V.E. Lukash

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.

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.

Disruption Scenarios, their Mitigation and Operation Window in ITER

The impacts of plasma disruptions on ITER have been investigated in detail to confirm the robustness of the design of the machine to the potential consequential loads. The loads include both electro-magnetic (EM) and heat loads on the in-vessel components and the vacuum vessel. Several representative disruption scenarios are specified based on newly derived physics guidelines for the shortest current quench time as well as the maximum product of halo current fraction and toroidal peaking factor arising from disruptions in ITER. Disruption simulations with the DINA code and EM load analyses with a 3D finite element method code are performed for these scenarios. Some margins are confirmed in the EM load on in-vessel components due to induced eddy and halo currents for these representative scenarios. However, the margins are not very large. The heat load on various parts of the first wall due to the vertical movement and the thermal quench (TQ) is calculated with a 2D heat conduction code based on the database of heat deposition during disruptions and simulation results with the DINA code. For vertical displacement event, it is found that the beryllium (Be) wall does not melt during the vertical movement, prior to the TQ. Significant melting is anticipated for the upper Be wall and the tungsten divertor baffle due to TQ after the vertical movement. However, its impact could be substantially mitigated by implementing a reliable detection system of the vertical movement and a mitigation system, e.g. massive noble gas injection. Some melting of the upper Be wall is anticipated at major disruptions. At least several tens of unmitigated disruptions must be considered even if an advanced prediction/mitigation system is implemented. With these unmitigated disruptions, the loss of the Be layer is expected to be within ?30?100??m/event out of a 10?mm thick Be first wall.

Development of ITER 15 MA ELMy H-mode inductive scenario

The poloidal field (PF) coil system on ITER, which provides both feedforward and feedback control of plasma position, shape, and current, is a critical element for achieving mission performance. Analysis of PF capabilities has focused on the 15 MA Q = 10 scenario with a 300-500 s flattop burn phase. The operating space available for the 15 MA ELMy H-mode plasma discharges in ITER and upgrades to the PF coils or associated systems to establish confidence that ITER mission objectives can be reached have been identified. Time dependent self-consistent free-boundary calculations were performed to examine the impact of plasma variability, discharge programming, and plasma disturbances. Based on these calculations a new reference scenario was developed based upon a large bore initial plasma, early divertor transition, low level heating in L-mode, and a late H-mode onset. Equilibrium analyses for this scenario indicate that the original PF coil limitations do not allow low li (<0.8) operation or lower flux states, and the flattop burn durations were predicted to be less than the desired 400 s. This finding motivates the expansion of the operating space, considering several upgrade options to the PF coils. Analysis was also carried out to examine the feedback current reserve required in the CS and PF coils during a series of disturbances and a feasibility assessment of the 17 MA scenario was undertaken. Results of the studies show that the new scenario and modified PF system will allow a wide range of 15 MA 300-500 s operation and more limited but finite 17 MA operation.

Development of the ITER baseline inductive scenario

Sustainment of Q ~ 10 operation with a fusion power of ~500 MW for several hundred seconds is a key mission goal of the ITER Project. Past calculations and simulations predict that these conditions can be produced in high-confinement mode operation (H-mode) at 15 MA relying on only inductive current drive. Earlier development of 15 MA baseline inductive plasma scenarios provided a focal point for the ITER Design Review conducted in 2007–2008. In the intervening period, detailed predictive simulations, supported by experimental demonstrations in existing tokamaks, allow us to assemble an end-to-end specification of this scenario consistent with the final design of the ITER device. Simulations have encompassed plasma initiation, current ramp-up, plasma burn and current ramp-down, and have included density profiles and thermal transport models producing temperature profiles consistent with edge pedestal conditions present in current fusion experiments. These quasi-stationary conditions are maintained due to the presence of edge-localized modes that limit the edge pressure. High temperatures and densities in the pedestal region produce significant edge bootstrap current that must be considered in modelling of feedback control of shape and vertical stability. In this paper we present new results of transport simulations fully consistent with the final ITER design that remain within allowed limits for the coil system and power supplies. These self-consistent simulations increase our confidence in meeting the challenges of the ITER program.

Current ramps in tokamaks: from present experiments to ITER scenarios

In order to prepare adequate current ramp-up and ramp-down scenarios for ITER, present experiments from various tokamaks have been analysed by means of integrated modelling in view of determining relevant heat transport models for these operation phases. A set of empirical heat transport models for L-mode (namely, the Bohm–gyroBohm model and scaling based models with a specific fixed radial shape and energy confinement time factors of H96−L = 0.6 or HIPB98 = 0.4) has been validated on a multi-machine experimental dataset for predicting the li dynamics within ±0.15 accuracy during current ramp-up and ramp-down phases. Simulations using the Coppi–Tang or GLF23 models (applied up to the LCFS) overestimate or underestimate the internal inductance beyond this accuracy (more than ±0.2 discrepancy in some cases). The most accurate heat transport models are then applied to projections to ITER current ramp-up, focusing on the baseline inductive scenario (main heating plateau current of Ip = 15 MA). These projections include a sensitivity study to various assumptions of the simulation. While the heat transport model is at the heart of such simulations (because of the intrinsic dependence of the plasma resistivity on electron temperature, among other parameters), more comprehensive simulations are required to test all operational aspects of the current ramp-up and ramp-down phases of ITER scenarios. Recent examples of such simulations, involving coupled core transport codes, free-boundary equilibrium solvers and a poloidal field (PF) systems controller are also described, focusing on ITER current ramp-down.

