Gyrokinetic modeling of energetic ion response to arbitrary-wavelength electromagnetic fluctuations in magnetized plasmas

Abstract Energetic ions (EIs) are responsible for driving most meso-scale Alfvénic instabilities and can also couple with micro-scale turbulence and macro-scale magnetohydrodynamic modes driven by bulk plasmas. In this work, we demonstrate the extension of gyrokinetic EI capability for the multiscale analysis for plasma stabilities (MAS) code (Bao et al 2023 Nucl. Fusion 63 076021) that treats bulk plasma instabilities of different spatio-temporal scales and polarizations on the same footing by a five-field Landau-fluid model, which then forms a comprehensive Landau-fluid–gyrokinetic hybrid model for analyzing the linear interactions between EIs and unstable/damped bulk plasma modes in a non-perturbative manner in general geometry. An efficient numerical scheme is proposed for evaluating EI moments in the MAS formulation that greatly decreases computational cost; this numerically integrates the EI distribution function in phase space with the adoption of well-circulating and deeply–trapped approximations for passing and trapped particle species, respectively, so that the effects of finite Larmor radius and finite orbit width (FOW) can be accurately retained for arbitrary-wavelength electromagnetic fluctuations together with dominant wave–particle resonances. In the long-wavelength limit, the EI moments in the MAS formulation can recover early theory on the response functions. These EI upgrades to the MAS code have been verified by simulating an EI-excited reverse shear Alfvén eigenmode (RSAE) based on a well-benchmarked DIII-D equilibrium case, which exhibits good agreement with other codes for the mode structure and dispersion relation, and FOW stabilization on the RSAE is found to be important in the regime of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> <mml:mtext>⩾</mml:mtext> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> (where ρ d is the magnetic drift orbit size).