Global linear stability analysis of kinetic trapped ion mode (TIM) in tokamak plasma using the spectral method

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 Psi dependency of the equilibrium Hamiltonian H-eq(Psi) in both the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function F-eq. 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 psi dependent equilibrium Hamiltonian, are investigated. The growth rate depends on the logarithmic gradient of temperature K-T, density K-n and equilibrium Hamiltonian K-lambda. With the exact psi 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.