Trapped ion modes (TIMs) belong to the family of ion temperature gradient (ITG) modes, which are one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis by considering the magnetic flux ψ dependency of the equilibrium Hamiltonian in both the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function . Using this spectral method, linear growth rates of TIM instability in the presence of different temperature profiles and precession frequencies of trapped ions, with an approximated constant Hamiltonian and the exact ψ dependent equilibrium Hamiltonian, are investigated. The growth rate depends on the logarithmic gradient of temperature κT, density κn and equilibrium Hamiltonian . With the exact ψ dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with an approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with good accuracy. This spectral method is very fast and requires much less computation resources compared to a linear version of the Vlasov-solver based on a semi-Lagrangian scheme.
捕捉离子模（TIM）属于离子温度梯度（ITG）模家族，是托卡马克等离子体中离子尺度热湍流输运的重要组成之一。本文对捕捉离子模的约化回旋-反弹动力学模型进行了全局线性分析，并提出了一种求解色散关系的谱方法。重要的是，在线性分析中，通过考虑平衡哈密顿量对磁通ψ的依赖，在准中性方程和平衡回旋-反弹平均分布函数中均计入了粒子漂移速度的径向分布。利用该谱方法，研究了在不同温度分布和捕捉离子进动频率条件下，采用常数近似哈密顿量与精确的ψ依赖平衡哈密顿量时TIM不稳定性的线性增长率。结果表明，增长率依赖于温度对数梯度κT、密度对数梯度κn以及平衡哈密顿量。与采用常数近似哈密顿量的情形相比，采用精确的ψ依赖哈密顿量时，增长率与势函数分布均发生显著修正。所有全局线性分析结果均与基于半拉格朗日格式的线性Vlasov求解器结果吻合良好。该谱方法计算速度快，与基于半拉格朗日格式的线性Vlasov求解器相比，所需计算资源大幅减少。