Time-dependent Transport Simulations Research Articles

Perturbative studies of toroidal momentum transport in KSTAR H-mode and the effect of ion temperature perturbation

Perturbative experiments have been carried out using tangential neutral beam injection (NBI) and non-resonant magnetic perturbation (NRMP) to analyze the momentum transport properties in KSTAR H-modes. Diffusive and non-diffusive terms of momentum transport are evaluated from the transient analysis. Although the operating conditions and methodologies applied in the two cases are similar, the momentum transport properties obtained show clear differences. The estimated momentum diffusivity and pinch obtained in the NBI modulation experiments is larger than that in the NRMP modulation experiments. We found that this discrepancy could be a result of uncertainties in the assumption for the analysis. By introducing time varying momentum transport coefficients depending on the temperature gradient, the linearized equation shows that if the temperature perturbation exists, the evolution of toroidal rotation perturbation could be faster than the transport rate of mean quantity, since the evolution of toroidal rotation perturbation is related to , a momentum diffusivity from perturbative analysis. This could explain the estimated higher momentum diffusivity using time independent transport coefficients in NBI experiments with higher ion temperature perturbation compared to that in NRMP modulation experiments. The differences in the momentum transport coefficient with NRMP and NBI are much reduced by considering time varying momentum transport coefficients in the time dependent transport simulation.

External heating and current drive source requirements towards steady-state operation in ITER

Steady state scenarios envisaged for ITER aim at optimizing the bootstrap current, while maintaining sufficient confinement and stability to provide the necessary fusion yield. Non-inductive scenarios will need to operate with internal transport barriers (ITBs) in order to reach adequate fusion gain at typical currents of 9 MA. However, the large pressure gradients associated with ITBs in regions of weak or negative magnetic shear can be conducive to ideal MHD instabilities, reducing the no-wall limit. The E × B flow shear from toroidal plasma rotation is expected to be low in ITER, with a major role in the ITB dynamics being played by magnetic geometry. Combinations of heating and current drive (H/CD) sources that sustain reversed magnetic shear profiles throughout the discharge are the focus of this work. Time-dependent transport simulations indicate that a combination of electron cyclotron (EC) and lower hybrid (LH) waves is a promising route towards steady state operation in ITER. The LH forms and sustains expanded barriers and the EC deposition at mid-radius freezes the bootstrap current profile stabilizing the barrier and leading to confinement levels 50% higher than typical H-mode energy confinement times. Using LH spectra with spectrum centred on parallel refractive index of 1.75–1.85, the performance of these plasma scenarios is close to the ITER target of 9 MA non-inductive current, global confinement gain H98 = 1.6 and fusion gain Q = 5.

Formation and sustainment of internal transport barriers in the International Thermonuclear Experimental Reactor with the baseline heating mix

Plasmas with internal transport barriers (ITBs) are a potential and attractive route to steady-state operation in ITER. These plasmas exhibit radially localized regions of improved confinement with steep pressure gradients in the plasma core, which drive large bootstrap current and generate hollow current profiles and negative magnetic shear. This work examines the formation and sustainment of ITBs in ITER with electron cyclotron heating and current drive. The time-dependent transport simulations indicate that, with a trade-off of the power delivered to the equatorial and to the upper launcher, the sustainment of steady-state ITBs can be demonstrated in ITER with the baseline heating configuration.

