R.R. Khayrutdinov

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.

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.

Inter-code comparison benchmark between DINA and TSC for ITER disruption modelling

Results of 2D disruption modelling for validation of benchmark ITER scenarios using two established codes—DINA and TSC, are compared. Although the simulation models employed in those two codes ought to be equivalent in the resistive time scale, quite different defining equations and formulations are adopted in their approaches. Moreover there are considerable differences in the implemented model of solid conducting structures placed on the periphery of the plasma such as the vacuum vessel and blanket modules. Thus it has long been unanswered whether the one of the two codes is really able to reproduce the others results correctly, since a large number of code-wise differences render the comparison task exceedingly complicated. In this paper, it is demonstrated that after the simulations are set up accounting for the model differences, a reasonably good agreement is generally obtained, corroborating the correctness of the code results. When the halo current generation and its poloidal path in the first wall are included, however, the situation is more complicated. Because of the surface averaged treatment of the magnetic field (current density) diffusion equation, DINA can only approximately handle the poloidal electric currents in the first wall that cross the field lines. Validation is carried out for DINA simulations of the halo current generation by comparing with TSC simulations, where the treatment of halo current dynamics is more justifiable. The specific details of each code, affecting the consequence in ITER disruption prediction, are highlighted and discussed.

Achieving and sustaining advanced scenarios in ITER modelled by CRONOS and DINA-CH

The heating and current drive characteristics for accessing advanced scenarios in ITER, close to those obtained in present-day experiments, are analysed together with the plasma performance using the prescribed-boundary CRONOS suites of codes. For the hybrid scenario, a sensitivity analysis shows the sensitivity to the parameter range which leads to an appropriate control of the safety factor and pressure profiles. A steady-state regime with no internal transport barrier is obtained as a natural extension of the hybrid regime. These prescribed-boundary scenario developments are used as an initial step for a complete free-boundary simulation carried out with the DINA-CH code coupled to CRONOS, which once again underlines how sensitive the ITER advanced scenarios are to small plasma geometry changes. Both scenarios were achieved within the technical limits of ITER, specifically the poloidal field coil currents, voltages, forces and fields.

Local and integral forces on the vacuum vessel during thermal quench in the ITER tokamak

The forces arising during an early stage of disruption in tokamaks are studied here. The analysis is based on DINA calculations and comparison with recent analytical predictions (Pustovitov 2015 Plasma Phys. Rep. 41 952). One such prediction was that a large radial force on the vacuum vessel wall can be generated by a thermal quench (TQ) alone, even before the plasma current is changed. The numerical results presented here confirm this and provide precise quantitative characteristics. The calculations are performed for the International Thermonuclear Experimental Reactor (ITER) geometry by using the DINA code. It is shown, in particular, that the TQ-produced radial force in ITER can reach ~70 MN. Its poloidal distribution has a peak ~2.8 times larger than the average. The relevant details of physics models are also presented.

Synthesis and modeling of the H ∞ -system of magnetic control of the plasma in the tokamak-reactor

The article deals with the development of a two-contour system of magnetic control of the position, current, and shape of the plasma in the tokamak-reactor. The H∞-theory of control is used for the synthesis of a scalar and a multidimensional feedback controller. The controllers are synthesized on the basis of the multidimensional linear model DINA-L of an object (plasma in the tokamak). The linear model DINA-L is obtained from the nonlinear model implemented by the plasmophysical DINA code for conditions of the international thermonuclear experimental reactor (ITER). The numerical modeling of a closed control system is carried out on the linear DINA-L model and the nonlinear DINA model of an object at disturbances of the type of small disruptions. The modeling results for both of the cases were superimposed on each other, which showed their good coincidence at the acceptable quality of control of the synthesized system.

Edge safety factor at the onset of plasma disruption during VDEs in JT-60U

Detailed examinations of the value of the edge safety factor (qa) at the onset of thermal quench (TQ) during intentional vertical displacement event (VDE) experiments in JT-60U are carried out using two different reconstruction methods, FBI/FBEQU and DINA. The results from the two methods are very similar and show that the TQ occurs when the qa value is in the range between 1.5 and 2. This result suggests that the predictive simulations for VDEs should be performed within this range of q to examine the subsequent differences in the halo currents, plasma movement and other plasma behaviour during the current quench.

Plasma vertical stabilisation in ITER

This paper describes the progress in analysis of the ITER plasma vertical stabilisation (VS) system since its design review in 2007–2008. Two indices characterising plasma VS were studied. These are (1) the maximum value of plasma vertical displacement due to free drift that can be stopped by the VS system and (2) the maximum root mean square value of low frequency noise in the dZ/dt measurement signal used in the VS feedback loop. The first VS index was calculated using the PET code for 15 MA plasmas with the nominal position and shape. The second VS index was studied with the DINA code in the most demanding simulations for plasma magnetic control of 15 MA scenarios with the fastest plasma current ramp-up and early X-point formation, the fastest plasma current ramp-down in a divertor configuration, and an H to L mode transition at the current flattop. The studies performed demonstrate that the VS in-vessel coils, adopted recently in the baseline design, significantly increase the range of plasma controllability in comparison with the stabilising systems VS1 and VS2, providing operating margins sufficient to achieve ITERs goals specified in the project requirements. Additionally two sets of the DINA code simulations were performed with the goal of assessment of the capability of the PF system with the VS in-vessel coils: (i) to control the position of runaway electrons generated during disruptions in 15 MA scenarios and (ii) to trigger ELMs in H-mode plasmas of 7.5 MA/2.65 T scenarios planned for the early phase of ITER operation. It was also shown that ferromagnetic structures of the vacuum vessel (ferromagnetic inserts) and test blanket modules insignificantly affect the plasma VS.

Integrated modelling of DEMO-FNS current ramp-up scenario and steady-state regime

An approach to the integrated modelling of plasma regimes in the projected neutron source DEMO-FNS based on different codes is developed. The consistency check of the steady-state regime is carried out, namely, the possibility of the plasma current ramp-up, acceptance of growth rates of MHD modes in the steady-state regime, heat loads to the wall and divertor plates and neutron yield value. The following codes are employed for the integrated modelling. ASTRA transport code for calculation of plasma parameters in the steady-state regime, NUBEAM Monte Carlo code for NBI incorporated into the ASTRA code, DINA free boundary equilibrium and evolution code, SPIDER free boundary equilibrium and equilibrium reconstruction code, KINX ideal MHD stability code, TOKSTAB rigid shift vertical stability code, edge and divertor plasma B2SOLPS5.2 code and Semi-analytic Hybrid Model (SHM) code for self-consistent description of the core, edge and divertor plasmas based on the experimental scaling laws. The consistent steady-state regime for the DEMO-FNS plasma and the plasma current ramp-up scenario are developed using the integrated modelling approach. Passive copper coils are suggested to reduce the plasma vertical instability growth rate to below ∼30 s −1 .The outer divertor operation in the ‘high-recycling’ regime is numerically demonstrated with a maximal heat flux density of 7–9 MW m −2 that is technically acceptable.