Nonlinear reversed shear Alfvén eigenmode saturation due to spontaneous zonal current generation

Abstract

General nonlinear equations describing reversed shear Alfvén eigenmode (RSAE) self-modulation via zero-frequency zonal structure (ZFZS) generation are derived using nonlinear gyrokinetic theory, which are then applied to study the spontaneous ZFZS excitation as well as RSAE nonlinear saturation. It is found that both electrostatic zonal flow and electromagnetic zonal current can be preferentially excited by finite-amplitude RSAE, depending on specific plasma parameters. The modification to local shear Alfvén wave continuum is evaluated using the derived saturation level of zonal current, which is shown to play a comparable role in saturating RSAE with the ZFZS scattering.

Core localized alpha-channeling via low frequency Alfven mode generation in reversed shear scenarios

“…and is comparable with or slightly higher than typical threshold condition for other dominant nonlinear mode coupling processes, e.g., ZS generation [35,52]. This threshold amplitude, is also consistent with typical SAW instability intensity observed in experiments [53].…”

“…As a final remark, several channels may contribute to the RSAE nonlinear saturation, e.g., self-consistent re-distribution of EPs [55], and zonal field generation generation [52] with notably the effects of zonal current on modifying the local SAW continuum structures. For the proper evaluation of EP confinement, the nonlinear dynamics of RSAE including saturation level is required, which is determined by the relative importance of these channels; and thus, more in-depth investigation including nonlinear gyrokinetic simulation [56] is required.…”

Gyrokinetic theory of the nonlinear saturation of a toroidal Alfvén eigenmode

“…Furthermore, it is also worth noting that the "preferential channel via ZC excitation" is connected with the properties of the TAE of interest here, for which RS and MX nearly cancel each other. This argument cannot be straightforwardly generalized to other SAW instabilities; e.g., BAE with |k V A /ω| ≪ 1 will predominantly excite ZF [60,61]; while for reversed shear Alfvén eigenmode (RSAE) with frequency between TAE and BAE frequency range, depending on the specific |nq min − m| value, both ZF and/or ZC excitation can be preferred [62]. For ZC excitation with ∆ T /ω 0 > 0 and typical parameters of most unstable TAE with k ⊥ ρ E ∼ O(1), the threshold condition can be estimated as…”

“…The TAE induced fusion alpha particle transport, can be obtained from nonlinear gyrokinetic transport theory [9,18], with the expected magnetic fluctuation level given by equation (62). Here, taking circulating EP as an example, whose transport is mainly caused by resonance overlapping induced EP orbit stochasticity [71], the quasilinear transport equation for EP equilibrium distribution function evolution is [18,72] ∂…”

Nonlinear excitation of geodesic acoustic mode by reversed shear Alfvén eigenmodes in non-uniform plasmas

“…This present investigated process, while very sensitive to plasma parameters, may have a comparable cross-section with other dominant nonlinear mode coupling channels, e.g. zero-frequency zonal structure generation (Wei et al 2021;Wang et al 2022).…”