Confinement Scaling Laws Research Articles

ENN's roadmap for proton-boron fusion based on spherical torus

ENN Science and Technology Development Co., Ltd. (ENN) is committed to generating fusion energy in an environmentally friendly and cost-effective manner, which requires abundant aneutronic fuel. Proton-boron (p-11B or p-B) fusion is considered an ideal choice for this purpose. Recent studies have suggested that p-B fusion, although challenging, is feasible based on new cross section data, provided that a hot ion mode and high wall reflection can be achieved to reduce electron radiation loss. The high beta and good confinement of the spherical torus (ST) make it an ideal candidate for p-B fusion. By utilizing the new spherical torus energy confinement scaling law, a reactor with a major radius R0=4 m, central magnetic field B0=6 T, central temperature Ti0=150 keV, plasma current Ip=30 MA, and hot ion mode Ti/Te=4 can yield p-B fusion with Q>10. A roadmap for p-B fusion has been developed, with the next-generation device named EHL-2. EHL stands for ENN He-Long, which literally means “peaceful Chinese Loong.” The main target parameters include R0≃1.05 m, A≃1.85, B0≃3 T, Ti0≃30 keV, Ip≃3 MA, and Ti/Te≥2. The existing ST device EXL-50 was simultaneously upgraded to provide experimental support for the new roadmap, involving the installation and upgrading of the central solenoid, vacuum chamber, and magnetic systems. The construction of the upgraded ST fusion device, EXL-50U, was completed at the end of 2023, and it achieved its first plasma in January 2024. The construction of EHL-2 is estimated to be completed by 2026.

Isotope mass scaling and transport comparison between JET Deuterium and Tritium L-mode plasmas

The dimensionless isotope mass scaling experiment between pure Deuterium and pure Tritium plasmas with matched ρ∗ , ν∗ , β n , q and Te/Ti has been achieved in JET L-mode with dominant electron heating (NBI+ohmic) conditions. 28% higher scaled energy confinement time BtτE,th/A is found in favour of the Tritium plasma. This can be cast in the form of the dimensionless energy confinement scaling law as ΩiτE,th∼A0.48±0.16 . This significant isotope mass scaling is consequently seen in the scaled one-fluid heat diffusion coefficient Aχeff/Bt which is around 50% lower in the Tritium plasma throughout the whole plasma radius. The isotope mass dependence in the particle transport channel is negligible, supported also by the perturbative particle transport analysis with gas puff modulation. The comparison of the edge particle fuelling or ionisation profiles from the EDGE2D-EIRENE simulations show that the absolute density differences that are necessary for the dimensionless match in the confined plasma dominate over any isotope mass dependencies of particle fuelling and ionization profiles at the plasma edge. Local GENE simulation results indicate a mild anti-gyroBohm effect at ρtor = 0.6 and thereby a small isotope mass dependence in favour of Tritium on heat transport and a negligible effect on particle transport. A significant fraction of the isotope scaling and reduced heat transport observed in the Tritium plasma is not captured in the GENE and ASTRA-TGLF-SAT2 simulations by simply changing the isotope mass for the same input profiles.

Massive parametric study for prospective design space of a compact tokamak fusion reactor

Using a novel computational algorithm that integrates tokamak systems analysis with neutron transport calculations, the minimum major radius (R0) and resulting maximum magnetic field at the plasma center (BT) can be determined uniquely for a given plasma performance. Plasma performance was varied extensively using a supercomputer (KAIROS) and scanning over a wide range of physics, technology, and system parameters to derive the optimal design space for a compact tokamak fusion reactor. Given the design goals of fusion gain Q > 20.0, net electric power > 100 MW, neutron wall loading < 2.0 MW/m2, indicator of divertor power handling PSOL/R0 < 25 MW/m, direct capital cost < $4.0 billion, and steady-state operation, a prospective design space was determined depending on the levels of physics and technology. Advanced engineering features, such as maximum allowable magnetic field at the toroidal field coil (Bmax = 23 T), were implemented by adopting high-temperature superconducting magnet technology, using an advanced shield material such as tungsten carbide (WC), and a plug-bucked magnet support structure. It was found that by exceeding the energy confinement scaling laws of IPB98y2, a design space of R0 < 4.0 m could be accessed under the following conditions for a conventional tokamak: confinement enhancement factor H > 1.7, bootstrap current fraction fBS > 0.55, magnetic field at the magnetic axis BT > 4.0 T, fusion power Pfusion > 600 MW, and thermodynamic efficiency ηth > 0.33. For a spherical tokamak, these conditions were H > 1.3, fBS > 0.6, BT 〈 6.0 T, and Pfusion 〉 500 MW. Sensitivity studies on the energy confinement scaling laws showed that stricter conditions on the physics parameters were required with the ITPA20 scaling law, whereas the conditions were mitigated with the β-independent scaling law.

