Field-reversed Configuration Plasma Research Articles

A New Device Concept of Magnetic Confinement Deuterium–Deuterium Fusion

A two-stage cascade magnetic compression scheme based on field reversed configuration plasma is proposed. The temperature and density of plasma before and after magnetic compression are analyzed. In addition, the suppression of the two-fluid effect and the finite Larmor radius effect on the tilting mode and the rotating mode of major magnetic hydrodynamic instability is studied, and finally, the key physical and engineering parameters of the deuterium–deuterium fusion pulse device are introduced. Further analysis shows that the fusion neutrons can be produced at an energy flux of more than 2 MW/m2 per year, which meets the material testing requirements for the fusion demonstration reactor (DEMO). If the recovery of magnetic field energy is taken into account, net energy outputs may be achieved, indicating that the scheme has a potential application prospect as a deuterium–deuterium pulse fusion energy.

Quasi-static magnetic compression of field-reversed configuration plasma: amended scalings and limits from two-dimensional MHD equilibrium

In this work, several key scaling laws of the quasi-static magnetic compression of field reversed configuration (FRC) plasma (Spencer et al 1983 Phys. Fluids 26 1564) are amended from a series of two-dimensional FRC MHD equilibriums numerically obtained using the Grad–Shafranov equation solver NIMEQ. Based on the new scaling for the elongation and the magnetic fields at the separatrix and the wall, the empirically stable limits for the compression ratio, the fusion gain, and the neutron yield are evaluated, which may serve as a more accurate estimate for the upper ceiling of performance from the magnetic compression of FRC plasma as a potential fusion energy as well as neutron source devices.

Development of multichord ion Doppler spectroscopy system for toroidal flow measurement of field-reversed configuration.

A double-chord ion Doppler spectroscopy (IDS) system was developed to measure the ion temperature and flow velocity of field-reversed configuration (FRC) plasmas in the FRC amplification via a translation-collisional merging (FAT-CM) device. Adopting a Czerny-Turner mount monochromator and 16-channel photomultiplier tube array, the developed IDS system achieves high wavelength resolution and fast time response. In addition, two vertically aligned optical paths share the optical system up to the monochromator and then branch just before the detector, successfully reducing crosstalk to <1%. The Doppler broadening was measured at two measurement points in the FAT-CM device, simultaneously, and ion temperatures of ∼50eV were measured. Toroidal spin-up from 7 to 15 km/s and a steady flow velocity of ∼10 km/s were estimated from the Doppler shift obtained by the developed system. The observation of the toroidal flow velocity and the spatial profile of the ion temperature of the FRC plasma in the FAT-CM device were realized. These spectroscopic diagnostic's double chord capabilities will aid in understanding and improving the FRC plasmas.

Helium line ratio imaging in the C-2W divertor.

A 2D imaging instrument has been designed and deployed on C-2W ("Norman") [H. Gota et al., Nucl. Fusion 61, 106039 (2021)] to study the plasma in the expander divertor by simultaneously measuring three neutral helium spectral lines. Ratios of these images, in conjunction with a collisional-radiative model, yield 2D maps of electron temperature and density. Almost the entire radial plasma cross-section (∼60cm) can be mapped with a spatial resolution ≲1cm. These data can, in principle, be acquired at 3kHz. The neutral helium target is provided by a custom-built supersonic gas injector located inside the divertor vessel, which injects helium toward the magnetic axis and perpendicular to the camera sight-cone. Images of helium emission and reconstructed electron density and temperature profiles of the plasma produced from an end gun are presented. Voltages applied to concentric annular electrodes located in the divertors are used to stabilize beam-driven field reversed configuration plasmas. Magnetic field expansion is also employed to thermally isolate electrons from the end electrodes. Measurements of electron temperature and density in the divertor are important in order to study the effects of both the electrostatic biasing and the divertor magnetic field on electron confinement, neutral gas transport, and the overall machine performance.

High-fidelity inference of local impurity profiles in C-2W using Bayesian tomography.

In C-2W (also called "Norman") [1], beam-driven field reversed configuration plasmas embedded in a magnetic mirror are produced and sustained in a steady state. A multi-chord passive Doppler spectroscopy diagnostic provides line-integrated impurity emission measurements near the center plane of the confinement vessel with fast time resolution. The high degree of plasma non-uniformity across optical sightlines can preclude direct fitting of the measured line-integrated spectra. To overcome this challenge, local impurity profiles are inferred using Bayesian tomography, a superior analysis technique based on a complete forward model of the diagnostic. The measured emission of O4+ triplet lines near 278.4nm is modeled assuming two independent populations: thermal and beam ions. Gaussian processes are used to generate and infer local profiles. The inference incorporates details of the geometrical arrangement of the diagnostic, instrument function, intensity calibration, and a noise model. Markov chain Monte Carlo (MCMC) sampling of the posterior distribution of solutions provides high-fidelity uncertainty estimates. The reconstructed O4+ impurity profiles are consistent with data from other diagnostics and show good agreement with expected physics based on previously developed models of biasing circuit and impurity transport.

Upgraded main ion charge exchange recombination spectroscopy on the C-2W field reversed configuration (FRC) plasma.

