Speaker
Description
Most nonlinear simulations of Alfvén Eigenmode (AE) stability study one toroidal mode family at a time, yet in a real tokamak discharge several toroidal mode numbers $n$ are unstable simultaneously. When these families coexist, they compete for the same free energy, couple through three-wave interactions, and collectively drive zonal flows, none of which a single-$n$ model can describe. To explore these effects in a concrete experimental setting, we carried out nonlinear gyrofluid simulations of multi-$n$ Toroidal Alfvén Eigenmode (TAE) dynamics in KSTAR geometry using the FAR3D code, stepping up from a single-$n$ baseline to a full multi-$n$ run to see what changes and why.
Here we presents the nonlinear gyrofluid simulations of Alfvén Eigenmode (AE) stability in KSTAR plasma to investigate the effect of energetic particle (EP) drive on the nonlinear coupling of co-existing Alfvén wave families. All simulations are performed for the KSTAR equilibrium (discharge 21695), with EP beta $\beta_f \approx 0.020$, Lundquist number $S = 5\times10^6$. The single-$n$ baseline, where $n{=}2$ TAE grows ($n{=}2$, with 16 poloidal modes, $m = \pm2$–$\pm9$) gives a clean reference. The $m{=}{-}5/n{=}2$ TAE grows at $\gamma_\mathrm{lin} = 0.075\ \tau_A^{-1}$, saturates around $t \approx 50$–$100 tau_A$, and evolves to $t = 200\;\tau_A$. Extending the basis to include $n{=}1$ shifts dominance entirely to that family, whose saturation energy exceeds $n{=}2$ significantly. Next the simulation pushes further, evolving $n{=}1$, $2$, and $3$ simultaneously (with42 dynamic modes) with $m{=}0/n{=}0$ as a dynamic field.
These simulations reveal how strongly the $n$-families compete. Once $n{=}1$ is present it dominates, effectively suppressing $n{=}2$, unlike any single-$n$ study. In the full multi-$n$ run the dominant linear mode shifts to $m{=}{-}8/n{=}3$ ($\gamma_\mathrm{lin} = 0.059;\tau_A^{-1}$), and at saturation the energy is spread broadly across all three families; which mode dominates depends entirely on which families are simultaneously active. Beyond the mode competition, the multi-$n$ runs reveal genuine inter-$n$ energy transfer through the reduced-MHD Poisson bracket, ${\phi(m_1,n_1),,\phi(m_2,n_2)} \to \phi(m_1{+}m_2,,n_1{+}n_2)$: $n{=}1$ and $n{=}2$ modes drive $n{=}3$ sidebands (upward cascade), while $n{=}2$ and $n{=}{-}2$ drive a $n{=}0$ zonal flow (inverse transfer). The zonal potential $\phi_{00}(r,t)$ builds up from the onset and never decays; it persists at $r/a \approx 0.4$–$0.6$ throughout the entire $t = 0$–$1000;\tau_A$ run, coinciding with the peak of the TAE eigenfunctions. This is not a transient, it looks like a self-sustained zonal state driven continuously by the TAEs. To quantify what is driving this zonal flow we have compute the Reynolds stress (RS) and Maxwell stress (MS) at every timestep using the Wronskian. The analysis of saturation phase shows that the Maxwell stress has a similar shape but smaller magnitude than the Reynolds stress, so it is the electrostatic Reynolds channel that does most of the driving, with the electromagnetic piece playing a supporting role.
The most intriguing observation comes from the frequency-vs-radius spectrograms, computed for each $n$-family and overlaid with the Alfvén continua calculated by ALCON code. Each $n$ mode sits within its own continuum gap at a distinct radial band i.e., lower $n$ near the core, $n{=}2$ slightly outward, $n{=}3$ more localized. As the simulation enters deep saturation, new spectral features appear that were not there at linear onset, power at a higher frequency ($\omega \approx 0.35$–$0.40\;\mathrm{rad}/\tau_A$, above the primary TAE band near $0.20$–$0.25\;\mathrm{rad}/\tau_A$) and at a lower frequency ($\omega \lesssim 0.1\;\mathrm{rad}/\tau_A$). These two features sit near continuum accumulation points in the ALCON overlay, suggesting a three-wave decay of the TAE into a higher-frequency daughter (possibly an EAE or higher-gap EPM) and a lower-frequency mode (possibly a BAE or sub-TAE Alfvénic branch). A definitive mode identification is still under investigation, but the spectral signatures are consistent and reproducible across runs.
These results demonstrate that the nonlinear physics of co-existing multi-$n$ TAEs is not a quantitative correction to single-$n$ results, it is qualitatively different. The dominant mode shifts, the saturation level changes, a long-lived zonal flow appears, and new frequency branches emerge, collectively suggesting that multi-$n$ nonlinear mode coupling must be accounted for in reliable EP transport predictions for KSTAR and next-step burning plasma devices.