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. Fusion61 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.
High and low frequency Alfvén modes in tokamaks