Drift-Type Waves in Rotating Tokamak Plasma

The concept of energy production through the fusion of two light nuclei has been studied since the 1950’s. One of the major problems that fusion scientists have encountered is the confinement of the hot ionised gas, i.e. the plasma, in which the fusion process takes place. The most common way to contain the plasma is by using at magnetic field configuration, in which the plasma takes a doughnut-like shape. Experimental devices of this kind are referred to as tokamaks. For the fusion process to proceed at an adequate rate, the temperature of the plasma must exceed 100,000,000C. Such a high temperature forces the plasma out of thermodynamical equilibrium which plasma tries to regain by exciting a number of turbulent processes. After successfully quenching the lager scale magnetohydrodynamic turbulence that may instantly disrupt the plasma, a smaller scale turbulence revealed itself. As this smaller scale turbulence behaved contrary to the common theory at the time, it was referred to as anomalous. This kind of turbulence does not directly threaten existents of the plasma, but it allows for a leakage of heat and particles which inhibits the fusion reactions. It is thus essential to understand the origin of anomalous turbulence, the transport it generates and most importantly, how to reduce it. Today it is believed that anomalous transport is due to drift-type waves driven by temperature and density inhomogeneities and the theoretical treatment of these waves is the topic of this thesis.The first part of the thesis contains a rigorous analytical two-fluid treatment of drift waves driven solely by density inhomogeneities. Effects of the toroidal magnetic field configuration, the Landau resonance, a peaked diamagnetic frequency and a sheared rotation of the plasma have been taken into account. These effects either stabilise or destabilise the drift waves and to determine the net result on the drift waves requires careful analysis. To this end, dispersion relations have been obtained in various limits to determine when to expect the different effects to be dominant. The main result of this part is that with a large enough rotational shear, the drift waves will be quenched.In the second part we focus on temperature effects and thus treat reactive drift waves, specifically ion temperature gradient and trapped electron modes. In fusion plasmas the α-particles, created as a by-product of the fusion process, transfer the better part of their energy to the electrons and hence the electron temperature is expected to exceed the ion temperature. In most experiments until today, the ion temperature is greater than the electron temperature and this have been proven to improve the plasma confinement. To predict the performance of future fusion plasmas…


1. Description of drift waves in static equilibrium
1.1 The Universal Instability
1.1.1 Analytical Description of Drift Waves in Slab Geometry
1.2 The Landau Resonance
1.2.1 A Qualitative Picture of Wave-Particle Interaction
1.2.2 Physical Description of Landau Damping
1.2.3 Analytical Description of Landau Damping
1.3 Magnetic Shear Damping
1.4 Toroidal Mode Coupling
1.4.1 Propagating or localised drift modes?
2. The Weiland Model
2.1 The Interchange Instability
2.2 The Competition between Density and Temperature Inhomogeneities
2.3 Reactive Drift Modes
2.3.1 Ion Temperature Gradient Modes
2.3.2 Trapped Electron Modes
3. Summary of the Papers
Paper I
Paper II and III
Paper IV

Author: Asp, Elina

Source: Uppsala University Library

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