A. Polevoi

Chapter 2: Plasma confinement and transport

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

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.

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.

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.

Integrated modelling of the current profile in steady-state and hybrid ITER scenarios

We present integrated modelling of steady-state and hybrid scenarios for ITER parameters using several predictive transport codes. These employ models for non-inductive current drive sources in conjunction with various theory-based and semi-empirical transport models. In conjunction with the simulation effort, the current drive models are being evaluated in a series of cross-code and code-experiment comparisons under ITER-relevant conditions. New benchmark evaluations of current drive from injection of neutral beams (NBCD), electron cyclotron waves (ECCD) and lower hybrid waves (LHCD) are reported. Simulations using several transport modelling codes self-consistently calculate the heating and current drive sources using ITER design parameters. Operating constraints are also taken into account, although the calculations reported here still require further refinement. The modelling addresses both the final stationary state and dynamic access to it. The simulations indicate that generation and control of internal and edge barriers to access and maintain high confinement will be a major undertaking for future simulations, as well as a challenge for the ITER steady-state and hybrid experimental programme.

Performance of ITER as a burning plasma experiment

Recent performance analysis has improved confidence in achieving Q (= fusion power/auxiliary heating power)≥ 10 in inductive operation in ITER. Performance analysis based on empirical scalings shows the feasibility of achieving Q ≥ 10 in inductive operation, particularly with improved modelling of helium exhaust. Analysis has also indicated the possibility that ITER can potentially demonstrate Q ~ 50, enabling studies of self-heated plasmas. Theory-based core modelling indicates the need for a high pedestal temperature (3.2–5.3 keV) to achieve Q ≥ 10, which is in the range of projections with presently available pedestal scalings. Pellet injection from the high-field side would be useful in enhancing Q and reducing edge localized mode (ELM) heat load in high plasma current operation. If the ELM heat load is not acceptable, it could be made tolerable by further tilting the target plate. Steady state operation scenarios at Q = 5 have been developed with modest requirements on confinement improvement and beta (HH98(y,2) ≥ 1.3 and βN ≥ 2.6). Stabilization of the resistive wall modes (RWMs), required in such regimes, is feasible with the present saddle coils and power supplies with double-wall structures taken into account. Recent analysis shows a potential of high power steady state operation with a fusion power of 0.7 GW at Q ~ 8. Achievement of the required βN ~ 3.6 by RWM stabilization is a possibility. Further analysis is also needed on reduction of the divertor target heat load.

Assessment of current drive efficiency and the synergetic effect for ECCD and LHCD and the possibility of long pulse operation in ITER

Steady state operation is preferable for fusion reactors. The possibility of extending the pulse length in ITER is considered taking into account the capabilities of the planned electron-cyclotron current drive (ECCD) and low-hybrid current drive (LHCD). The ECCD efficiency for current drive at different locations is assessed. The possibility of extending the pulse length by the increase in the current drive efficiency due to the synergetic effect for combined ECCD and LHCD at the same location is assessed. The calculated synergetic effect of ECCD and LHCD on the current drive efficiency is less than 10% for ITER parameters. Long pulse operation with the energy multiplication factor Pfus/Paux = Q > 5 and duration t > 3000 s will be possible in the case of enhanced confinement with respect to the ELMy H-mode scaling HH98y,2 ~ 1.3–1.4.

Evolution of plasma parameters in the termination phase of high confinement H-modes at JET and implications for ITER

The evolution of the parameters of the plasma in the termination phase of high confinement H-modes at JET with carbon fibre composite plasma facing components (JET-C) has been analysed with a view to predict the dynamics of the plasma energy decrease for sudden terminations of the ITER QDT = 10 scenario caused by malfunction of additional heating systems. JET-C experiments show that the rate of decay of the plasma energy in the high performance H-mode termination phase is predominantly determined by the duration of the type III ELMy H-mode phase after the end of the type I ELMy H-mode regime. Longer type III ELMy H-mode phase durations lead to slower plasma energy decay rates. The duration of the type III ELMy H-mode phase is itself determined by the margin of the edge power flow (dominated by the rate of collapse of the plasma energy) over the H-mode threshold power in the termination phase, with larger margins leading to longer type III ELMy H-mode phase durations. For most of the JET-C discharges analysed the timescale for the plasma energy decrease in the termination of high energy confinement H-modes is comparable to the energy confinement time of the plasma in the high confinement phase rather than half of this value, which is to be expected for instantaneous H–L transitions. Modelling of the termination phase of ITER QDT = 10 H-modes (with transport assumptions in this phase validated against JET-C experiments) shows that similar to JET-C results the timescale for the decrease of the plasma energy is comparable and can even be longer than the energy confinement time of the burning phase, provided that ELM control can be maintained. This is due to the long sustainment of the type III ELMy H-mode by the substantial edge power flow compared to the H-mode threshold power during this phase. The large edge power flow in the termination phase of ITER high QDT plasmas is provided by the decrease of the plasma energy and the slow collapse of the alpha heating. Operational strategies in ITER to control the energy decay rate as well as the consequences of the lack of ELM control in the high QDT termination phase are presented.

Analysis of fuelling requirements in ITER H-modes with SOLPS-EPED1 derived scalings

Fuelling requirements for ITER are analysed in relation to pellet fuelling and ELM pacing, and a divertor power load control consistent with the ITER pumping and fuel throughput capabilities. The plasma parameters at the separatrix and the particle sources are derived from scalings based on SOLPS simulations. Effective transport coefficients in the H-mode pedestal are derived from EPED1 + SOLPS scalings for the pedestal height and width. 1.5D transport is simulated in the ASTRA framework. The operating window for ITER DT plasmas with the required fusion performance and level of ELM, and divertor power load control compatible with ITER fuelling and pumping capabilities, is determined. It is shown that the flexibility of the ITER fuelling systems, comprising pellet and gas injection systems, enables operation with Q = 10, which was found to be marginal in previous studies following a similar approach but with different assumptions. The present assessment shows that a reduction of by a factor ~2 (from 9 to 5 × 1019 m−3) in 15 MA H-mode plasmas leads to a reduction in the required pellet fuelling rate by a factor of four. Results of the analysis of the fuelling requirements for a range of ITER scenarios are found to be similar to those obtained with the JINTRAC code that included 2D modelling of the edge plasma.

Comprehensive evaluation of the linear stability of Alfvén eigenmodes driven by alpha particles in an ITER baseline scenario

The linear stability of Alfven eigenmodes in the presence of fusion-born alpha particles is thoroughly assessed for two variants of an ITER baseline scenario, which differ significantly in their core and pedestal temperatures. A systematic approach based on CASTOR-K (Borba and Kerner 1999 J. Comput. Phys. 153 101; Nabais et al 2015 Plasma Sci. Technol. 17 89) is used that considers all possible eigenmodes for a given magnetic equilibrium and determines their growth rates due to alpha-particle drive and Landau damping on fuel ions, helium ashes and electrons. It is found that the fastest growing instabilities in the aforementioned ITER scenario are core-localized, low-shear toroidal Alfven eigenmodes. The largest growth-rates occur in the scenario variant with higher core temperatures, which has the highest alpha-particle density and density gradient, for eigenmodes with toroidal mode numbers . Although these eigenmodes suffer significant radiative damping, which is also evaluated, their growth rates remain larger than those of the most unstable eigenmodes found in the variant of the ITER baseline scenario with lower core temperatures, which have and are not affected by radiative damping.