The magnetohydrodynamic-kinetic (MHD-kinetic) hybrid model (Park et al 1992 Phys. Fluids B 4 2033–7) has been widely applied in studying energetic particles (EPs) problems in fusion plasmas for past decades. The pressure-coupling scheme or the current-coupling scheme is adopted in this model. However, two noteworthy issues arise in the model application: firstly, the coupled term introduced in the pressure-coupling scheme, , is often simplified by , which is equivalent to neglecting the parallel inertial term of EPs; secondly, besides the contribution caused by changing in the EP distribution function, the magnetic field perturbation (the contribution) generated during development of the instabilities should also be considered, but it is often ignored in existing hybrid simulations. In this paper, we derive the analytical formulations under these two coupling schemes and then numerically study the representative case of the linear stability of the internal kink mode (IKM) (Fu et al 2006 Phys. Plasmas13 052517) by using the CLT-K code. It is found that the approximated models can still yield reasonable results when EPs are isotopically distributed. But it fails completely in cases with anisotropic EP distributions. In addition, we further investigate the influence of EP's orbit width on the stability of IKM and verify the equivalence between pressure-coupling scheme and the current-coupling scheme.
This paper examines the impact of two important factors on MHD-kinetic hybrid simulations of fusion plasmas: the parallel inertial term of energetic particles and the magnetic field perturbation (δB) contribution. The authors find that neglecting these factors can lead to inaccurate results, especially for anisotropic energetic particle distributions. The study provides insights into the stability of the 1/1 internal kink mode, which is crucial for fusion energy research.