Turbulent transport in tokamak advanced scenarios

Nuclear fusion has the potential of providing a high baseline, environmentally friendly, and sustainable source of energy. A plasma consisting of the hydrogen isotopes deuterium and tritium, heated to temperatures of ~ 108 K, can sustain fusion reactions at a sufficiently high rate for energy production. In a reactor the plasma must be confined and insulated from the walls. The leading confinement concept is the tokamak, where the plasma is trapped in a toroidal chamber by helical magnetic fields. The confinement is then limited by turbulent transport, which leads to leakage of heat and particles at a rate higher than expected from collisional transport. The poloidal component of the helical field is produced by toroidal current in the plasma itself. This current is in standard operation induced by a transformer in the centre of torus, where the plasma loop acts as the secondary circuit. The use of a transformer is not ideal for reactor operation; the discharge pulse times are limited since the transformer current cannot be infinitely ramped. The underlying question motivating the work in this thesis is thus: can an achievable tokamak operational scenario be developed which allows for significantly longer pulses, compatible with reactor requirements? One such scenario developed in present-day tokamaks is the ‘hybrid-scenario’. The scenario operates at reduced plasma current compared with fully inductive scenarios, and has an increased non-inductive current fraction through increased external current drive. Importantly, hybrid scenarios display better confinement than expected from empirical scaling laws, which can compensate the confinement lost due to the reduced plasma current. This holds great promise for the extrapolation of this scenario to future machines, and may even pave the way towards a long-pulse reactor scenario. This thesis focuses on an a particular factor which may partially explain the improved confinement - the impact of the broad current profile which characterises hybrid scenarios, on the turbulent transport which limits plasma confinement. The particular instabilities studied are those driven by the ion temperature gradient (ITG). This the dominant source of turbulence in the tokamak regimes studied. The current profile characteristics are represented by the following quantities derived thereof: the q-profile and magnetic shear (ˆs). Hybrid scenario q-profiles are characterised by high ˆs/q at high radii and low-ˆs at low radii. The beneficial effects of increased ˆs/q at high radii for increasing ITG critical gradient thresholds are quantified in an extrapolation of the hybrid scenario to the ITER tokamak (currently under construction) by integrated modelling with the CRONOS suite of codes coupled to the GLF23 transport model for predicted heat transport. The confinement is optimised by tailoring the q-profile with external current drive sources. It is predicted that for a mix of off-axis neutral beam injection (NBI) and electron cyclotron current drive (ECCD), an ITER hybrid scenario satisfying q > 1, Q = 5, and t > 3000 s can be achieved for an edge transport barrier (pedestal) temperature of Tped > 4keV . The fusion gain factor is defined as Q = Pfus Pinput. It is also predicted that ion cyclotron resonance heating (ICRH) and lower hybrid current drive (LHCD) are not beneficial for the ITER hybrid scenario main burn phase, since they do not provide beneficial q-profile shaping. These results are validated versus experimental discharges. Two pairs of hybrid scenario discharges from both the JET and ASDEX-Upgrade tokamaks are analysed. Each pair is characterised by similar pedestal heights but differences in q-profile and core confinement. The degree to which the differences in core confinement can be attributed to the ˆs/q effect is studied. CRONOS and GLF23 are used for predictive simulations of the discharges, as in the ITER extrapolation. These predictions are then compared to the actual experimental data. The effect of ˆs/q can be isolated in the simulations since all the various parameters and profiles in the simulations can be interchanged independently. Particularly for the JET pair, it is found that ˆs/q can indeed explain a major component of the core confinement difference. However, including the rotational flow shear turbulence suppression model in GLF23 leads to significant overprediction of the ion temperatures for all discharges studied. This raises questions regarding the importance of plasma shaping effects, and the validity of the parallel velocity gradient (PVG) destabilisation in the model. The beneficial effect of reduced temperature profile stiffness at low-ˆs in inner radii is assessed with non-linear modelling using the GENE gyrokinetic code. It is found that at low-ˆs the turbulence correlation lengths are decreased and the non-linear frequency broadening increases compared to high-ˆs cases. Both these effects may be related to the observed increase in zonal flow activity, and leads to a reduction in the predicted flux compared to the high-ˆs cases. With these results, the validity of an advanced quasilinear transport model, QuaLiKiz, was extended to low-ˆs parameter space. The underlying assumptions of the model are examined, and the mixing length rule improved with guidance from the non-linear simulations. This work improves the confidence in using the QuaLiKiz transport model in the future for hybrid scenario predictions. Finally, the experimentally observed stiffness reduction at low-ˆs and high flow shear was investigated with non-linear modelling. This topic is also of importance to hybrid scenarios, to further understand the relative importance of the various factors contributing to improved confinement. Hybrid scenarios on present-day machines also tend to be associated with high levels of flow shear. The simulations do not predict the degree of reduced stiffness as experimentally observed, and this question is thus still open. Experimental measurements of the poloidal rotation profile in this class of discharge may shed more light on the matter, as we assumed that the rotation is purely toroidal due to the expected neoclassical poloidal damping. Nevertheless, additional insights were gained into the non-linear nature of ITG turbulence. From electromagnetic simulations, the non-linear ße (ratio of electron pressure to magnetic pressure) stabilisation of ITG turbulence is observed to be significantly greater than the well-known linear ße stabilisation. This may be related to the observed increase in zonal flow activity within the ße range studied. Beyond the increase in fundamental understanding, this effect could also be important for furthering the interpretation of transport in hybrid scenarios, which tend to operate at higher ße than in inductive scenarios.