Perturbative studies of toroidal momentum transport using neutral beam injection modulation in the Joint European Torus: Experimental results, analysis methodology, and first principles modeling

Perturbative experiments have been carried out in the Joint European Torus [Fusion Sci. Technol. 53(4) (2008)] in order to identify the diffusive and convective components of toroidal momentum transport. The torque source was modulated either by modulating tangential neutral beam power or by modulating in antiphase tangential and normal beams to produce a torque perturbation in the absence of a power perturbation. The resulting periodic perturbation in the toroidal rotation velocity was modeled using time-dependent transport simulations in order to extract empirical profiles of momentum diffusivity and pinch. Details of the experimental technique, data analysis, and modeling are provided. The momentum diffusivity in the core region (0.2<ρ<0.8) was found to be close to the ion heat diffusivity (χϕ/χi∼0.7–1.7) and a significant inward momentum convection term, up to 20 m/s, was found, leading to an effective momentum diffusivity significantly lower than the ion heat diffusivity (χϕeff/χieff∼0.4). These results have significant implications on the prediction of toroidal rotation velocities in future tokamaks and are qualitatively consistent with recent developments in momentum transport theory. Detailed quantitative comparisons with the theoretical predictions of the linear gyrokinetic code GKW [A. G. Peeters et al., Comput. Phys. Commun. 180, 2650 (2009)] and of the quasilinear fluid Weiland model [J. Weiland, Collective Modes in Inhomogeneous Plasmas (IOP, Bristol, 2000)] are presented for two analyzed discharges.

Toroidal and poloidal momentum transport studies in JET

This paper reports on the recent studies of toroidal and poloidal momentum transport in JET. The ratio of the global energy confinement time to the momentum confinement is found to be close to τE/τϕ = 1 except for the low density or low collisionality discharges where the ratio is τE/τϕ = 2–3. On the other hand, local transport analysis of around 40 discharges shows that the ratio of the local effective momentum diffusivity to the ion heat diffusivity is χϕ/χi ≈ 0.1–0.4 (averaged over the radial region r/a = 0.4–0.7) rather than unity, as expected from the global confinement times and used often in ITER predictions. The apparent discrepancy in the global and local momentum versus ion heat transport can be at least partly explained by the fact that momentum confinement within edge pedestal is worse than that of the ion heat and thus, momentum pedestal is weaker than that of ion temperature. In addition, while the ion temperature profile shows clearly strong profile stiffness, the toroidal velocity profile does not exhibit stiffness, as exemplified here during a giant ELM crash. Predictive transport simulations with the self-consistent modelling of toroidal velocity using the Weiland model and GLF23 also confirm that the ratio χϕ/χi ≈ 0.4 reproduces the core toroidal velocity profiles well and similar accuracy with the ion temperature profiles. Concerning poloidal velocities on JET, the experimental measurements show that the carbon poloidal velocity can be an order of magnitude above the neo-classical estimate within the ITB. This significantly affects the calculated radial electric field and therefore, the E × B flow shear used for example in transport simulations. Both the Weiland model and GLF23 reproduce the onset, location and strength of the ITB well when the experimental poloidal velocity is used while they do not predict the formation of the ITB using the neo-classical poloidal velocity in time-dependent transport simulation. The most plausible explanation for the generation of the anomalous poloidal velocity is the turbulence driven flow through the Reynolds stress. Both CUTIE and TRB turbulence codes show the existence of an anomalous poloidal velocity, being significantly larger than the neo-classical values. And similarly to experiments, the poloidal velocity profiles peak in the vicinity of the ITB and seem to be dominantly caused by flow due to the Reynolds stress. However, it is important to note that both the codes treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes (GAMs). Therefore, the results should be considered as indicative, and most probably provide an upper bound of the mean poloidal velocity as results from other codes including GAM dynamics show that they often serve as a damping mechanism to flows.

Fully predictive time-dependent transport simulations of ITB plasmas in JET, JT-60U and DIII-D

