Allen H. Boozer

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.

Monte Carlo evaluation of transport coefficients

A method is developed for evaluating transport coefficients in asymmetric geometries using the Monte Carlo method. The method is applied to the stellarator.

Plasma equilibrium with rational magnetic surfaces

The self‐consistent classical plasma equilibrium with diffusion is studied in a toroidal geometry having a sheared magnetic field. Near each rational surface it is found that the pressure gradient is zero unless the Fourier component of 1/B2, which resonates with that surface, vanishes. Despite the resonances, the overall plasma confinement is, in practice, only slightly modified by the rational surfaces.

Guiding center drift equations

The equations for particle drift orbits are given in a new magnetic coordinate system. This form of the equations separates the fast motion along the magnetic field lines from the slow motion across the lines. In addition, less information is required about the magnetic field structure than in alternative forms of the drift equations.

Evaluation of the structure of ergodic fields

A method of analyzing ergodic magnetic fields is given, including a generalization of magnetic coordinates to such fields. The results of this analysis can be used in existing Monte Carlo codes to assess the enhanced transport associated with imperfect surfaces. The Hamiltonian for a general magnetic field is given as part of this analysis.

Principal physics developments evaluated in the ITER design review

As part of the ITER Design Review and in response to the issues identified by the Science and Technology Advisory Committee, the ITER physics requirements were reviewed and as appropriate updated. The focus of this paper will be on recent work affecting the ITER design with special emphasis on topics affecting near-term procurement arrangements. This paper will describe results on: design sensitivity studies, poloidal field coil requirements, vertical stability, effect of toroidal field ripple on thermal confinement, material choice and heat load requirements for plasma-facing components, edge localized modes control, resistive wall mode control, disruptions and disruption mitigation.

Establishment of magnetic coordinates for a given magnetic field

A method is given for expressing the magnetic field strength in magnetic coordinates for an arbitrary toroidal, scalar pressure, equilibrium with magnetic surfaces. The field strength in magnetic coordinates is central to the study of equilibrium, stability, and transport in asymmetric plasmas. While doing these calculations, it is assumed that the plasma equilibrium is known.

Modeling of active control of external magnetohydrodynamic instabilities

A general circuit formulation of resistive wall mode (RWM) feedback stabilization developed by Boozer [Phys. Plasmas 5, 3350 (1998)] has been used as the basis for the VALEN computer code that calculates the performance of an active control system in arbitrary geometry. The code uses a finite element representation of a thin shell structure in an integral formulation to model arbitrary conducting walls. This is combined with a circuit representation of stable and unstable plasma modes. Benchmark comparisons of VALEN results with large aspect ratio analytic model of the current driven kink mode are in very good agreement. VALEN also models arbitrary sensors, control coils, and the feedback logic connecting these sensors and control coils to provide a complete simulation capability for feedback control of plasma instabilities. VALEN modeling is in good agreement with experimental results on DIII-D [Garofalo et al., Nucl. Fusion 40, 1491 (2000)] and HBT-EP [Cates et al., Phys. Plasmas 7, 3133 (2000)]. VALEN ...

Computation of three-dimensional tokamak and spherical torus equilibria

A nominally axisymmetric plasma configuration, such as a tokamak or a spherical torus, is highly sensitive to nonaxisymmetric magnetic perturbations due to currents outside of the plasma. The high sensitivity means that the primary interest is in the response of the plasma to very small perturbations, i.e., ∣b∕B∣≈10−2 to 10−4, which can be calculated using the theory of perturbed equilibria. The ideal perturbed equilibrium code (IPEC) is described and applied to the study of the plasma response in a spherical torus to such external perturbations.

Theory of mode-induced beam-particle loss in tokamaks

Large‐amplitude rotating magnetohydrodynamic modes are observed to induce significant high‐energy beam particle loss during high‐power perpendicular netural beam injection on the poloidal divertor experiment (PDX). A Hamiltonian formalism for drift orbit trajectories in the presence of such modes is used to study induced particle loss analytically and numerically. Results are in good agreement with experiment.