Global gyrokinetic models for energetic particle driven Alfv\'{e}n instabilities in 3D equilibria*

The GTC global gyrokinetic PIC model has been adapted to 3D VMEC equilibria and provides a new method for the analysis of Alfv\'{e}nic instabilities in stellarators, 3D tokamaks, and helical RFP states. The gyrokinetic orderings (k$_{\vert \vert }$/k$_{\bot }$ \textless \textless 1, $\omega $/$\Omega _{ci}$ \textless \textless 1, $\rho_{EP}$/L \textless \textless 1) are applicable to a range of energetic particle driven instabilities that have been observed in 3D configurations. Applications of this model to stellarators have indicated that a variety of different Alfv\'{e}n instabilities can be excited, depending on the toroidal mode number, fast ion average energy and fast ion density profile. Both an LHD discharge [1] where bursting n $=$ 1 Alfv\'{e}n activity in the TAE gap was observed and a W7-X case [2] have been examined. TAE,/EAE/GAE modes have been found in the simulations, depending on the mode family and fast ion profiles used. The dynamical evolution of the instabilities shows the field period coupling between n and n $+$ Nfp expected for a stellarator. The development of gyrofluid reduced models that can capture relevant physics aspects of the gyrokinetic models will also be discussed. \\[4pt] [1] M. Osakabe, et al., Nuclear Fusion 46, S911 (2006).\\[0pt] [2] A. Mischenko, A. K\"{o}nies, et al. Nuclear Fusion 54, 104003 (2014).