Plasma Shape Research Articles

Effect of anisotropic thermal transport on tearing mode stability in negative versus positive triangularity plasmas

The combined effects of anisotropic thermal transport and the plasma shaping, including negative triangularity, on the n = 1 (n is the toroidal mode number) tearing mode (TM) stability are numerically investigated utilizing the MARS-F code [Liu et al., Phys. Plasmas 7, 3681–3690 (2000)]. While varying the plasma boundary triangularity, the TM stability is found to be dictated by the competing effects of the Shafranov shift induced stabilization and the bad-curvature induced destabilization. The negative triangularity shape increases the Shafranov shift (stabilizing) in the plasma core but also enlarges bad-curvature regions (destabilizing) near the plasma edge, with the net effect being largely destabilizing for the TM as compared to the positive triangularity counter-part. Large negative triangularity however can also lead to more stabilization for the plasma core-localized TM. Anisotropic thermal transport reduces the stabilizing effect on the TM associated with the favorable averaged curvature, resulting in more unstable core-localized TMs in both negative and positive triangularity plasmas. But the opposite effect can also take place for the edge-localized TM in finite-pressure plasmas with negative triangularity.

Angular Distribution of Bremsstrahlung Spectral Temperature Measured in a Full Dimension of ECR Ion Source Using NaI(TI) Detector

Measurement of angular distribution (AD) of the bremsstrahlung spectral temperature from a full dimension of the Electron Cyclotron Resonance Ion Source (ECRIS) along the beam axis is challenging. To overcome some challenges, this paper presents the AD of the bremsstrahlung spectral temperature measured in a full dimension of the ECRIS along the beam axis using data obtained from the Busan Center of Korea Basic Science Institute (KBSI). The bremsstrahlung spectral temperature from 28-GHz ECR Ion source at the KBSI was measured in six, three, and nine azimuthal angles at the injection, centre, and extraction sides of the ECRIS using three round type thallium-activated sodium iodide (NaI(TI)) scintillation detectors. Monte Carlo simulation based on the Geant4 software package was performed to take the geometrical acceptance and energy-dependent detection efficiency into account due to large non-uniformity in the material budget. True bremsstrahlung energy spectra from the 28-GHz ECR ion source were obtained using the inverse-matrix deconvolution method. The unfolding method was based on a full geometry of the Geant4 model of the ECRIS plasma. The results show that in all three measurement locations, the highest value of the spectral temperature was at an angle of 30∘ coincident with one of the maximum angles of the ECRIS plasma shape.

Influence of the magnetic configuration on the high-field side scrape-off layer at ASDEX Upgrade and the role of the secondary separatrix

In tokamaks, radial transport is ballooning, meaning it is enhanced at the low-field side (LFS). This work investigates the effect of the magnetic configuration on the high-field side (HFS) scrape-off layer. Our experiments involved L-mode and H-mode discharges at ASDEX Upgrade, in which we scanned the magnetic configuration from a lower to an upper single-null shape, thus varying the location of the secondary separatrix. We show that the secondary separatrix determines the width of the HFS scrape-off layer, meaning that the density is much lower in the region that is magnetically disconnected from the LFS scrape-off layer, outside the secondary separatrix. Furthermore, we observe that the large density often seen in the HFS divertor drastically decreases as the separation between the primary and secondary separatrices falls below a particular value. This value is different for L-mode and H-mode plasmas and closely matches the power decay length measured at the LFS midplane. We also show how the HFS scrape-off layer density is smaller in an upper single-null than in a lower single-null, when the ionic grad-B drift points down. This difference is likely caused by reversing the E×B drifts in the active divertor when switching the active X-point from the bottom to the top. We further observe that the neutral density in the lower divertor also correlates with the plasma shape and the high-density region in the HFS scrape-off layer. During the shape scans analyzed here, the HFS divertor remained partially detached throughout, with transitory reattachment modulated by ELM activity in H-mode. This work provides novel experimental data that can be leveraged to further the modeling capabilities and understanding of scrape-off layer physics in highly shaped plasmas.

