X. Garbet

Trapped ion modes (TIM) 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. It is essential to properly estimate their linear growth rate to understand their influence on ion-scale turbulent transport. 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 H_{eq}(ψ) in the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function F_{eq} . Using this spectral method, linear growth-rates of TIM instability in 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 κ_{T} , density κ_{n} and equilibrium Hamiltonian κ_Λ . With the exact ψ dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with a good accuracy. This spectral method is very fast and requires very less computation resources compared to a linear version of Vlasov-solver based on a semi-Lagrangian scheme.

Present-days Reversed Field Pinches (RFPs) are characterized by quasi-laminar magnetic configurations in their core, whose boundaries feature sharp internal transport barriers, in analogy with tokamaks and stellarators. The abatement of magnetic chaos leads to the reduction of associated particle and heat transport along wandering field lines. At the same time, the growth of steep temperature gradients may trigger drift microinstabilities. In this work we summarize the work recently done in the RFP RFX-mod in order to assess the existence and the impact upon transport of such electrostatic and electromagnetic microinstabilities as Ion Temperature Gradient (ITG), Trapped Electron Modes (TEM) and microtearing modes.