Understanding and controlling plasma rotation in tokamaks

Fusion energy is an attractive candidate for future energy production. At very high temperatures the nuclei of two hydrogen isotopes, deuterium and tritium, fuse, producing helium, a neutron and a very large amount of energy. The high temperatures that are needed to make fusion reactions possible can be reached in a plasma that is magnetically confined. The most successful concept for the magnetic confinement of a plasma is the tokamak. However, despite the success of the tokamak, several challenges still lie ahead. One of these challenges is the magnetic stability. If we want to assure the magnetic stability of a tokamak, it is necessary to know what causes magnetic instabilities. An important class of magnetohydrodynamic instabilities are so-called tearing modes or magnetic islands. These tearing modes can be triggered by an external magnetic error field, which can be due to misalignment of field coils, asymmetries in the tokamak vessel et cetera. It has been observed on several tokamaks that the excitation of these error field induced modes depends strongly on the plasma rotation. Also theories have been developed to describe this dependency. The TEXTOR tokamak is very well suited to investigate the relation between plasma rotation and the excitation of tearing modes. Two tangential neutral beam injectors give us complete control over the plasma rotation. A set of perturbation coils, called the dynamic ergodic divertor (DED), provide a fully adjustable perturbation field. With the tangential neutral beams and the DED, dedicated experiments were carried out to test the theory on mode excitation. When an external perturbation field is applied, the plasma rotation is expected change until the rotation velocity is so that tearing modes would be at rest in the frame of the perturbation field. Once this rotation velocity is reached, large tearing modes will develop in the plasma. This is called mode excitation or mode penetration. A too low perturbation field may not induce enough change in plasma rotation to reach the rotation velocity for which the tearing modes are at rest in the frame of the perturbation field. This means that the perturbation level needs to reach a certain threshold in order to excite tearing modes. The theory found in the literature predicts a monotonic change in the plasma rotation. It also predicts that the threshold for mode excitation increases with the plasma rotation velocity. The direction of the rotation, within the frame of the perturbation field, is not important, hence the threshold as a function of the rotation velocity is symmetric around the minimal threshold. The results of our experiments deviate from the predictions made by the theory. Instead of a monotonic change in the plasma rotation, we found that the plasma has an initial tendency to rotate in the co-current direction when the DED is applied. For a plasma that rotates faster in the co-current direction than the DED field, this means that the plasma first accelerates and only at a high perturbation strength starts to slow down. Not only the measured change in plasma rotation was different than expected. Also the relation between the plasma rotation and the threshold for mode excitation was not in agreement with the theory. Instead of the predicted symmetry around the minimal threshold, we measured that the threshold increases faster with increasing plasma corotation than with increasing counter-rotation. The reason for this discrepancy between theory and experiment was found in the plasma edge. An external perturbation field creates a stochastic zone in the plasma edge. Fast electron transport parallel to the stochastic field lines leads to a radial electron loss current. Ambipolarity requires this loss current to be balanced by a perpendicular return current, that in turn exerts a j × B-force onto the plasma. This stochastic torque is always in the co-current direction and saturates for a high perturbation strength. In most tokamaks the stochastic region will be very small and the stochastic force can be ignored. In TEXTOR however, the stochastic force is quite large, because one of the main objectives of the DED is to significantly perturb the plasma edge. The conventional theory of mode excitation does not take this stochastic force into account. The change in plasma rotation and the threshold as a function of plasma rotation is found by balancing an electromagnetic torque at the position of the mode with a viscous torque that opposes any change in the plasma rotation. Because the stochastic torque can not be ignored, in TEXTOR the balance of the EM torque, the viscous torque and the stochastic torque has to be taken. With the stochastic force included in the mode excitation model, the measurements of the plasma rotation and the rotation dependence of the mode excitation could be explained. For co-rotating plasmas the EM torque tries to slow the plasma down, while the stochastic torque tries to increase the plasma velocity. In an initial stage the stochastic torque is dominant and the plasma rotation increases. When the perturbation field is increased the EM torque takes over, the plasma slows down and mode excitation occurs. The stochastic torque opposes the EM torque, resulting in a high the excitation threshold. For counter-rotating plasmas, both the stochastic and the EM torque slow down the plasma. As a result the threshold for mode excitation is not as high for counter-rotating plasmas as it is for plasmas rotating with the same speed in the co-direction. Two conclusions can be drawn from this work: (a) In absence of a stochastic field the conventional mode excitation theory is valid. (b) The introduction of a stochastic edge field is beneficial for co-rotating plasmas: the threshold for mode excitation increases and – for moderate perturbations – the rotation itself also increases. ITER is expected to rotate in the co-direction. It may be therefore worthwhile to look into the possibility of a stochastic edge. Especially because, apart from a higher mode threshold and a faster rotation, stochasticity also suppresses unfavourable ELM’s in H-mode. Both with and without a stochastic edge region, the fact remains that a fast rotating plasma is less sensitive to tearing modes than a slowly rotating plasma. In present day tokamaks neutral beam injectors provide the necessary high rotation speed. For the next generation of fusion reactors the neutral beams will not be able to deliver enough momentum to a plasma. Other sources of momentum input are therefore needed. A promising source of momentum input is ion cyclotron resonance heating (ICRH). The effect of ICRH on plasma rotation is, however, still not very well understood. Depending on the plasma Understanding and controlling plasma rotation in tokamaks conditions ICRH can induce both co- or counter-rotation. In TEXTOR it was found that ICRH acts as a source of momentum in the counter-current direction. If ICRH changes the plasma rotation, we may assume that also electron cyclotron resonance heating (ECRH) has an influence on the plasma rotation. In TEXTOR it was found that the changes in rotation during ECRH were related to changes in the local transport. This opens perspectives for local shaping of the rotation profile. Especially the possibility to locally increase the velocity gradient is interesting, because a sheared velocity suppresses turbulence and thus increases the confinement