Energy Confinement Time Research Articles

Start of experiments in the design configuration of the GOL-NB multiple-mirror trap

A multiple-mirror confinement is an alternative concept in fusion energy development that improves the particle and energy confinement times in open traps (linear magnetic systems). The paper discusses the development progress of the GOL-NB multiple-mirror experiment that was recently commissioned at BINP. The reference description of the GOL-NB hardware is presented. Properties of a low-temperature start plasma are discussed. The first results from test experiments with injection of one 25 keV neutral beam are shown. Methods of plasma stabilization in the non-min-B configuration are discussed. In general, the ongoing commissioning progress and results of the preliminary experiments are modestly optimistic for the expected device performance.

Core‐SOL simulations of high‐power JET‐ILW pulses fuelled with gas and/or with pellets

AbstractExperimental analysis of two couples of pulses in the range of input power of 26–32 MW, shows that addition of pellet throughput to high gas dosing pulses does not modify the plasma energy, but leads to better conditions as far as the tungsten concentration and core radiation are concerned. Significantly decreasing the gas dosing with addition of high pellet throughput causes the increase of plasma energy, but the W concentration increases from 5.2 × 10−5 to 6.9 × 10−5 and the core radiation from 7.5 to 11 MW. From the numerical results of the self‐consistent core‐SOL COREDIV code two mechanisms appear to be responsible for the observed different W concentrations: the core residence time of W, which is related to the energy and particle confinement time, and the divertor impurity screening efficiency, dependent on the electron density and on the perpendicular transport coefficient in the SOL.

An Unsupervised Spectrogram Cross-Correlation Method to Assess ELM Triggering Efficiency by Pellets

The high confinement mode (H-mode) is considered the optimal regime for the production of energy through nuclear fusion for industrial purposes since it allows to increase the energy confinement time of the plasma roughly by a factor of two. Consequently, it has been selected at the moment as the standard scenario for the next generation of devices, such as ITER. However, pressure-driven edge instabilities, known as edge localized modes (ELMs), are a distinct feature of this plasma regime. Their extrapolated thermal and particle peak loads on the plasma-facing components (PFC) of the next generation of devices are expected to be so high as to damage such structures, compromising the normal operations of the reactors themselves. Consequently, the induced loads have to be controlled; this can be achieved by mitigating ELMs. A possibility then lays in increasing the ELMs frequency to lower the loads on the PFCs. As already demonstrated at JET, the pellet pacing of ELMs is considered one of the most promising techniques for such scope, and its optimization is therefore of great interest for present and future operations of nuclear fusion facilities. In this work, we suggest a method to access primary pieces of information to perform statistics, assess and characterize the pacing efficiency. The method, tested on JET data, is based on the clustering (k-means) of convoluted signals, using so-called spectrogram cross-correlation, between the measured pellets and ELMs time traces. Results have also been obtained by taking advantage of a new type of diagnostic for measuring the ELMs dynamic, based on synthetic diamond sensors, faster than the standard spectroscopic cameras used at JET.

Transport hysteresis in electromagnetic microturbulence caused by mesoscale zonal flow pattern-induced mitigation of high β turbulence runaways

Electromagnetic microturbulence at finite normalized plasma pressure β=n0T0/(B02/2μ0) (n0 is the equilibrium density, T0 the equilibrium temperature, B0 the equilibrium magnetic field, and μ0 the permeability of free space) is investigated within a local gradient-driven gyrokinetic framework. The focus lies on the well-known high β turbulence runaways [R. E. Waltz, Phys. Plasmas 17, 072501 (2010)] that have been proposed to set a nonlinear upper threshold βc, also known as the nonzonal transition [M. J. Pueschel, Phys. Rev. Lett. 110, 155005 (2013)]. In this paper, it is shown that persistent mesoscale zonal flow patterns, developing self-consistently on long time scales, mitigate high β turbulence runaways. The application of such mesoscale zonal flow states as initial conditions allows for the access of an improved β-regime, that is, β>βc, in which no turbulence runaway occurs. Various aspects of those mesoscale zonal flow-dominated improved states are investigated, such as (i) the stability constraints with respect to the mesoscale zonal flow level for the triggering of turbulence runaways, (ii) the influence of mesoscale zonal flows on magnetic stochasticity [W. M. Nevins, Phys. Rev. Lett. 106, 065003 (2010)], and (iii) the transfer processes connected to the drive and damping of mesoscale zonal flows. This work implies that βc does not set the upper limit in the normalized plasma pressure for stationary operation, provided persistent mesoscale zonal flow patterns can develop. Since variations of β occur on the energy confinement time, which is large compared to the time required for mesoscale zonal flows to develop, the reported mesoscale zonal flow-dominated improved β-regime is expected to be the experimentally relevant branch. Furthermore, this work highlights the need for sufficiently long simulation time traces of at least a few ∼103 R0/vth,i (R0 is the major radius, and vth,i is the ion thermal velocity), also within kinetic electron frameworks, to capture non-negligible long-term dynamics.