The dependence of tokamak L-mode confinement on magnetic field and plasma size, from a magnetic field scan experiment at ASDEX Upgrade to full-radius integrated modelling and fusion reactor predictions

The dependence of the confinement of a tokamak plasma in L-mode on the magnetic field is explored with a set of dedicated experiments in ASDEX Upgrade and with a theory-based full-radius modelling approach, based on the ASTRA transport code and the TGLF-SAT2 transport model and only using engineering parameters in input, like those adopted in scaling laws for the confinement time. The experimental results confirm the weak dependence of the global confinement on the magnetic field, consistent with the scaling laws for L-mode plasmas and in agreement with the full-radius TGLF-SAT2 predictions. The modelling approach is then extended to numerically investigate the confinement dependence on magnetic field, plasma current and plasma size. The weak dependence of the L-mode confinement on the magnetic field at constant plasma current and plasma size is shown to be produced by a balance between the decrease of confinement mainly produced by the reduction of the E×B shearing rate and the increase of confinement provided by the reduced gyro-Bohm factor, when the magnetic field is increased. The ASTRA/TGLF-SAT2 predicted increase of confinement with increasing plasma size is investigated in comparison with the predictions of the global confinement scaling laws for L-mode plasmas and the Bohm and gyro-Bohm dependencies of confinement, highlighting interesting similarities and important differences. Full-radius TGLF-SAT2 simulations with increasing plasma size are then extended to dimensions which are compatible with reactor relevant fusion power production, using ITER and the European DEMO as references. ASTRA/TGLF-SAT2 predictions of fusion power and confinement of an L-mode fusion reactor are presented at both 5.7 T and 10 T of magnetic field on the magnetic axis.

Quantum Confinement of Electron-Phonon Coupling in Graphene Quantum Dots.

On the basis of first-principles calculations and the special displacement method, we demonstrate the quantum confinement scaling law of the phonon-induced gap renormalization of graphene quantum dots (GQDs). We employ zigzag-edged GQDs with hydrogen passivation and embedded in hexagonal boron nitride. Our calculations for GQDs in the sub-10 nm region reveal strong quantum confinement of the zero-point renormalization ranging from 20 to 250 meV. To obtain these values we introduce a correction to the Allen-Heine theory of temperature-dependent energy levels that arises from the phonon-induced splitting of 2-fold degenerate edge states. This correction amounts to more than 50% of the gap renormalization. We also present momentum-resolved spectral functions of GQDs, which are not reported in previous contributions. Our results lay the foundation to systematically engineer temperature-dependent electronic structures of GQDs for applications in solar cells, electronic transport, and quantum computing devices.

New assessment of the fast ion energy in ASDEX upgrade H-mode discharges

Confinement scaling laws such as IPB98(y, 2) are widely used to extrapolate the performance of present tokamaks to next-step devices such as ITER or DEMO. The thermal energy of the plasma (W th), which is used to determine the energy confinement time for most scaling laws, is difficult to measure, due to the sizeable uncertainties in the experimental kinetic profiles. The common approach in the tokamak community is to derive W th as the difference between the measured magnetohydrodynamic (MHD) energy and some simulation-based estimate of the fast ion energy W fi. In H-mode plasmas W fi can be as high as W th, in presence of neutral beam injection (NBI) or ion cyclotron radio frequency heating (ICRF), therefore an accurate assessment of W fi is crucial to have a somewhat reliable H-factor, regardless of the power-scaling of a given scaling law. In this paper we aim at evaluating the current approach to estimate W fi, by comparing its predictions with a wide database of calculations using validated NBI codes. Systematic deviations and trends, as well as statistical scatter are discussed. We use a comprehensive database of AUG H-mode deuterium plasmas, with significant variations of plasma current, NBI power and plasma density. We neglect thereby the fast-ion losses caused by MHD modes and the synergy effect between NBI and ICRF. A new approach is proposed based on the newly developed fast NBI code RABBIT.

