  In this work, we focus on the development of the particle-in-cell scheme and
the application to the studies of Alfv\'en waves and energetic particle physics
in tokamak plasmas. The $\delta f$ and full $f$ schemes are formulated on the
same footing adopting mixed variables and the pullback scheme for
electromagnetic problems. The TRIMEG-GKX code [Lu et al. J. Comput. Phys. 440
(2021) 110384] has been upgraded using cubic spline finite elements and full
$f$ and $\delta f$ schemes. The EP-driven TAE has been simulated for the
ITPA-TAE case featured by a small electron skin depth $\sim
1.18\times10^{-3}\;{\rm m}$, which is a challenging parameter regime of
electromagnetic simulations, especially for the full $f$ model. The simulation
results using the $\delta f$ scheme are in good agreement with previous work.
Excellent performance of the mixed variable/pullback scheme has been observed
for both full $f$ and $\delta f$ schemes. Simulations with mixed full $f$ EPs
and $\delta f$ electrons and thermal ions demonstrate the good features of this
novel scheme in mitigating the noise level. The full $f$ scheme is a natural
choice for EP physics studies which allows a large variation of EP profiles and
distributions in velocity space, providing a powerful tool for kinetic studies
using realistic experimental distributions related to intermittent and
transient plasma activities.

Plasma Physics