Plasma surrogate modelling using Fourier neural operators

Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier neural operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (Mean Squared Error in the normalised domain ≈10−5 ). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations, and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e. cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full (available) duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

Free boundary equilibrium determination of HL-3 discharges

In 2022–2023, HL-3 (previously known as HL-2M) realized the divertor discharge after its first plasma campaign. To analyze equilibrium configurations of HL-3, a free boundary equilibrium code FEEQS, based on the finite element method, has been used in recent experiments. Free boundary equilibrium determinations are carried out for discharges performed in both limiter and divertor configurations. Compared with the experimental diagnostic data from fast camera photos and saturated ion current signals.etc, various time evolution of plasma parameters are well reproduced, such as plasma shape, currents in the poloidal field coils, strike-point displacement. The use of FEEQS successfully supported the operations in HL-3, and physics study as well, which laid a foundation for the application of free boundary equilibrium integration simulation in the next step.

Decoupled magnetic control of spherical tokamak divertors via vacuum harmonic constraints

Power exhaust is a critical challenge for spherical tokamak reactors, making the design, optimisation and control of advanced divertor configurations crucial. These tasks are greatly simplified if the poloidal magnetic fields in the core and divertor regions can be varied independently. We present a novel method which facilitates decoupling of the core plasma equilibrium from the divertor geometry optimisation and control, using vacuum spherical harmonic (SH) constraints. This has the advantage that it avoids iterative solution of the Grad–Shafranov equation, making it easy to use, rapid and reliable. By comparing a large number of MAST-U equilibrium reconstructions against their approximations using SHs, a small number ( ∼4 ) of harmonics is found to be sufficient to closely reproduce the plasma boundary shape. We show experimentally that poloidal field changes designed to leave harmonics unaffected indeed have no effect on the core plasma shape. When augmented with divertor geometry constraints, this approach gives a powerful tool for creating advanced magnetic configurations, and its simplicity brings improvements in speed and robustness when solving coil position optimisation problems. We discuss the clear benefits to real-time feedback control, feed-forward scenario design and coilset optimisation with a view to future reactors.

An overview of the evolution of the modeling of reflectometry diagnostics in fusion plasmas using finite-difference time-domain codes

Microwave reflectometry, having its origins in ionosphere probing techniques to evaluate electronic density, has become one of the most important diagnostics for the same quantity in fusion plasmas. Reflectometry will play a major role in next-generation machines, in particular in DEMO, where it is expected to provide plasma positioning, shaping, and tracking data. The ability to have an ever-increasing comprehensive description of reflectometry is particularly important since it allows us to assess the measuring capabilities of existing experimental systems and to predict the performance of new diagnostic concepts based on probing waves. Furthermore, wave propagation in a thermonuclear plasma with fluctuating electronic densities is far from straightforward and the need for a numerical full-wave treatment becomes fundamental. We will present the reader with the fundamentals of this technique and introduce the usage and evolution of FDTD in reflectometry, using as an example, the synthetic diagnostics setup that uses the family of REFMUL* codes, which is employed in the assessment of the performance of several reflectometry systems in different fusion machines.

Evaluation of the impact of plasma operation scenarios on the fusion reactor blanket design using an integrated numerical plasma and neutronics analysis suite

A very limited operation scenario has been used for fusion neutronics for the design of tritium breeding blankets. However, many advanced operation scenarios are under development and the impact of choosing a plasma operation scenario for fusion neutronics, which requires integration of neutronics analysis with plasma analysis, needs to be evaluated. An automated process from plasma analysis to neutronics analysis to create a viable fusion plasma neutron source was considered using a few different codes. In this work, we develop an integrated suite combining plasma modeling codes and neutronics codes. McCARD, a Monte-Carlo neutron-photon transport simulation code, is integrated into TRIASSIC, a tokamak reactor integrated automation suite for simulation and calculation, as the module for neutronics analysis of various plasma operation scenarios. McCARD integration allows TRIASSIC to perform neutronics analysis along with analytical and predictive plasma simulations. To evaluate this integrated suite, KSTAR experimental data were used to calculate the neutron flux at the first wall via TRIASSIC with the McCARD module in three different cases. First, the effect of plasma shape parameters, elongation and triangularity, on neutron flux is analyzed. Second, plasma scenario with the changes to the shape and the performance of plasma over time is studied to evaluate the time varying simulation. Third, two different plasma scenarios are compared to analyze the impact of plasma performance on neutron flux.

