Double Null Configuration Research Articles

Validating reduced models for detachment onset and reattachment times on MAST-U

Two reduced models for predicting detachment onset and divertor reattachment times are validated on MAST Upgrade (MAST-U). These models are essential for future tokamak reactor design, providing rapid calculations based primarily on engineering parameters. The first model predicts detachment onset using a qualifier developed on ASDEX Upgrade (AUG) and later tested on JET, while the second model provides an estimate for the time required for a given transient to burn through the neutral particles in the divertor. Experiments in H-mode plasma scenarios were conducted on MAST-U with double-null and single-null configurations, which involved D2 fuelling ramps and N2 seeding. The detachment onset was determined by monitoring divertor parameters, including the target heat flux profile, electron temperature, and electron density, with measurements showing consistency with AUG-derived predictions. Reattachment times were assessed during dynamic vertical shifts of the plasma centroid position, with observations indicating reattachment within milliseconds, consistent with model predictions. Overall, the results confirm the applicability of both reduced models to MAST-U, extending their validation beyond AUG and JET.

A simple and fast method to calculate the coil currents and the external poloidal flux and magnetic field for fixed boundary equilibria

A simple and fast method to calculate the coil currents and the external poloidal flux and magnetic field consistent with a given internal magnetohydrodynamic (MHD) equilibrium and coil geometry is presented. The constrained optimization technique employed allows to fix the exact position of the X-points. The external poloidal flux and field are calculated using Green’s functions expressed in terms of elliptic integrals that are calculated using a fast and accurate routine. The calculation can be limited to the region between the plasma and the device wall. An example for a double null configuration is presented.

Radiated power and soft x-ray diagnostics in the SMART tokamak.

A multi-energy soft x-ray diagnostic is planned to operate in the small aspect ratio tokamak (SMART), consisting of five cameras: one for core measurements, two for edge, and two for divertors. Each camera is equipped with four absolute extreme ultra-violet diodes, with three of them filtered by Ti and Al foils for C and O line emissions, respectively, and Be foils for temperature measurements. In addition, two spectrometers will be installed with a vertical line of sight for impurity control. This study introduces a synthetic model designed to characterize radiated power and soft x-ray emissions. The developed code extracts the radiated power and Zeff values by leveraging distributions of electron density, temperatures, and impurity concentrations. The investigation is centered on the predicted scenarios of SMART's first phase of operation (Ip = 100kA; Bt = 0.1T), employing a double-null configuration with positive and negative triangularity. The anticipated impurities encompass C (1%) and Fe (0.01%) from the vessel, as well as O and N (0.1%) from air and water. For simplicity, the distribution is assumed to be homogeneous within the plasma, considering different mixtures with Zeff values ranging between 1 and 2. Finally, the model estimates signal strength for the diagnostic design, proving its feasibility.

Plasma burn-mind the gap.

The programme to design plasma scenarios for the Spherical Tokamak for Energy Production (STEP), a reactor concept aiming at net electricity production, seeks to exploit the inherent advantages of the spherical tokamak (ST) while making conservative assumptions about plasma performance. This approach is motivated by the large gap between present-day STs and future burning plasmas based on this concept. It is concluded that plasma exhaust in such a device is most likely to be manageable in a double null (DN) configuration, and that high core performance is favoured by positive triangularity (PT) plasmas with an elevated central safety factor. Based on a full technical and physics assessment of external heating and current drive (CD) systems, it was decided that the external CD is provided most effectively by microwaves. Operation with active resistive wall mode (RWM) stabilization as well as high elongation is needed for the most compact solution. The gap between existing devices and STEP is most pronounced in the area of core transport, owing to high normalized plasma pressure in the latter which changes qualitatively the nature of the turbulence controlling transport. Plugging this gap will require dedicated experiments, particularly on high-performance STs, and the development of reduced models that faithfully represent turbulent transport at high normalized pressure. Plasma scenarios in STEP will also need to be such that edge localized modes (ELMs) either do not occur or are small enough to be compatible with material lifetime limits. The high current needed for a power plant-relevant plasma leads to the unavoidable generation of high runaway electron beam current during a disruption, where novel mitigation techniques may be needed. This article is part of the theme issue 'Delivering Fusion Energy - The Spherical Tokamak for Energy Production (STEP)'.

