Development of a diamagnetic loop in KAIMIR.

We developed a diamagnetic loop for the estimation of plasma stored energy in the KAIST Magnetic Mirror magnetic mirror device [Oh et al., J. Plasma Phys. 90, 975900202 (2024)]. Diamagnetic loops are used to estimate the plasma stored energy from measurements of the diamagnetic flux in plasma with an applied external magnetic field. However, diamagnetic flux measurements are accompanied by the vacuum flux, which generally exceeds the diamagnetic flux by over 10 000 times. Therefore, it is critical to attain a high signal-to-noise ratio with minimized noise in diamagnetic flux measurements. In this study, we employed a novel method to reduce background noise and improve the signal-to-noise ratio. Using two identical loops with opposite polarities, we successfully removed parasitic capacitive noise from the external insulation while amplifying the inductive signal two times. To eliminate the vacuum flux, we utilized two coaxial loops with different radii positioned at the same axial location. Results obtained from six paired loops confirmed the successful removal of the vacuum flux. The plasma stored energy was also found to agree well with Langmuir probe measurements, which verifies the diamagnetic flux measurements using the developed loop.

GS-DeepNet: mastering tokamak plasma equilibria with deep neural networks and the Grad-Shafranov equation.

The force-balanced state of magnetically confined plasmas heated up to 100 million degrees Celsius must be sustained long enough to achieve a burning-plasma state, such as in the case of ITER, a fusion reactor that promises a net energy gain. This force balance between the Lorentz force and the pressure gradient force, known as a plasma equilibrium, can be theoretically portrayed together with Maxwell's equations as plasmas are collections of charged particles. Nevertheless, identifying the plasma equilibrium in real time is challenging owing to its free-boundary and ill-posed conditions, which conventionally involves iterative numerical approach with a certain degree of subjective human decisions such as including or excluding certain magnetic measurements to achieve numerical convergence on the solution as well as to avoid unphysical solutions. Here, we introduce GS-DeepNet, which learns plasma equilibria through solely unsupervised learning, without using traditional numerical algorithms. GS-DeepNet includes two neural networks and teaches itself. One neural network generates a possible candidate of an equilibrium following Maxwell's equations and is taught by the other network satisfying the force balance under the equilibrium. Measurements constrain both networks. Our GS-DeepNet achieves reliable equilibria with uncertainties in contrast with existing methods, leading to possible better control of fusion-grade plasmas.

A sustained high-temperature fusion plasma regime facilitated by fast ions.

Nuclear fusion is one of the most attractive alternatives to carbon-dependent energy sources1. Harnessing energy from nuclear fusion in a large reactor scale, however, still presents many scientific challenges despite the many years of research and steady advances in magnetic confinement approaches. State-of-the-art magnetic fusion devices cannot yet achieve a sustainable fusion performance, which requires a high temperature above 100 million kelvin and sufficient control of instabilities to ensure steady-state operation on the order of tens of seconds2,3. Here we report experiments at the Korea Superconducting Tokamak Advanced Research4 device producing a plasma fusion regime that satisfies most of the above requirements: thanks to abundant fast ions stabilizing the core plasma turbulence, we generate plasmas at a temperature of 100 million kelvin lasting up to 20 seconds without plasma edge instabilities or impurity accumulation. A low plasma density combined with a moderate input power for operation is key to establishing this regime by preserving a high fraction of fast ions. This regime is rarely subject to disruption and can be sustained reliably even without a sophisticated control, and thus represents a promising path towards commercial fusion reactors.

A machine learning approach to identify the universality of solitary perturbations accompanying boundary bursts in magnetized toroidal plasmas.

