Magnetic Confinement Fusion Research Articles

Meta variance reduction for Monte Carlo estimation of energetic particle confinement during stellarator optimization

This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplicative amount of variance reduction. The proposed meta estimators are particularly efficient within outer-loop applications when the input distribution of the uncertainties changes during the outer loop, which is often the case in reliability-based design and shape optimization. We derive asymptotic bounds of the variance reduction of the meta estimators in the limit of convergence of the outer-loop results. We demonstrate the meta estimators, using data-driven surrogate models and biasing densities, on a design problem under uncertainty motivated by magnetic confinement fusion, namely the optimization of stellarator coil designs to maximize the estimated confinement of energetic particles. The meta estimators outperform all of their constituent variance reduction techniques alone, ultimately yielding two orders of magnitude speedup compared to standard Monte Carlo estimation at the same computational budget.

Development of a High Sampling Rate Data Acquisition System Working in a High Pulse Count Rate Region for Radiation Diagnostics in Nuclear Fusion Plasma Research

In this study, a high sampling rate data acquisition system with the ability to provide timestamp, pulse shape information, and waveform simultaneously under a sub megahertz pulse counting rate was developed for radiation diagnostics for magnetic confinement nuclear fusion plasma research. The testing of the data acquisition system under the high pulse counting rate condition using real signals was performed in an accelerator-based deuterium-deuterium fusion neutron source (Fast Neutron Source) at the Japan Atomic Energy Agency. We found that the pulse counts acquired by the system linearly increased up to 6 × 105 cps, and the count loss at 106 cps was estimated to be ~10%. The data acquisition system was applied to deuterium-deuterium neutron profile diagnostics in the deuterium gas operation of a helical-type magnetic confinement plasma device, called the Large Helical Device, to observe the radial profile of neutron emissivity for the first time in a three-dimensional magnetic confinement fusion device. Time-resolved measurements of the deuterium-deuterium fusion emission profile were performed. The experimentally observed radial neutron emission profile was consistent with numerical predictions based on the orbit-following models using experimental data. The data acquisition system was shown to have the desired performance.

The research on the influence mechanism of internal deformation for the performance of Bi-2212

Cable-in-conduit conductor (CICC), one of the most promising conductors for manufacturing magnets in magnetic confinement fusion devices, has attracted lots of attention. In the production of CICC, porosity control is necessary for its stability. The porosity control is usually realized by the diameter-reducing process, which would also lead to indentation damages to the elements of CICC-superconducting wires. In this article, systematic research of indentation damages was carried out on the next generation of high-temperature superconducting materials–Bi-2212 wires. The results indicate that the current carrying capacity of the indentation-damaged wire would first keep steady and then show exponential decline with the increase of indentation depth. The wires subjected to pre-overpressure (pre-OP) treatment exhibit slightly improved resistance against indentation damage at shallow indentation depths. However, their critical current (I c) deteriorates more rapidly at greater indentation depths when compared to wires that have not undergone the per-OP process. The following structural characterization analyzed the reasons for the property changes with the help of scanning electron microscopy, energy dispersive x-ray spectroscopy, computed tomography, and hardness tester. Misalignment between the Bi-2212 grains and shaped filaments was found in the indentation-damaged wires, with which the degradation in I c of the wires and the differences in properties of the two kinds of wires were further discussed.

Experimental and model study of LIBS depth profile for multilayer deposition materials

The patterns of erosion and deposition occurred in the plasma-facing materials (PFMs) of a magnetic confinement fusion device are crucial for the investigation of plasma-wall interaction (PWI). The deposition behavior can be identified by the elemental depth profile of the deposition layer. As an effective remote monitoring method for the wall in nuclear fusion devices, laser-induced breakdown spectroscopy (LIBS) shows excellent potential for the depth profiling of the deposition layer on the PFMs. However, some potentially influencing factors lead to the difficulty of distinguishing and identifying the interfaces between the deposition layers and substrate. The measuring accuracy of the deposition layer thickness plays an essential role in PWI research. In this paper, depth profiling of multilayer samples with Ni layers on Cu were performed using LIBS with an ns-pulse laser. The experiment was carried out under 5 × 10−5 mbar to simulate the operation of a nuclear fusion device. Meanwhile, a two-dimensional model for multi-pulse LIBS depth analysis based on the laser beam profile factor and interface roughness factor was established to reconstruct and predict the elemental depth profile distribution of NiCu multilayer materials. The correlation coefficients between the experimental and modeling data were all >0.99. We introduced a locating approach for the interface based on model prediction, and the relative errors of all Ni layer thicknesses were < 5.1%, demonstrating the feasibility and accuracy of the model. All the results show that the two-dimensional numerical model can improve the accuracy of LIBS depth profile on layer thickness analysis and further promote the application of in situ LIBS diagnosis in PWI research.