First SOLPS-ITER predictions of the impact of cross-field drifts on divertor and scrape-off layer conditions in double-null configuration of STEP

Introduction of cross-field drifts in SOLPS-ITER simulations of connected double-null plasmas in STEP with the ion ∇B×B drift towards the upper divertors was found to enhance the detachment of the inner divertors with decreased target densities and ion and heat fluxes, while simultaneously complicating the access to detachment in the outer lower divertor by increasing the target temperature and heat loads to levels above the engineering limits. The ∇B×B drift was observed to significantly affect the radial heat transport between the core and the scrape-off layer (SOL), altering the poloidal temperature and pressure profiles and, consequently, the poloidal conductive and convective heat transport in the SOL. As a result, up-down asymmetries of 52:48 and 58:42 biased towards the outer lower and upper inner divertors, respectively, were observed to arise in the unmitigated power entering the divertor regions, breaking the up-down symmetry seen in simulations without the drift terms and contradicting with earlier experimental observations on the low-field side. Moreover, the upstream electron density was found to decrease noticeably in the core and separatrix regions following the activation of the drifts due to an increased share of the neutrals arriving from D2 injections near the upper and lower X-points ionizing already in the private flux regions.

Investigation of performance enhancement by balanced double-null shaping in KSTAR

We report experimental observations on the effect of plasma boundary shaping towards balanced double-null (DN) configuration on the plasma performance in KSTAR. The transition from a single-null to a DN configuration resulted in improved plasma performance, manifested through changes in the pedestal region, decreased density, and core MHD activity variation. Specifically, the DN transition led to a wider and higher pedestal structure, accompanied by grassy edge-localized modes (ELMs) characteristics. The density decrease was a prerequisite for performance enhancement during DN shaping, increasing fast ion confinement. Optimizing the plasma near the core region was associated with the suppression of sawtooth instabilities and the occurrence of fishbone modes during the DN transition. Integrated modeling demonstrated that secondary effects of the DN shaping could increase core thermal energy confinement.

The investigation of the neutronic responses of components in the K-DEMO

The neutronic response of consisting materials of the Korean fusion DEMOnstration reactor (K-DEMO) in its fusion neutron environment is a crucial consideration factor from the conceptual design stage of the K-DEMO. Especially in the design of in-vessel components (IVCs) of the K-DEMO that are placed in the most extreme neutron irradiation field, neutronic damage of constituent components is a major limiting factor that determines the lifetime of IVCs. From the analysis of the neutronic response of IVCs of the K-DEMO, the neutron wall loading (NWL) related to the tritium breeding ratio and nuclear heating of IVCs can be quantified to assess the self-sufficient supply of tritium, and thermal energy transferred from fusion neutrons, respectively. The calculated NWL shows that the harmonizing design of the cooling configuration of each blanket segment with the corresponding NWL is critical thermos-hydraulic design issue for the efficient utilization of thermal energy in the blanket. Another finding is that the double null magnetic field configuration and related blanket configuration with a water-cooled pebble bed of the K-DEMO make a self-sufficient tritium supply challenging. The implicated lifetime of the first plasma-facing tungsten wall of the K-DEMO is around 2 full power years (FPY) in the severely neutron-irradiated region. For the reduced activation ferritic/martensitic steel layers in the blanket, the lifetime of it is estimated around 4 FPY in the inboard region. Based on the response analysis results of this study, optimization of the design of the K-DEMO will continue iteratively in the future.

SOLPS-ITER analysis of a proposed STEP double null geometry: impact of the degree of disconnection on power-sharing

To mitigate the issue of plasma exhaust in reactor scale tight aspect ratio tokamaks such as Spherical Tokamak for Energy Production (STEP), a double-null (DN) configuration is thought to be advantageous over a single-null (SN) configuration. However, practical control of the plasma vertical stability will likely lead to an oscillation around the symmetry point, which may lead to transient loading of the divertors. In this work we investigated the impact of disconnection of the two separatrices on the power-sharing between the divertors in disconnected-double-null configurations for the initial iteration of STEP design using the SOLPS-ITER code without drifts. The power fraction to the primary divertor increased with , reaching ∼95% at the highest which is representative of SN. The total power fraction to the inner divertors (upper + lower), however, did not show an increase with for , where λ q is the parallel heat flux decay length, and even at the highest it showed only ∼30% increase from connected-double-null (CDN), unlike the experimental results for current conventional aspect ratio machines. We found two underlying mechanisms that could explain this result—the total flux compression from the outer midplane to the primary inner divertor target and the parallel current in the primary SOL (between the two separatrices). This work implies that the benefit of DN over SN in power load onto the inner divertor in STEP may be less than found experimentally in conventional tokamaks due to its tight aspect ratio. Further investigations through experiments, especially on STs and simulations with additional physics such as drifts, are the subject of a future investigation.