Magnetics only real-time equilibrium reconstruction on ASDEX Upgrade

Real-time reconstruction of the magnetic equilibrium provides fundamental control of plasma shape and position in a tokamak. Details of the implementation of the equilibrium reconstruction code developed for the ASDEX Upgrade tokamak (JANET++) are summarized. Cubic Hermite splines are introduced as current density basis functions for solving the Grad–Shafranov equation. The choice of the optimal Tikhonov regularization parameter is discussed. The code is validated by comparing the results of the equilibrium reconstruction with those of further equilibrium reconstructions available on ASDEX Upgrade (CLISTE and IDE). In a high time resolution study of a discharge with edge localized modes (ELM), the poloidal asymmetry of the fits and magnetic probe measurements suggest that the real-time equilibrium reconstruction captures the essential features of the current density redistribution in an ELMing edge plasma. An efficient algorithm to locate multiple X-points and identify the active one in advanced X-divertor and snowflake divertor configurations is presented.

Recent Upgrade of the Magnetic Diagnostic System in the Alvand-U Tokamak

The main acting parameters in tokamak plasma experiments, such as currents and electric and magnetic fields, are present inside and outside the plasma volume. To analyze the changes in the shape of tokamak plasma, it is necessary to use experimental data obtained from magnetic measurements. Until recently, a four-digit magnetic probe (MP) was used for qualitative analysis of the magnetic field, but its accuracy was low, and it could not be practically used as a diagnostic system. Following the Magnetic Confinement Group, Tokamak Laboratories’ approach to optimize and improve the measurement of plasma parameters, the use of a richer array of MPs to accurately measure changes in the magnetic field and identify plasma parameters in the Alvand tokamak was considered. In order to upgrade the magnetic diagnostic system, two MP arrays were designed and manufactured. Each array contains 12 poloidal and radial probes. The MPs of each array were attached to Mylar belts and mounted on the vacuum vessel of the tokamak. In addition, an integrator unit was designed and installed as a magnetic diagnostic subsystem. The conducted research involved the MP and calibration setup followed by preliminary tests of the array probe.

Criterion for long sustained highly peaked ion temperature in diverted configuration of KSTAR tokamak

In the context of KSTAR plasma research, the discovery of the fast ion regulated enhanced mode is noteworthy due to its remarkable ability to maintain ion temperatures exceeding up to 10 keV for a few tens of seconds, avoid impurity accumulation, and keep low loop voltages. This new plasma operating scenario is achieved in a diverted configuration plasma by avoiding the H-mode transitions with sufficient additional power for the transition. Keeping the density low is the primary method for the avoidance. Additionally, adjustments to other parameters (plasma shape, neutral beam injection, and toroidal magnetic field) associated with the H-mode threshold power are applied to inhibit the transition process. This paper includes an experimental analysis and discussion of these findings.

Kinetic-ballooning-bifurcation in tokamak pedestals across shaping and aspect-ratio

We use a new gyrokinetic threshold model to predict a bifurcation in tokamak pedestal width-height scalings that depends strongly on plasma shaping and aspect-ratio. The bifurcation arises from the first and second stability properties of kinetic-ballooning-modes that yields wide and narrow pedestal branches, expanding the space of accessible pedestal widths and heights. The wide branch offers potential for edge-localized-mode-free pedestals with high core pressure. For negative triangularity, low-aspect-ratio configurations are predicted to give steeper pedestals than conventional-aspect-ratio. Both wide and narrow branches have been attained in tokamak experiments.

A new quasilinear model for turbulent momentum transport in tokamaks with flow shear and plasma shaping

In tokamak experiments, sufficiently strong E × B flow shear reduces turbulent transport, thereby improving the prospects for fusion power plants. It is therefore of great importance to efficiently explore parameter space to find where strong plasma flow can be achieved. To this end, we propose a new, physically motivated quasi-linear model for estimating momentum transport from turbulence in the presence of toroidal flow shear and plasma shaping. The method gives good estimates of momentum transport for up–down asymmetric geometries as well as low magnetic shear and tight aspect ratio. The results are benchmarked with high-fidelity nonlinear GENE simulations, demonstrating that it provides a fast and accurate estimate of momentum transport.

On multiple solutions of the Grad–Shafranov equation

The Grad–Shafranov equation (GSE) for axisymmetric MHD equilibria is a nonlinear, scalar PDE which in principle can have zero, one or more non-trivial solutions. The conditions for the existence of multiple solutions has been little explored in the literature so far. We develop a simple analytic model to calculate multiple solutions in the large aspect ratio limit. We compare the results to the recently developed deflated continuation method to find multiple solutions in a realistic geometry and right-hand side of the GSE using the finite element method. The analytic model is surprisingly accurate in calculating multiple solutions of the GSE for given boundary conditions and the two methods agree well in limiting cases. We examine the effect of plasma shaping and aspect ratio on the multiple solutions and show that shaping generally does not alter the number of solutions. We discuss implications for predictive modelling, equilibrium reconstruction, plasma stability and disruptions.

