Tokamak Energy Confinement Research Articles

Analysis of the highest energy confinement in tokamaks based on thermodynamic approach

We analyze the highest energy confinement in tokamak plasmas based on thermodynamic approach (plasma self-organization). The energy transport coefficients in the saturated confinement regimes are calculated from experiments in the T-10 tokamak. Using these coefficients, we estimate the maximal energy confinement for JET, ASDEX Upgrade, JT-60U, DIII-D and KSTAR tokamaks. Calculated energy confinement is in a good agreement with measured ones. Obtained results allow us to predict the maximal energy confinement in newly constructed machines up to a fusion reactor. The energy confinement for two basic scenarios for ITER is accessed.

Improvement of plasma energy confinement in tokamak under radiative cooling of the edge plasma

Improvement of plasma energy confinement in the T-10 tokamak by injection of impurity gases was studied experimentally. Injection of Ne and He in the ohmic and ECR heating regimes allows one to separate the dependences of energy confinement on the plasma density and on the edge plasma cooling rate. It is shown that the well-known dependence of the energy confinement time on the plasma density is, in fact, the dependence on the radiative loss power. This phenomenon can be explained by plasma self-organization. The experiments are described by a thermodynamic model for self-organized plasma in which the transport coefficient depends on the difference between the actual and self-consistent pressure profiles. The reduction in the heat flux at the plasma edge due to radiative cooling leads to a decrease in the transport coefficient in this region and, accordingly, improves energy confinement. Results of approximate model calculations for experiments with Ne injection are presented.

Discovery of stationary operation of quiescent H-mode plasmas with net-zero neutral beam injection torque and high energy confinement on DIII-D

Recent experiments in DIII-D [J. L. Luxon et al., in Plasma Physics and Controlled Nuclear Fusion Research 1996 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] have led to the discovery of a means of modifying edge turbulence to achieve stationary, high confinement operation without Edge Localized Mode (ELM) instabilities and with no net external torque input. Eliminating the ELM-induced heat bursts and controlling plasma stability at low rotation represent two of the great challenges for fusion energy. By exploiting edge turbulence in a novel manner, we achieved excellent tokamak performance, well above the H98y2 international tokamak energy confinement scaling (H98y2 = 1.25), thus meeting an additional confinement challenge that is usually difficult at low torque. The new regime is triggered in double null plasmas by ramping the injected torque to zero and then maintaining it there. This lowers E × B rotation shear in the plasma edge, allowing low-k, broadband, electromagnetic turbulence to increase. In the H-mode edge, a narrow transport barrier usually grows until MHD instability (a peeling ballooning mode) leads to the ELM heat burst. However, the increased turbulence reduces the pressure gradient, allowing the development of a broader and thus higher transport barrier. A 60% increase in pedestal pressure and 40% increase in energy confinement result. An increase in the E × B shearing rate inside of the edge pedestal is a key factor in the confinement increase. Strong double-null plasma shaping raises the threshold for the ELM instability, allowing the plasma to reach a transport-limited state near but below the explosive ELM stability boundary. The resulting plasmas have burning-plasma-relevant βN = 1.6–1.8 and run without the need for extra torque from 3D magnetic fields. To date, stationary conditions have been produced for 2 s or 12 energy confinement times, limited only by external hardware constraints. Stationary operation with improved pedestal conditions is highly significant for future burning plasma devices, since operation without ELMs at low rotation and good confinement is key for fusion energy production.

Application of symbolic regression to the derivation of scaling laws for tokamak energy confinement time in terms of dimensionless quantities

In many scientific applications, it is important to investigate how certain properties scale with the parameters of the systems. The experimental studies of scalings have traditionally been addressed with log regression, which limits the results to power laws and to theoretical and not data-driven dimensionless quantities. This has also been the case in nuclear fusion, in which the scaling of the energy confinement time is a crucial aspect in understanding the physics of transport and in the design of future devices. Traditionally two main assumptions are at the basis of the most widely accepted empirical scaling laws for the confinement time: (a) the dimensionless variables used are the ones derived from the symmetries of the Vlasov equation; (b) the final scalings have the mathematical form of power laws. In this paper, it is shown how symbolic regression (SR), implemented with genetic programming (GP) techniques, can be used to test these hypotheses. Neither assumption is confirmed by the available data of the multi-machine International Tokamak Physics Activity (ITPA) of validated tokamak discharges. The statistically soundest expressions are not power laws and cannot be formulated in terms of the traditional dimensionless quantities. The consequences of the data-driven scaling laws obtained are both practical and theoretical: the confinement time for the ITER can be significantly shorter than foreseen by power laws and different dimensionless variables should be considered for theoretical investigations. On the other hand, higher quality databases should be built to reduce the uncertainties in the extrapolations. It is also worth emphasising that the proposed methodology is fully general and therefore can be applied to any field of science.