Multiphysics Modeling of Impurity Transport for FNSF Startup Scenario with ERO2.0

This study focuses on performing a multiphysics study using the ERO2.0 and UEDGE codes for two standard double null configurations for the Fusion Nuclear Science Facility: (a) 100% recycling and (b) 99% recycling. Results show that the main contributor to tungsten erosion along the divertor plates is impurities from the midplane waveguides. In addition, the standard high-recycling case (100% recycling) shows a significantly higher buildup of impurities along the divertor tiles during the startup phase, which can lead to a higher increase of energy loss in the plasma during steady-state operation. Last, for high recycling, anomalous diffusion can dominate over parallel field diffusion. The work performed in this study can be iteratively applied to a full operation scenario with additional physics such as those from neutrals, wall shaping, and additional external fields.

The GBS code for the self-consistent simulation of plasma turbulence and kinetic neutral dynamics in the tokamak boundary

A new version of GBS (Ricci et al. (2012) [27]; Halpern et al. J. Comput. Phys. 315 (2016) 388-408; Paruta et al. (2018) [11]) is described. GBS is a three-dimensional, flux-driven, global, two-fluid turbulence code developed for the self-consistent simulation of plasma turbulence and kinetic neutral dynamics in the tokamak boundary. In the new version presented here, the simulation domain is extended to encompass the whole plasma volume, avoiding an artificial boundary with the core, hence retaining the core-edge-SOL interplay. A toroidal coordinate system is introduced to increase the code flexibility, allowing for the simulation of arbitrary magnetic configurations (e.g. single-null, double-null and snowflake configurations), which can also be the result of the equilibrium reconstruction of an experimental discharge. The implementation of a new iterative solver for the Poisson and Ampère equations is presented, leading to a remarkable speed-up of the code with respect to the use of direct solvers, therefore allowing for efficient electromagnetic simulations that avoid the use of the Boussinesq approximation. The self-consistent kinetic neutral model, initially developed for limited configurations, is ported to the magnetic configurations considered by the present version of GBS and carefully optimized. A new MPI parallelisation is implemented to evolve the plasma and neutral models in parallel, thus improving the code scalability. The numerical implementation of the plasma and neutral models is verified by means of the method of manufactured solutions. As an example of the simulation capabilities of the new version of GBS, a simulation of a TCV tokamak discharge is presented.

Linear simulation of magnetohydrodynamic plasma response to three-dimensional magnetic perturbations in high-β P plasmas

We report the numerical analyses of the linear magnetohydrodynamics (MHD) plasma response to applied three-dimensional magnetic perturbations (MPs) in a joint DIII-D/EAST collaboration on high-β P (poloidal beta) plasmas, utilizing the extended-MHD code M3D-C1, with the purpose of gaining a better understanding of the existing experiment in which n = 3 MPs were applied to such high-β P plasmas attempting to control large-amplitude type-I edge-localized modes (ELMs). These high-β P plasmas obtained at the DIII-D tokamak feature an upper-biased double-null configuration, a high edge safety factor q 95 ∼ 6.4, and a stable internal transport barrier (ITB), leading to relatively high core pressures. Single-fluid simulations show that the plasma response to n = 3 MPs, including both non-resonant/kinking and resonant components, is significantly weaker than that to n = 1 or 2 MPs. To survey the impact of q 95 on the plasma response to applied MPs, the self-consistent equilibrium-generating workflow for analysis module, developed in the OMFIT integrated modeling framework, is employed to generate a series of equilibria with a wide range of q 95, while other key parameters, including the normalized beta, electron density at the pedestal top, and plasma shape, are kept fixed. Compared to the vacuum response, single-fluid M3D-C1 simulations predict a much more significant decrease in resonant plasma response to the applied n = 3 MPs at the maximum penetration radii as q 95 increases. In contrast to single-fluid simulation results, showing that resonant penetration occurs only near the pedestal top where the E × B toroidal rotation frequency is zero, two-fluid simulations show two comparable resonant penetrations located near the pedestal top and the ITB foot, where the perpendicular electron rotation frequency is zero. Such resonant field penetration near the ITB foot may be responsible for the observed formation of a staircase structure in both the electron density and temperature profiles, and thereby a considerable deterioration in the global plasma performance, when MPs are applied in high-β P plasmas. Motivated by this numerical work, we provide some ideas for future research, with the purpose of realizing effective ELM control in such high-β P plasmas in the DIII-D and EAST devices.

