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Description
Quasilinear simulations can be an effective reduced tool for predicting and interpreting fast ion transport in fusion devices. At the core of these transport models is the form of their diffusion coefficients (or resonance functions), which have a leading role in determining the resonant wave saturation levels. While conventional quasilinear theory requires a random phase approximation to be satisfied via resonance overlap, it has been shown [V. N. Duarte, N. N. Gorelenkov, R. B. White, and H. L. Berk, Phys. Plasmas 26, 120701 (2019)] that near-threshold instabilities are naturally in the quasilinear regime even in the absence of any overlap, provided that the effective scattering rate felt by resonance particles well exceeds the instability net growth rate. This further motivates the deployment of resonance broadened quasilinear models to predict the dynamics of discrete Alfvénic eigenmodes upon their interaction with energetic ions, as they may alternate between the isolated and overlapping regimes.
Abstract This work describes how a generalization of the resonance function can be constructed to automatically enforce quasilinear simulations to replicate saturation levels obtained analytically from nonlinear theory in the limiting cases of marginal and strongly driven instabilities. The resonance function $R\left(\Omega\right)$ is intuitively proposed in a convolutional form in phase space, $R\left(\Omega\right)=\int_{-\infty}^{\infty}R_{\text{ampl}}\left(h\right)R_{\text{scatt}}\left(\Omega-h\right)dh$, to encode the following properties: (i) its characteristic broadening is the sum of the broadenings of the two individual components due to the effective scattering frequency $R_{\text{scatt}}\left(\Omega\right)$ and due to wave amplitude $R_{\text{ampl}}\left(\Omega\right)$, (ii) the resonance function integrates to the unity, as physically expected for a broadened function replacing a delta function, and (iii) it exactly recovers either of its constituents in the limits of marginal or strongly driven instability.
Abstract Stability boundaries between pulsating and quasi-steady amplitudes are investigated in quasilinear simulations and the results are compared with fully nonlinear kinetic simulations. It is found that the resonance broadening width is the key parameter that determines the mode evolution properties, with the resonance function exact shape playing a sub-dominant role. A discrepancy is found for the location of the parameter-space boundary between pulsating and quasi-steady saturation scenarios in quasilinear vs in nonlinear simulations in scenarios of low stochasticity. Such lack of agreement is verified to be largely a consequence of the diffusive resonant dynamics assumption embedded in quasilinear theory, rather than a lack of accuracy in the prescription of the resonance function.
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