Comparing DINA code simulations with TCV experimental plasma equilibrium responses

The DINA nonlinear time-dependent simulation code has been validated against an extensive set of plasma equilibrium response experiments carried out on the TCV tokamak. Limited and diverted plasmas are found to be well modelled during the plasma current flat top. In some simulations the application of the poloidal field coil voltage stimulation pulse sufficiently changed the plasma equilibrium that the vertical position feedback control loop became unstable. This behaviour was also found in the experimental work, and cannot be reproduced using linear time-independent models. A single null diverted plasma discharge was also simulated from start-up to shut-down and the results were found to accurately reproduce their experimental equivalents. The most significant difference noted was the penetration time of the poloidal flux, leading to a delayed onset of sawtoothing in the DINA simulation. The complete set of frequency stimulation experiments used to measure the open-loop tokamak plasma equilibrium response was also simulated using DINA and the results were analysed in an identical fashion to the experimental data. The frequency response of the DINA simulations agrees with the experimental results. Comparisons with linear models are also discussed in order to identify areas of good and only occasionally less good agreement.

Runaway current termination in JT-60U

Termination of the runaway electron current generated during plasma disruptions is found in JT-60U during simulated vertical plasma displacement events where the safety factor at the plasma surface qs decreases. For all discharges with runaway electron generation, the runaway current disappears for qs≥2 with the appearance of spikes in the magnetic fluctuations. The growth rate of the spikes in the magnetic fluctuations decreases by an order of magnitude during the termination of runaway current. Corresponding to the loss of runaway electrons by magnetic fluctuations, heat flux pulses are measured at the inner divertor plates, which indicates interaction of the wall with the runaway electrons. The halo current during runaway termination is small and increases after runaway termination with a dominant toroidal mode of n = 1.

Comparing TCV experimental VDE responses with DINA code simulations

The DINA free-boundary equilibrium simulation code has been implemented for TCV, including the full TCV feedback and diagnostic systems. First results showed good agreement with control coil perturbations and correctly reproduced certain non-linear features in the experimental measurements. The latest DINA code simulations, presented in this paper, exploit discharges with different cross-sectional shapes and different vertical instability growth rates which were subjected to controlled vertical displacement events (VDEs), extending previous work with the DINA code on the DIII-D tokamak. The height of the TCV vessel allows observation of the non-linear evolution of the VDE growth rate as regions of different vertical field decay index are crossed. The vertical movement of the plasma is found to be well modelled. For most experiments, DINA reproduces the S-shape of the vertical displacement in TCV with excellent precision. This behaviour cannot be-modelled using linear time-independent models because of the predominant exponential shape due to the unstable pole of any linear time-independent model. The other most common equilibrium parameters like the plasma current I-p, the elongation kappa, the triangularity delta, the safety factor q, the ratio between the averaged plasma kinetic pressure and the pressure of the poloidal magnetic field at the edge of the plasma beta(p), and the internal self inductance l(i) also show acceptable agreement. The evolution of the growth rate gamma is estimated and compared with the evolution of the closed-loop growth rate calculated with the RZIP linear model, confirming the origin of the observed behaviour.

Full tokamak discharge simulation of ITER by combining DINA-CH and CRONOS

A full tokamak discharge simulator has been developed by combining a free-boundary equilibrium evolution code, DINA-CH, and an advanced transport modelling code, CRONOS. The combined tokamak discharge simulator provides a full simulation of a whole tokamak discharge, including non-linear coupling effects between the evolution of the free-boundary plasma equilibrium and transport. The free-boundary plasma equilibrium evolution is self-consistently calculated with the plasma current diffusion, in response to currents flowing in the PF coils and the surrounding conducting system. The heat and current source profiles calculated taking the free-boundary plasma equilibrium are used for the plasma transport. The constraints in operating a tokamak, such as the PF coil current and voltage limits, are taken into account. The potential of the combined tokamak discharge simulator is demonstrated by simulating whole operation phases of the inductive 15 MA ELMy H-mode ITER scenario 2. Issues related to ITER operation, such as respecting the coil current limit, vertical instability and poloidal flux consumption, are investigated. ITER hybrid mode operation is studied focusing on the capability of operating the plasma with a stationary flat safety factor profile.