Abstract Details
Abstracts
Author: Tommaso Barberis
Requested Type: Consider for Invited
Submitted: 2025-02-21 15:07:16
Co-authors: V.N. Duarte, N.N. Gorelenkov, E.J. Hartigan-O’Connor
Contact Info:
Princeton Plasma Physics Laboratory
100 Stellarator Rd
Princeton, New Jersey 08540
United States
Abstract Text:
The saturation of energetic particle (EP)-driven instabilities has been extensively studied in tokamak plasmas. Two main nonlinear mechanisms govern the saturation of these instabilities: wave-particle interactions and wave-wave nonlinearities.
Wave-particle interactions can be described in the framework of the Berk-Breizman model, which explains how mode growth is constrained by the EP distribution function in presence of sources and sinks. In the diffusive transport regime, this mechanism can be modeled by the Resonance Broadened Quasilinear (RBQ) code, which predicts the saturation amplitude of EP-driven modes while accounting for resonance broadening due to wave amplitude and EP scattering.
On the other hand, several simulation studies showed that wave-wave nonlinearities, and in particular the generation of zonal modes (ZM), can limit the growth of EP-driven instabilities. This effect is more pronounced when the linear growth rate of the instability is sufficiently high, and the mode is strongly driven. In such cases, an accurate prediction of the saturation amplitude requires a combined treatment of wave-particle and wave-wave nonlinearities. In this work, we present a simplified approach to include the effects of ZM alongside wave-particle nonlinearities on the saturation amplitude. We develop an intuitive model that integrates the self-generation of ZM within the framework used in RBQ. The model assumes that the ZM grow rate is twice that of the original (pump) wave, consistent with a beat-driven generation mechanism. We show a comparison between the model’s analytical results and nonlinear 1D bump-on-tail simulations.
Despite its simplifying assumptions, the model exhibits good agreement with more comprehensive simulations for realistic parameter values. We discuss how the simplicity of the model enables its integration into the RBQ code to enhance the code's predictive capabilities, as well as its application for analyzing recent DIII-D experiments.
Characterization: 1.0
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