For the first time, the predictive capabilities of the mixed Bohm/GyroBohm, Weiland and ‘retuned’ GLF23 transport models are investigated with ITB discharges from the ITPA ITB database with fully predictive, time-dependent transport simulations. A range of plasma conditions is examined for JET, JT-60U and DIII-D discharges with internal transport barriers (ITBs). The simulations show that the Bohm/GyroBohm model is able to follow the time evolution of the discharge from the preheating phase without an ITB through the ITB onset phase until the high performance phase with fair accuracy in most cases in JET and JT-60U. This indicates the importance of the interplay between the magnetic shear and ωE×B flow shear in ITB formation since these are the mechanisms that govern the ITB physics in the model. In order to achieve good agreement in DIII-D, the α-stabilization had to be included in the model, emphasizing the role played by the α-stabilization in the physics of the ITBs. The Weiland and GLF23 transport models show limited agreement between the model predictions and experimental time evolution of the ITB and kinetic plasma profiles. The Weiland model does not form a clear ITB in any of the three tokamaks despite varying plasma profiles, such as the q-profile. On the other hand, the average temperatures and density are often in fair agreement with experimental values. The GLF23 model often predicts an ITB, but its radial location is often too far inside the plasma, or shrinks as the simulations proceed in time. Consequently, the central temperatures at the end of the simulations during the high performance phase are usually underestimated. It is worth noting that GLF23 features in general better predictions of the Te and Ti profiles outside the ITB than the other models studied. Achieving the quantitative capability to predict the multi-channel ITB dynamics with fully predictive, time-dependent transport simulations has turned out to be extremely challenging.

Observation of the bootstrap current reduction at magnetic island in a neoclassical tearing mode plasma

Evolution of the current density profile associated with magnetic island formation in a neoclassical tearing mode plasma is measured for the first time in JT-60U by using a motional Stark effect diagnostic. As the island grows, the current density profile turns flat at the radial region of the island and a hollow structure appears at the rational surface. As the island shrinks the deformed region becomes narrower and finally diminishes after the disappearance of the island. In a quiescent plasma without magnetohydrodynamic instabilities, on the other hand, no deformation is observed. The observed deformation in the current density profile associated with the tearing mode is reproduced in a time dependent transport simulation assuming the reduction of the bootstrap current in the radial region of the island. Comparison of the measurement with a calculated steady-state solution also shows that the reduction and recovery of the bootstrap current at the island explains the temporal behaviours of the current density and safety factor profiles. From the experimental observation and simulations, we reach the conclusion that the bootstrap current decreases within the island O-point.

Predictive transport simulations of real-time profile control in JET advanced tokamak plasmas

Predictive, time-dependent transport simulations with a semi-empirical plasma model have been used in closed-loop simulations to control the q-profile and the strength and location of the internal transport barrier (ITB). Five transport equations (Te, Ti, q, ne, vΦ) are solved, and the power levels of lower hybrid current drive, NBI and ICRH are calculated in a feedback loop determined by the feedback controller matrix. The real-time control (RTC) technique and algorithms used in the transport simulations are identical to those implemented and used in JET experiments (Laborde L. et al 2005 Plasma Phys. Control. Fusion 47 155 and Moreau D. et al 2003 Nucl. Fusion 43 870). The closed-loop simulations with RTC demonstrate that varieties of q-profiles and pressure profiles in the ITB can be achieved and controlled simultaneously. The simulations also showed that with the same RTC technique as used in JET experiments, it is possible to sustain the q-profiles and pressure profiles close to their set-point profiles for longer than the current diffusion time. In addition, the importance of being able to handle the multiple time scales to control the location and strength of the ITB is pointed out. Several future improvements and perspectives of the RTC scheme are presented.

Profile formation and sustainment of autonomous tokamak plasma with current hole configuration