Radial transport and electron-cyclotron-current drive in the TCV and DIII-D tokamaks.

Calculation of electron-cyclotron-current drive (ECCD) with the comprehensive CQL3D Fokker-Planck code for a TCV tokamak shot gives 550 kA of driven toroidal current, in marked disagreement with the 100-kA experimental value. Published ECCD efficiencies calculated with CQL3D in the much larger, higher-confinement DIII-D tokamak are in excellent agreement with experiment. The disagreement is resolved by including in the calculations electrostatic-type radial transport at levels given by global energy confinement in tokamaks. The radial transport of energy and toroidal current are in agreement.

Overview of RF techniques in new confinement regimes with modified shear

It has been shown that the core energy confinement in tokamaks can be significantly improved by modifying the plasma current profile. Plasma regimes where the transport is reduced to its neoclassical value in the centre of the plasma within a region called the internal transport barrier (ITB) can be achieved with a zero or negative magnetic shear. In this paper the role of the radio frequency (RF) methods: electron cyclotron resonance, ion cyclotron resonance and lower hybrid current drive in producing these ITBs is reviewed. Combined techniques where RF waves are used to modify the magnetic shear together with a central heating method (neutral beam injection or RF) are described. Application of RF methods to high fusion yield plasmas in JET with modified shear are presented together with a discussion on the prospects of achieving steady-state high-performance plasmas. RF techniques are already playing an important role in these `advanced scenarios' and are likely to become indispensable tools for future steady-state tokamak reactors.

Local Cooling Effect of Rotation and Formation of Thermal Transport Barrier in Tokamaks

A simple model, rotation-inducing local cooling, for the mechanism on the formation of thermal transport barrier and the increase in rotation velocity is presented. It is shown that the sheared rotation can make electron temperature profile Te(r) steepen near the rotation layer and ▿Te > 0 on some location inside it, in agreement with the experimental observations in tokamaks, such as JT-60U with (poloidal or toroidal) sheared rotation and HL-1M with a biased electrode. Such temperature profile can remarkably improve the energy confinement in tokamaks.

Global energy confinement under coupling of the transport process with magnetohydrodynamic modes

Macroscopic instabilities are governed by transport-determined plasma profiles and transport, in turn, is affected by instabilities. It is clear that neither transport process nor the behavior of instabilities can be treated in isolation. A model is developed for investigating the effects of the instabilities on global energy confinement in tokamaks. The results clearly demonstrate that magnetohydrodynamic (MHD) instabilities coupled with the transport process change not only the value of global energy confinement time, but also, perhaps more importantly, the energy confinement scaling law. While considering MHD effects, global energy confinement becomes sensitively dependent on the boundary transport conditions, and the cases with and without MHD stability can result in quite different parameter behavior of the global energy confinement. Such coupling should be considered when attempts are made to analyze the global energy confinement in tokamaks.

Quantitative predictions of tokamak energy confinement from first-principles simulations with kinetic effects

A first-principles model of anomalous thermal transport based on numerical simulations is presented, with stringent comparisons to experimental data from the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. This model is based on nonlinear gyrofluid simulations, which predict the fluctuation and thermal transport characteristics of toroidal ion-temperature-gradient-driven (ITG) turbulence, and on comprehensive linear gyrokinetic ballooning calculations, which provide very accurate growth rates, critical temperature gradients, and a quasilinear estimate of χe/χi. The model is derived solely from the simulation results. More than 70 TFTR low confinement (L-mode) discharges have been simulated with quantitative success. Typically, the ion and electron temperature profiles are predicted within the error bars, and the global energy confinement time within ±10%. The measured temperatures at r/a≂0.8 are used as a boundary condition to predict the temperature profiles in the main confinement zone. The dramatic transition to the improved confinement in the supershot regime is also qualitatively explained. Further work is needed to extend this model of core heat transport to include particle and momentum transport, the edge region, and other operating regimes besides the ITG-dominated L mode. Nevertheless, the present model is very successful in predicting thermal transport in the main plasma over a wide range of parameters.

