Tokamak Research Articles

Toroidal vs cylindrical analytical description of the magnetic field outside the elongated evolving plasma in tokamaks

In the plasma equilibrium theory, Gajewski's analytical expression [Gajewski, Phys. Fluids 15, 70 (1972)] for the poloidal magnetic flux ψ outside the plasma is known. It was obtained as a solution of the two-dimensional Laplace equation outside an infinite straight cylinder with an elliptical cross section and a uniform current density j ζ. An example of its use for analysis of static configurations is given in the study by Porcelli and Yolbarsop [Phys. Plasmas 26, 054501 (2019)]. Here, we consider the question of its applicability in dynamic problems including, for example, the current quench (CQ) or vertical displacement event (VDE), when the electromagnetic response of the vacuum vessel to the plasma magnetic field evolution has to be accounted for. It is shown that the mentioned cylindrical model does not provide enough information for calculation of the current induced in the wall. Mathematically, this manifests itself in the fact that Gajewski's expression contains an indefinite constant of integration ψ b (hereinafter it is ψ at the plasma boundary), which, in analytical applications, is replaced either by zero or by a value that makes ψ = 0 on the magnetic axis. This does not affect the magnitude of the magnetic field B, but it would incorrectly give the electric field at ∂ B / ∂ t ≠ 0. To eliminate this shortcoming, an additional block of calculations in the toroidal geometry is needed. Here, the problem is solved analytically. The resulting final expression with ψ b well-defined in the toroidal configuration also includes the effects of the Shafranov's shift and inhomogeneity of j ζ. The proposed extensions allow generalization of the earlier results to a wider area and cover such events as CQ or VDE.

Core-localized toroidal Alfvén eigenmodes in spherical tokamaks

Spherical Tokamaks (STs) with a high normalised plasma pressure parameter βT are promising alternative pathways for net gain magnetic fusion reactors. Toroidal Alfvén eigenmodes (TAEs) excited via wave-particle resonances by fusion-born alpha-particles are of major concern for burning deuterium-tritium (D-T) plasmas in magnetic fusion as AEs cause a radial re-distribution of alpha-particles affecting their plasma heating efficiency and causing alpha-losses to the first wall. Tokamak plasmas with high pressure gradients were found to suppress toroidally induced Alfvén eigenmodes (TAEs) in ideal incompressible MHD and the high plasma βT attained by STs is expected to facilitate access to these TAE-free regimes. However, the low magnetic shear inherent to STs can lead to the formation of multiple AEs, which may increase transport due to the larger resonance area of the alpha-particle phase space. A suite of MHD codes HELENA, MISHKA and CS_MISH are used to investigate the discrete AE spectrum in high-pressure STs in the current paper. TAEs for an experimental ST40 magnetic equilibrium are computed and through varying βT and the current density profile the suppression of TAEs is investigated. The critical βT (above which no TAE modes are found) is shown to decrease with increased ellipticity, increased toroidal field (relative to a fixed plasma current) and a flatter current density profile. Despite the increase in the number of core-localised TAEs at low magnetic shear, the modes appear more sensitive to increases in βT and disappear at lower thresholds.

SITAR: A Code for ICRH Antenna–Plasma Coupling

We have developed an ICRF (ion cyclotron range of frequency) heating antenna code, SITAR (Simulation of ICRH anTennA Resistance), for stripline antenna to find out its impedance in the presence of plasma. The antenna is of finite poloidal and toroidal dimensions and screened from the plasma by the Faraday shield that shorts out the toroidal components of the radio frequency field. Antenna lead current as well as toroidal and poloidal current of antenna have been taken into account. A slab geometry model for coupling of antenna with tokamak plasma and a linear model of the perpendicular refractive index for the propagation of ICRF wave in the evanescent region have been considered. The plasma in the coupling region is described by a cold plasma dielectric tensor with nonuniform density and toroidal magnetic field along the radial direction.

