Control of plasma profiles and stability through localised Electron Cyclotron Current Drive

Abstract

The work presented in this thesis addresses several topics from the physics of the magnetically confined plasma inside a tokamak. At the moment, the tokamak is the most successful concept for becoming a future thermonuclear reactor. However, there are plenty of physics and engineering problems to surpass before the prototype can become an economically and environmentally feasible device. The plasma in the tokamak experiences periodic oscillations of the central temperature and density when the safety factor, q, drops below unity on-axis. These oscillations are called the sawtooth instability and are the subject of the first part of this thesis. The sawtooth oscillations are characterised by the relatively slow rise phase, when the central temperature increases, and a following crash phase, when the central temperature drops. The energy, particles and plasma current are redistributed during the sawtooth crash. Obviously, this leads to a confinement degradation and moreover, the sawtooth instability can trigger potentially other more dangerous instabilities, such as a neoclassical tearing mode. The sawtooth period control is realised on the basis of the sawtooth trigger model, derived by Porcelli. The main idea of this model is that the sawtooth crash is triggered when the magnetic shear at the q=1 surface, s1, reaches a critical value which depends on the local plasma parameters. The magnetic shear, s, is a measure for the rate of change in the direction of the field line as a function of the position in the plasma. The sawtooth period can be changed by affecting the evolution of s1. The effects of the electron cyclotron current drive (ECCD) on the shear evolution are studied with a simple model for the poloidal field evolution. The results of the model are summarised in a form of a criterion for the amount of the non-inductive current drive required for sawtooth period control. The effects of the ECCD have been studied in the TEXTOR tokamak in order to confirm the outcome of the model. The observations are complicated by the unavoidable presence of concurrent heating, which also affects the sawtooth period. The effects of additional heating have been separated from the effects of current drive by normalising the sawtooth period, as a function of the power deposition radius, to a case with heating only. The results are in qualitative agreement with the predictions of the theory and confirm that the shear around the q=1 surface determines the moment of the sawtooth crash. The next topic addresses the current diffusion in the presence of the ECCD. It is known that the synergy between non-inductively driven current and the ohmic current can affect the current penetration. However, the standard method of calculations, which assumes neoclassical plasma resistivity, cannot describe the synergistic effects. We propose a model which combines a Fokker-Planck code and magnetic diffusion calculation in a self-consistent manner; where the plasma resistivity is approximated from the Fokker-Planck code at every time step. In this way the parallel electric field is no longer a constant input profile for the Fokker-Planck code, but is a result of calculations of the magnetic diffusion. This model allowed us to identify situations where the synergy between the driven and the ohmic currents becomes significant and affects the current penetration. Both the ECCD power and the electron density have been varied over a wide range of parameters, thus changing the well known non-linearity criterion for ECCD after Harvey. This criterion indicates the non-linear behaviour of the current drive efficiency and also appears to be a good predictor for the synergistic effects. The results are compared with the standard method of calculations which were supplied by the ASTRA transport code. The standard method and the Fokker-Planck code with the self-consistent electric field show similar results in the absence of the synergy and therefore for low values of the Harvey parameter. For co-ECCD and high values of the Harvey parameter substantial synergy between ECCD and the ohmic current is observed and leads to the generation of a large population of suprathermal electrons and slows down the current penetration. The synergy between counter-ECCD and the inductive current results in a decrease of the total driven current and a much smaller population of suprathermal electrons. Another plasma stability problem has been studied during the current ramp-up phase. Quiet and MHD free current ramp-up is a necessary requirement for a long and efficient flat-top phase. The current penetration in the plasma scenarios with various plasma ramp-up rates has been modelled with the ASTRA transport code. It is shown that in the absence of MHD activity the predictions of the ASTRA code are in a agreement with the experimental results.