Q. Yu

Numerical modelling of error field penetration

Error field (or externally applied helical field) penetration is studied numerically based on the two fluids equations. It is shown that there is a minimum in the required field amplitude when the applied helical field frequency is the same as the mode frequency being determined by both the background equilibrium plasma rotation and the diamagnetic drift. The mode penetration threshold significantly increases as the field frequency deviates from the mode frequency and can become asymmetric on the two sides of the minimum due to parallel heat transport. After mode penetration the nonlinear saturated island width is found to be smaller for a larger electron diamagnetic drift frequency.

Control of MHD Instabilities by ECCD: ASDEX Upgrade Results and Implications for ITER

The requirements for control of MHD instabilities by electron cyclotron current drive (ECCD) are reviewed. It is shown that a localized current drive is needed for control of both sawteeth and neoclassical tearing modes (NTMs). In the case of NTMs, the deposition width should be smaller than the island width for efficient control. At island widths smaller than the deposition width, as is predicted to occur in ITER, theory suggests that efficient control is possible only by modulating the ECCD power in phase with the island. These predictions are experimentally confirmed in ASDEX Upgrade for NTM control. Narrow deposition has also been used to extend the operational range of NTM stabilization in ASDEX Upgrade to lower q95 and in the improved H-mode scenario. Our results suggest that, for the ITER ECCD system, good localization of the driven current profile as well as the capability to modulate the ECCD in phase with rotating modes will be needed for efficient MHD control by ECCD.

Plasma response to externally applied resonant magnetic perturbations

Based on recent finding that applied resonant magnetic perturbation (RMP) can either increase or decrease the local electron density gradient around the resonant surface (Yu and Gunter 2009 Nucl. Fusion 49 062001), the plasma response to the RMP of a single helicity is studied numerically by further taking into account the electron energy transport. It is found that the changes in the local electron density and temperature by RMPs are coupled. If the local parallel heat diffusivity and/or the island width are sufficiently large, the local electron temperature profile flattens, which enhances the change in the local electron density gradient. Depending on the plasma parameters, either the plasma rotation frequency or the electron diamagnetic frequency (electron pressure gradient) can be significantly changed by RMPs, and these two changes affect each other. With a reduced set of equations that does not include the electron energy transport equation, the particle transport in stochastic magnetic fields is found to be similar to that across a single magnetic island.

Effect of the dynamic ergodic divertor in the TEXTOR tokamak on MHD stability, plasma rotation and transport

With the dynamic ergodic divertor in TEXTOR fundamental effects of the coupling of external magnetic field perturbations to the confined plasma have been studied. The non-linear coupling between external (m/n = 12/4) and internal modes (m/n = 3/1) has been investigated. The critical perturbation field (m/n = 3/1) for the excitation of an m/n = 2/1 tearing mode depends not only on the magnitude but also on the direction of the toroidal angular momentum input by neutral beam injection (NBI). Below the excitation threshold of this mode a toroidal spin-up of the plasma has been observed, which only depends on the strength of the perturbation field. It is independent of both the rotation direction of the external perturbation field and the toroidal angular momentum supplied by the NBI.

Fast sawtooth reconnection at realistic Lundquist numbers

Magnetic reconnection, a ubiquitous phenomenon in astrophysics, space science and magnetic confinement research, frequently proceeds much faster than predicted by simple resistive MHD theory. Acceleration can result from the break-up of the thin Sweet–Parker current sheet into plasmoids, or from two-fluid effects decoupling mass and magnetic flux transport over the ion inertial length or the drift scale depending on the absence or presence of a strong magnetic guide field. We describe new results on the modelling of sawtooth reconnection in a simple tokamak geometry (circular cylindrical equilibrium) pushed to realistic Lundquist numbers for present day tokamaks. For the resistive MHD case, the onset criteria and the influence of plasmoids on the reconnection process agree well with earlier results found in the case of vanishing magnetic guide fields. While plasmoids are also observed in two-fluid calculations, they do not dominate the reconnection process for the range of plasma parameters considered in this study. In the two-fluid case they form as a transient phenomenon only. The reconnection times become weakly dependent on the S-value and for the most complete model—including two-fluid effects and equilibrium temperature and density gradients—agree well with those experimentally found on ASDEX Upgrade

Numerical modelling of sawtooth crash using two-fluid equations

The nonlinear growth of internal kink modes is studied numerically using two-fluid equations. As already reported earlier (Gunter et al 2015 Plasma Phys. Control. Fusion 57 014017), short sawtooth crash times (<100 μs) are found for typical ASDEX Upgrade parameters, in agreement with experimental observations. These fast sawtooth crashes are associated with large parallel electric field perturbations, giving rise to the generation of supra-thermal electrons. Slow sawtooth crashes (~ms) are obtained only for a sufficiently small () and a large local electron diamagnetic drift frequency at the surface, where q0 is the value of the safety factor q at the magnetic axis. Kink modes are shown to drive sheared plasma rotation, propagating from the surface towards the magnetic axis during the nonlinear phase. After the sawtooth crash, the driven plasma rotation is in the co- (counter-) current direction inside (outside) the surface, as observed in experiments.

Conversion of the dominantly ideal perturbations into a tearing mode after a sawtooth crash

Forced magnetic reconnection is a topic of common interest in astrophysics, space science, and magnetic fusion research. The tearing mode formation process after sawtooth crashes implies the existence of this type of magnetic reconnection and is investigated in great detail in the ASDEX Upgrade tokamak. The sawtooth crash provides a fast relaxation of the core plasma temperature and can trigger a tearing mode at a neighbouring resonant surface. It is demonstrated for the first time that the sawtooth crash leads to a dominantly ideal kink mode formation at the resonant surface immediately after the sawtooth crash. Local measurements show that this kink mode transforms into a tearing mode on a much longer timescale (10−3s−10−2s) than the sawtooth crash itself (10−4s). The ideal kink mode formed after the sawtooth crash provides the driving force for magnetic reconnection and its amplitude is one of the critical parameters for the length of the transition phase from a ideal into an resistive mode. Nonlinear ...

Seed island formation by forced magnetic reconnection

Neoclassical tearing modes observed in experiments often grow from seed magnetic islands induced by triggers like sawteeth. The formation of seed islands is studied in this paper using both the reduced MHD and two-fluid equations, with the trigger being modelled by externally applied resonant magnetic perturbations. In the linear phase the growth rate of the driven mode is found to be the same as that of the trigger. A slowly growing trigger drives a tearing mode, while a fast one drives a kink-like mode, which becomes a tearing mode later when the triggers growth slows down. A finite ion sound Larmor radius (ion Larmor radius by using electron temperature) and electron inertia are found to lead to a larger seed island for a given external perturbation. The electron diamagnetic drift and plasma rotation, if increasing the relative rotation between the trigger and the driven mode, decrease the seed island width.

Utilizing resonant magnetic perturbations to enhance neoclassical tearing mode stabilization by rf current

A new method to stabilize the rotating neoclassical tearing mode (NTM) by using both the rf current drive and the static resonant magnetic perturbation (RMP) is investigated. When a non-uniform mode rotation is induced by the RMP, the stabilization of NTM by the rf current is found to be enhanced if the RMP phase has a half period difference from that of the rf wave deposition along the helical angle. The required rf current for mode stabilization is reduced by about one third if an appropriate RMP amplitude is applied.