The effect of plasma shaping on high density H-mode SOL profiles and fluctuations in TCV

The impact of plasma shaping on the properties of high density H-mode scrape-off layer (SOL) profiles and transport at the outer midplane has been investigated on Tokamakà configuration variable. The experimental dataset has been acquired by evolving the upper triangularity while keeping the other parameters constant. The scan comprises δup values between 0.0 and 0.6, excluding negative triangularity scenarios. Within this study, a transition from type-I edge localised modes to the quasi-continuous exhaust regime takes place from low to high δup . The modification of the upstream SOL profiles has been assessed, in terms of separatrix quantities, within the αt turbulence control parameter theoretical framework (Eich et al 2020 Nucl. Fusion 60 056016). The target parallel heat load and the upstream near-SOL density profiles have been shown to broaden significantly for increasing αt . Correspondingly, in the far SOL a density shoulder formation is observed when moving from low to high δup . These behaviours have been correlated with an enhancement of the SOL fluctuation level, as registered by wall-mounted Langmuir probes as well as the thermal helium beam diagnostic. Specifically, both the background and the filamentary-induced fluctuating parts of the first wall ion saturation current signal are larger at higher δup , with filaments being ejected more frequently into the SOL. Comparison of two pulses at the extremes of the δup scan range, but with otherwise same input parameters, shows that the midplane neutral pressure does not change much during the H-mode phase of the discharge. This indicates that indirect effects of the change in geometry, linked to first wall recycling sources, should not play a significant role. The total core radiation increases at high δup , on account of a stronger plasma–wall interaction and resulting larger carbon impurity intake from the first wall. This is likely associated to the enhanced first wall fluctuations, as well as a smaller outer gap and the close-to-double-null magnetic topology at high shaping.

First measurements of an imaging heavy ion beam probe at the ASDEX Upgrade tokamak.

The imaging heavy ion beam probe (i-HIBP) diagnostic has been successfully commissioned at ASDEX Upgrade. The i-HIBP injects a primary neutral beam into the plasma, where it is ionized, leading to a fan of secondary (charged) beams. These are deflected by the magnetic field of the tokamak and collected by a scintillator detector, generating a strike-line light pattern that encodes information on the density, electrostatic potential, and magnetic field of the plasma edge. The first measurements have been made, demonstrating the proof-of-principle of this diagnostic technique. A primary beam of 85/87Rb has been used with energies ranging between 60 and 72keV and extracted currents up to 1.5 mA. The first signals have been obtained in experiments covering a wide range of parameter spaces, with plasma currents (Ip) between 0.2 and 0.8 MA and on-axis toroidal magnetic field (Bt) between 1.9 and 2.7T. Low densities appear to be critical for the performance of the diagnostic, as signals are typically observed only when the line integrated density is below 2.0-3.0 × 1019m-2 in the central interferometer chord, depending on the plasma shape. The strike line moves as expected when Ip is ramped, indicating that current measurements are possible. Additionally, clear dynamics in the intensity of the strike line are often observed, which might be linked to changes in the edge profile structure. However, the signal-to-background ratio of the signals is hampered by stray light, and the image guide degradation is due to neutron irradiation. Finally, simulations have been carried out to investigate the sensitivity of the expected signals to plasma density and temperature. The results are in qualitative agreement with the experimental observations, suggesting that the diagnostic is almost insensitive to fluctuations in the temperature profile, while the signal level is highly determined by the density profile due to the beam attenuation.

A new flux coordinates-based solver for fixed-boundary tokamak equilibrium with toroidal flow

The plasma equilibrium plays a crucial role in nuclear fusion studies, serving as the foundation for various aspects of fusion research, including plasma stability, transport, and current drive. In this paper, a new Grad–Shafranov equation solver is developed for the fixed-boundary plasma equilibria with toroidal flow. This solver utilizes the pressure profile, safety factor profile (not current profile), and any two profiles of the toroidal angular velocity, plasma temperature, and square of the Mach number as inputs. The numerical results obtained by this solver exhibit good agreement with known analytic solution under identical parameters, and the potential applications of the solver are demonstrated through several numerical equilibria with toroidal flow. It is very convenient to apply this code to simulate the tokamak equilibrium with a smooth plasma shape. In addition, the effect of toroidal flow on the plasma equilibria is investigated as a simple application. The results reveal a notable outward shift in the contour profiles of magnetic flux surface, density, pressure, and temperature induced by toroidal flow.