Role of impurities in modifying isotope scaling law of ion temperature gradient turbulence driven transport in tokamak

Tokamak experiments show that the plasma empirical energy confinement scaling law varies with plasma ion mass (Ai) in a certain range under conditions of different plasma parameters or different devices. In order to understand such a modification of the empirical energy confinement scaling law, the isotope mass dependence of ion temperature gradient (ITG, including impurity modes) turbulence driven transport in the presence of tungsten impurity ions in tokamak plasma is studied by employing the gyrokinetic theory. The effect of heavy (tungsten) impurity ions on ITG and impurity mode is revealed to modify significantly the isotope mass dependence and effective charge effect. As the charge number of impurity ions (Z) or impurity charge concentration (fz) changes, the theoretical scaling law of ITG turbulence transport varies substantially in a relatively large range. The maximum growth rate of ITG mode scales as Mi-0.48 -0.12, whilst that of impurity mode scales as Mi-0.46 -0.3. Here, Mi is the mass number of primary ion in the plasma. In both cases the fitting index with Mi deviates further away from -0.5 when impurity charge concentration fz increases. The isotope mass dependence of ITG turbulence gradually weakens when the effective charge number Zeff increases. The isotope mass dependence of impurity mode turbulence also weakens with Zeff increasing for the same impurity ion charge number (Z). In contrast, the isotope mass dependence gradually strengthens with effective charge number Zeff increasing for the same impurity charge concentration (fz). On average, the maximum growth rates of impurity mode scale roughly as max~Mi-0.35Zeff1.5 and max~Mi-0.4Zeff1, respectively, for Zeff 3 and Zeff 3. The reason for the deviation of isotope scaling law from the normal case is investigated deliberately, and it is demonstrated that the isotope scaling index deviates from -0.5 more or less due to the fact that the impurity species, charge number and impurity concentrations vary in a certain range. These results demonstrate that it is impossible to deduce a unique isotope scaling law due to the variety of micro-instabilities and various plasma parameter regimes in tokamak plasma, which is consistent with the experimental observations. These results may contribute to the transport study involving heavy (tungsten) impurity ions in ITER discharge scenario investigation.

Confinement Tuning of a 0-D Plasma Dynamics Model

Investigations of tokamak dynamics, especially as they relate to the challenge of burn control, require an accurate representation of energy and particle confinement times. While the ITER-98 scaling law represents a correlation of data from a wide range of tokamaks, confinement scaling laws will need to be fine-tuned to specific operational features of specific tokamaks in the future. A methodology for developing, by regression analysis, tokamak- and configuration-specific confinement tuning models is presented and applied to DIII-D as an illustration. It is shown that inclusion of tuning parameters in the confinement models can significantly enhance the agreement between simulated and experimental temperatures relative to simulations in which only the ITER-98 scaling law is used. These confinement tuning parameters can also be used to represent the effects of various heating sources and other plasma operating parameters on overall plasma performance and may be used in future studies to inform the selection of plasma configurations that are more robust against power excursions.

Radiation and confinement in 0D fusion systems codes

In systems modelling for fusion power plants, it is essential to robustly predict the performance of a given machine design (including its respective operating scenario). One measure of machine performance is the energy confinement time that is typically predicted from experimentally derived confinement scaling laws (e.g. IPB98(y,2)). However, the conventionally used scaling laws have been derived for ITER which—unlike a fusion power plant—will not have significant radiation inside the separatrix.In the absence of a new high core radiation relevant confinement scaling, we propose an ad hoc correction to the loss power used in the ITER confinement scaling and the calculation of the stored energy by the radiation losses from the ‘core’ of the plasma . Using detailed ASTRA / TGLF simulations, we find that an appropriate definition of is given by 60% of all radiative losses inside a normalised minor radius . We consider this an improvement for current design predictions, but it is far from an ideal solution. We therefore encourage more detailed experimental and theoretical work on this issue.