Experimental observations assisted by 2-D imaging diagnostics on the KSTAR tokamak show that a solitary perturbation (SP) emerges prior to a boundary burst of magnetized toroidal plasmas, which puts forward SP as a potential candidate for the burst trigger. We have constructed a machine learning (ML) model based on a convolutional deep neural network architecture for a statistical study to identify the SP as a boundary burst trigger. The ML model takes sequential signals detected from 19 toroidal Mirnov coils as input and predicts whether each temporal frame corresponds to an SP. We trained the network in a supervised manner on a training set consisting of real signals with manually annotated SP locations and synthetic burst signals. The trained model achieves high performances in various metrics on a test data set. We also demonstrated the reliability of the model by visualizing the discriminative parts of the input signals that the model recognizes. Finally, we applied the trained model to new data from KSTAR experiments, which were never seen during training, and confirmed that the large burst at the plasma boundary that can fatally damage the fusion device always involves the emergence of SP. This result suggests that the SP is a key to understanding and controlling of the boundary burst in magnetized toroidal plasmas.

Imputation of faulty magnetic sensors with coupled Bayesian and Gaussian processes to reconstruct the magnetic equilibrium in real time.

A Bayesian with Gaussian process-based numerical method to impute a few missing magnetic signals caused by impaired magnetic probes during tokamak operations is developed such that the real-time reconstruction of magnetic equilibria, whose performance strongly depends on the measured magnetic signals and their intactness, is affected minimally. Likelihood of the Bayesian model constructed with Maxwell's equations, specifically Gauss's law for magnetism and Ampère's law, results in an infinite number of solutions if two or more magnetic signals are missing. This undesirable characteristic of the Bayesian model is remediated by coupling the model with the Gaussian process. Our proposed numerical method infers nine non-consecutive missing magnetic signals correctly in less than 1 ms suitable for the real-time reconstruction of magnetic equilibria during tokamak operations.

Solitary perturbations in the steep boundary of magnetized toroidal plasma.

Solitary perturbations (SPs) localized both poloidally and radially are detected within ~100 µs before the partial collapse of the high pressure gradient boundary region (called pedestal) of magnetized toroidal plasma in the KSTAR tokamak device. The SP develops with a low toroidal mode number (typically unity) in the pedestal ingrained with quasi-stable edge-localized mode (QSM) which commonly appears during the inter-collapse period. The SPs have smaller mode pitch and different (often opposite) rotation velocity compared to the QSMs. Similar solitary perturbations are also frequently observed before the onset of complete pedestal collapse, suggesting a strong connection between the SP generation and the pedestal collapse.

An upgrade of the magnetic diagnostic system of the DIII-D tokamak for non-axisymmetric measurements.

The DIII-D tokamak magnetic diagnostic system [E. J. Strait, Rev. Sci. Instrum. 77, 023502 (2006)] has been upgraded to significantly expand the measurement of the plasma response to intrinsic and applied non-axisymmetric "3D" fields. The placement and design of 101 additional sensors allow resolution of toroidal mode numbers 1 ≤ n ≤ 3, and poloidal wavelengths smaller than MARS-F, IPEC, and VMEC magnetohydrodynamic model predictions. Small 3D perturbations, relative to the equilibrium field (10(-5) < δB/B0 < 10(-4)), require sub-millimeter fabrication and installation tolerances. This high precision is achieved using electrical discharge machined components, and alignment techniques employing rotary laser levels and a coordinate measurement machine. A 16-bit data acquisition system is used in conjunction with analog signal-processing to recover non-axisymmetric perturbations. Co-located radial and poloidal field measurements allow up to 14.2 cm spatial resolution of poloidal structures (plasma poloidal circumference is ~500 cm). The function of the new system is verified by comparing the rotating tearing mode structure, measured by 14 BP fluctuation sensors, with that measured by the upgraded B(R) saddle loop sensors after the mode locks to the vessel wall. The result is a nearly identical 2/1 helical eigenstructure in both cases.

Toroidal mode number estimation of the edge-localized modes using the KSTAR 3-D electron cyclotron emission imaging system.