Experimental confirmation of efficient island divertor operation and successful neoclassical transport optimization in Wendelstein 7-X

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.

Power balance in the smallest tokamak

The ion temperature of the smallest tokamak, the major radius of 0.1 m, is measured using Doppler broadening spectroscopy. Experiments are performed for helium discharge. Ion temperature Ti = 0.7eV is obtained from the Doppler broadened line spectrum of the helium ion. The electron temperature and density measured using line emission intensities of the helium atom are Te = 4.7eV and ne = 3.2 × 1018m−3. The major radius R0 = 0.11m and the minor radius a = 0.03m are obtained from magnetic measurements. Then, the energy flow from the electron to the ion is evaluated as well as ohmic heating and power losses due to atomic processes. The main loss channel for electron stored energy is conduction even though the tokamak is immersed in the residual neutral gas. Total energy confinement time τE = 2.3µs is determined from the power balance, which is comparable with that deduced from the neo-Alcator scaling law.

Explaining the lack of power degradation of energy confinement in wide pedestal quiescent H-modes via transport modeling

Wide pedestal quiescent H (WPQH)-mode is an attractive scenario for future burning plasmas as they operate without ELMs. WPQH is characterized by formation of a wider and higher pedestal (than quiescent H-mode), and broadband fluctuations in the pedestal. Unlike conventional H-modes, where the energy confinement time reduces with increasing heating power, the WPQH plasmas reported in this paper do not show power degradation of the energy confinement. As the injected neutral beam power was increased, reduced core (ρ ⩽ 0.45) transport calculated by transp, as well as increased core temperatures, pressure gradient and diamagnetic E × B shear rate were observed. The reduction in the heat transport and rapid decrease in the ion temperature gradient scale length suggest the formation of an ion internal transport barrier (ITB) that was accompanied by increased stored energy in the core. Quasilinear turbulent transport modeling using the trapped gyro Landau fluid (tglf) code was used to predict the ITB and its turbulence stability properties. By using profiles and equilibria produced by matching the transp transport fluxes with the tglf transport model within the tgyro transport solver, the energy confinement time captures the experimentally observed insensitivity to the increased P NBI. Linear stability analysis reveals that drift-wave instabilities in the core are stabilized by E × B shear, T i/T e ratio and Shafranov shift; the latter was found to have the strongest effect on the turbulence suppression at the highest heating level.

Considerations on Stellarator’s Optimization from the Perspective of the Energy Confinement Time Scaling Laws

The Stellarator is a magnetic configuration considered a realistic candidate for a future thermonuclear fusion commercial reactor. The most widely accepted scaling law of the energy confinement time for the Stellarator is the ISS04, which employs a renormalisation factor, fren, specific to each device and each level of optimisation for individual machines. The fren coefficient is believed to account for higher order effects not ascribable to variations in the 0D quantities, the only ones included in the database used to derive ISS04, the International Stellarator Confinement database. This hypothesis is put to the test with symbolic regression, which allows relaxing the assumption that the scaling laws must be in power monomial form. Specific and more general scaling laws for the different magnetic configurations have been identified and perform better than ISS04, even without relying on any renormalisation factor. The proposed new scalings typically present a coefficient of determination R2 around 0.9, which indicates that they basically exploit all the information included in the database. More importantly, the different optimisation levels are correctly reproduced and can be traced back to variations in the 0D quantities. These results indicate that fren is not indispensable to interpret the data because the different levels of optimisation leave clear signatures in the 0D quantities. Moreover, the main mechanism dominating transport, in reasonably optimised configurations, is expected to be turbulence, confirmed by a comparative analysis of the Tokamak in L mode, which shows very similar values of the energy confinement time. Not resorting to any renormalisation factor, the new scaling laws can also be extrapolated to the parameter regions of the most important reactor designs available.

