Heavy impurity transport in the presence of 3D MHD ideal perturbations

Heavy impurity accumulation poses a problem for the operation of tokamaks featuring tungsten plasma facing components. Early termination of the plasma due to tungsten accumulation is often observed following long living 3D MHD perturbations. Such scenarios areoften observed in present tokamaks like JET and ASDEX-U, and may be of concern for futuremachines like ITER and the European DEMO. Finding a way of designing high performancescenarios while preventing tungsten accumulation is therefore crucial. This thesis aims atunderstanding and modelling heavy impurity transport in tokamak plasmas in the presenceof long living 3D MHD ideal perturbations. In the first part of the thesis, we develop thetheoretical framework to treat the problem, building on stellarator theory for the main ions,while including the effect of strong toroidal rotation that is only present in tokamaks. Theorderings of the background ion species and the heavy impurity species are developed indetail. The background ions are subsonic which allows for the calculation of their flows usingthe stellarator 1/Μ collisional regime, while the heavy impurities flow supersonically whichrequires the inclusion of centrifugal effects for the impurity description. An expression forthe neoclassical heavy impurity flux is obtained which helps identify the contrasting physicsinvolved. In the second part of the thesis, we present the development of the numerical toolsused to model the problem according to the theoretical framework presented. The usage ofthe VMEC code to obtain suitable 3D MHD equilibria is explained. Also, the development ofnew codes for calculating the background ion and heat flux flow of the ions, and the impurityflow from such magnetic equilbria is described. The heavy impurities are followed in thisbackground plasma using the VENUS-LEVIS code. This code describes the guiding-centermovement of the heavy impurities, accounting for the centrifugal and Coriolis drifts, as wellas for the correct effect of friction and thermal forces exerted by the background ions onthe impurities through a newly implemented collision operator. Finally, the numerical toolsdeveloped in this thesis are used to model the impact of long living 1/1 internal kink modeson heavy impurity transport. Heavy impurity accumulation is observed to occur rapidly inthe presence of a 1/1 internal kink mode, contrary to what is observed in axisymmetry, inwhich off-axis accumulation occurs due to the strong rotation. These cases agree well witha JET pulse where tungsten accumulates following rapid growth of a continuous 1/1 mode.In the weakly 3D phase of the pulse, off-axis accumulation of tungsten is observed, whilstin the strong 3D phase of the pulse, strong tungsten on-axis accumulation is observed. Thetheoretical developments allow us to break down all the relevant physics effects. It is seen thatsuch on-axis accumulation is due to the synergetic effect of the 1/1 mode, the strong toroidalrotation and the NTV ambipolar electric field.