A linear theoretical study of instabilities driven by passing energetic particles in weak magnetic shear configurations

Based on drift kinetic theory, we derive the eigenvalue equation and dispersion relation for the instability excited by passing energetic particles in a weak magnetic shear configuration. By numerically solving the eigenvalue equation with experimental parameters, the growth rate and frequency of the linear instability of the energetic particle mode are calculated. The influence of parameters such as the precession frequency and energetic particle beta on instability is discussed in detail.