Applying FAIR4RS principles to develop an integrated modeling environment for the magnetic confinement fusion

Over the decades, the integrated modeling (IM) environment for magnetically confined fusion has evolved from a single, isolated, proprietary numerical computing software to an open, flexible platform emphasizing sharing, communication, and workflow. This development direction is consistent with the FAIR4RS principles put forward by the scientific community in recent years. In this article, we describe how the FAIR4RS principles were put into practice during the development of the IM management tool FyDev for the Experimental Advanced Superconducting Tokamak (EAST). FyDev integrates the process of building, deploying, and invoking research software, automating the entire process. FyDev can also assign a unique ID for each software, convert the software ID to a Python module, and encapsulate a package management tool to enhance the software building process, ensuring consistency throughout the entire phase of the research software find, access, use, and invocation in a uniform contextual environment.

Lagrangian Chaotic Mixing in a Nonlinear Model of Resistive Drift-wave Turbulence in Tokamak Plasmas

In fusion plasma, numerical simulations are commonly employed to investigate the confinement properties of plasma in the bulk region of tokamaks. The modified Hasegawa-Wakatani (MHW) equations are used to model the behavior of the plasma, which enables us to understand the radial transport in two-dimensional numerical simulations of electrostatic resistive drift-wave turbulence. By utilizing the MHW equations, we have gained insights into the low-to-high confinement (L-H) transitions that occur spontaneously in the plasma when it moves from a low confinement stage, characterized by turbulent flow, to a turbulence-suppressed regime known as zonal flow. To investigate these transitions, we vary the value of a control parameter \(\alpha\), which is related to adiabaticity, in numerical simulations, and observe the transition between the two regimes. This simplified model of L-H transitions can provide valuable information for tokamaks. To identify the Lagrangian coherent structures (LCS) and to better characterize the chaotic mixing during the L-H transition, we computed the finite-time Lyapunov exponent (FTLE) of the calculated velocity field derived from the electrostatic potential. We further compared the statistics of the chaotic mixing of the two regimes. The results of our study offer insights into the turbulent transport processes in magnetic confinement fusion plasmas.

Propagation of short-wavelength electromagnetic surface waves along the transition layer between two plasma-like half-spaces in the Voigt geometry

The dispersion properties of surface type electromagnetic waves are studied. The waves are considered to propagate along a slab transition layer located between two infinite homogeneous plasma regions of different particle densities. The wavelength is assumed to be short as compared with the layer width. The waves propagate across a static magnetic field, which is parallel to the layer interface. The influence of the smoothness of the gradient of the plasma particle density within the layer on the surface wave propagation/disappearance is discussed. The conclusions derived in the present paper are of interest in the fields of plasma electronics, nano-technologies, plasma-antenna systems, plasma production, and magnetic confinement fusion.

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. The formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

Steady-state burning plasma: a new stage in the development of magnetic confinement fusion energy.

Over the past 20 years, advances in tokamak physics and technology have prepared the field of magnetic confinement fusion research for the next step toward a steady-state burning plasma.

