P. Helander

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.

A simple avalanche model as an analogue for magnetospheric activity

The power law dependence of the power spectrum of auroral indices, and in-situ magnetic field observations in the earths geotail, may be evidence that the coupled solar wind-magnetospheric system exhibits scale free self organised criticality and can to some extent be described by avalanche models. In contrast, the intensity of, and time interval between, substorms both have well defined probability distributions with characteristic scales. We present results from a simple cellular automaton that models avalanches in a one dimensional “sandpile”; here we examine the simplest case of constant inflow. This model generates a probability distribution of energy discharges due to internal reorganization that is a power law implying SOC, whereas systemwide discharges (flow of “sand” out of the system) form a distinct group which do not exhibit SOC. The energy dissipated in a systemwide discharge follows a probability distribution with a well defined mean, as does the time interval between one systemwide discharge and the next. Internal and external avalanches can therefore in principle be identified with distinct processes in the dynamic geotail. If so, the avalanche model places restrictions on the class of physical process that may be invoked to explain the observed geomagnetic dynamics.

Runaway acceleration during magnetic reconnection in tokamaks

In this paper, the basic theory of runaway electron production is reviewed and recent progress is discussed. The mechanisms of primary and secondary generation of runaway electrons are described and their dynamics during a tokamak disruption is analysed, both in a simple analytical model and through numerical Monte Carlo simulation. A simple criterion for when these mechanisms generate a significant runaway current is derived, and the first self-consistent simulations of the electron kinetics in a tokamak disruption are presented. Radial cross-field diffusion is shown to inhibit runaway avalanches, as indicated in recent experiments on JET and JT-60U. Finally, the physics of relativistic post-disruption runaway electrons is discussed, in particular their slowing down due to emission of synchrotron radiation, and their ability to produce electron–positron pairs in collisions with bulk plasma ions and electrons.

Solar flares as cascades of reconnecting magnetic loops

A model for the solar coronal magnetic field is proposed where multiple directed loops evolve in space and time. Loops injected at small scales are anchored by footpoints of opposite polarity moving randomly on a surface. Nearby footpoints of the same polarity aggregate, and loops can reconnect when they collide. This may trigger a cascade of further reconnection, representing a solar flare. Numerical simulations show that a power law distribution of flare energies emerges, associated with a scale-free network of loops, indicating self-organized criticality.

Suppression of runaway electron avalanches by radial diffusion

The kinetic theory of runaway electron avalanches caused by close Coulomb collisions is extended to account for radial diffusion. This is found to slow down the growth of avalanches. An approximate analytical formula for the growth rate is derived and is verified by a three-dimensional Monte Carlo code constructed for this purpose. As the poloidal magnetic flux that is available to induce an electric field in a tokamak is limited, avalanches can be prevented altogether by sufficiently strong radial diffusion. The requisite magnetic fluctuation level is sensitive to the mode structure and the speed of the disruption. It is estimated to be δB/B∼10−3 for parameters typical of large tokamaks.

Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas

In this work, we examine the validity of several common simplifying assumptions used in numerical neoclassical calculations for nonaxisymmetric plasmas, both by using a new continuum drift-kinetic code and by considering analytic properties of the kinetic equation. First, neoclassical phenomena are computed for the LHD and W7-X stellarators using several versions of the drift-kinetic equation, including the commonly used incompressible-E × B-drift approximation and two other variants, corresponding to different effective particle trajectories. It is found that for electric fields below roughly one third of the resonant value, the different formulations give nearly identical results, demonstrating the incompressible E × B-drift approximation is quite accurate in this regime. However, near the electric field resonance, the models yield substantially different results. We also compare results for various collision operators, including the full linearized Fokker-Planck operator. At low collisionality, the radial transport driven by radial gradients is nearly identical for the different operators; while in other cases, it is found to be important that collisions conserve momentum.

Runaway electron drift orbits in magnetostatic perturbed fields

Disruptions in large tokamaks can lead to the generation of a relativistic runaway electron beam that may cause serious damage to the first wall. To mitigate the disruption and suppress the runaway beam the application of resonant magnetic perturbations has been suggested. In this work we investigate the effect of resonant magnetic perturbations on the confinement of runaway electrons by simulating their drift orbits in magnetostatic perturbed fields and calculating the orbit losses for various initial energies and magnetic perturbation magnitudes. In the simulations we use a TEXTOR-like configuration and solve the relativistic, gyro-averaged drift equations for the runaway electrons including synchrotron radiation and collisions. The results indicate that runaway electrons are well confined in the core of the device, but the onset time of runaway losses closer to the edge is dependent on the magnetic perturbation level and thereby can affect the maximum runaway current. However, the runaway current damping rate is not sensitive to the magnetic perturbation level, in agreement with experimental observations.

Sandpiles, silos and tokamak phenomenology : a brief review

Increasing attention is being given to the possibility that some key features of tokamak confinement physics may not be specific to the plasma state. In particular, there appear to be parallels between sandpiles and transport in tokamaks. Aspects of sandpile physics involving self-organized criticality (SOC) have been suggested by Carreras, Diamond, Newman and co-workers (for example, 1996 Phys. Plasmas 3 1858, 2903 and 3745) as a paradigm for certain tokamak phenomena. However, the range of confinement physics displayed by sandpiles (in particular, by real experimental sandpiles) and also by related systems such as silos is substantially broader than so far considered for application to tokamak plasmas. It is reviewed in this paper, and additional candidate phenomena for sandpile modelling in tokamak physics, such as edge-localized modes and Berk - Breizman dynamics, are identified. The behaviour of sandpile-like systems is varied, and is sometimes sensitive to details in the experimental set-up or the theoretical model, so the role of SOC is not entirely clear. Recent theoretical progress in the modelling of experimental sandpiles is described, showing that the internal dynamics of a sandpile-type system may be governed by SOC even when this is not observed in the flow of matter from the system.

Destabilization of magnetosonic-whistler waves by a relativistic runaway beam

Magnetosonic-whistler waves may be destabilized by runaway electrons both in fusion and astrophysical plasmas. A linear instability growth rate of these waves in the presence of a runaway avalanche is calculated both perturbatively and by numerical solution of the full dispersion equation. The local threshold of the instability depends on the fraction of runaways, the magnetic field, and the temperature of the background plasma. The quasilinear analysis shows that the main result of the instability is the scattering of the electrons in pitch-angle. It appears possible that this instability could explain why the number of runaway electrons generated in tokamak disruptions depends on the strength of the magnetic field.

Overview of recent experimental results on MAST

Note: Proc. 19th IAEA Fusion Energy Conference, Lyon, France, October 2002, IAEA-CN-94/EX/OV2-3 Reference CRPP-CONF-2002-068 Record created on 2008-05-13, modified on 2017-05-12