S. Günter

Chapter 3: MHD stability, operational limits and disruptions

Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document (1999 Nucl. Fusion 39 2137-2664), is reviewed. Recent theoretical and experimental research has made important advances in both understanding and control of MHD stability in tokamak plasmas. Sawteeth are anticipated in the ITER baseline ELMy H-mode scenario, but the tools exist to avoid or control them through localized current drive or fast ion generation. Active control of other MHD instabilities will most likely be also required in ITER. Extrapolation from existing experiments indicates that stabilization of neoclassical tearing modes by highly localized feedback-controlled current drive should be possible in ITER. Resistive wall modes are a key issue for advanced scenarios, but again, existing experiments indicate that these modes can be stabilized by a combination of plasma rotation and direct feedback control with non-axisymmetric coils. Reduction of error fields is a requirement for avoiding non-rotating magnetic island formation and for maintaining plasma rotation to help stabilize resistive wall modes. Recent experiments have shown the feasibility of reducing error fields to an acceptable level by means of non-axisymmetric coils, possibly controlled by feedback. The MHD stability limits associated with advanced scenarios are becoming well understood theoretically, and can be extended by tailoring of the pressure and current density profiles as well as by other techniques mentioned here. There have been significant advances also in the control of disruptions, most notably by injection of massive quantities of gas, leading to reduced halo current fractions and a larger fraction of the total thermal and magnetic energy dissipated by radiation. These advances in disruption control are supported by the development of means to predict impending disruption, most notably using neural networks. In addition to these advances in means to control or ameliorate the consequences of MHD instabilities, there has been significant progress in improving physics understanding and modelling. This progress has been in areas including the mechanisms governing NTM growth and seeding, in understanding the damping controlling RWM stability and in modelling RWM feedback schemes. For disruptions there has been continued progress on the instability mechanisms that underlie various classes of disruption, on the detailed modelling of halo currents and forces and in refining predictions of quench rates and disruption power loads. Overall the studies reviewed in this chapter demonstrate that MHD instabilities can be controlled, avoided or ameliorated to the extent that they should not compromise ITER operation, though they will necessarily impose a range of constraints.

Experiments on neoclassical tearing mode stabilization by ECCD in ASDEX Upgrade

The reduction of neoclassical tearing modes by ECCD is demonstrated experimentally. It is shown that with an averaged ECCD power of only 4-8% of the total heating power injected into the discharge, the island width can be reduced by 40%, provided that the centre of deposition is very close to the resonant surface. The reduction in mode amplitude results in a partial recovery of the loss of stored energy induced by the mode. This experimental result is well reproduced by modelling calculations.

ELM pace making and mitigation by pellet injection in ASDEX upgrade

In ASDEX Upgrade, experimental efforts aim to establish pace making and mitigation of type-I edge localized modes (ELMs) in high confinement mode (H-mode) discharges. Injection of small size cryogenic deuterium pellets (~(1.4?mm)2 ? 0.2?mm ? 2.5 ? 1019?D) at rates up to 83?Hz imposed persisting ELM control without significant fuelling, enabling for investigations well inside the type-I ELM regime. The approach turned out to meet all required operational features. ELM pace making was realized with the driving frequency ranging from 1 to 2.8 times the intrinsic ELM frequency, the upper boundary set by hardware limits. ELM frequency enhancement by pellet pace making causes much less confinement reduction than by engineering means like heating, gas bleeding or plasma shaping. Confinement reduction is observed in contrast to the typical for engineering parameters. Matched discharges showed triggered ELMs ameliorated with respect to intrinsic counterparts while their frequency was increased. No significant differences were found in the ELM dynamics with the available spatial and temporal resolution. By breaking the close correlation of ELM frequency and plasma parameters, pace making allows the establishment of fELM as a free parameter giving enhanced operational headroom for tailoring H-mode scenarios with acceptable ELMs. Use was made of the pellet pace making tool in several successful applications in different scenarios. It seems that further reduction of the pellet mass could be possible, eventually resulting in less confinement reduction as well.

Type-I ELM substructure on the divertor target plates in ASDEX Upgrade

In the ASDEX Upgrade tokamak, the power deposition structures on the divertor target plates during type-I edge localized modes (ELMs) have been investigated by infrared thermography. In addition to the axisymmetric strike line, several poloidally displaced stripes are resolved, identifying an ELM as a composite of several subevents. This pattern is interpreted as being a signature of the helical perturbations in the low field side edge during the non-linear ELM evolution. Based on this observation, the ELM related magnetic perturbation in the midplane can be derived from the target load pattern. In the start phase of an ELM collapse, average toroidal mode numbers around n ≈ 3–5 are found evolving to values of n ≈ 12–14 during the ELM power deposition maximum. Further information about the non-linear evolution of the ELM mode structure is obtained from statistical analyses of the spatial distribution, heat flux amplitudes and number of single stripes.

