Self-consistent transport simulation of ITER scenarios is a very important tool for the exploration of the operational space and for scenario optimization. It also provides an assessment of the compatibility of developed scenarios (which include fast transient events) with machine constraints, in particular with the poloidal field coil system, heating and current drive, fuelling and particle and energy exhaust systems. This paper discusses results of predictive modelling of all reference ITER scenarios and variants using two suites of linked transport and equilibrium codes. The first suite consisting of the 1.5D core/2D SOL code JINTRAC (Wiesen S. et al 2008 JINTRAC-JET modelling suite JET ITC-Report) and the free-boundary equilibrium evolution code CREATE-NL (Albanese R. et al 2003 ISEM 2003 (Versailles, France); Albanese R. et al 2004 Nucl. Fusion 44 999), was mainly used to simulate the inductive D–T reference Scenario-2 with fusion gain Q = 10 and its variants in H, D and He (including ITER scenarios with reduced current and toroidal field). The second suite of codes was used mainly for the modelling of hybrid and steady-state ITER scenarios. It combines the 1.5D core transport code CRONOS (Artaud J.F. et al 2010 Nucl. Fusion 50 043001) and the free-boundary equilibrium evolution code DINA-CH (Kim S.H. et al 2009 Plasma Phys. Control. Fusion 51 105007).

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.

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Many challenging plasma control problems still need to be addressed in order for the ITER plasma control system (PCS) to be able to maintain the plasma within a predefined operational space and optimize the plasma state evolution in the tokamak, which will greatly aid in the successful achievement of ITER's goals. Firstly in this work, a general control-oriented, physics-based modeling approach is developed to obtain first-principles-driven (FPD) models of the plasma magnetic profile and stored energy evolutions valid for high performance, high confinement (H-mode) scenarios, with the goal of developing model-based closedloop algorithms to control the safety factor profile (q profile) and stored energy evolutions in the tokamak. The FPD model is tailored to H-mode burning plasma scenarios in ITER by employing the DINA-CH & CRONOS free-boundary tokamak simulation code, and the FPD model's prediction capabilities are demonstrated by comparing the prediction to data obtained from DINA-CH & CRONOS. Secondly, a model-based feedback control algorithm is designed to simultaneously track target q profile and stored energy evolutions in H-mode burning plasma scenarios in ITER by embedding the developed FPD model of the magnetic profile evolution into the control design process. The feedback controller is designed to ensure that the closed-loop system is robust to uncertainties in the electron density, electron temperature and plasma resistivity, and is tested in simulations with the developed FPD model. The effectiveness of the controller is demonstrated by first tracking nominal q profile and stored energy target evolutions, and then modulating the generated fusion power while maintaining the q profile in a stationary condition. In the process, many key practical issues for plasma profile control in ITER are investigated, which will be useful for the development of the ITER PCS that has recently been initiated. Some of the more pertinent investigated issues are the time necessary to drive the q profile and stored energy to a target evolution, and whether plasma control can be achieved through the use of separate individual control algorithms or whether a more fully integrated approach is required.

The energy eigenvalues of the class of non-Hermitian -symmetric Hamiltonians H = p2 + x2(ix)ϵ (ϵ ⩾ 0) are real, positive and discrete. The behavior of these eigenvalues has been studied perturbatively for small ϵ. However, until now no other features of H have been examined perturbatively. In this paper the small-ϵ expansion of the operator and the equivalent isospectral Dirac–Hermitian Hamiltonian h are derived.