INGRID: An interactive grid generator for 2D edge plasma modeling

A fusion boundary-plasma domain is defined by axisymmetric magnetic surfaces where the geometry is often complicated by the presence of one or more X-points; and modeling boundary plasmas usually relies on computational grids that account for the magnetic field geometry. The new grid generator INGRID (Interactive Grid Generator) presented here is a Python-based code for calculating grids for fusion boundary plasma modeling, for a variety of configurations with one or two X-points in the domain. INGRID first performs partitioning over the domain consisting of a small number of patches conforming to the magnetic field and wall geometry; then it generates a subgrid on each of the patches and joins them into a global grid. This domain partitioning strategy makes possible a uniform treatment of various configurations with one or two X-points in the domain. This includes single-null, double-null, and other configurations with two X-points in the domain. The INGRID design allows generating grids either interactively, via a parameter-file driven GUI, or using a non-interactive script-controlled workflow. Results of testing demonstrate that INGRID is a flexible, robust, and user-friendly grid-generation tool for fusion boundary-plasma modeling. Program summaryProgram Title: INGRID: Interactive Grid Generator for Tokamak Boundary RegionCPC Library link to program files:https://doi.org/10.17632/w3hbdgbndk.1Developer's repository link:https://github.com/LLNL/INGRIDLicensing provisions: MITProgramming language: PythonNature of problem: Modeling of tokamak boundary edge plasma physics is essential for the design and optimization of future fusion reactors. A crucial component of certain edge transport modeling codes is the computational grid representing the magnetic topology and plasma facing components within a tokamak. Generation of grids can be a tedious process that requires frequent intervention from the user of the grid generator. Despite their importance, robust simple-to-use grid-generation tools are nonexistent. The creation of a grid generator capable of both modeling and automatically identifying advanced divertor configurations is of great importance.Solution method: INGRID utilizes user-provided MHD equilibrium data and the target plates and limiter geometry to automatically identify magnetic topology, and generate the appropriate computational grid in block structured manner. First, the magnetic topology identification algorithm decides how the computational domain is partitioned. Within each partition, a local subgrid is generated which is used to construct the global grid ready for export.

Design and feasibility of breeding blanket vertical segment-based architecture

A design integration study (KDII4) was conducted in the DEMO Pre-Concept Design Phase with the primary goal to develop a pre-concept feasibility design and concept of operation for the Vertical Blanket Segment Architecture. The primary goal was to develop two workable variants for removal of large in-vessel components. This, prompted by two earlier studies, highlighting the integration challenge finding a self-consistent DEMO design point (KDII) and secondly the complexity of operation required to ensure compatibly with the proposed port-based maintenance schemes. Initially, only a single null (SN) divertor configuration was considered, but due to additional identified issues and technical challenges centred on the extraction of the BB segments, a double null (DN) alternative variant has also been investigated. This was prompted by other KDII's studies, especially KDII1 (Design, performance and feasibility of wall protection limiters during plasma transients) and KDII3 (Advanced Magnetic Configurations). Alternative forms of vertical maintenance architecture have been investigated by breaking down the study into Ports, In-vessel Components, Operations and Safety. SN and DN configurations were studied with split and full blankets numbering seven variants in total. Each variant was studied in some detail, comparatively assessing each on its merits. However, no viable solution has been found for down-selection. Nevertheless, the question of vertical maintenance is now better understood. This paper will describe the findings of KDII4 in conjunction with the Remote Maintenance (RM) technology work package, which suggests that the current ‘reference’ design envelope available for RM is too constrained.

