Theory-based Transport Model Research Articles

Comparison of Saturation Rules Used for Gyrokinetic Quasilinear Transport Modeling

Theory-based transport modeling has been widely successful and is built on the foundations of quasilinear theory. Specifically, the quasilinear expression of the flux can be used in combination with a saturation rule for the toroidal mode amplitude. Most transport models follow this approach. Saturation rules are heuristic and difficult to rigorously derive. We compare three common saturation rules using a fairly accurate quasilinear expression for the fluxes computed using local linear gyrokinetic simulation. We take plasma parameters from experimental H-mode profiles and magnetic equilibrium and include electrons, deuterium, and carbon species. We find that the various saturation rules provide qualitatively similar behavior. This may help to explain why the different theory-based transport models can all predict core tokamak profiles reasonably well. Comparisons with nonlinear local and global gyrokinetic simulations are discussed.

Predicting the Lattice Thermal Conductivity in Nitride Perovskite LaWN3 from ab initio Lattice Dynamics.

Using a density functional theory-based thermal transport model, which includes the effects of temperature (T)-dependent potential energy surface, lattice thermal expansion, force constant renormalization, and higher-order quartic phonon scattering processes, it is found that the recently synthesized nitride perovskite LaWN3 displays strong anharmonic lattice dynamics manifested into a low lattice thermal conductivity (κL ) and a non-standard κL ∝T-0.491 dependence. At high T, the departure from the standard κL ∝T-1 law originates in the dual particle-wave behavior of the heat carrying phonons, which includes vibrations tied to the N atoms. While the room temperature κL =2.98 W mK-1 arises mainly from the conventional particle-like propagation of phonons, there is also asignificant atypical wave-like phonon tunneling effect, leading to a 20% glass-like heat transport contribution. The phonon broadening effect lowers the particle-like contribution but increases the glass-like one. Upon T increase, the glass-like contribution increases and dominates above T = 850 K. Overall, the low κL with a weak T-dependence points to a new utility for LaWN3 in energy technology applications, and motivates synthesis and exploration of nitrideperovskites.

The local nature of the plasma response to cold pulses with electron and ion heating at ASDEX Upgrade

In low density Ohmic heated tokamak plasmas a fast increase of the central electron temperature is regularly observed in response to a drop at the edge produced by the cold pulse of an impurity ablation. This observation has challenged the physical understanding and the theory-based local transport modelling for several decades. Recent experimental results in C-Mod and related modelling (Rodriguez-Fernandez et al 2018 Phys. Rev. Lett. 120 075001) have for the first time provided an explanation for this phenomenology, which results from the stabilization of trapped electron mode turbulence caused by the sudden flattening of the electron density profile as a consequence of the impurity ablation. Starting from this breakthrough result, recent cold pulse experiments in ASDEX Upgrade produced by laser ablation of carbon in deuterium plasmas demonstrate that the fast increase of the central electron temperature is only observed in the presence of dominant electron heating, whereas no fast increase is observed in dominantly ion heated plasmas, even at the same low density. The measured fast flattening of the density profile is shown to be large enough to produce a strong stabilization of the trapped electron mode turbulence in the case where the electron temperature largely exceeds the ion temperature, allowing the fast increase of the central electron temperature, consistent with the C-Mod modelling results. In contrast, it produces a destabilization of the electron temperature gradient modes when the electron and ion temperatures are closer, preventing the increase of the central electron temperature. Finally, modelling which also includes the dynamical evolution of the density profile with a local theory-based transport model shows that the impurity penetration transiently modifies the local turbulence causing a fast penetration of the particles, which explains the observation of a very fast flattening of the electron density profile. By this, the complex density and temperature behaviours in response to a cold pulse are demonstrated to be fully explained by multi-channel interactions within a local model.

Improved Multi-Mode anomalous transport module for tokamak plasmas

The Multi-Mode anomalous transport module version 7.1 (MMM7.1) is a theory-based transport model that is used to predict temperature, density and rotation profiles for tokamak plasmas in integrated whole device modeling codes. The theoretical foundation of the current version, MMM7.1, has been significantly advanced since the first released version in 1995, MMM95. The latest version of the Multi-Mode model, MMM7.1, includes an improved Weiland model for the ITG, TEM, and MHD modes, the Horton model for short wavelength ETG modes and the Rafiq model for the drift resistive inertial ballooning modes (DRIBMs). The ETG transport threshold in the Horton model is refined by using the threshold obtained from toroidal gyrokinetic ETG turbulence simulations. The different components of the MMM7.1 model provide contributions to transport in the different regions of plasma discharge. To facilitate the implementation of the latest version of the Multi-Mode module in integrated predictive modeling codes, a clearly specified interface is described and a test program is provided in order to examine the predictions provided by MMM7.1. MMM7.1 is documented and organized as a standalone module, which fully complies with the National Transport Code Collaboration (NTCC) standards. The MMM7.1 module has been used both with a standalone driver program as well as within the PTRANSP code. Results are presented to illustrate the extent to which the various component models contribute to transport in both L-mode and H-mode discharges.