Benchmarking calculations of excitation energies and transition properties with spectroscopic accuracy of highly charged ions used for the fusion plasma and astrophysical plasma

Atomic radiative data such as excitation energies, transition wavelengths, radiative rates, and level lifetimes with high precision are the essential parameters for the abundance analysis, simulation, and diagnostics in fusion and astrophysical plasmas. In this work, we mainly focus on reviewing our two projects performed in the past decade. One is about the ions with Z ≲ 30 that are generally of astrophysical interest, and the other one is about the highly charged krypton (Z = 36) and tungsten (Z = 74) ions that are relevant in research of magnetic confinement fusion. Two different and independent methods, namely, multiconfiguration Dirac–Hartree–Fock (MCDHF) and the relativistic many-body perturbation theory (RMBPT) are usually used in our studies. As a complement/extension to our previous works for highly charged tungsten ions with open M-shell and open N-shell, we also mainly focus on presenting and discussing our complete RMBPT and MCDHF calculations for the excitation energies, wavelengths, electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transition properties, and level lifetimes for the lowest 148 levels belonging to the 3l 3 configurations in Al-like W61+. We also summarize the uncertainties of our systematical theoretical calculations, by cross-checking/validating our datasets from our RMBPT and MCDHF calculations, and by detailed comparisons with available accurate observations and other theoretical calculations. The data are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.10569.

Design and Feasibility Assessment of an HTS Sector Shaped High-Current Conductor for Fusion Coils

Technologies based on High Temperature Superconductors (HTS) are evolving rapidly toward maturity. Within the magnetic confinement fusion environment, several projects are demonstrating the possibility to integrate HTS in the coil systems. With respect to Low Temperature Superconducting (LTS) technologies, HTS could allow extending the operating space of fusion coils, either at higher temperatures, or at higher magnetic field levels, and in any case with larger operating margins. Different perspectives and development strategies are proposed, depending on whether HTS is considered a technology to completely substitute LTS, or to integrate and extend its performance range. A fundamental common requirement is the assessment of the layout, the feasibility, and performance demonstration of high-current conductors. Starting from the results achieved with the Al-slotted core cable-in-conduit conductor, and with a view on existing concepts for standard copper and aluminum cables, we have designed a new HTS sector-cable concept, to allow a flexible conductor design and a robust industrial processing. Several trials have been carried out, to verify the manufacturing approach, using either Al- or Cu-based stabilizers. Prototype sub-cables have been characterized at 77 K and self-field, as a necessary step toward the final target of a CICC operating stably with 60 kA at 4.2 K and 18 T, that is presently of interest for the EU-DEMO Central Solenoid Coil.

Modeling of subcooled flow boiling for hypervapotron in divertor of fusion reactor based on RPI model

The divertor is the key in-vessel component to remove the high heat flux and impurities in magnetic confinement fusion reactor. Hypervapotron (HV) has been developed as one of the candidates for cooling structure of divertor, owing to its excellent heat transfer performance in subcooled flow boiling. To address the design and development requirements of divertor, a suitable model for single-phase and two-phase flow of HV are developed. Four combination models of boiling properties expressed by different empirical correlations are evaluated. The results indicate that the LC-UN (Lemmert-Chawla, Unal) model shows a good agreement with the experimental results of Lim et al. (2022), with average deviation of 8.15%. Moreover, for the first time, the model successfully predicts the onset of fully developed nucleate boiling (OFDB) point of HV. Based on the LC-UN model, the detailed heat transfer and flow characteristics of HV are revealed. It shows that the boiling process is independent between each slot due to the fin barrier, and the bubbles are condensed by the subcooled main stream after leaving the wall. The “double vortex” in HV intensifies the interaction between vapor and liquid phase, preventing the aggregation of bubbles, allowing it has excellent heat transfer performances.

Gyrokinetic simulations of neoclassical electron transport and bootstrap current generation in tokamak plasmas in the TRIMEG code