Initial boronization of the DIII–D tokamak

A system has been installed to deposit a thin film of elemental boron on the walls of the DIII–D tokamak, in order to reduce the influx of impurities during plasma discharges. Subsequently new regimes of substantially improved tokamak energy confinement were obtained. The deposition of the boron layer is achieved during a glow-discharge session using a helium-diborane gas mixture and a film of ≊100 nm is deposited. The boronization system includes special storage and handling precautions for the diborane, a delivery and metering system for the glow discharge, modifications to the tokamak’s residual gas analyzer system, and a dedicated system for handling and neutralizing the exhaust gas from the tokamak. Tokamak discharges with similar parameters before and after boronization are used to characterize the effects of the boron film. Nickel has been reduced by a factor of 30, while impurities such as oxygen and carbon are reduced fivefold. A system of pulsing the glow discharge has been developed in order to improve the uniformity of the film applied

Neural network approach to energy confinement scaling in Tokamaks

Empirical studies of the scaling of Tokamak energy confinement times with machine parameters constitute a useful point of contact with physics-based transport theories. They also form the basis for the design of next-step and reactor grade Tokamaks. In most cases a simple power law (or sometimes offset linear) functional form is fitted to the data. Such linear regression techniques have the advantage of computational simplicity, but otherwise have little a-priori justification. Neural networks provide a powerful general purpose technique for nonlinear regression which exhibits no essential limitations on the functional form which can be fitted. The authors apply neural networks to the problem of energy confinement scaling and they illustrate the technique using the data from the JET (Joint European Torus) Tokamak. The results show that the neural network approach leads to a substantial improvement in the ability to predict the energy confinement times as compared with linear regression. The significance of this result is discussed.

Transport barrier in ion temperature gradient driven turbulence

Fluid simulations of long ηi modes are presented that demonstrate that the density profile plays a much more profound role in controlling global energy confinement than would be expected from simple marginal stability considerations. Specifically, local steepening of the density gradient produces an effective transport barrier that allows ion global confinement to improve dramatically. The threshold value ηi =d ln(Ti)/d ln(n) required for instability ηic plays a fundamental role in the formation of the transport barrier—no transport barrier forms for ηic<1. The implication of these results for understanding ion energy confinement in tokamaks is discussed.

Study of toroidal ion temperature gradient electrostatic drift waves

The toroidal ion temperature gradient electrostatic drift waves are investigated including the effect of ion dynamics parallel to the ambient magnetic fields. By using the transport equations of Braginskii, the mode equations are derived. The local as well as nonlocal dispersion relations are obtained and various limiting cases are discussed. Also addressed is the issue of the anomalous ion energy transport that is caused by the nonthermal ion temperature gradient drift waves. A possible stationary solution of the nonlinear mode coupling equations is presented. The relevance of our investigation to the ion energy confinement in tokamaks is pointed out.

Extrapolation of tokamak energy confinement to Next Step Devices

The extrapolation of energy confinement to the conditions of a Next Step tokamak, to operate with an ignited DT plasma, is an essential ingredient of the data base needed for such a device. The present knowledge on energy confinement and the approaches used for providing a basis for the extrapolation are concisely described. The lines of further research are indicated which have to be followed to be able, in a few years, to extrapolate energy confinement to a Next Step tokamak with improved accuracy.

A unified physical scaling law for tokamak energy confinement

From the equations which describe local transport in a turbulent plasma the scaling of the local diffusivity with the plasma parameters can be established. It is shown that, by appropriate choices of time and length scales for the turbulence, the scaling of the global energy confinement can be cast in two limiting forms: a short and a long wavelength scaling. The scaling laws consist of a leading term and a function F whose arguments are the dimensionless normalized plasma collisionality and beta. The scaling of the leading term in the short wavelength expression for global confinement is shown to fit both L-mode and H-mode confinement data from JET. The function F which describes the precise physical mechanism of the turbulence is found to increase with collisionality, but its dependence on the plasma beta remains uncertain. Several theoretical models are found to be a reasonable fit to the JET confinement data; others, however, such as that for the dissipative trapped electron mode, can be discarded. The short wavelength confinement scaling is shown to unify a multiplicity of existing theoretical/empirical scaling laws by suitable choices of the function F. These scaling laws all exhibit a similar dependence of F upon collisionality but have different dependences upon the plasma beta. It is shown that for the JET data it is very difficult to determine the beta dependence and this explains why so many apparently different scaling laws produce reasonable fits to the data. Using the leading term of the scaling, the fusion product can be extrapolated to reactor conditions (ITER) with an uncertainty factor of four. This uncertainty can be reduced to ±30% by the use of a similarity technique in which F is determined directly from the JET data.

