Speaker
Description
Computationally inexpensive integrated codes simulating interactions between Alfvén waves and fast ions in tokamak plasmas make use of perturbative models for the intermediate and slow processes of instability growth, saturation, chirping and busting, and associated fast ion transport. Meanwhile, the processes by which an Alfvén mode's spatiotemporal structure forms are assumed to have been completed more rapidly, within the mode's oscillation period, $\tau_0 \equiv 2\pi/\omega_0$. This separation of time scales, together with the assumption of a robust spatial mode structure, underlies the computational efficiency of perturbative models, where the Alfvén mode's time-dependence is reduced to that of a scalar signal $s(t) = A(t)\sin(-\omega_0 t - \phi(t))$ with variable amplitude $A(t)$ and phase $\phi(t)$. For Alfvén eigenmodes residing in gaps between continua, eigensolvers can provide the required accurate input data in the form of the spatial structure $\delta\Phi({\mathbf{x}})$, damping rate $\gamma_{\rm d}$, and initial frequency $\omega_0$. For continuum modes, a reasonable guess for $\delta\Phi(\mathbf{x})$ and $\gamma_{\rm d}$ (if necessary, in frequency-dependent form) could be inferred from the typical fast ion orbit width and continuum structure, but it is difficult to guess the correct seed frequency $\omega_0$. Here, we report results of numerical experiments demonstrating that it is possible to find $\omega_0$ by taking advantage of a prompt frequency shift that was previously discovered with the ORBIT code and interpreted as a product of prompt resonant auto-optimization [1]. Since the terms required for such fast dynamics were truncated in the derivation of the perturbative model, the prompt frequency shift is incomplete but suffices for an iterative optimization scheme.
[1] Bierwage, Duarte & White, Plasma Fus. Res. 16 (2021) 1403087. Link: https://doi.org/10.1585/pfr.16.1403087.