Influence of rotation on axisymmetric plasma equilibria: double-null DTT scenario

We study the influence of toroidal plasma rotation on some relevant tokamak equilibrium quantities. The Grad–Shafranov equation generalised to the rotating case is analytically solved employing two different representations for the homogenous solution. Using an expression in terms of polynomials, we describe the separatrix shape by a few geometrical parameters, reproducing different plasma scenarios such as double-null and inverse triangularity. In this setting, the introduction of toroidal rotation corresponds to variations on relevant plasma quantities, most notably an enhancement of the poloidal beta. Using a more general expression in terms of Bessel functions, we reconstruct the full plasma boundary of the double-null configuration proposed for the upcoming Divertor Tokamak Test experiment, demonstrating how said configuration is compatible with different values of the plasma velocity.

Single and double null equilibria in the SMART Tokamak

The SMall Aspect Ratio Tokamak (SMART) device is a novel, compact (R geo = 0.42 m, a = 0.22 m, A ≥ 1.70) spherical tokamak, currently under development at the University of Seville. The SMART device is being developed over 3 phases, with target on-axis toroidal magnetic fields between 0.1 ≤ B ϕ ≤ 1.0 T, and target plasma currents of between 35 ≤ I p ≤ 400 kA; with phases 2 and 3 enabling access to a wide range of elongations (κ ≤ 2.30) and triangularities ( − 0.50 ≤ δ ≤ 0.50). SMART employs four internal divertor coils with two internal and two external poloidal field coils, enabling operation in lower-single, upper-single and double-null configurations. This work examines phase 3 of the SMART device, presenting a prospective L-mode discharge scenario without external heating, before examining five highly-shaped equilibria, including: two double null triangular configurations, two single null triangular configurations and a baseline double null configuration. All equilibria are obtained via an axisymmetric Grad-Shafranov force balance solver (Fiesta), in combination with a circuit equation rigid current displacement model (RZIp) to obtain time-resolved vessel and plasma currents.

Detachment in conventional and advanced double-null plasmas in TCV

Divertor detachment is investigated on the Tokamak à Configuration Variable (TCV) for conventional and alternative double-null (DN) magnetic geometries in L-mode, Ohmic density ramps and then compared to precisely matched single-null (SN) geometries. The poloidal flux expansion at the outer strikepoint(s) is varied by a factor 2 and the total flux expansion by 30% in lower single null (LSN) and DN configurations. Leg power sharing for DN and near-DN in attached conditions is in line with previous studies in other devices, with balanced power partition between upper and lower divertor achieved for |δR sep| ≲ λ q /2. This results in a reduction in the lower outer target integral and peak heat flux compared to a LSN by 30%. Unlike previous studies, λ q is fairly insensitive to δR sep. The detachment threshold in these geometries is investigated from target measurements with wall-embedded Langmuir probes and two-dimensional CIII line emissivity profiles across the two divertor regions. DN plasmas display clear benefits compared to their LSN counterparts. Transitioning from a LSN to DN shows a substantial reduction, of approx. 20%–25%, in the detachment threshold for the active divertor legs as well as a 50% higher radiated fraction at all . The density limit is simultaneously reduced in DN by 10%–20%. Across the explored range, poloidal flux expansion has only a small effect on the detachment threshold in LSN (as seen in previous experiments), and no effect in DN, with similar observations for the total flux expansion. In general, no strong benefits of increased poloidal or total flux expansion are observed across the explored range.

Magnetic equilibrium design for the SMART tokamak

The SMall Aspect Ratio Tokamak (SMART) device is a new compact (plasma major radius Rgeo≥0.40 m, minor radius a≥0.20 m, aspect ratio A≥1.7) spherical tokamak, currently in development at the University of Seville. The SMART device has been designed to achieve a magnetic field at the plasma center of up to Bϕ=1.0 T with plasma currents up to Ip=500 kA and a pulse length up to τft=500 ms. A wide range of plasma shaping configurations are envisaged, including triangularities between −0.50≤δ≤0.50 and elongations of κ≤2.25. Control of plasma shaping is achieved through four axially variable poloidal field coils (PF), and four fixed divertor (Div) coils, nominally allowing operation in lower-single null, upper-single null and double-null configurations. This work examines phase 2 of the SMART device, presenting a baseline reference equilibrium and two highly-shaped triangular equilibria. The relevant PF and Div coil current waveforms are also presented. Equilibria are obtained via an axisymmetric Grad-Shafranov force balance solver (Fiesta), in combination with a circuit equation rigid current displacement model (RZIp) to obtain time-resolved vessel and plasma currents.