Interpretation of tokamak self-consistent pressure profiles

The phenomenon of a pressure profiles self-consistency in tokamak plasmas is interpreted in the framework of a ‘thermodynamic’ approach, used successfully in complex non-equilibrium systems studies. The solutions for the self-consistent pressure profiles are in accordance with experimental pressure profiles. The heat transport features in the vicinity of the minimum of the free energy are analysed. The deduced energy confinement scaling law is in qualitative agreement with the empirical so-called IPB98(y,2) scaling law.

Symbolic regression via genetic programming for data driven derivation of confinement scaling laws without any assumption on their mathematical form

Many measurements are required to control thermonuclear plasmas and to fully exploit them scientifically. In the last years JET has shown the potential to generate about 50 GB of data per shot. These amounts of data require more sophisticated data analysis methodologies to perform correct inference and various techniques have been recently developed in this respect. The present paper covers a new methodology to extract mathematical models directly from the data without any a priori assumption about their expression. The approach, based on symbolic regression via genetic programming, is exemplified using the data of the International Tokamak Physics Activity database for the energy confinement time. The best obtained scaling laws are not in power law form and suggest a revisiting of the extrapolation to ITER. Indeed the best non-power law scalings predict confinement times in ITER approximately between 2 and 3 s. On the other hand, more comprehensive and better databases are required to fully profit from the power of these new methods and to discriminate between the hundreds of thousands of models that they can generate.

Fluctuation Measurements and Their Link with Transport on Tore Supra

Measurement of turbulence properties provides key insight to understand anomalous transport in magnetic fusion devices. On Tore Supra, scattering diagnostics and reflectometers have been used to measure density fluctuations in the plasma core. A cross-polarization scattering diagnostic was also the first diagnostic to measure the turbulence magnetic fluctuations in a fusion plasma core. This paper presents the principle and the experimental setup of these diagnostics, with chosen results illustrating their capabilities to determine the spatial structure of the turbulence and to assess the link between energy transport and fluctuations. These flexible and complementary measurements made it possible to analyze the confinement and fluctuation scaling laws with nondimensional parameters, which requires a wide variety of plasma conditions.

On the extrapolation to ITER of discharges in present tokamaks

An expression for the extrapolated fusion gain G = Pfusion/5Pheat (Pfusion being the total fusion power and Pheat the total heating power) of ITER in terms of the confinement improvement factor (H) and the normalized beta (βN) is derived in this paper. It is shown that an increase in normalized beta can be expected to have a negative or neutral influence on G depending on the chosen confinement scaling law. Figures of merit like should be used with care, since large values of this quantity do not guarantee high values of G, and might not be attainable with the heating power installed on ITER.

The beta scaling of energy confinement in ELMy H-modes in JET

The disagreement between the weak dependence of the energy confinement time on normalized pressure, β, observed in dedicated scans and the strongly negative dependence in the confinement scaling laws used for the design of next step tokamaks and future reactors, remains an outstanding problem. As such, scans of β have been undertaken in single null, low triangularity (δ ≈ 0.2) ELMy H-mode plasmas in JET with the MarkIIGB-SRP divertor. The scans varied β by a factor of 2.8 (normalized β from 0.72 to 2.04) and covered a range of magnetic fields (1.5–2.3 T), plasma currents (1.5–2.75 MA) and safety factors (q95 = 2.8 and 3.3). A weak β dependence was observed both globally (B0τE varied less than 9% across any one scan) and locally. A scan within Type I ELMy H-modes suggests that this weaker dependence is not due to ELM regimes. A statistical analysis indicates that these results are consistent with log–linear regressions performed on a wide JET database of ELMy H-modes, if correlations in this database are considered.

Flux driven turbulence in tokamaks

The work presented deals with tokamak plasma turbulence in the case wherefluxes are fixed and profiles are allowed to fluctuate. These systemsare intermittent. In particular, radially propagating fronts areusually observed over a broad range of time and spatial scales. Theexistence of these fronts provides one possible way to understand thefast transport events sometimes observed in tokamaks. It is also shownthat the confinement scaling law can still be of the gyro-Bohm type inspite of these large scale transport events. Some departure from thegyro-Bohm prediction is observed at low flux, i.e. when the gradientsare close to the instability threshold. Finally, it is found that thediffusivity is not the same for a turbulence calculated at fixed fluxas for a turbulence calculated at fixed temperature gradient, with thesame time averaged profile.