On the role of density fluctuations in the core turbulent transport of Wendelstein 7-X

A recent characterization of core turbulence carried out with a Doppler reflectometer in the optimized stellarator Wendelstein 7-X (W7-X) found that discharges achieving high ion temperatures at the core featured an ITG-like suppression of density fluctuations driven by a reduction of the gradient ratio (Carralero et al 2021 Nucl. Fusion 61 096015). In order to confirm the role of ITG turbulence in this process, we set out to establish experimentally the relation between core density fluctuations, turbulent heat flux and global confinement. With this aim, we consider the scenarios found in the previous work and carry out power balance analysis for a number of representative ones, including some featuring high ion temperature. We also evaluate the global energy confinement time and discuss it in the context of the ISS04 inter-stellarator scaling. We find that when turbulence is suppressed as a result of a reduction of η i , there is a reduction of ion turbulent transport, and global performance is improved as a result. This is consistent with ITG turbulence limiting the ion temperature at the core of W7-X. In contrast, when turbulence is reduced following a decrease in collisionality, no changes are observed in transport or confinement. This could be explained by ITG modes being combined with TEM turbulence when the latter is destabilized at low collisionalities.

A Study of the Requirements of p-11B Fusion Reactor by Tokamak System Code

Most tokamak devices including ITER exploit the deuterium-tritium reaction due to its high reactivity, but the wall loading caused by the associated 14-MeV neutrons will limit the further development of fusion performance at high beta. To explore the p-11B fusion cycle, a tokamak system code is extended to incorporate the relativistic bremsstrahlung since the temperature of electrons approaches the electron rest energy. By choosing an optimum p-11B mix and ion temperature, some representative sets of parameters of the p-11B tokamak reactor, whose fusion gain exceeds 1, have been found under the thermal wall loading limit and beta limit when synchrotron radiation loss is neglected. However, the fusion gain greatly decreases when the effect of synchrotron radiation loss is considered. Helium ash also plays an important role in the fusion performance, and we have found that the helium confinement time must be below the energy confinement time to keep the helium concentration ratio in an acceptable range.

Overview of GLOBUS-M2 spherical tokamak results at the enhanced values of magnetic field and plasma current

The paper provides an overview of the results obtained on the spherical tokamak Globus-M2 in 2019–2020. The experiments were performed with the toroidal magnetic field up to 0.8 T and plasma current up to 0.4 MA (80% of the design values). The temperature of electrons 1 keV and ions 800 eV at the plasma density of 1020 m−3 were recorded at neutral beam injection (850 kW, 28.5 keV). Heat conductivity analysis was made by means of the codes ASTRA 7.0, NCLASS, SPIDER, NUBEAM, 3D fast ion tracking algorithm on the basis of the experimental data. A scaling for spherical tokamaks, which demonstrates strong τ E dependence on magnetic field and moderate dependence on plasma current, has been confirmed for the magnetic field up to 0.8 T. For Globus-M/M2 it is . The dependence of the normalized energy confinement time (B T τ E) on collisionality (ν*) in a wide range 0.02 < ν* < 0.2 was determined as . A non-inductively driven current was recorded during the launch of the electromagnetic waves of the lower hybrid frequency range (2.45 GHz) with the help of a toroidally oriented grill. The fraction of noninductively driven current has exceeded 70% in the discharge with a total current of 0.2 MA. The achieved values of efficiency η = (0.15–0.4) × 1019 A m−2 W−1 are comparable with the results obtained on conventional tokamaks. This paper presents the results of experiments on the study of Alfvén modes. The resulting scaling for the loss of fast ions caused by toroidal Alfvén eigenmodes demonstrates their decrease with increasing magnetic field and plasma current. Observation of Alfvén cascades made it possible to apply the method of MHD spectroscopy to determine the evolution of q min in a discharge. Also presented are the results of SOL investigation. Attention is also paid to the development of diagnostics.

Suppression of toroidal Alfvén eigenmodes by the electron cyclotron current drive in KSTAR plasmas

Advanced operation scenarios such as high poloidal beta (β P) or high q min are promising concepts to achieve the steady-state high-performance fusion plasmas. However, those scenarios are prone to substantial Alfvénic activity, causing fast-ion transport and losses. Recent experiments with the advanced operation scenario on KSTAR tokamak have shown that the electron cyclotron current drive (ECCD) is able to mitigate and suppress the beam-ion driven toroidal Alfvén eigenmodes (TAEs) for over several tens of global energy confinement time. Co-current directional intermediate off-axis ECCD lowers the central safety factor slightly and tilts the central q-profile shape so that the continuum damping in the core region increases. Besides, the rise of central plasma pressure and increased thermal-ion Landau damping contribute to TAE stabilization. While the TAEs are suppressed, neutron emission rate and total stored energy increase by approximately 45% and 25%, respectively. Fast-ion transport estimated by TRANSP calculations approaches the classical level during the TAE suppression period. Substantial reduction in fast-ion loss and neutron deficit is also observed. Enhancement of fast-ion confinement by suppressing the TAEs leads to an increase of non-inductive current fraction and will benefit the sustainment of the long-pulse high-performance discharges.