Influence of up-down asymmetry in plasma shape on RMP response

Shaping effect on the plasma response to the externally applied resonant magnetic perturbation field is investigated for both DIII-D and MAST experiments, utilizing toroidal modeling. The plasma boundary shape is systematically varied ranging from single-null (SN) to double-null (DN) configurations, while other equilibrium quantities are kept largely unchanged. The relative amplitude of the computed plasma surface displacement, between the top/bottom of the torus and the outboard mid-plane, is identified as the most reliable indicator that distinguishes the plasma response between the SN and DN configurations. The underlying physics is the weakening of the edge-peeling component in the plasma response with increasing up-down symmetry of the plasma boundary shape.

The advanced tokamak path to a compact net electric fusion pilot plant

Physics-based simulations project a compact net electric fusion pilot plant with a nuclear testing mission is possible at modest scale based on the advanced tokamak concept, and identify key parameters for its optimization. These utilize a new integrated 1.5D core-edge approach for whole device modeling to predict performance by self-consistently applying transport, pedestal and current drive models to converge fully non-inductive stationary solutions, predicting profiles and energy confinement for a given density. This physics-based approach leads to new insights and understanding of reactor optimization. In particular, the levering role of high plasma density is identified, which raises fusion performance and self-driven ‘bootstrap currents’, to reduce current drive demands and enable high pressure with net electricity at a compact scale. Solutions at 6–7 T, ∼4 m radius and 200 MW net electricity are identified with margins and trade-offs possible between parameters. Current drive comes from neutral beam and ultra-high harmonic (helicon) fast wave, though other advanced approaches are not ruled out. The resulting low recirculating power in a double null configuration leads to a divertor heat flux challenge that is comparable to ITER, though reactor solutions may require more dissipation. Strong H-mode access (x2 margin over L–H transition scalings) and ITER-like heat fluxes are maintained with ∼20%–60% core radiation, though effects on confinement need further analysis. Neutron wall loadings appear tolerable. The approach would benefit from high temperature superconductors, as higher fields would increase performance margins while potential for demountability may facilitate nuclear testing. However, solutions are possible with conventional superconductors. An advanced load sharing and reactive bucking approach in the device centerpost region provides improved mechanical stress handling. The prospect of an affordable test device which could close the loop on net-electric production and conduct essential nuclear materials and breeding research is compelling, motivating research to validate the techniques and models employed here.

Assessment of measurement performance for a low field side IDTT plasma position reflectometry system

The Italian Divertor Test Tokamak (IDTT) facility will study advanced exhaust solutions applicable to DEMO. This new machine also opens the possibility to test and validate relevant non-magnetic control diagnostics in support of a DEMO design implementation. Reflectometry, compatible with a full grade reactor implementation, has been proposed as a source of real-time (RT) plasma position and shape measurements for control purposes, in replacement or complement of standard magnetic measurements, to ensure reliability and safety on the machine. Additionally, such a system can be useful to obtain the characteristics of edge turbulence, useful for Neoclassical Tearing Mode (NTM) control or to improve the efficiency of other diagnostics as Collective Thomson Scattering (CTS). This new control technique based on multiple, poloidally distributed, non-magnetic measurements, must be tested, in all of its aspects, before it can be fully implemented in future fusion reactors. IDTT will be one of the best candidates to implement and build a knowledge database of nonstandard reflectometry (away from the equatorial plane) that will be needed on DEMO and is currently unavailable. The performance of three Ordinary mode (O-mode) Plasma Position Reflectometers (PPR) at the Lower Field Side (LFS) on IDTT is assessed using the two-dimensional (2D) full-wave Finite-Difference Time-Domain (FDTD) code, REFMULF, in two of the foreseen IDTT plasma scenarios: 5MA Single Null (SN) and Double Null (DN) configurations.