Ion temperature gradient mode in the weak density limit

Including the Righi–Leduc ion heat flux in the energy equation, the ion temperature gradient mode (ITG mode) is reconsidered for flat density profiles in a plasma with inhomogeneous ion temperature and magnetic field gradients. The stability boundary is (re)derived and is compared with those derived recently using either an ad hoc model or the numerical analysis of the kinetic dispersion relation. The impact of ITG mode turbulence on the ion energy confinement in tokamaks is discussed.

Nonlinear coupling of waves in the ion cyclotron range of frequencies to tokamak trapped electron modes

The results of a theoretical study of nonlinear coupling of waves in the ion cyclotron range of frequencies (ICRF) to tokamak dissipative trapped electron modes (DTEM) via sidebands of the ICRF source wave are presented. These interactions can affect the stability of the DTEM spectrum and thus tokamak energy confinement. Explicit expressions are derived for the nonlinear growth rates of DTEM both for fast magnetosonic and ion Bernstein source waves. Fast wave coupling is found to be destabilizing for frequencies in the ICRF at low plasma ion beta, but can be stabilizing for wave frequencies well above the ion gyrofrequency (ω0≳ωciβ−1/2i). Ion Bernstein coupling can also be stabilizing or destabilizing depending on details of the source wave. Waves with ω0>ωci, k0>k, and k0 ρi≳1 appear better suited for stabilization (k0, k are the wavenumbers of the source wave, DTEM). For example, if these conditions are met and 2k0y<k (k0y is the poloidal source wavenumber), it is shown that the whole DTEM spectrum for kρi <1 can be stabilized. Analytic expressions for the ICRF wave electric field strengths for DTEM stabilization are given.

A comparison of energy confinement in tokamaks and stellarators

We overview and compare the energy confinement behaviour of tokamaks andstellarators at high heating powers. Tokamaks show in all parameter ranges ananomalous enhancement of electron energy losses. At high heating powers abifurcation is observed in the plasma energy vs. heating power diagram, withthe low energy (L-regime) branch showing a clear deterioration of confinementtime with power. Divergent results exist concerning the corresponding behaviorof the high energy (H-regime) branch. Experiments with ECR-heating ofnet-current-free stellarator plasmas can be to a large extent explained byneoclassical electron heat conduction losses, including ripple effects. Inthese experiments anomalous transport enhancement has been identified only inthe outer plasma layers and at low temperatures and densities, which in thisform should not affect reactor aspects. At a given density, neoclassicalelectron heat conduction losses scale however in a similar manner with heatingpower as the L-regime losses observed in tokamaks. For a better discrimination- important due to the differing variation with size expected for the twotypes of losses - density scans over a range not accessible with present dayECRH-systems are needed. Corresponding experiments with NBI-heating on thehigh shear Heliotron-E device indeed gave evidence for a confinement anomalyincreasing with heating power, although not well fitted by tokamak L-regimeexpressions. For low shear systems, conclusive evidence is expected fromNBI-heating experiments on W VII-AS.

The use of scaling laws for the design of high beta tokamaks

Several different empirical scaling laws for the tokamak energy confinement time are used to estimate the auxiliary heating power required for a laboratory experiment capable of testing tokamak confinement at high beta and techniques to access the second stability regime. Since operating experience in the second stability regime does not yet exist, these laws predict a wide range of possible power requirements, especially at large aspect ratios. However, by examining a model DT fusion power reactor with reasonable restrictions on the fusion island weight, neutron loading, and maximum magnetic field of the external coils, only a limited range of operating conditions are found for both first and second regime tokamaks, and only a subset of the scaling laws predict ignition. These particular scaling laws are then used to set confinement goals which if demonstrated by the laboratory experiment would indicate favourable scaling to a reactor.

Enhancement of confinement in tokamaks

A plausible interpretation of the experimental evidence is that energy confinement in tokamaks is governed by two separate considerations: (1) the need for resistive MHD kink-stability, which limits the permissible range of current profiles-and therefore normally also the range of temperature profiles; and (2) the presence of strongly anomalous microscopic energy transport near the plasma edge, which calibrates the amplitude of the global temperature profile, thus determining the energy confinement time tau E. The present analysis begins by identifying a hypothetical model of tokamak confinement that is designed to take into account the conflict between Te(r)-profile shapes arising from microscopic transport and J(r)-profile shapes required for gross stability. On the basis of this model, a number of hypothetical lines of advance are developed. Some TFTR experiments that may point the way to a particularly attractive type of tokamak reactor regime are discussed.