Implementation and Validation of the Chirping criterion in NOVA-K as of November 2021

Microturbulence was predicted [1] and validated at the same time recently [2 -4] to mediate the transitions between distinct nonlinear characters of the AE instabilities in certain scenarios. The ability to predict  highly nonlinear evolution of Alfvénic oscillations (fixed-frequency, leading to diffusive losses, or chirping/avalanching, leading to convective losses) is of considerable advantage for experimentally observed fast ion transport. For example, for the case of dominant diffusive losses, reduced modelling such as a resonance broadened quasi-linear theory, is expected to be sufficient to capture the essence of the self-consistent evolution of the fast ion distribution function. Spherical tokamaks tend to exhibit Alfvénic chirping and avalanching, accompanied by wave amplitude bursting, while conventional tokamaks have Alfvénic waves oscillating with a nearly fixed frequency and a quasi-steady amplitude. To be able to explain this puzzling observation, a criterion for the likelihood of chirping oscillations was developed based on previous analytical works on the theory of driven, kinetic instabilities near threshold with dissipation [5,6] and evaluated for a number of NSTX, DIII-D and TFTR discharges [7,8] using the stability hybrid, MHD-kinetic code NOVA-K [11].  The micro-turbulence can be a strong mediator between the mode transition from fixed-frequency to chirping and vice-versa due to an enhancement of the fast ion stochasticity. In spherical tokamaks, particles spend more time on the good curvature region and experience higher relative rotation shear. Therefore, STs naturally exhibit lower anomalous transport with respect to conventional tokamaks. For example, on NSTX the total thermal ion diffusivity has been found to be of order of its neoclassical level [9]. These distinct turbulence features have been found to explain why chirping instabilities are rare in conventional tokamaks and common in spherical tokamaks since the turbulence acts to effectively increase the scattering experienced by the resonant fast ions [10] and therefore to prevent the chirping and avalanching responses. An example of the emergence of chirping correlating with low turbulence is shown in the following Figure.

References:
[1] V. N. Duarte, H. L. Berk, N. N. Gorelenkov,  t al., "Prediction of nonlinear evolution character of energetic-particle-driven instabilities," Nucl. Fusion, vol. 57, no. 5, p. 054 001, 2017
[2] P. Lauber et al., "Strongly non-linear energetic particle dynamics in asdex upgrade scenarios with core impurity accumulation," in 27th IAEA Fusion Energy Conference (FEC), 2018;
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[4]  V. N. Duarte, N. N. Gorelenkov et al., "Study of the likelihood of alfvenic mode bifurcation in nstx and
predictions for iter baseline scenarios," Nucl. Fusion, vol. 58, no. 8, p. 082 013, 2018.
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Nazikian, D. C. Pace, M. Podesta, and M. A. V. Zeeland, "Theory and observation
of the onset of nonlinear structures due to eigenmode destabilization by fast ions
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[10] J. Lang and G.-Y. Fu, "Nonlinear simulation of toroidal Alfv ́en eigenmode with microturbulence-induced radial diffusion," Phys. Plasmas, vol. 18, no. 5, p. 055 902, 2011. doi: 10.1063/1.N. 3574503.
[11] N. N. Gorelenkov, C. Z. Cheng, G. Y. Fu, Phys. Plasmas 6 (1999) 2802.
ChirpCrit