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Gyrokinetic theory of toroidal Alfvén eigenmode saturation via nonlinear wave–wave coupling

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Abstract

Nonlinear wave–wave coupling constitutes an important route for the turbulence spectrum evolution in both space and laboratory plasmas. For example, in a reactor relevant fusion plasma, a rich spectrum of symmetry-breaking shear Alfvén wave (SAW) instabilities is expected to be excited by energetic fusion alpha particles, and self-consistently determines the anomalous alpha particle transport rate by the saturated electromagnetic perturbations. In this work, we will show that the nonlinear gyrokinetic theory is a necessary and powerful tool in qualitatively and quantitatively investigating the nonlinear wave–wave coupling processes. More specifically, one needs to employ the gyrokinetic approach to account for the breaking of the “pure Alfvénic state” in the short-wavelength kinetic regime, due to the short-wavelength structures associated with nonuniformity intrinsic to magnetically confined plasmas. Using well-known toroidal Alfvén eigenmode (TAE) as a paradigm case, three nonlinear wave–wave coupling channels expected to significantly influence the TAE nonlinear dynamics are investigated to demonstrate the strength and necessity of nonlinear gyrokinetic theory in predicting crucial processes in a future reactor burning plasma. These are: 1. the nonlinear excitation of meso-scale zonal field structures via modulational instability and TAE scattering into short-wavelength stable domain; 2. the TAE frequency cascading due to nonlinear ion-induced scattering and the resulting saturated TAE spectrum; and 3. the cross-scale coupling of TAE with micro-scale ambient drift wave turbulence and its effect on TAE regulation and anomalous electron heating.

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Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Notes

  1. For more information and activities of CNPS, one may refer to the CNPS homepage at https://www.afs.enea.it/zonca/CNPS/.

  2. Interested readers may refer to Ref. Chen and Zonca (2012) for the detailed analysis of the threshold condition on ZFS excitation. The analysis is presented following Eq. (24) therein.

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Acknowledgements

This work was supported by the National Science Foundation of China under Grant Nos. 12275236 and 12261131622, Italian Ministry for Foreign Affairs and International Cooperation Project under Grant No. CN23GR02, and “Users of Excellence program of Hefei Science Center CAS” under Contract No. 2021HSC-UE016. This work was supported by the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No. 101052200 EUROfusion). The views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

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  1. Institute for Fusion Theory and Simulation, School of Physics, Zhejiang University, Hangzhou, 310027, China

    Zhiyong Qiu, Liu Chen & Fulvio Zonca

  2. Center for Nonlinear Plasma Science and C. R. ENEA Frascati, C. P. 65, 00044, Frascati, Italy

    Zhiyong Qiu, Liu Chen & Fulvio Zonca

  3. Department of Physics and Astronomt, University of California, Irvine, 92697-4575, CA, USA

    Liu Chen

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Qiu, Z., Chen, L. & Zonca, F. Gyrokinetic theory of toroidal Alfvén eigenmode saturation via nonlinear wave–wave coupling. Rev. Mod. Plasma Phys. 7, 28 (2023). https://doi.org/10.1007/s41614-023-00130-7

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