties of LFMs in EAST with weak/reversed magnetic shear are studied numerically and analytically based on a general fishbone-like dispersion relation. Without considering the contribution of energetic ions, it is shown that the LFM with Alfvénic polarization is an MHD-unstable kinetic ballooning mode with frequency of the order of the ion diamagnetic drift frequency. Several important factors for the excitation of LFM instability are analyzed: (1) the role of energetic ions is unimportant, and the LFMs can be excited under the two conditions of with/without energetic ions; (2) the higher τ = T e/T i with larger η i = L ni /L Ti are required, namely the normalized pressure gradient α ∝ (1 + τ)(1 + η i) should be large enough to overcome the stability effect of finite field line bending; (3) the weak/reversed shear q-profile with q min ⩽ 2 and suitable S ≡ (r/q)(q″)1/2 are required.

The linear wave properties of the low-frequency Alfvén modes (LFAMs) observed in the DIII-D tokamak experiments with reversed magnetic shear (Heidbrink et al 2021 Nucl. Fusion 61 016029) are theoretically studied and delineated based on the general fishbone-like dispersion relation. By adopting representative experimental equilibrium parameters, it is found that, in the absence of energetic ions, the LFAM is a reactive-type kinetic ballooning mode instability with a dominant Alfvénic polarization. More specifically, due to diamagnetic and trapped particle effects, the LFAM can be coupled with the beta-induced Alfvén-acoustic mode in the low-frequency region (frequency much less than the thermal-ion transit and/or bounce frequency) or with the beta-induced Alfvén eigenmode in the high-frequency region (frequency higher than or comparable to the thermal-ion transit frequency), resulting in reactive-type instabilities. Moreover, the ‘Christmas light’ and ‘mountain peak’ spectral patterns of LFAMs as well as the dependence of instability drive on the electron temperature observed in the experiments can be theoretically interpreted by varying the relevant physical parameters. Conditions for when dissipative-type instabilities may set in are also discussed.

Multiple broadband Alfvénic chirping modes (CMs), with frequencies in the wide range of f ∼ 35–150 kHz and chirping down rapidly, are found in HL-2A neutral beam injection plasmas, and the CMs can even coexist. The frequency chirping down process can be completed within ∼1 ms, and the frequency shift can reach 30–50 kHz. The CMs propagate in ion diamagnetic drift directions poloidally. The toroidal mode number is confirmed to be n = 1, 2, 3 and 4 for the f ∼ 35–65, 55–90, 70–120 and 100–150 kHz CMs, respectively. The CMs are more like to be energetic-particle continuum modes (EPMs), since the modes almost locate on the Alfvén continuum.

Theoretical and numerical studies of the two-dimensional (2D) global stability and mode structures of high-n beta-induced Alfvén eigenmodes excited by magnetically trapped energetic electrons in tokamaks are carried out by employing the WKB-ballooning mode representation along with the generalized fishbone-like dispersion relation. Depending on parameter regimes, it is found that (i) the mode growth rate has a maximum with increasing energetic electron density at the ground radial eigenstate; (ii) the ground and excited radial eigenstates can be unstable simultaneously, and the most unstable mode is related not only to the pressure gradient of energetic electrons, but also to the width of the mode itself; (iii) the corresponding 2D mode structures are twisted due to the anti-Hermitian contribution from wave-energetic electron interaction and show opposite deformation directions compared with that in the presence of energetic ions; and (iv) the mode structures, especially, the mode width and its radial asymmetry, can be affected by radial eigen-mode number, energetic electron density, and magnetic shear. Finally, the radial symmetry breaking of the localized e-BAE mode structure with respect to parallel wave-number has a potential impact on toroidal momentum transport.