On the impact of electric field fluctuations on microtearing turbulence

The magnetic drift and the electric potential play an important role in microtearing destabilization by increasing the growth rate of this instability in the presence of collisions, while in electrostatic plasma micro-turbulence, zonal electric potentials can have a strong impact on turbulent saturation. A reduced model has been developed, showing that the Rechester–Rosenbluth model is a good model for the prediction of electron heat diffusivity by microtearing turbulence. Here, nonlinear gyrokinetic flux-tube simulations are performed in order to compute the characteristics of microtearing turbulence and the associated heat fluxes in tokamak plasmas and to assess how zonal flows and zonal fields affect saturation. This is consistent with a change in saturation mechanism from temperature corrugations to zonal field- and zonal flow-based energy transfer. It is found that removing the electrostatic potential causes a flux increase, while linearly stabilization is observed.

Observation of tearing mode triggering by sawtooth crash with high-Z impurity accumulation in EAST

The high-Z impurity accumulation in the plasma core could degrade the plasma performance and may affect sawtooth crash and trigger tearing modes (TMs) in experimental advanced superconducting tokamak (EAST). Triggering of m/n = 3/2 TM (m and n are the poloidal and toroidal mode numbers, respectively) and m/n = 2/1 TM by a large sawtooth crash is observed and studied under the condition of high-Z impurity accumulation in core plasma in EAST tokamak. This work mainly focuses on the relationship among impurity, sawtooth crashes, and TMs. When there is a certain amount of impurity in the plasma core, sawtooth crash leads to impurity transport, resulting the changes in impurity concentration, and by inducing the density perturbation near the rational surface, TMs become destabilized. The experimental analyses indicate that the outward impurity transport after a sawtooth crash plays an important role in the destabilization of TMs.

Development of electromagnetic pellet injector for disruption mitigation of tokamak plasma

Disruption remains to be a serious threat to large tokamaks like the International Thermonuclear Experimental Reactor (ITER). The injection speed of disruption mitigation systems (DMS) driven by high pressure gas is limited by the sound speed of the propellant gas. When extrapolating to ITER-like tokamaks, long overall reaction duration and shallow penetration depth due to low injection speed make it stricter for plasma control system to predict the impending disruptions. Some disruptions with a short warning time may be unavoidable. Thus, a fast time response and high injection speed DMS is essential for large scale devices. The electromagnetic pellet-injection (EMPI) system is a novel massive material injection system aiming to provide rapid and effective disruption mitigation. Based on the railgun concept, EMPI can accelerate the payload to over 1000 m/s and shorten the overall reaction time to a few milliseconds. To verify the injection ability and stability of the EMPI, the prototype injector EMPI-1 has been designed and assembled. The preliminary test has been carried out using a 5.9 g armature to propel a dummy pellet and the results suggest that the EMPI configuration has a great potential to be the DMS of the large scale fusion devices.

Tokamak and ITER plasma with the Quantum Alfven waves

The hydrodynamical model of quantum mechanics based on the Schrodinger equation is combined with the magnetohydrodynamical term to form so called quantum magnetohydrodynamic equation. It is shown that the quantum correction to the Alfven waves follows from this new equation. The possible generalization is considered for the so called nonlinear Schrodinger equation and for the situation where dissipation is described by the Navier-Stokes equation.

Plasma diagnostics using fast cameras at the GOLEM tokamak

Tomographic inversion of radiation determines spatial distribution of tokamak plasma radiation sources using line integrated plasma projections data. For measurements of the projections, fast visible radiation matrix cameras became broadly applied on tokamaks in recent past. These novel cameras opened new possibilities in high temperature plasma studies.The GOLEM tokamak of the Czech Technical University in Prague strives to implement up-to-date diagnostics with enhanced temporal and spatial resolution. Therefore, a novel diagnostic system of two crossed monochrome cameras Photron FASTCAM MINI UX50 was integrated into the GOLEM diagnostics. The proposed contribution will detail their novel port mounts (vertical and horizontal) at the GOLEM tokamak which have been designed so that additional optical measurements of the plasma core (e.g. plasma spectroscopy) is possible.As the main purpose of this study, we shall focus in particular on the frame rate potential which is high enough to make detection and observation of highly transient phenomena in the GOLEM plasmas possible. Progress in solving specific challenges of the ill-conditioned tomographic inversion via the algorithm optimization and testing for the GOLEM tokamak will be presented together with the first tomographic results.

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.

