O. Sauter

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.

Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime

Expressions for the neoclassical resistivity and the bootstrap current coefficients in terms of aspect ratio and collisionality are widely used in simulating toroidal axisymmetric equilibria and transport evolution. The formulas used are in most cases based on works done 15-20 years ago, where the results have been obtained for large aspect ratio, small or very large collisionality, or with a reduced collision operator. The best expressions to date and to our knowledge are due to Hirshman [S. P. Hirshman, Phys. Fluids 31, 3150 (1988)] for arbitrary aspect ratio in the banana regime and Hinton-Hazeltine [F. L. Hinton and R. D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976)] for large aspect ratio and arbitrary collisionality regime. A code solving the Fokker-Planck equation with the full collision operator and including the variation along the magnetic field line, coupled with the adjoint function formalism, has been used to calculate these coefficients in arbitrary equilibrium and collisionality regimes. The coefficients have been obtained for a wide variety of plasma and equilibrium parameters and a comprehensive set of formulas, which have been fitted to the code results within 5%, is proposed for evaluating the neoclassical conductivity and the bootstrap current coefficients. This extends previous works and also highlights inaccuracies in the previous formulas in this wide plasma parameter space

Beta limits in long-pulse tokamak discharges

The maximum normalized beta achieved in long-pulse tokamak discharges at low collisionality falls significantly below both that observed in short pulse discharges and that predicted by the ideal MHD theory. Recent long-pulse experiments, in particular those simulating the International Thermonuclear Experimental Reactor (ITER) [M. Rosenbluth et al., Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1995), Vol. 2, p. 517] scenarios with low collisionality nu(e)*, are often limited by low-m/n nonideal magnetohydrodynamic (MHD) modes. The effect of saturated MHD modes is a reduction of the confinement time by 10%-20%, depending on the island size and location, and can lead to a disruption. Recent theories on neoclassical destabilization of tearing modes, including the effects of a perturbed helical bootstrap current, are successful in explaining the qualitative behavior of the resistive modes and recent results are consistent with the size of the saturated islands. Also, a strong correlation is observed between the onset of these low-m/n modes with sawteeth, edge localized modes (ELM), or fishbone events. consistent with the seed island required by the theory. We will focus on a quantitative comparison between both the conventional resistive and neoclassical theories, and the experimental results of several machines, which have all observed these low-min nonideal modes. This enables us to single out the key issues in projecting the long-pulse beta limits of ITER-size tokamaks and also to discuss possible plasma control methods that can increase the soft beta limit, decrease the seed perturbations, and/or diminish the effects on confinement

A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation

A new code is presented here, named Gyrokinetic SEmi-LAgragian (GYSELA) code, which solves 4D drift-kinetic equations for ion temperature gradient driven turbulence in a cylinder (r,θ,z). The code validation is performed with the slab ITG mode that only depends on the parallel velocity. This code uses a semi-Lagrangian numerical scheme, which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been validated in the linear and non-linear regimes. The GYSELA code is found to be stable over long simulation times (more than 20 times the linear growth rate of the most unstable mode), including for cases with a high resolution mesh (δr ∼ 0.1 Larmor radius, δz ∼ 10 Larmor radius).

A global collisionless PIC code in magnetic coordinates

A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), delta f scheme, 3D cubic B-splines finite elements for the field solver and several numerical noise reduction techniques. A particular feature is the use of straight-field-1 line magnetic coordinates and a field-aligned Fourier filtering technique that dramatically improves the performance of the code in terms of both the numerical noise reduction and the maximum time step allowed. Another feature is the capability to treat arbitrary axisymmetric ideal MHD equilibrium configurations. The code is heavily parallelized, with scalability demonstrated up to 4096 processors and 109 marker particles. Various numerical convergence tests are performed. The code is validated against an analytical theory of zonal flow residual, geodesic acoustic oscillations and damping, and against other codes for a selection of linear and nonlinear tests. (c) 2007 Elsevier B.V. All rights reserved.

The CHEASE code for toroidal MHD equilibria

The CHEASE code (Cubic Hermite Element Axisymmetric Static Equilibrium) solves the Grad-Shafranov equation for toroidal MHD equilibria using a Hermite bicubic finite element discretization with pressure, current profiles and plasma boundaries specified by analytical forms or sets of experimental data points. Moreover, CHEASE allows the automatic generation of pressure profiles marginally stable to ballooning modes or with a prescribed fraction of bootstrap current. The code provides equilibrium quantities for several stability and global wave propagation codes.

Overview of the ITER EC upper launcher

The ITER electron cyclotron (EC) upper port antenna (or launcher) is nearing completion of the detailed design stage and the final build-to-print design stage will soon start. The main objective of this launcher is to drive current locally to stabilize the neoclassical tearing modes (NTMs) (depositing ECCD inside of the island that forms on either the q = 3/2 or 2 rational magnetic flux surfaces) and control the sawtooth instability (deposit ECCD near the q = 1 surface). The launcher should be capable of steering the focused beam deposition location to the resonant flux surface over the range in which the q = 1, 3/2 and 2 surfaces are expected to be found for various plasma equilibria susceptible to the onset of NTMs and sawteeth. The aim of this paper is to provide the design status of the principal components that make up the launcher: port plug, mm-wave system and shield block components. The port plug represents the chamber that provides a rigid support structure that houses the mm-wave and shield blocks. The mm-wave system comprises the components used to guide the RF beams through the port plug structure and refocus the beams far into the plasma. The shield block components are used to attenuate the nuclear radiation from the burning plasma, protecting the fragile in-port components and reducing the neutron streaming through the port assembly. The design of these three subsystems is described; in addition, the relevant thermo-mechanical and electro-magnetic analyses are reviewed for critical design issues.

On the physics guidelines for a tokamak DEMO

The physics base for the ITER Physics Design Guidelines is reviewed in view of application to DEMO and areas are pointed out in which improvement is needed to arrive at a consistent set of DEMO Physics Design Guidelines. Amongst the proposed improvements, the area of power exhaust plays a crucial role since predictive capability of present-day models is low and this area is expected to play a major role in limiting DEMO designs due to the much larger value of Ptot/R in DEMO than in present-day devices and even ITER.

Creation and control of variably shaped plasmas in TCV

During the first year of operation, the TCV tokamak has produced a large variety of plasma shapes and magnetic configurations, with 1.0<or=Btor<or=1.46 T, Ip<or=800 kA, kappa <or=2.05, -0.7<or= delta <or=0.7. A new shape control algorithm, based on finite element reconstruction of the plasma current in real time, has been implemented. Vertical growth rates of 800 sec-1 corresponding to a stability margin f=1.15, have been stabilized. Ohmic H-modes, with energy confinement times reaching 80 ms, normalized beta ( beta toraB/Ip) of 1.9 and tau E/ITER89-P of 2.4 have been obtained in single-null X-point deuterium discharges with the ion grad B drift towards the X-point. Limiter H-modes with maximum line averaged electron densities of 1.7*1020m-3 have been observed in D-shaped plasmas with 360 kA<or=Ip<or=600 kA.

Snowflake divertor plasmas on TCV

Starting from a standard single null X-point configuration, a second order null divertor (snowflake (SF)) has been successfully created on the Tokamak a Configuration Variable (TCV) tokamak. The magnetic properties of this innovative configuration have been analysed and compared with a standard X-point configuration. For the SF divertor, the connection length and the flux expansion close to the separatrix exceed those of the standard X-point by more than a factor of 2. The magnetic shear in the plasma edge is also larger for the SF configuration.