Effect of plasma parameter profiles on a thermonuclear reaction operation

The operation of a thermonuclear reactor on an alternative to D-T fuel (D-D, Cat-DD, D-3He, p-11B, p-6Li) requires a higher temperature of the fuel mixture and an increased plasma energy confinement time. It is shown that at a fixed power of thermonuclear reaction, an increase in the peaking of plasma parameters leads to a decrease in power, which is necessary to its addition heating. Moreover, the peaking of the plasma parameters leads to decrease of its radiation losses. All this reduces the requirements for the operating conditions of thermonuclear reactor. Keywords: thermonuclear reactor, alternative fuel, picking.

Влияние пространственного распределения параметров плазмы на работу термоядерного реактора

The operation of a thermonuclear reactor on an alternative to D-T fuel (D-D, Cat-DD, D−3He, p−11B, p−6Li) requires a higher temperature of the fuel mixture and an increased plasma energy confinement time. It is shown that at a fixed power of thermonuclear reaction, an increase in the peaking of plasma parameters leads to a decrease in power, which is necessary to its addition heating. Moreover, the peaking of the plasma parameters leads to decrease of its radiation losses. All this reduces the requirements for the operating conditions of thermonuclear reactor.

Energy confinement in the spherical tokamak Globus-M2 with a toroidal magnetic field reaching 0.8 T

The work presents the results of the energy confinement study carried out on the compact spherical tokamak Globus-M2 with a toroidal magnetic field as high as 0.8 T. A reproducible and stable discharge was obtained with the average plasma density (5–10) × 1019 m−3. Despite the increase in the magnetic field, the neutral beam injection (NBI) led to clear and reproducible transition to the H-mode accompanied by a decrease in the turbulence level at the plasma edge. NBI allowed effectively heat the plasma: electron and ion temperatures in the plasma core exceeded 1 keV. Compared to the previous experiments carried out with a toroidal magnetic field as high as 0.4 T plasma total stored energy was increased by a factor of 4. The main reason or this phenomenon is a strong dependence of the energy confinement time on the toroidal magnetic field in the spherical tokamak. It was experimentally confirmed that such kind of dependence is valid for ST with magnetic field up to 0.8 T. It has also been shown that the enhancement of the energy confinement in Globus-M2 with collisionality decrease is associated with an improvement of both electron and ion thermal insulation.

Simulating fusion alpha heating in a stellarator reactor

Gyrocenter following simulations of fusion born alpha particles in a stellarator reactor are preformed using the BEAMS3D code. The Wendelstein 7-X high mirror configuration is scaled in geometry and magnetic field to reactor relevant parameters. A m−3 density plasma with 20 keV core temperatures is assumed and fusion birth rates calculated for various fusion products assuming a 50/50 deuterium-tritium mixture. It is found that energetic He4 ions comprise the vast majority of the energetic particle inventory. Slowing down simulations of the He4 population suggest plasma heating consistent with scaled energy confinement times for a stellarator reactor. Losses for this configuration appear large suggesting optimization beyond the scope of the W7-X device is key to a future fusion reactor. These first simulations are designed to demonstrate the capability of the BEAMS3D code to provide fusion alpha birth and heating profiles for stellarator reactor designs.

Validation of a full-plasma integrated modeling approach on ASDEX Upgrade

In this work we present the extensive validation of a refined version of the integrated model based on engineering parameters (IMEP) introduced in reference (Luda et al 2020 Nucl. Fusion 60 036023). The modeling workflow is now fully automated, computationally faster thanks to the reduced radial resolution of the TGLF calculation, and it includes the modeling of the toroidal rotation, which was still taken from experimental measurements in our previous work. The updated model maintains the same accuracy as its previous version when tested on the cases presented in the initial publication. The confined plasma, from the magnetic axis to the separatrix, is simulated without using any experimental information from profiles measurements, and the inputs of IMEP are the same engineering parameters used when programming a plasma discharge. The model validation database consists of 50 ASDEX Upgrade (AUG) stationary (over a few energy confinement time) H-mode phases, which largely cover the entire AUG operational domain. The prediction of IMEP is compared with experimental measurements and with scaling laws, such as the IPB98(y,2), the ITPA20-IL, and AUG specific regressions. This modeling framework has proven to be very accurate over the entire set of 50 cases, with a significantly lower mean relative error with respect to each of the scaling laws considered, accurately reproducing the change in pedestal and core confinement caused by a change in plasma current, heating power, fueling rate, triangularity, magnetic field, NBI voltage (i.e. the effect of a change in the core particle source), and heating mix (e.g. correctly predicting the effect on confinement caused by a change in T e/T i). Plasma confinement is correctly described by IMEP also for two particular operating regimes, such as the ITER baseline scenario, and the QCE regime (quasi continuous exhaust, also referred as type-II and small ELMs). This work clearly demonstrates the power of this approach in pulling out physics mechanisms to interpret subtle interdependencies and that a 1D integrated model can reproduce experimental results over very large parameter variations with a higher accuracy than any statistical regression. This approach has therefore the potential to improve the prediction of the fusion performance in future tokamak reactors.