The IAEA DEMO Programme Workshop Series: 2012–2021 report

The IAEA DEMO Programme Workshop Series was initiated to be the reference forum to debate, evaluate and establish the next steps to be taken within the international fusion community to deliver fusion as a reliable source of clean energy. The DEMO programme refers predominantly to a future magnetic confinement Tokamak design concept, after the ITER project, with a goal of delivering electricity to the grid. To enable this, the programme workshop series provides a unique frame where the discussion and analysis of the progress and findings of the various DEMO programmes, and not just the presentation of results being the major goals. More recently, due to the construction development of ITER, the workshop has also provided a forum to bring together the fusion community and industry. This is an important development for DEMO programmes, which will be more reliant on industry given their focus on devices proximate to a commercial fusion power plant. In this paper a summary of all editions of this workshop (2012–2013–2015–2016–2018–2019) up to 2021 are summarized. Topics addressed are listed and findings and open questions pointed out for each edition.

FERMI: Fusion Energy Reactor Models Integrator

The Fusion Energy Reactor Models Integrator (FERMI) is an integrated simulation environment under development for the coupled simulation of the plasma, first wall, and blanket of fusion reactor designs. The FERMI goals are to shorten the overall design cycle while guaranteeing unprecedented accuracy, thus integrating fusion design activities, facilitating an optimal reactor design, and reducing development risks. These goals are achieved by coupling single-physics solvers into a multiphysics simulation environment (FERMI). The Integrated Plasma Simulator (IPS)–FASt TRANsport (IPS-FASTRAN) simulation framework is used for the following: plasma physics, MCNP/Shift codes for neutron and photon transport, OpenFoam for computational fluid dynamics and magnetohydrodynamics (MHD), HyPerComp Incompressible MHD solver for Arbitrary Geometry (HIMAG) for dual-coolant lead-lithium (DCLL) blankets, and DIABLO for structural mechanics simulations. These codes are coupled using the open-source library named precise Code Interaction Coupling Environment (preCICE). FERMI’s features are tested with the analysis of the liquid immersion blanket (LIB) [proposed in the Affordable Robust Compact (ARC)–class tokamak design], the DCLL blanket [proposed in the Fusion Pilot Plant (FPP) design], and other benchmark cases. The calculated figures of merit are the tritium breeding ratio, material activation, displacements per atom, shutdown dose rate, heat deposited in the vacuum vessel and blanket, temperature hot spots, and displacements caused by swelling and creep. A critical technical problem is multiphysics code coupling, which is tackled here, and the first three-dimensional (3D) simulations of the DCLL-FPP and LIB-ARC blankets are presented. To the authors’ knowledge, FERMI represents the first effort to perform 3D simulations of nuclear fusion first wall and blankets in a fully coupled multiphysics manner.

Coherent mode induced by supersonic molecular beam injection in EAST Ohmic plasmas

A coherent mode (CM) induced by the supersonic molecular beam injection (SMBI) was observed in Ohmic plasmas of EAST tokamak. The CM existed in the spectra of the electron temperature fluctuation and density fluctuation, but not in the spectrum of Mirnov fluctuation. The radial location of the CM was about 10 cm inside the separatrix (normalized minor radius ). In most cases, the CM has multiple discrete frequencies between with an interval of ∼1 kHz. Occasionally, there is only one dominant frequency. The poloidal scale of the CM (poloidal wavenumber , poloidal mode number ) is between that of typical ion turbulence and macroscopic magnetohydrodynamic activities. Statistical analysis results suggest that the onset of the CM requires a high temperature gradient and a relatively low density gradient. Furthermore, the transport analysis shows that the SMBI-caused perturbation propagates inward faster in plasmas with stronger CM, which implies that the CM might be correlated to a high local transport level. However, the impact of the CM on macroscopic plasma parameters including stored energy, energy confinement time, and SMBI-caused mean density fluctuation is too weak to be found in comparison with the random fluctuation and the measurement errors, which suggests that the CM does not have a clear influence on the global confinement.

Global linear stability analysis of kinetic trapped ion mode (TIM) in tokamak plasma using the spectral method

Trapped ion modes (TIMs) belong to the family of ion temperature gradient (ITG) modes, which are one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis by considering the magnetic flux ψ dependency of the equilibrium Hamiltonian in both the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function . Using this spectral method, linear growth rates of TIM instability in the presence of different temperature profiles and precession frequencies of trapped ions, with an approximated constant Hamiltonian and the exact ψ dependent equilibrium Hamiltonian, are investigated. The growth rate depends on the logarithmic gradient of temperature κ T , density κ n and equilibrium Hamiltonian . With the exact ψ dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with an approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with good accuracy. This spectral method is very fast and requires much less computation resources compared to a linear version of the Vlasov-solver based on a semi-Lagrangian scheme.