We have investigated the profile formation and sustainment of tokamak plasmas with the current hole (CH) configuration by using 1.5 dimensional time-dependent transport simulations. A model of the current limit inside the CH on the basis of the Axisymmetric Tri-Magnetic-Islands equilibrium is introduced into the transport simulation. We found that a transport model with the sharp reduction of anomalous transport in the reversed-shear (RS) region can reproduce the time evolution of profiles observed in JT-60U experiments. The transport becomes neoclassical-level in the RS region, which results in the formation of profiles with internal transport barrier (ITB) and CH. The CH plasma has an autonomous property because of the strong interaction between a pressure profile and a current profile through the large bootstrap current. The ITB width determined by the neoclassical-level transport agrees well with that measured in JT-60U. The energy confinement inside the ITB agrees with the scaling based on the JT-60U data. The scaling means that the core plasma inside ITB is governed by the MHD equilibrium limit, i.e. the autonomous limitation of energy confinement in the CH plasma. The plasma with the large CH is sustained with the full current drive by the bootstrap current. The plasma with the small CH and the small bootstrap current fraction shrinks due to the penetration of inductive current. This shrink is prevented and the CH size can be controlled by the appropriate external current drive (CD). The CH plasma is found to respond autonomically to the external CD. The application of the CH plasma to the tokamak reactor is discussed.

Modelling of ECH modulation experiments in ASDEX Upgrade with an empirical critical temperature gradient length transport model

The relevance of the assumption of critical gradient length in electron heat transport is tested against the results of electron cyclotron heating (ECH) modulation experiments carried out on ASDEX Upgrade, using time-dependent transport simulations. A general χe model based on a ∇Te/Te threshold is proposed, which can provide two different heat pulse (HP) propagation regimes, with respect to the power balance (PB) diffusion coefficient χePB: χeHP = χePB occurs if ∇Te/Te<(∇Te/Te)c, while χeHP>χePB if ∇Te/Te⩾(∇Te/Te)c. By a careful choice of the model parameters, the experimental Te response to ECH modulations is simulated with excellent accuracy, and the transition between the two propagation regimes is, without ambiguity, ascribed to a ∇Te/Te threshold. Our findings are consistent with theoretical expectations, as well as with experimental observations made on TORE SUPRA. This global consistency shows the relevance of the main physical factors involved in our model, in particular the assumption of critical temperature gradient length.

Status of advanced tokamak scenario modelling with off-axis electron cyclotron current drive in DIII-D

The status of modelling work focused on developing the advanced tokamak (AT) scenarios in DIII-D is discussed. The objective of the work is twofold: (a) to develop AT scenarios with ECCD using time dependent transport simulations, coupled with heating and current drive models, consistent with MHD equilibrium and stability; and (b) to use time dependent simulations to help plan experiments and to understand the key physics involved. Time dependent simulations based on transport coefficients derived from experimentally achieved target discharges are used to perform AT scenario modelling. The modelling indicates that off-axis ECCD with approximately 3 MW absorbed power can maintain high performance discharges with qmin > 1 for 5-10 s. The resultant equilibria are calculated to be stable to n = 1 pressure driven modes. The plasma is well into the second stability regime for high-n ballooning modes over a large part of the plasma volume. The role of continuous localized ECCD is studied for stabilizing m/n = 2/1 tearing modes. Progress towards validating current drive and transport models, consistent with experimental results, and developing self-consistent, integrated high performance AT scenarios is discussed.

`Non-local' response of RTP ohmic plasmas to peripheral perturbations

A `non-local' response of the plasma core triggered by peripheral plasma perturbations other than laser ablation is found in the RTP tokamak. Oblique pellet injection (OPI) has been used to induce fast cooling of the peripheral plasma. In response, an inward cold pulse (Te drop) and a slightly delayed core Te rise are observed. A somewhat similar `non-local' response is observed when the peripheral plasma is heated by modulated electron cyclotron heating or by fast current ramps, i.e. the core temperature drops in response to the peripheral heating. The plasma conditions for the occurrence of the `non-local' response have been investigated. The core Te rise following OPI is associated with the formation of a large temperature gradient in the region 1 < q < 2. The Te rise is largest at low electron density and for large pellet deposition radii. Above a critical density the Te rise disappears and only the (weaker) drop in core Te is observed. Time dependent transport simulations show that the propagation of the inward cold pulse is consistent with local transport, while the core Te rise is a slower phenomenon requiring a large transient drop of χe in the region 1 < q < 2.