State of the art of gyrokinetic and hybrid MHD-kinetic codes through non-linear benchmarking to study reactor relevant burning plasmas

Abstract After a brief introduction on present day simulation and modeling of burning plasmas in magnetically confined devices, the results of a non-linear benchmark are presented, undertaken among several state-of-the-art codes available to study the self-consistent interaction of an Energetic Particle (EP) population with shear Alfvén waves: HYMAGYC, MEGA, ORB5 and XTOR-K. The first two codes, HYMAGYC and MEGA, are hybrid codes: HYMAGYC is a MHD-Gyrokinetic code (the bulk plasma is represented by MHD equations, while the EP species is treated using the gyrokinetic formalism), while MEGA is an MHD-Drift-Kinetic code (the bulk plasma is represented by MHD equations, while the EP species is treated using the drift-kinetic formalism, with the possibility of an ad-hoc gyroaveraging); ORB5 is a global electromagnetic gyrokinetic code (both bulk and EP species are treated using the gyrokinetic formalism); XTOR-K is a non-linear kinetic-MHD code (the bulk plasma is described by a set of non-linear resistive two-fluid MHD equations, extended to include kinetic effects of multiple ion species with a fully kinetic PIC module). The equilibrium of the so-called NLED-AUG reference case, in its version with peaked off-axis EP density profile, has been used, while considering a $$|n|=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>n</mml:mi> <mml:mo>|</mml:mo> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> perturbation. This non-linear benchmark is the natural continuation of the linear benchmark already considered in the recent past, and represent a first-ever code comparison in the deep non-linear stage. In the present study fluid non-linearities are omitted, and the focus will be on comparing wave-particle interactions effects across codes. Characteristics of the non-linear saturation of the mode, self-consistent modification to the EP density profile and other features are compared among the considered codes. This brief review presents the state of the art of gyrokinetic and hybrid MHD-kinetic codes emerging as tools for studying reactor-relevant burning plasmas in realistic conditions.