Scenario optimization for the tokamak ramp-down phase in RAPTOR: Part A. Analysis and model validation on ASDEX Upgrade

We discuss how the combination of experimental observations and rapid modeling has enabled to improve understanding of the tokamak ramp-down phase in ASDEX Upgrade. A series of dedicated experiments has been performed, to disentangle the effect of individual actuators like plasma current, auxiliary heating and plasma shaping. Optimized discharge termination strategies with increased margin with respect to radiative and vertical stability limits are proposed and tested in experiment. Radiative collapse of the edge Te profile after the HL back-transition is avoided by initially maintaining auxiliary heating during L-mode, showing beneficial effects even after the auxiliary heating is turned off. The capability of the RAPTOR code to model the time evolution of the internal inductance has been validated, including the effect of a change in the Ip ramp-down rate and the HL transition timing. The reduction of caused by rapid compression of the plasma cross-section has been quantitatively recovered in simulations. Successful modeling of the time evolution is essential to optimize ramp-down scenarios for future fusion reactors, for which vertical stability and power balance control will be more challenging.

Development of high-performance long-pulse discharge in KSTAR

High-performance long-pulse plasma operation is essential for producing economically viable fusion energy in tokamak devices. To achieve such discharges in KSTAR, firstly, the rapid increase in the temperature of plasma-facing components was mitigated. The temperature increase of the poloidal limiter, especially, was associated with beam-driven fast ion orbit loss and the discrepancy of the equilibrium reconstructed with heated magnetic probes of signal drift. The fast ions lost to the poloidal limiter were reduced by optimizing the plasma shape and the composition of neutral beam injection (NBI). This nonlinear signal drift was successfully reduced by a new thermal shielding protector on the magnetic probes. Secondly, a lower loop voltage approach was implemented to reduce a poloidal flux consumption rate. A plasma current of 400 kA and a line-averaged electron density of ∼2.0 × 1019 m−3 were chosen by considering the L–H power threshold, fast ion orbit loss, and beam shine-through power loss for low loop voltage in KSTAR. In addition, the application of electron cyclotron heating also helped maintain the plasma with low loop voltage (∼25 mV) by enhancing the NBI-driven current and achieving a high poloidal beta (β P) state. KSTAR has achieved a long pulse (∼90 s) operation with the high performance of β P ⩽ 2.7, thermal energy confinement enhancement factor (H98y2) ∼ 1.1, and fraction of non-inductive current (f NI) ⩽ 0.96. Still, gradual degradation of the plasma performance has been observed over time in the discharges. In one of the long-pulse discharges, β P reduced by ∼18% over the time of ∼8τ R (current relaxation time, τ R ∼ 5 s) and ∼1067τ E,th (thermal energy confinement time, τ E,th ∼ 45 ms). The degradation may be closely associated with weak, yet growing, and persistent toroidal Alfvén eigenmodes and their effect on fast ion confinement.

Real-Time Plasma Magnetic Control System with Equilibrium Reconstruction Algorithm in the Feedback for the Globus-M2 Tokamak

To control the plasma shape during a tokamak discharge, it is necessary to calculate the plasmashape in real-time. The rate requirements for the shape calculations are especially high for tokamaks with asmall radius, such as Globus-M2 (St. Petersburg, Russia). A real-time magnetic plasma control system forthe Globus-M2 tokamak with flux and current distribution identification (FCDI) algorithm for the plasmaequilibrium reconstruction in feedback is presented. The control system contains discrete one-dimensionaland matrix proportional-integral-derivative controllers synthesized by the matrix inequality method usingthe plasma LPV model calculated on experimental data, and carries out the coordinated control of the plasmaposition and shape as well as the compensation for the scattered field of the central solenoid. The FCDI algorithmis improved for the operation in the real-time mode, and makes it possible to reconstruct the plasmashape in 20 μs. The digital control system with a feedback algorithm was simulated on a real-time test bench,consisting of two Speedgoat Performance Real-Time Target Machines (RTTM), and demonstrated the averageTask Execution Time (TET) value in 67 μs.