A potentially robust plasma profile control approach for ITER using real-time estimation of linearized profile response models

An active plasma profile control approach for ITER, which is potentially robust by being tolerant to changing and uncertain physics, has been explored in this work, using a technique based on real-time estimation of linearized profile response models. The linearized models approximate static responses of the plasma profiles to power changes in auxiliary heating and current drive systems. These models are updated in real-time, differing from the model-based technique which deduces a dynamic model from identification experiments. The underlying physics is simplified with several assumptions to allow real-time update of the profile response models; however, without significant loss of information necessary for feedback control of the plasma profiles. The response of the electron temperature profile is modelled by simplifying the electron heat transport equation. The response of the safety factor profile is computed by directly relating it to the changes in source current density profiles. The required actuator power changes are directly computed by inverting the response matrix using the singular value decomposition technique. The saturation of the actuator powers is taken into account and the capability of using quantized auxiliary powers is provided. The potential of our active control approach has been tested by applying it to simulations of the ITER hybrid mode operation using CRONOS. In these simulations, either a global transport model or a theory-based local transport model has been used and the electron temperature and safety factor profiles were well controlled either independently or simultaneously.

Integrated modelling of steady-state scenarios and heating and current drive mixes for ITER

Recent progress on ITER steady-state (SS) scenario modelling by the ITPA-IOS group is reviewed. Code-to-code benchmarks as the IOS group's common activities for the two SS scenarios (weak shear scenario and internal transport barrier scenario) are discussed in terms of transport, kinetic profiles, and heating and current drive (CD) sources using various transport codes. Weak magnetic shear scenarios integrate the plasma core and edge by combining a theory-based transport model (GLF23) with scaled experimental boundary profiles. The edge profiles (at normalized radius ρ = 0.8–1.0) are adopted from an edge-localized mode-averaged analysis of a DIII-D ITER demonstration discharge. A fully noninductive SS scenario is achieved with fusion gain Q = 4.3, noninductive fraction fNI = 100%, bootstrap current fraction fBS = 63% and normalized beta βN = 2.7 at plasma current Ip = 8 MA and toroidal field BT = 5.3 T using ITER day-1 heating and CD capability. Substantial uncertainties come from outside the radius of setting the boundary conditions (ρ = 0.8). The present simulation assumed that βN (ρ) at the top of the pedestal (ρ = 0.91) is about 25% above the peeling–ballooning threshold. ITER will have a challenge to achieve the boundary, considering different operating conditions (Te/Ti ≈ 1 and density peaking). Overall, the experimentally scaled edge is an optimistic side of the prediction. A number of SS scenarios with different heating and CD mixes in a wide range of conditions were explored by exploiting the weak-shear steady-state solution procedure with the GLF23 transport model and the scaled experimental edge. The results are also presented in the operation space for DT neutron power versus stationary burn pulse duration with assumed poloidal flux availability at the beginning of stationary burn, indicating that the long pulse operation goal (3000 s) at Ip = 9 MA is possible. Source calculations in these simulations have been revised for electron cyclotron current drive including parallel momentum conservation effects and for neutral beam current drive with finite orbit and magnetic pitch effects.

Confinement and transport properties during current ramps in the ASDEX Upgrade tokamak

A detailed analysis of experimental data from the ASDEX Upgrade tokamak is carried out to shed light on the properties of confinement and transport in the current ramp-up and ramp-down phases of the plasma discharge. The experimental database is used to identify the relevant ranges of parameters explored during the ramp-up and the ramp-down. The energy confinement time observed in the two ramps displays interesting evolution, in many cases attaining different values at the same current level between ramp-up and ramp-down. The possible reasons for this behaviour are investigated. Interpretative transport simulations are used as a tool to clarify the interplay between different parameters, which are coupled in a non-linear way. In addition, a theory-based transport model is used to understand the behaviour of confinement as observed in the experiment, evidencing the role of both turbulent and neoclassical transport. Linear gyrokinetic calculations are performed to identify the relevant turbulence regime, showing that a broad range of frequencies, in the trapped electron modes (TEMs) and in the ion temperature gradient modes (ITGs) regimes, is explored during both the ramp-up and ramp-down. In the same framework, a quasi-linear model is applied to calculate the value of the local logarithmic density gradient and compare it with the experimental value. Finally, first non-linear simulations of heat transport during the current ramps are presented.