Analytical solutions to the Grad–Shafranov equation

Two families of exact analytical solutions of the Grad–Shafranov equation are presented by specifying the highest polynomial dependence of the plasma current density on the flux function Ψ in such a way that the Grad–Shafranov equation becomes a linear inhomogeneous differential equation. Both the pressure profile and the poloidal current profile each have two free parameters. X-points can be represented by superposition of solutions. Examples of the exact equilibrium solution are given for both a D-shaped plasma and a toroidally diverted plasma.

Interaction of energetic particles with large and small scale instabilities

Beyond a certain heating power, measured and predicted distributions of NBI driven currents deviate from each other, in a form that can be explained by the assumption of a modest diffusion of fast particles. Direct numerical simulation of fast test particles in a given field of electrostatic turbulence indicates that for reasonable parameters fast and thermal particle diffusion indeed are similar. High quality plasma edge plasma profiles on ASDEX Upgrade, used in the linear, gyrokinetic, global stability code LIGKA give excellent agreement with the eigenfunction measured by a newly extended reflectometry system for ICRH-excited TAE-modes. They support the hypothesis of TAE-frequency crossing of the continuum in the edge region as explanation of the high TAE-damping rates measured on JET.A new fast ion loss detector with 1MHz time resolution allows frequency and phase resolved correlation between low frequency magnetic perturbation, giving, together with modelling of the particle orbits, new insights into the mechanism of fast particle losses during NBI and ICRH due to helical perturbations.

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.

LIGKA: A linear gyrokinetic code for the description of background kinetic and fast particle effects on the MHD stability in tokamaks

Abstract In a plasma with a population of super-thermal particles generated by heating or fusion processes, kinetic effects can lead to the additional destabilisation of MHD modes or even to additional energetic particle modes. In order to describe these modes, a new linear gyrokinetic MHD code has been developed and tested, LIGKA (linear gyrokinetic shear Alfven physics) [Ph. Lauber, Linear gyrokinetic description of fast particle effects on the MHD stability in tokamaks, Ph.D. Thesis, TU Munchen, 2003; Ph. Lauber, S. Gunter, S.D. Pinches, Phys. Plasmas 12 (2005) 122501], based on a gyrokinetic model [H. Qin, Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks, Ph.D. Thesis, Princeton University, 1998]. A finite Larmor radius expansion together with the construction of some fluid moments and specification to the shear Alfven regime results in a self-consistent, electromagnetic, non-perturbative model, that allows not only for growing or damped eigenvalues but also for a change in mode-structure of the magnetic perturbation due to the energetic particles and background kinetic effects. Compared to previous implementations [H. Qin, mentioned above], this model is coded in a more general and comprehensive way. LIGKA uses a Fourier decomposition in the poloidal coordinate and a finite element discretisation in the radial direction. Both analytical and numerical equilibria can be treated. Integration over the unperturbed particle orbits is performed with the drift-kinetic HAGIS code [S.D. Pinches, Ph.D. Thesis, The University of Nottingham, 1996; S.D. Pinches et al., CPC 111 (1998) 131] which accurately describes the particles’ trajectories. This allows finite-banana-width effects to be implemented in a rigorous way since the linear formulation of the model allows the exchange of the unperturbed orbit integration and the discretisation of the perturbed potentials in the radial direction. Successful benchmarks for toroidal Alfven eigenmodes (TAEs) and kinetic Alfven waves (KAWs) with analytical results, ideal MHD codes, drift-kinetic codes and other codes based on kinetic models are reported.

Internal transport barrier triggering by rational magnetic flux surfaces in tokamaks

The formation of internal transport barriers (ITBs) has been experimentally associated with the presence of rational q surfaces in both JET and ASDEX Upgrade. The triggering mechanisms are related to the occurrence of magneto-hydrodynamic (MHD) instabilities such as mode coupling and fishbone activity. These events could locally modify the poloidal velocity and increase transiently the shearing rate to values comparable with the linear growth rate of ion temperature gradient modes. For JET reversed magnetic shear scenarios, ITB emergence occurs preferentially when the minimum q reaches an integral value. In this case, transport effects localized in the vicinity of zero magnetic shear and close to rational q values may be at the origin of ITB formation. The role of rational q surfaces in ITB triggering stresses the importance of q profile control for an advanced tokamak scenario and could assist in substantially lowering the access power to these scenarios in next step facilities.

On fully three-dimensional resistive wall mode and feedback stabilization computations

Resistive walls, located close to the plasma boundary, reduce the growth rates of external kink modes to resistive time scales. For such slowly growing resistive wall modes, the stabilization by an active feedback system becomes feasible. The fully three-dimensional stability code STARWALL, and the feedback optimization code OPTIM have been developed [P. Merkel and M. Sempf, 21st IAEA Fusion Energy Conference 2006, Chengdu, China (International Atomic Energy Agency, Vienna, 2006, paper TH/P3-8] to compute the growth rates of resistive wall modes in the presence of nonaxisymmetric, multiply connected wall structures and to model the active feedback stabilization of these modes. In order to demonstrate the capabilities of the codes and to study the effect of the toroidal mode coupling caused by multiply connected wall structures, the codes are applied to test equilibria using the resistive wall structures currently under debate for ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)] and ASDEX Upgrade [W. K...