  Verification and validation of the internal kink instability in tokamak have
been performed for both gyrokinetic (GTC) and kinetic-MHD codes (GAM-solver,
M3D-C1-K, NOVA, XTOR-K). Using realistic magnetic geometry and plasma profiles
from the same equilibrium reconstruction of the DIII-D shot #141216, these
codes exhibit excellent agreement for the growth rate and mode structure of the
internal kink mode when all kinetic effects are suppresed. The simulated radial
mode structures agree quantitatively with the electron cyclotron emission
measurement after adjusting, within the experimental uncertainty, the safety
factor q=1 flux-surface location in the equilibrium reconstruction.
Compressible magnetic perturbations strongly destabilize the kink, while
poloidal variations of the equilibrium current density reduce the growth rate
of the kink. Furthermore, kinetic effects of thermal ions are found to decrease
the kink growth rate in kinetic-MHD simulations, but increase the kink growth
rate in gyrokinetic simulations, due to the additional drive of the ion
temperature gradient and parallel electric field. Kinetic thermal electrons are
found to have negligible effects on the internal kink instability.