Effect of energetic ion loss on ICRF heating efficiency and energy confinement time in heliotrons

The ICRF heating efficiency and the global energy confinement time duringICRF heating are investigated, including the effect of energetic ion loss in heliotrons.The approximate formula of ICRF heating efficiency is derived using results based on Monte Carlo simulations (Murakami, S., et al., Fusion Eng. Des. 26 (1995) 209). The global energy confinement time including the energetic ion effect can be expressed in heliotrons in terms of ICRF heating power, plasma density and magnetic field strength. Results in plasmas at CHS show a systematic decrease of the global energy confinement time due to energetic ion loss from the assumed energy confinement scaling law, which is consistent with the experimental observations. The model is also applied to ICRF minority heating in LHD plasmas in two cases of typical magnetic configurations. A clear increase of the global energy confinement time due to the stored energy of energetic tail ions is obtained in the `orbit improved' configuration, while a decrease is observed in the `standard' configuration.

Profile control for steady-state operation

Large departures from standard L-mode confinement scaling laws are now being observed in most tokamaks which appear promising for relaxing the plasma current constraint and therefore open the route to high-performance steady-state operation with high bootstrap current fraction. Prospects of the weak or reversed magnetic shear scenarios for steady-state tokamak operation are presented in the light of recent experimental progress to control pressure and current profiles with the combined use of various heating and current drive schemes. Implications of the present experiments on the modelling of future non-inductive operation in existing tokamaks and in ITER are addressed.

Experimental scaling of fluctuations and confinement with Lundquist number in the reversed-field pinch

The scaling of the magnetic and velocity fluctuations with Lundquist number (S) is examined experimentally over a range of values from 7×104 to 106 in a reversed-field pinch (RFP) plasma. Magnetic fluctuations do not scale uniquely with the Lundquist number. At high (relative) density, fluctuations scale as b̃∝S−0.18, in agreement with recent numerical results. Fluctuations are almost independent of S at low (relative) density, b̃∝S−0.07. The range of measured exponents is narrow and is in clear disagreement with theories predicting b̃∝S−1/2. At high relative density, the scaling of the energy confinement time follows expectations for transport in a stochastic magnetic field. A confinement scaling law (nτE∝β4/5⋅T−7/10⋅a−3/5⋅Iφ2) is derived, assuming the persistent dominance of stochastic magnetic diffusion in the RFP and employing the measured scaling of magnetic fluctuations. The peak velocity fluctuations during a sawtooth cycle scale marginally stronger than magnetic fluctuations but weaker than a simple Ohm’s law prediction. The sawtooth period is determined by a resistive-Alfvénic hybrid time (Tsaw∝τRτA) rather than a purely resistive time.

Consequences of core and edge similarity for experiments

The role of similarity parameters for core and edge phenomena in tokamaks, and the possibility to use sets of matching discharges on different devices under identical dimensionless parameters are discussed. Such experiments, carried out so far have show that the Kadomtsev set of dimensionless parameters is well suited to describe global confinement, and also the L-to-H transition phenomenon, at least in the intermediate density regime. The comparison of the existing empirical data base for the observed density limit in tokamaks with the prediction of similarity laws suggest a role of finite-β effects in the explanation of this phenomenon. Finally we discuss the possibility to simulate the interference between confinement scaling laws and operating boundaries in similarity experiments.

Analysis of Convective Heat Losses in JT-60U Neutral Beam Injection Experiments

The role of convective heat losses in tokamak plasmas is studied analytically and numerically. One of the natural forms of the energy confinement scaling law is suggested. The ion temperature limit in the steady-state neutral beam injection discharges caused by convective heat losses is obtained. A new technique for the determination of convective heat losses from experimental measurements is applied to the analysis of a JT-60U NBI discharge. The particle source and convective heat losses calculated directly from the experimental data are in a good agreement with ASTRA calculations. The convective heat loss obtained from the data is about 50% of the absorbed NB power.