Speaker
Description
The nonlinear 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 are well described by the theoretical framework of the Berk-Breizman model [1], which explains how mode growth is constrained by the available free energy in the EP distribution function in presence of sources and sinks. In the diffusive transport regime, this mechanism can be effectively modeled by the Resonance Broadened Quasilinear (RBQ) code [2], which predicts the saturation amplitude of multiple EP-driven modes while accounting for pitch angle scattering resonance broadening. On the other hand, several simulation studies showed that wave-wave nonlinearities, and in particular the generation of zonal modes, can further limit the growth of EP-driven instabilities. This effect is particularly pronounced when the linear growth rate of the instability is 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 incorporate the effects of zonal modes alongside wave-particle nonlinearities in the determination of the saturation amplitude. We develop an intuitive analytical model that integrates the self generation of zonal modes within the same framework used in RBQ. The model assumes that the zonal perturbations grow at a rate twice that of the original (pump) wave, consistent with a beat-driven (or force-driven) generation mechanism. The model has been implemented in the nonlinear 1D BOT code [3], and preliminary results are presented. We also discuss potential comparisons between the model’s predictions and more comprehensive simulations of recent DIII-D discharges. The simplicity of the model facilitates its integration into the RBQ code, aiming to enhance its predictive capabilities for strongly driven modes.
References
[1] H. L. Berk and B. N. Breizman, Physics of Fluids B, vol. 2, no. 9, pp. 2235–2245, 1990.
[2] N. N. Gorelenkov et al., Nucl. Fusion, vol. 58, p. 082 016, 2018.
[3] M. K. Lilley et al., Phys. Plasmas, vol. 17 (9), p. 092 305, 2010.
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