  The hybrid method combining particle-in-cell and magnetohydrodynamics can be
used to study the interaction between energetic particles and global plasma
modes. In this paper we introduce the M3D-C1-K code, which is developed based
on the M3D-C1 finite element code solving the magnetohydrodynamics equations,
with a newly developed kinetic module simulating energetic particles. The
particle pushing is done using a new algorithm by applying the Boris pusher to
the classical Pauli particles to simulate the slow-manifold of particle orbits,
with long-term accuracy and fidelity. The particle pushing can be accelerated
using GPUs with a significant speedup. The moments of the particles are
calculated using the $\delta f$ method, and are coupled into the
magnetohydrodynamics simulation through pressure or current coupling schemes.
Several linear simulations of magnetohydrodynamics modes driven by energetic
particles have been conducted using M3D-C1-K, including fishbone, toroidal
Alfv\'en eigenmodes and reversed shear Alfv\'en eigenmodes. Good agreement with
previous results from other eigenvalue, kinetic and hybrid codes has been
achieved.