Integrated modelling of ITER reference scenarios

The ITER Scenario Modelling Working Group (ISM WG) is organized within the European Task Force on Integrated Tokamak Modelling (ITM-TF). The main responsibility of the WG is to advance a pan-European approach to integrated predictive modelling of ITER plasmas with the emphasis on urgent issues, identified during the ITER Design Review. Three major topics are discussed, which are considered as urgent and where the WG has the best possible expertize. These are modelling of current profile control, modelling of density control and impurity control in ITER (the last two topics involve modelling of both core and SOL plasma). Different methods of heating and current drive are tested as controllers for the current profile tailoring during the current ramp-up in ITER. These include Ohmic, NBI, ECRH and LHCD methods. Simulation results elucidate the available operational margins and rank different methods according to their ability to meet different requirements. A range of ‘ITER-relevant’ plasmas from existing tokamaks were modelled. Simulations confirmed that the theory-based transport model, GLF23, reproduces the density profile reasonably well and can be used to assess ITER profiles with both pellet injection and gas puffing. In addition, simulations of the SOL plasma were launched using both H-mode and L-mode models for perpendicular transport within the edge barrier and in the SOL. Finally, an integrated approach was also used for the predictive modelling of impurity accumulation in ITER. This includes helium ash, extrinsic impurities (such as argon) and impurities coming from the wall (including tungsten). The relative importance of anomalous and neo-classical pinch contributions towards impurity penetration through the edge transport barrier and further accumulation in the core was assessed.

Analytical solutions of gas transport problems in inorganic/organic hybrid structures for gas barrier applications

The analytical solutions of the ideal laminate theory-based gas transport model are obtained for inorganic/organic hybrid structures used in gas barrier applications. Nondimensionalized solutions are provided for two cases that can be encountered in real applications: (1) gas diffusion-into and (2) gas transmission-through the barrier structures. The two cases represent (1) gas absorption into flexible organic electronic devices encapsulated by barrier structures and (2) the conventional gas transmission test conditions of barrier structures, respectively. The solutions are utilized to address gas transport behavior in two important practical applications.

Analysis of DEMO scenarios with the CRONOS suite of codes

The CRONOS suite of codes and the GLF23 theory-based transport model are used to perform a 1.5D analysis of the DEMO design. The study uses plasma parameters similar to those obtained in the European Power Plant Conceptual Study in the case of a scenario with moderate inductive current, high bootstrap current fraction, relatively small major radius R = 7.5 m and minor radius a = 2.5 m and high elongation and triangularity. It is shown how it is possible to obtain a high fusion power of 2600 MW and high fusion gain Q = 26.5 by adding 98 MW off-axis neutral beam at a moderately high Greenwald fraction of 1.2. A non-inductive current fraction of 88% is obtained mainly from the bootstrap current at the plasma edge, where a high pedestal of 7.8 keV has been considered in order to optimize the alpha power. It is also shown how by adding 66 MW of electron cyclotron waves to the previous scenario a 100% non-inductive current steady-state scenario can be obtained with a reversed q profile. However, in this case the fusion gain drops to 17.2 due to the higher input power. The application of LH waves is also discussed.

The first transport code simulations using the trapped gyro-Landau-fluid model

The first transport code simulations using the newly developed trapped gyro-Landau-fluid (TGLF) theory-based transport model are presented. TGLF has comprehensive physics to approximate the turbulent transport due to drift-ballooning modes in tokamaks. The TGLF model is a next generation gyro-Landau-fluid model that improves the accuracy of the trapped particle response and the finite Larmor radius effects compared to its predecessor, GLF23. The model solves for the linear eigenmodes of trapped ion and electron modes, ion and electron temperature gradient modes, and electromagnetic kinetic ballooning modes in either shifted circle or shaped geometry. A database of over 400 nonlinear gyrokinetic simulations using the GYRO code has been created. A subset of 83 simulations with shaped geometry has been used to find a model for the saturation levels. Using a simple quasilinear (QL) saturation rule, remarkable agreement with the energy and particle fluxes from a wide variety of GYRO simulations is found for both shaped or circular geometry and also for low aspect ratio. Using this new QL saturation rule along with a new E×B shear quench rule for shaped geometry, the density and temperature profiles have been predicted in over 500 transport code runs and the results compared against experimental data from 96 tokamak discharges. Compared to GLF23, the TGLF model demonstrates better agreement between the predicted and experimental temperature profiles. Surprisingly, TGLF predicts that the high-k modes are found to play an important role in the central core region of low and high confinement plasmas lacking transport barriers.