For magnetic confinement fusion in tokamak plasmas, some of the limitations to the particle and energy confinement times are caused by turbulence and collisions between particles in toroidal geometry, which determine the “anomalous” and the neoclassical transport, respectively. Neoclassical effects are also responsible for the intrinsically generated bootstrap current, and only the self-consistent modeling of neoclassical and turbulent processes can ultimately give accurate predictive results. In this work, we focus on the implementation of neoclassical physics in the gyrokinetic code TRIMEG, which is a TRIangular MEsh-based Gyrokinetic code that can handle both the closed and open field line geometries of a divertor tokamak. We report on the implementation of a simplified Lorentz collision operator in TRIMEG. For comparison with neoclassical theory, the calculation of flux surface averages is necessary. Since the code uses an unstructured mesh, a procedure for calculating the flux surface averages of particle and energy fluxes and the bootstrap current is derived without relying on the poloidal coordinate, which is useful also for other simulations in unstructured meshes. With the newly implemented collision operator, we study electron transport and bootstrap current generation in a plasma with a finite density gradient but uniform temperature for various simplified and realistic geometries. Compared with neoclassical theory, good agreement is obtained for the large aspect ratio case regarding the particle and energy fluxes as well as the bootstrap current. However, some discrepancies are observed at moderate aspect ratio and for a case with the realistic geometry of the ASDEX Upgrade tokamak. These deviations can be explained by different treatments and approximations in theory and simulation. In this paper, we demonstrate the capability to calculate the electron transport and bootstrap current generation in TRIMEG, which will allow for the self-consistent inclusion of neoclassical effects in gyrokinetic simulations in the future.

Study on the effect of neutron shielding design on tritium breeding based on water-cooled ceramic blanket for CFETR

The Chinese Fusion Engineering Test Reactor (CFETR) is a magnetic confinement fusion reactor independently designed and developed by China, which is based on the ITER design experience. As one of the candidates for the CFETR, the water cooled ceramic blanket (WCCB) mainly carries out many important tasks, such as tritium breeding and radiation shielding. The high tritium breeding ability is one of the most significant goals of the blanket. For the design of the CFETR, in addition to meeting the requirements of tritium breeding, the design of the blanket must also consider meeting relevant shielding limits. Due to the limited space of the blanket, the improvement in tritium breeding space will inevitably lead to the reduction in neutron shielding space behind the breeding area, and vice versa. Therefore, under the premise of meeting the requirements of neutron shielding, increasing the tritium breeding space as much as possible is the focus of research. In this work, a three-dimensional neutronics model containing the WCCB blanket is developed, and the neutronics performance is calculated based on 1.5 GW fusion power. A set of nuclear analyses are carried out by the MCNP code, including analysis of the neutron wall load, tritium breeding ratio (TBR), and fast neutron fluence of the TF coil. It is found that the shielding space of certain blanket modules could be optimized. After the shielding optimization, the global TBR increased from 1.168 to 1.186, an increase of 0.018 TBR. The current research has important guiding significance for the future design and optimization of the WCCB for the CFETR.

Surface production of negative deuterium ions from plasma-exposed boron doped diamond and graphite: work function measurements using photoemission yield spectroscopy

Negative-ion sources are of considerable interest for applications such as materials processing and neutral beam injection for magnetic confinement fusion. The efficient production of negative ions in these sources often relies on surface production. Work function measurements are critical to enable a detailed understanding of the mechanisms that underpin this. In this study we used a combination of photoemission yield spectroscopy and the Fowler method to determine the work functions of boron doped diamond (BDD) and highly oriented pyrolytic graphite (HOPG) directly after exposure to a low-pressure inductively coupled deuterium plasma (150 W, 2 Pa). A magnetised retarding field energy analyser is used to measure the negative ion current from the samples. During plasma exposure, samples are biased at −130 V or −60 V and their temperature is varied between 50 ∘C and 750 ∘C. The results show that the increasing work function of the plasma exposed HOPG occurs over the same sample temperature range as the decreasing negative-ion current. In contrast, the work function of BDD does not show a clear relationship with negative-ion current, suggesting that different mechanisms influence the negative-ion production of metal-like HOPG and dielectric-like BDD. The necessity for an additional fitting parameter for the Fowler fits to BDD suggests that its electronic properties are changing under plasma exposure, unlike HOPG. For both materials, the maximum photocurrent measured from the samples displays a strong similarity with negative-ion current, suggesting they are driven by a common mechanism. The in-situ measurement of the work function using non-invasive techniques is of interest for the development of negative ion sources.