A new and more accurate technique is presented for determining the toroidal mode number n of edge-localized modes (ELMs) using two independent electron cyclotron emission imaging (ECEI) systems in the Korea Superconducting Tokamak Advanced Research (KSTAR) device. The technique involves the measurement of the poloidal spacing between adjacent ELM filaments, and of the pitch angle α* of filaments at the plasma outboard midplane. Equilibrium reconstruction verifies that α* is nearly constant and thus well-defined at the midplane edge. Estimates of n obtained using two ECEI systems agree well with n measured by the conventional technique employing an array of Mirnov coils.

Diamagnetic loop measurement in Korea Superconducting Tokamak Advanced Research machine.

Diamagnetic loop (DL), which consists of two poloidal loops inside the vacuum vessel, is used to measure the diamagnetic flux during a plasma discharge in the Korea Superconducting Tokamak Advanced Research (KSTAR) machine. The vacuum fluxes in the DL signal can be compensated up to 0.1 mWb by using the coefficients, which are obtained from experimental investigations, in the vacuum flux measurements during vacuum shots under same operational conditions of magnetic coils for plasma experiment in the KSTAR machine. The maximum error in the diamagnetic flux measurement due to the errors of the coefficients was estimated as ∼0.22 mWb. From the diamagnetic flux measurements for the ohmically heated circular plasmas in the KSTAR machine, the stored energy agrees well with the estimated kinetic energy within the discrepancy of 25%. When the electron cyclotron heating, the neutral beam injection, and the ion cyclotron resonance heating are added to the ohmically heated limiter plasmas, the additional heating effects can be clearly observed from the increase of the stored energy evaluated in the DL measurement.

The first experimental results from x-ray imaging crystal spectrometer for KSTAR.

The x-ray imaging crystal spectrometer (XICS) for the Korea Superconducting Tokamak Advanced Research has been first applied for the experimental campaign in 2009. The XICS was designed to provide measurements of the profiles of the ion and electron temperatures from the heliumlike argon (Ar XVII) spectra. The basic functions of the XICS are properly working although some satellites lines are not well matched with the expected theoretical values. The initial experimental results from the XICS are briefly described.

Diagnostics for first plasma and development plan on KSTAR.

The first plasma with target values of the plasma current and the pulse duration was finally achieved on June 13, 2008 in the Korea Superconducting Tokamak Advanced Research (KSTAR). The diagnostic systems played an important role in achieving successful first plasma operation for the KSTAR tokamak. The employed plasma diagnostic systems for the KSTAR first plasma including the magnetic diagnostics, millimeter-wave interferometer, inspection illuminator, H(alpha), visible spectrometer, filterscope, and electron cyclotron emission (ECE) radiometer have provided the main plasma parameters, which are essential for the plasma generation, control, and physics understanding. Improvements to the first diagnostic systems and additional diagnostics including an x-ray imaging crystal spectrometer, reflectometer, ECE radiometer, resistive bolometer, and soft x-ray array are scheduled to be added for the next KSTAR experimental campaign in 2009.

Spectral resolution measurement of an x-ray imaging crystal spectrometer for KSTAR.

A spectral resolution measurement of the x-ray imaging crystal spectrometer for the Korea Superconducting Tokamak Advanced Research machine utilizing a segmented position-sensitive detector and time-to-digital converter based delay-line readout electronics was performed by using an x-ray tube in a laboratory. The measured spectral resolution is about 12,600, which means the actual energy resolution is 0.32 eV for the x-ray tube's bremsstrahlung peak energy of 4 keV. The results from the spectral resolution measurement are described.

Magnetic diagnostics for the first plasma operation in Korea Superconducting Tokamak Advanced Research.

Magnetic diagnostics for the first plasma operation in the Korea Superconducting Tokamak Advanced Research device are described. The main discussion is the feasibility studies from the magnetic flux and field measurements utilizing the superconducting poloidal field coils before the first plasma generation.

Diamagnetic loop for the first plasma in the KSTAR machine.