A theory-based transport model with comprehensive physics

A new theory-based transport model with comprehensive physics (trapping, general toroidal geometry, fully electromagnetic, electron-ion collisions, impurity ions) has been developed. The core of the model is the new trapped-gyro-Landau-fluid (TGLF) equations, which provide a fast and accurate approximation to the linear eigenmodes for gyrokinetic drift-wave instabilities (trapped ion and electron modes, ion and electron temperature gradient modes, and kinetic ballooning modes). The new TGLF transport model is more accurate, and has an extended range of validity, compared to its predecessor GLF23. The TGLF model unifies trapped and passing particles in a single set of gyro-Landau-fluid equations. A model for the averaging of the Landau resonance by the trapped particles makes the equations work seamlessly over the whole drift-wave wave-number range from trapped ion modes to electron temperature gradient modes. A fast eigenmode solution method enables unrestricted magnetic geometry. The transport model uses the TGLF eigenmodes to compute quasilinear fluxes of energy and particles. A model for the saturated intensity of the turbulence completes the flux calculation. The intensity model is constructed to fit a large set of nonlinear gyrokinetic turbulence simulations with kinetic electrons. The TGLF model is valid in new physical regimes that GLF23 was not. These include the low aspect ratio spherical torus, which has both a high trapped fraction and strong shaping of magnetic flux surfaces. The TGLF model is also valid close to the magnetic separatrix so the transport physics of the H-mode pedestal region can be explored.

Comparison of turbulent transport models of L- and H-mode plasmas

Theory-based turbulent transport models have been proposed and used in transport simulations to predict the performance of the International Thermonuclear Experimental Reactor (ITER). We have selected the current diffusive ballooning mode (CDBM), GLF23 and Weiland models as typical transport models. Taking experimental data from the ITPA profile database, simulations have been carried out to compare the results with each other using our one-dimensional diffusive transport code. It is found that each model has unique dependence on devices and operation modes, and most reasonable results among the models can be obtained by the CDBM model for L-mode discharges and by the GLF23 model for H-modes. From an analysis of Te/Ti dependence, predictions of the CDBM and Weiland models could be better in the hot electron regime. The effect of the elliptic cross section of the plasma has been included in the CDBM model, and it is confirmed that an accuracy of the prediction is improved for H-mode discharges. Finally, heat transport simulations for a single particle species have indicated that the CDBM model reproduces Ti profiles more accurately than Te profiles.

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.

Theoretical predictions of the density profile in a tokamak reactor

Recent studies provide convincing evidence that the anomalous transport in a tokamak is governed by the combination of ion temperature gradient and trapped electron mode turbulence. In this paper, we employ the theory-based transport model GLF23 to study the density profile formation in ITER. It is shown that the plasma density can be noticeably more peaked than is usually assumed. The peaking is mainly due to the curvature drift as described by the GLF model and, independently, by the turbulent equipartition theory. This results in an approximately 30% enhancement of the fusion power in comparison with the standard conjecture of the flat density profile. The physical background of this density peaking and its possible further impact on the reactor performance are also discussed.

Comparison of ITER performance predicted by semi-empirical and theory-based transport models

The values of Q = (fusion power)/(auxiliary heating power) predicted for ITER by three different methods are compared. The first method utilizes an empirical confinement-time scaling and prescribed radial profiles of transport coefficients; the second approach extrapolates from specially designed ITER similarity experiments, and the third approach is based on partly theory-based transport models. The energy confinement time given by the ITERH-98(y, 2) scaling for an inductive scenario with a plasma current of 15 MA and a plasma density 15% below the Greenwald density is 3.7 s with one estimated technical standard deviation of ±14%. This translates, in the first approach, for levels of helium removal, and impurity concentration, that, albeit rather stringent, are expected to be attainable, into an interval for Q of [6–15] at the auxiliary heating power, Paux = 40 MW, and [6–30] at the minimum heating power satisfying a good confinement ELMy H-mode. All theoretical transport-model calculations have been performed for the plasma core only, whereas the pedestal temperatures were taken as estimated from empirical scalings. Predictions of similarity experiments from JET and of theory-based transport models that we have considered—Weiland, MMM, and IFS/PPPL—overlap with the prediction using the empirical confinement-time scaling within its estimated margin of uncertainty.