Refractive index measurement of hydrogen isotopologue mixture and applicability for homogeneity of hydrogen solid at cryogenic temperature in fusion fuel system

Deuterium (D)-Tritium (T) nuclear fusion reaction has potential as an energy source in the future. In both magnetic confinement and inertial confinement fusion reactors, solid D–T will generally be supplied as fusion fuel. The efficiency of the nuclear fusion reaction depends on the quality of solid D–T fuel, which is related to the composition, homogeneity, helium-3 (3He) content, and so on. However, there is no technique for in-situ examination of solid D–T fuel. In this study, we consider a simple and precise method for the characterization of solid hydrogen isotopologues at cryogenic temperature using refractive index measurement, and evaluate the distribution of hydrogen isotopologue composition and homogeneity. To evaluate without the effect of tritium decay, the homogeneity of the hydrogen (H2)-deuterium (D2) mixture is measured at first. By the in-situ refractive index measurement at cryogenic temperature, the homogeneity of solid H2–D2 mixture is roughly quantified. The phase diagram of the H2–D2 mixture shows a solid solution type. D2-rich crystal first appears from the liquid phase as a primary crystal. The composition of D2 in liquid phase ias homogeneous, whereas it reduces by obeying the liquidus line in the phase diagram with the crystallization. On the other hand, the composition of the H2–D2 mixture in solid phase is inhomogeneous because the mobility of H2 and D2 in solid phase was too slow to be homogeneous and solid. The compositions of H2–D2 mixture in liquid and solid phases could be evaluated by the in-situ refractive index measurement in time. Consequently, the refractive index measurement shows great potential as an inspection method of solid D–T fuel in fusion reactors.

Existence of global symmetries of divergence-free fields with first integrals

The relationship between symmetry fields and first integrals of divergence-free vector fields is explored in three dimensions in light of its relevance to plasma physics and magnetic confinement fusion. A Noether-type theorem is known: for each such symmetry, there corresponds a first integral. The extent to which the converse is true is investigated. In doing so, a reformulation of this Noether-type theorem is found for which the converse holds on what is called the toroidal region. Some consequences of the methods presented are quick proofs of the existence of flux coordinates for magnetic fields in high generality, without needing to assume a symmetry such as in the cases of magneto-hydrostatics or quasi-symmetry.

Influence of collisions on the validation of global gyrokinetic simulations in the edge and scrape-off layer of TCV

Understanding and predicting turbulent transport in the edge and scrape-off-layer (SOL) of magnetic confinement fusion devices is crucial for developing feasible fusion power plants. In this work, we present the latest improvements to the gyrokinetic turbulence code GENE-X and validate the extended model against experimental results in the TCV tokamak (“TCV-X21”). GENE-X features a full-f electromagnetic gyrokinetic model and is specifically targeted for edge and SOL simulations in diverted geometries. GENE-X can model the effect of collisions using either a basic Bhatnagar–Gross–Krook (BGK) or more sophisticated Lenard–Bernstein/Dougherty (LBD) collision operator. We present the results of a series of GENE-X simulations using the BGK or LBD collision models, contrasting them to collisionless simulations. We validate the resulting plasma profiles, power balance, and SOL heat flux against experimental measurements. The match to the experiment significantly improves with the fidelity of the collision model chosen. We analyze the characteristics of the turbulence and find that in almost all cases in the confined region the turbulence is driven by trapped electron modes (TEM). Both the simulations without collisions and those with the BGK collision operator do not accurately describe turbulence driven by TEMs. The more sophisticated LBD collision operator presents a minimum requirement for accurate gyrokinetic edge turbulence simulations.

A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries

Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.

Achievement of ion temperatures in excess of 100 million degrees Kelvin in the compact high-field spherical tokamak ST40

Ion temperatures of over 100 million degrees Kelvin (8.6 keV) have been produced in the ST40 compact high-field spherical tokamak (ST). Ion temperatures in excess of 5 keV have not previously been reached in any ST and have only been obtained in much larger devices with substantially more plasma heating power. The corresponding fusion triple product is calculated to be ni0Ti0τE≈6±2×1018m−3keVs . These results demonstrate for the first time that ion temperatures relevant for commercial magnetic confinement fusion can be obtained in a compact high-field ST and bode well for fusion power plants based on the high-field ST.