Description
The linear stability and nonlinear dynamics of Energetic Particle (EP)-driven modes is strongly dependent on the phase space gradients of EP distributions, since these modes are driven unstable by wave-particle resonances locally in phase space [1]. Even though EPs are far from thermodynamic equilibrium, their distribution function is often reduced in numerical modelling to local Maxwellians, or more realistic analytical forms taking into account the EP slowing-down physics, which tends to under-estimate the instabilities drive at high EP energy [2]. Therefore, for accurate predictions of EP-driven modes dynamics in upcoming burning plasmas and more importantly their cross-scale interaction with microturbulence, which depends heavily on the drive ratio between drift-waves and EP-driven modes [3], realistic numerical distributions are required in kinetic-MHD/gyrokinetic modelling.
In this contribution, we report progress made within the ITPA-EP activities, on the numerical verification and experimental validation of gyrokinetic and kinetic-MHD codes using realistic EP distributions. A DIII-D discharge has been chosen for this activity [4], where the stability of BAEs is influenced by changes in beam injection direction. Realistic EP distributions are obtained from NUBEAM [5]. Such inputs are generally too noisy to initialise $\delta F$ or full-F codes. They are therefore transformed into $\mathcal{C}^2$ distributions in the 3D constants of motion (CoM) space $(E,\mu,P_{\varphi})$ by the EPCoM code [6]. In addition to providing numerically smooth distributions, this approach enables a direct identification of instability drive in a phase space where wave-particle resonances can be explicitly identify.
In particular, results from the gyrokinetic codes GTC [7] and the kinetic-MHD codes M3D-C1 [8] and XTOR-K [9] will be presented. These codes agree well regarding the AE linear stability using either EP realistic distributions or equivalent Maxwellians. The AE drive with realistic beam distributions is much stronger than with equivalent Maxwellians. CoM space analysis reveals that although anisotropic beam EPs have less wave-particle resonances available, they lead to stronger drive because the local gradient drive $(n\partial_{P_{\varphi}}+\omega\partial_E)F_{EP}$ is 10 times stronger than its equivalent Maxwellian. The dependence of AE stability on beam injection angle will be compared between simulations and the experiment, as well as the modes nonlinear saturation and the associated EP transport.
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