Increased understanding of the dynamics and transport in ITB plasmas from multi-machine comparisons

Our understanding of the physics of internal transport barriers (ITBs) is being advanced by analysis and comparisons of experimental data from many different tokamaks worldwide. An international database consisting of scalar and two-dimensional profile data for ITB plasmas is being developed to determine the requirements for the formation and sustainment of ITBs and to perform tests of theory-based transport models in an effort to improve the predictive capability of the models. Analysis using the database indicates that: (a) the power required to form ITBs decreases with increased negative magnetic shear of the target plasma, and: (b) the E×B flow shear rate is close to the linear growth rate of the ion temperature gradient (ITG) modes at the time of barrier formation when compared for several fusion devices. Tests of several transport models (JETTO, Weiland model) using the two-dimensional profile data indicate that there is only limited agreement between the model predictions and the experimental results for the range of plasma conditions examined for the different devices (DIII-D, JET, JT-60U). Gyrokinetic stability analysis (using the GKS code) of the ITB discharges from these devices indicates that the ITG/TEM growth rates decrease with increased negative magnetic shear and that the E×B shear rate is comparable to the linear growth rates at the location of the ITB.

Comparison of theory-based and semi-empiricaltransport modelling in JET plasmas with ITBs

The theory-based Weiland transport model has been applied to JETdischarges with internal transport barriers (ITBs) for the first time. Theagreement of the modelling results with the experiments has been foundto be comparable with the agreement of the modelling results producedby the semi-empirical Bohm/gyro-Bohm transport model. Weiland modeloverestimates the width of the ITB and the electron temperature. Thereis evidence that the density gradient in the Weiland modelplays a more important role in governing the ITB formation dynamics forJET discharges than the suppression of turbulence by theωE×B flow shearing rate.

Theoretical transport modeling of Ohmic cold pulse experiments

The response of several theory-based transport models in Ohmically heated tokamak discharges to rapid edge cooling due to trace impurity injection is studied. Results are presented for the Institute for Fusion Studies—Princeton Plasma Physics Laboratory (IFS/PPPL), gyro-Landau-fluid (GLF23), Multi-mode (MM), and the Itoh–Itoh–Fukuyama (IIF) transport models with an emphasis on results from the Texas Experimental Tokamak (TEXT) [K. W. Gentle, Nucl. Technol./Fusion 1, 479 (1981)]. It is found that critical gradient models containing a strong ion and electron temperature ratio dependence can exhibit behavior that is qualitatively consistent with experimental observation while depending solely on local parameters. The IFS/PPPL model yields the strongest response and demonstrates both rapid radial pulse propagation and a noticeable increase in the central electron temperature following a cold edge temperature pulse (amplitude reversal). Furthermore, the amplitude reversal effect is predicted to diminish with increasing electron density and auxiliary heating in agreement with experimental data. An Ohmic pulse heating effect due to rearrangement of the current profile is shown to contribute to the rise in the core electron temperature in TEXT, but not in the Joint European Tokamak (JET) [A. Tanga and the JET Team, in Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 65] and the Tokamak Fusion Test Reactor (TFTR) [R. J. Hawryluk, V. Arunsalam, M. G. Bell et al., in Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 51]. While this phenomenon is not necessarily a unique signature of a critical gradient, there is sufficient evidence suggesting that the apparent plasma response to edge cooling may not require any underlying nonlocal mechanism and may be explained within the context of the intrinsic properties of electrostatic drift wave-based models.

Predicting temperature and density profiles in tokamaks

A fixed combination of theory-based transport models, called the Multi-Mode Model, is used in the BALDUR [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1988)] transport simulation code to predict the temperature and density profiles in tokamaks. The choice of the Multi-Mode Model has been guided by the philosophy of using the best transport theories available for the various modes of turbulence that dominate in different parts of the plasma. The Multi-Mode model has been found to provide a better match to temperature and density profiles than any of the other theory-based models currently available. A description and partial derivation of the Multi-Mode Model is presented, together with three new examples of simulations of the Tokamak Fusion Test Reactor (TFTR) [K. M. McGuire et al., Phys. Plasmas 2, 2176 (1995)]. The first simulation shows the strong effect of recycling on the ion temperature profile in TFTR supershot simulations. The second simulation explores the effect of a plasma current ramp—where the plasma energy content changes slowly on the energy confinement time scale. The third simulation shows that the Multi-Mode Model reproduces the experimentally measured profiles when tritium is used as the hydrogenic isotope in L-mode (low confinement mode) plasmas.