Divertor optimisation and power handling in spherical tokamak reactors

A key aspect in the design of a spherical tokamak reactor is the optimisation of the plasma equilibrium, together with a compatible divertor configuration, and the corresponding poloidal field system. This is a complex multi-disciplinary problem, integrating plasma physics and engineering in order to satisfy a multitude of often conflicting requirements and constraints. The equilibrium design process employed in this work takes into account the reference plasma operating scenario, the power exhaust solution, and the engineering limits.Managing the heat exhaust proves to be one of the most challenging issues in a compact device such as the UKAEA STEP reactor. With a smaller major radius, the available target area over which the scrape-off layer heat load must be deposited is relatively small as compared to conventional aspect ratio devices. Consequently, alternative and advanced divertor concepts need to be considered, having significant implications for the whole reactor design. Here we address the inner divertor power handling challenges. With very limited inboard space, and the small radius of the inner strike point, the associated heat loads are likely to exceed the power handling capacity of standard divertors (SD). An alternative divertor configuration approaching an X-divertor (XD), created by inducing a secondary X-point near the inner strike point, is compared with an SD configuration optimised for the maximal connection length and maximal poloidal flux expansion. The inner X-divertor, simultaneously achieving strong poloidal flux expansion, increased connection length and higher divertor volume, proved to be advantageous in reducing target heat loads and favouring detachment. Amongst a number of viable exhaust solutions considered, the inner-X divertor is indeed emerging as a promising candidate.

Enhancement of neoclassical impurity density up/down asymmetry and Pfirsch–Schlüter transport due to the plasma elongation in the tokamak plasmas

The standard neoclassical theory of the impurity transport in tokamak plasma is improved by including the plasma elongation effect. The neoclassical up/down asymmetry of the impurity density is largely enhanced by the plasma elongation and is under-predicted by the neoclassical theory with the circular cross section assumption. Accordingly, the impurity Pfirsch–Schlüter neoclassical transport is also enhanced by the plasma elongation.

Nonlinear second order electromagnetic gyrokinetic theory for a tokamak plasma

The steep plasma pressure gradient that forms at the edge of the high confinement, H-mode regime of tokamak operation provides free energy to drive electromagnetic micro-instabilities that are widely believed to influence the transport processes in this so-called pedestal region. This high pressure gradient also provides a high current density (bootstrap current), known to influence ballooning mode stability and to be important for driving kink modes in the ideal magneto-hydrodynamic plasma model (so-called peeling-ballooning modes). Furthermore, efficient, steady state future tokamak power plants must operate with a large bootstrap current in the core and especially concerning spherical tokamaks, confinement will be influenced by electromagnetic turbulence. To accommodate these important situations, conventional electromagnetic gyrokinetic theory is extended to incorporate neoclassical effects in the equilibrium drives, allowing (B 0 is the confining magnetic field, and B ϑ is its poloidal component). This provides a global gyrokinetic model that self-consistently captures the consequences of large bootstrap current fractions on the equilibrium distribution functions.

Peaking and hollowness of low-Z impurity profiles: an interplay between ITG and TEM induced turbulent transport

The transport of low-Z impurities in fusion plasmas is dominated, in many regimes of interest, by ion temperature gradient (ITG) and trapped electron mode (TEM) turbulence. We use a statistical test-particle approach to analyze the effects of these drift instabilities on the transport coefficients. It is found that the convection of motion by the polarization drift drives an outward radial pinch via ITG and an inward pinch via TEM turbulence. Opposite radial pinches are driven by turbulent motion along magnetic field-lines. The interplay between these effects can explain the co-existence of peaked and hollow impurity density profiles observed in tokamak plasmas. The theoretical framework is validated through comparison with experimental data on the transport of Boron impurities.

