Compressional Magnetic Fluctuations in Global Gyrokinetics*

Compressional magnetic field fluctuations are commonly ignored in gyrokinetic simulations. They tend not to have a large effect in core fusion plasmas, but may affect electromagnetic modes in the tokamak pedestal, the reconnection physics active in the solar corona, or the LAPD high-$\beta$ experiments. [Pueschel et al., PoP 22, 062105 (2015)]. The radially global gyrokinetic framework including compressional fluctuations is derived. Its implementation in the gyrokinetic turbulence code \textsc{Gene} is then compared against local flux-tube scenarios of a standard tokamak benchmark case, at LAPD high-$\beta$ experimental parameters, and for magnetic reconnection in 3D coronal loop geometry. Due to the usage of finite-element radial base function, the magnetic potential in the two directions perpendicular to the background magnetic field should be computed separately. This decouples the $B_\parallel$ from its gyroaveraged quantity $\bar{B}_\parallel$, thus a new gyroaverage procedure for the compressional magnetic field is also implemented.