Robust real-time feedback algorithms for plasma kinetic control in advanced tokamak scenarios

Robust real-time control algorithms for tracking plasma kinetic parameters in advanced tokamak scenarios are developed based on linear state-space (LSS) dynamic models. The real-time control algorithms under study comprise the robust control, the linear quadratic integral control and the internal model control. The plasma models used in this work are restricted to LSS models identified from dedicated simulation/experimental data, though the proposed control algorithms can conveniently be extrapolated to broadly incorporate linear models obtained from first-principles plasma theory. The control objective is to track plasma kinetic parameters of interest to desired operating points in advanced tokamak scenarios by actuating additional heating & current drive systems in real-time. Plasma kinetic parameters involve the poloidal pressure parameter β p , the internal inductance , the average toroidal rotation angular speed and the electron temperature on axis while the actuators are the ion cyclotron resonance heating and lower hybrid current drive systems. In order to achieve enhanced control performance, two control layers are designed. The outer layer, i.e. an internal model-based proportional-integral actuator controller, operating on a fast timescale ( the energy confinement time τ E ) aiming at tracking the commands requested by the inner kinetic controllers, while the inner layer, i.e. a kinetic controller chosen from various alternatives, running on a slow timescale () is dedicated to tailoring plasma kinetic parameters. Simulation results for the experimental advanced superconducting tokamak (EAST) tokamak are provided and compared to show the capabilities of each control approach. Dedicated kinetic control experiments conducted in an H-mode scenario on EAST are reported as well. The advantages and limits of these control algorithms are discussed and summarised.

Scaling laws of the energy confinement time in stellarators without renormalization factors

The most widely accepted unified scaling law for the energy confinement time in stellarators is a power law that contains a normalization factor for each individual device (and even for each sufficiently different magnetic configuration in a single machine). In the last decade, new and very powerful data analysis tools, based on symbolic regression (SR) via genetic programming (GP), have become quite consolidated and have provided very interesting results for tokamak configurations. The first application of SR via GP to the largest available multimachine stellarator database permits us to relax the power law constraint as an alternative to the use of renormalization factors. This approach, implemented with well-understood model selection criteria for the fitness function based on information theory and Bayesian statistics, has allowed convergence on very competitive global scaling laws, which present exponential terms, but do not contain any renormalization coefficient. Moreover, the exploratory application of SR via GP has revealed that the two main types of magnetic topology, those with and without shear, can be much better interpreted using two different models. The fact that these new scaling laws have been derived without recourse to any renormalization increases their interpretative value and confirms the dominant role of turbulence in determining the confinement properties of the stellarator. On the other hand, the techniques developed emphasise the need to improve the statistical basis before drawing definitive conclusions and providing reliable extrapolations.

Gas-puff induced cold pulse propagation in ADITYA-U tokamak

Short bursts (∼1 ms) of gas, injecting ∼1017–1018 molecules of hydrogen and/or deuterium, lead to the observation of cold pulse propagation phenomenon in hydrogen plasmas of the ADITYA-U tokamak. After every injection, a sharp increase in the chord-averaged density is observed followed by an increase in the core electron temperature. Simultaneously, the electron density and temperature decrease at the edge. All these observations are characteristics of cold pulse propagation due to the pulsed gas application. The increase in the core temperature is observed to depend on the values of both the chord-averaged plasma density at the instant of gas-injection and the amount of gas injected below a threshold value. Increasing the amount of gas-puff leads to higher increments in the core-density and the core-temperature. Interestingly, the rates of rise of density and temperature remain the same. The gas-puff also leads to a fast decrease in the radially outward electric field together with a rapid increase in the loop-voltage suggesting a reduction in the ion-orbit loss and an increase in Ware-pinch. This may explain the sharp density rise, which remains mostly independent of the toroidal magnetic field and plasma current in the experiment. Application of a subsequent gas-puff before the effect of the previous gas-pulse dies down, leads to an increase in the overall electron density and consequently the energy confinement time.