First 3D modelling of tungsten erosion and migration in WEST discharges adopting a toroidally non-symmetric wall geometry

Numerical analysis is a useful tool to investigate tungsten (W) sources and transport across plasma in W Environment Steady state Tokamak (WEST) plasma discharges, as it highlights physical mechanisms not always directly observable in experiments. Modelling activities were performed to study W erosion from WEST plasma-facing components (PFCs), as well as W migration through the plasma. For the first time, it was adopted a toroidally asymmetric wall geometry consisting of toroidally localized objects representing WEST antennas. To simulate WEST boundary plasma, 3D non-axisymmetric SOLEDGE transport simulations were performed with simplifying assumptions (pure deuterium plasma, a fluid model for neutrals). Results were then used as background for ERO2.0 runs to model W migration. On the sides of the toroidally localized objects, two thin stripes modelled WEST W antenna protections. Simulations suggest that particles eroded from the antennas protections may dominate the core W contamination in the analysed wall configuration. The findings suggest that these 3D non-axisymmetric models may be needed on a broader range of plasma conditions and wall configurations to accurately model the W migration in WEST.

Integrated deep learning framework for unstable event identification and disruption prediction of tokamak plasmas

The ability to identify underlying disruption precursors is key to disruption avoidance. In this paper, we present an integrated deep learning (DL) based model that combines disruption prediction with the identification of several disruption precursors like rotating modes, locked modes, H-to-L back transitions and radiative collapses. The first part of our study demonstrates that the DL-based unstable event identifier trained on 160 manually labeled DIII-D shots can achieve, on average, 84% event identification rate of various frequent unstable events (like H-L back transition, locked mode, radiative collapse, rotating MHD mode, large sawtooth crash), and the trained identifier can be adapted to label unseen discharges, thus expanding the original manually labeled database. Based on these results, the integrated DL-based framework is developed using a combined database of manually labeled and automatically labeled DIII-D data, and it shows state-of-the-art (AUC = 0.940) disruption prediction and event identification abilities on DIII-D. Through cross-machine numerical disruption prediction studies using this new integrated model and leveraging the C-Mod, DIII-D, and EAST disruption warning databases, we demonstrate the improved cross-machine disruption prediction ability and extended warning time of the new model compared with a baseline predictor. In addition, the trained integrated model shows qualitatively good cross-machine event identification ability. Given a labeled dataset, the strategy presented in this paper, i.e. one that combines a disruption predictor with an event identifier module, can be applied to upgrade any neural network based disruption predictor. The results presented here inform possible development strategies of machine learning based disruption avoidance algorithms for future tokamaks and highlight the importance of building comprehensive databases with unstable event information on current machines.

Characterization of the peak temperature on upper W divertor target during D and He plasma discharges in EAST

• The peak temperature on observed targets during both D and He discharges increase with the increase of heating power. • During the same heating power, the peak temperature during D discharges is generally lower than that during He discharges no matter L and H modes. • The sharp temperature leap induced by ELM induced transient heat load during D discharges is usually 2 times higher than that during He discharges. During the tokamak plasma discharge, the strong interaction between the edge plasma and the wall material leads to the overheating of the surface of divertor target plate and the possible melting of the material, which will seriously influence the safe operation of the device. Furthermore, transient heat load induced by edge localized modes (ELMs) is expected to cause surface damage of tungsten (W) based plasma-facing materials (PFMs) in future fusion devices. In order to ensure safe steady-state operation, it is prerequisite to obtain the peak temperature as well as distribution on the divertor target plate in real time. In EAST, a high temporal and spatial resolution infrared camera (IR) located in H port was built to observe the outer target on the L port of upper W divertor. Currently, the maximum temperature measured by IR camera has been characterized and analyzed during deuterium (D) and helium (He) plasma discharges. In addition, the ELM-induced temperature rise during H mode operations for D and He plasma discharges was specially studied. It is found that the maximum temperature on observed targets during both D and He discharges increase with the increase of heating power. In case of the same heating power, the maximum temperature during D discharges is generally lower than that during He discharges no matter L and H modes, which is more obvious when the total heating power exceeds 3 MW. However, the sharp temperature rise by ELM induced transient heat load during D discharges is usually higher than that during He discharges. Such qualitative and statistical analysis on the maximum temperature on upper outer divertor provide important reference for future operation of EAST and other tokamaks..