The diamagnetic loop (DL) is installed for the plasma diamagnetic measurement at the first plasma in the Korea superconducting tokamak advanced research (KSTAR) machine. Experimental results from the position measurement of the DL inside the KSTAR vacuum vessel and the vacuum flux measurement by using the DL for the evaluation of the geometrical data and the balance coefficient of the DL for the compensation of the vacuum flux in the diamagnetic measurement are described. In addition, a preliminary work of an instrument for a hardware compensation of the vacuum flux is presented.

Performance test of the integrator system for magnetic diagnostics in KSTAR.

Ten modules of the integrator system of the initial magnetic diagnostics for the first plasma operation have been simultaneously tested in the Korea superconducting tokamak advanced research device by measuring the magnetic flux density from various magnetic diagnostics sensors when a small current was applied to the superconducting poloidal field coils. The measured drifts from the integrators show between 1x10(-6) and 1x10(-5) Wb/s. The results from the field tests before the first plasma generation are described.

Calibration of an imaging crystal spectrometer for low x-ray energies.

An x-ray imaging crystal spectrometer was designed for the Hanbit magnetic mirror device to observe spectra of heliumlike neon at 13.4474 A. The spectrometer consists of a spherically bent mica crystal and an x-ray sensitive vacuum charge coupled device camera. This spectrometer can provide spatially resolved spectra, making it possible to obtain profiles of the ion charge state distribution from line ratios and profiles of the plasma rotation velocity from Doppler shift measurements. The paper describes measurements of spectral resolution of this instrument for low x-ray energies.

Data acquisition system for an advanced x-ray imaging crystal spectrometer using a segmented position-sensitive detector.

A versatile time-to-digital converter based data acquisition system for a segmented position-sensitive detector has been developed. This data acquisition system was successfully demonstrated to a two-segment position-sensitive detector. The data acquisition system will be developed further to support multisegmented position-sensitive detector to improve the photon count rate capability of the advanced x-ray imaging crystal spectrometer system.

Development of advanced x-ray imaging crystal spectrometer utilizing a large area segmented proportional counter for KSTAR.

An advanced x-ray imaging crystal spectrometer (XICS) for KSTAR tokamak has been developed by utilizing a segmented two dimensional (2D) position-sensitive multiwire proportional counter. The XICS for the KSTAR tokamak provides time-resolved measurements of the radial ion and electron temperature profiles, toroidal plasma rotation velocity, and ionization equilibrium. The segmented 2D detector with delay-line readout and supporting electronics has been adopted to improve the photon count rate capability. The current fabrication status of the XICS for the KSTAR tokamak and the first performance test results of the prototype segmented 2D detector are presented.

Analog integrator for the Korea superconducting tokamak advanced research magnetic diagnostics.

An analog integrator, which automatically compensates an integrating drift, has been developed for the magnetic diagnostics in the Korea superconducting tokamak advanced research (KSTAR). The compensation of the drift is done by the analog to digital converter-register-digital to analog converter in the integrator. The integrator will be used in the equilibrium magnetic field measurements by using inductive magnetic sensors during a plasma discharge in the KSTAR machine. Two differential amplifiers are added to the signal path between each magnetic sensor and the integrator in order to improve the performance of the integrator because a long signal cable of 100 m will be used for the measurement in the KSTAR machine. In this work, the characteristics of the integrator with two differential amplifiers are experimentally investigated.

Stabilization of interchange modes in mirror plasmas by a nonlinear rf-plasma wave coupling process.

Experimental and theoretical studies are made of the consequences of a nonlinear coupling process between pump rf waves and interchange modes in mirror plasmas. It is demonstrated that the interchange-stable operation window exists depending on the applied rf power and gamma=omega(0)/Omega(i), where omega(0) (Omega(i)) is the angular frequency of the applied rf wave (ion cyclotron frequency). Results are shown that the nonlinear wave coupling process gives rise to the operation window near the resonance (gamma approximately equal to 1), which is elucidated by theoretical analyses combined with full rf wave simulations.