Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

In this work, the gyrokinetic eigenvalue code LIGKA, the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of Reversed Shear Alfv\'en Eigenmodes (RSAEs). Using the parameters from an ASDEX-Upgrade plasma, a benchmark with the three different physical models for RSAE without and with Energetic Particles (EPs) is carried out. Reasonable agreement has been found for the mode frequency and the growth rate. Mode structure symmetry breaking (MSSB) is observed when EPs are included, due to the EPs' non-perturbative effects. It is found that the MSSB properties are featured by a finite radial wave phase velocity, and the linear mode structure can be well described by an analytical complex Gaussian expression $\Phi(s)=e^{- \sigma (s-s_0)^2}$ with complex parameters $\sigma$ and $s_0$, where $s$ is the normalized radial coordinate. The mode structure is distorted in opposite {manners} when the EP drive shifted from one side of $q_{min}$ to the other side, and specifically, a non-zero average radial wave number $\langle k_s\rangle$ with opposite signs is generated. The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport. The parallel velocity of EPs is generated in opposite directions, due to different values of the average radial wave number $\langle k_s\rangle$, corresponding to different initial EP density profiles with EP drive shifted away from the $q_{min}$.