Modelling of turbulent particle transport in finite-beta and multiple ion species plasma in tokamaks

Abstract

Recent experimental results carried out on Frascati Tokamak Upgrade (FTU) with the use of Liquid Lithium Limiter (LLL) show that the presence of lithium impurity can give rise to an improved particle confinement regime in which the main plasma constituents are transported towards the core whereas the impurity particles are driven outwards. The aim of our research was to further investigate this process using gyrokinetic simulations with the GKW code to calculate the particle flux in FTU-LLL discharges, and to provide a physical explanation of the above phenomena with a simplified multi-fluid description. The fluctuations in the FTU tokamak are dominantly electro-static (ES), magnetic perturbations are expected to be important in high beta tokamak plasmas, such as those in the Mega Amp`ere Spherical Tokamak (MAST). The effects of impurities on the electro-magnetic (EM) terms of turbulent particle transport are investigated in a typical MAST H-mode discharge. The first chapter of the thesis is dedicated to provide an understandable but thorough introduction to the gyrokinetic equation and the code GKW. It summarizes the concept of the Lie- transform perturbation method which forms the basis of the modern approach to gyrokinetics. The gyrokinetic Vlasov–Maxwell system of equations including the full electro-magnetic perturbation is derived in the Lagrangian formalism in a rotating frame of reference. The simulation code GKW is briefly introduced and the calculation of the particle fluxes is explained. In the second chapter the FTU-LLL and MAST experiments are introduced and the gy- rokinetic simulations of the two discharges are presented. It is shown that in an ES case the ITG driven electron transport is significantly reduced at high lithium concentration. This is accom- panied by an ion flow separation in order to maintain quasi-neutrality, and an inward deuterium pinch is obtained by a sufficiently high impurity density gradient. The EM terms are found to be negligible in the ion particle flux compared to the ExB contribution even at relatively high plasma beta. However, the EM effects drive a strong non-adiabatic electron response and thus prevent the ion flow separation in the analyzed cases. The third chapter provides a detailed description of a multi-fluid model that is used to gain insight into the diffusive, thermo-diffusive and pinch terms of the anomalous particle transport. It is based on the collisionless Weiland model, however, the trapped electron collisions are introduced (Nilsson & Weiland, NF 1994) in order to capture the micro-stability properties of the gyrokinetic simulations. The model is compared with analytical and numerical results in the two-fluid, adiabatic electron and large aspect ratio limits, showing good qualitative agreement. In the fourth chapter the fluid analysis of the FTU-LLL discharge is presented. It is shown that the inward deuterium pinch is achieved by a reduction of the diffusive term of the ITG driven main ion flux in presence of lithium impurities. The ITG mode responsible for the majority of the radial particle transport has been found to be the only unstable eigenmode rotating in the ion diamagnetic direction. Eigenmodes associated with the deuterium and lithium temperature gradients can be separately obtained when the Larmor-radius of the two ion species are more distinct, in which case the effect of lithium on the main ion transport is reduced and the inward deuterium flux is weaker