title: Structure Formation in Tokamak Turbulence : Impact of Collisions and Kinetic Electrons
Creators: name: Weikl, Arne
Publisher: name: University of Bayreuth
Year: 2019
Subjects: subject: plasma
subject: fusion
subject: tokamak
subject: turbulence
subject: gkw
subject: numerics
subject: collisions
subject: kinetic-electrons
subject: 530

description: In this thesis, the formation of structures in the zonal E ×B shear flow of the plasma in a Tokamak fusion reactor is studied with the nonlinear Eulerian gyro-kinetic code GKW. As this sheared zonal flow suppresses ion temperature gradient driven turbulence, structures in the zonal flow have a vast impact on the heat transport observed in a Tokamak and thus play a crucial role in developing an efficient fusion reactor. The formation of staircases in the shear of the zonal flow suppresses turbulence and leads to an upshift of the threshold in the temperature gradient, at which a significant heat flux is observed. The defining feature of this particular threshold, the so-called finite heat flux threshold, is that the heat flux does not go smoothly to zero when the threshold value is approached from above. An examination of the influence of ion-ion collisions reveals that this threshold is shifted to lower values due to collisions. Their influence is most prominent in the regime below the collisionless finite heat flux threshold and above the previously measured Dimits threshold. Investigating both the intensity as well as the radial profile of the E × B shear rate allows to reliably link the radial structure of the staircase to the observed behaviour. Fully developed staircases are observed below the finite heat flux threshold, while partially developed staircases are observed above. Increasing the collision frequency hinders the transgression from a partial to a fully developed staircase, leading to the observed reduction of the finite heat flux threshold. The results cannot be explained satisfactorily by solely considering the shear intensity alone, which bolsters the importance of the structure formation in the E×B shear. Investigating E × B shear structures in the zonal flow while treating the electrons as a fully kinetic species, reveals that the formation of staircases can be observed. However, in many cases strong small scale structures emerge in the shear rate, which appears to hinder staircase formation and prevents an efficient suppression of the turbulence induced heat transport. The small scale structures are linked to the self-interaction of turbulent modes through the double periodic boundary conditions of the toroidal geometry of a Tokamak plasma. Compared to simulations in the adiabatic electron limit, the influence of the boundary conditions is more prominent, because of the long extension of the mode structure along the field lines in the kinetic electron case. As the self-interaction is a newly discovered mechanism to drive the zonal flow, an extensive characterization is carried out. It is found that the driven structures scale with the normalized Larmor radius, are weakly affected by collisions and are also observed in global simulations. Changing the boundary conditions through the variation of the magnetic shear weakens the small scale structures, which leads to a reappearance of the staircase structure and most of its typical traits. The observation of the small scale structures driven by self-interaction in simulations with kinetic electrons raises the question, how effective certain zonal flow structures damp the ion temperature gradient instability driving the turbulence. To investigate this question, the growth rate of the turbulent modes after quenching is measured under the damping effect of a zonal flow profile. A quantitative measurement for the efficiency of a structure is provided by considering the damping in relation to the intensity of the zonal flow structure. All results of this examination lead to the conclusion that the damping is predominantly effected by zonal flow structures with a low radial wave vector.