A prototype main-ion CHarge Exchange Recombination Spectroscopy (mCHERS) diagnostic is providing measurements of the main-ion (hydrogen or deuterium) temperature and velocity in the C-2W field reversed configuration plasma using charge exchange Balmer-alpha emission at five different radial locations with 500Hz frequency and a per-pixel velocity resolution of 15 km/s. Measurement along the entire plasma radius of C-2W is enabled by a diagnostic neutral beam (DNB) that passes through the center of plasma, unlike the larger diameter heating neutral beams that have impact parameters of 20cm. DNB provides high time resolution via beam modulation and spatial resolution via its small cross section. The goals of the current mCHERS upgrade are to double the number of spatial channels, improve the per-pixel velocity resolution by three times, and increase the measurement frequency to match the maximum modulation frequency of the diagnostic neutral beam (∼10kHz). To accomplish these goals, a new astigmatism-free Isoplane spectrometer has been commissioned. Progress and results from the newly upgraded mCHERS system are detailed.

Improvement and test of high-voltage pulsed power supply for HFRC

Field-reversed theta-pinch (FRTP) is commonly used to form high-performance field-reversed configuration (FRC) plasmas, and it is employed for the initial plasma formation in the HFRC device. The high-voltage pulsed power supply which is used to feed the θ-pinch coils in HFRC has already demonstrated its importance for initial plasma formation. This paper presents two attempts to improve the performance of the high-voltage pulsed power supply. To reduce the space occupation and increase the accuracy of the triggers of hydrogen thyratron, a newly designed high-voltage floating trigger is proposed in this paper. Experimental tests show that the optimized trigger can work stably under a floating voltage of 35 kV with a voltage rising rate of about 12 kV/μs and a total jitter time of less than 60 ns. Besides, a high-voltage laminated busbar is proposed to reduce the stray parameters. Experimental tests show that it can withstand a voltage of 34 kV. The peak current and frequency of each branch of the power supply are increased by at least 10%. Tests of the entire power supply show that the power supply can work stably under a voltage of 34 kV. The oscillation frequency of the Pre-Ionization (PI) branch can reach 152.0 kHz and the peak current of the Main branch can reach 78.3 kA. The results show the validity and reliability of the improvements.

Fiber Bragg grating sensor array for detecting heat flux in vacuum.

In TAE Technologies' current experimental device, C-2W (also called "Norman"), record-breaking, advanced beam-driven field-reversed configuration plasmas are produced and sustained in steady state utilizing variable energy neutral beams, advanced divertors, edge-biasing electrodes, and an active plasma control system [Gota etal., Nucl. Fusion 61, 106039 (2021)]. A novel diagnostic has been developed by TAE Technologies to leverage an industrial fiber Bragg grating (FBG) sensor array to detect heat flux along the wall of the vacuum vessel from a plasma discharge. The system consists of an optical fiber with FBG sensors distributed along its length, housed in a pressurized steel sheath. Each FBG sensor is constructed to reflect a different wavelength, the exact value of which is sensitive to the strain and temperature at the location of the grating in the fiber. The fiber is illuminated with broadband light, and the data acquisition system analyzes the spectrum of reflected light to determine the temperature at the location of each FBG. We have installed four of these vacuum-rated FBG sensor arrays on the C-2W experiment, each with 30 individual FBG sensors spaced at 0.15m intervals along the 5m fiber, with a 100Hz acquisition rate. The measurement of temperature change due to a plasma discharge provides a single data point at each sensor location, creating a 120-point heat map of the vacuum vessel.

Simulation on formation process of field-reversed configuration

Collisional-merging is a way to form high-performance field-reversed configuration (FRC) plasma. An experiment device named HUST-FRC (HFRC) is under construction in Huazhong University of Science and Technology, which will be used to investigate the FRC formation through collisionalmerging. In this research, a magnetohydrodynamics simulation software called USim is used to study the effect of the initial density of plasma, the amplitude of the bias magnetic field, the configuration of the bias field, the rise time of the main field and the magnetic field ripple on the plasma parameters to facilitate the design and operation of HFRC. Preliminary simulation results show that cusp configuration, lower ripple, higher initial density, an initial bias field of −0.15 T or −0.2 T, and a rise time of 4 μs are conducive to the formation of high-performance FRC plasma in the HFRC device.

Project Design of a Pulsed D-D Fusion Neutron Source Based on Field Reversed Configuration

The fusion neutron source is of great significance for conducting material testing for future fusion reactors, as it can genuinely reflect the change of material properties under fusion neutron irradiation. The International Fusion Materials Irradiation Facility (IFMIF) is an accelerator-driven neutron source. It still has some differences from the ideal fusion neutron source in terms of fusion neutron energy spectrum, which has led to the reconsideration of the fusion neutron source approach. In this paper, the magnetic field configuration, heating scheme design, and related calculations are carried out regarding the fusion neutron source. The plasma temperature, density evolution process, and the corresponding neutron yield of the field reversed configuration (FRC) plasma after two-stage cascade magnetic compression are analyzed, and the suppression of the magnetic fluid instabilities such as tilted and rotating modes of the FRC plasma after considering the two-fluid effect and the finite Larmor radius effect are studied. The fundamental physical parameters of the fusion neutron source are finally given. The calculation results show that the neutron source is expected to obtain fusion neutrons with an annual average power density higher than 2 MW/m², which can meet the requirements of material testing of the demonstration reactors (DEMO). The power estimation also shows that the scheme has the potential to become an energy source based on the pulsed deuterium-deuterium fusion.

Numerical simulation of wave propagation and plasma response excited in field-reversed configuration plasma

A hybrid simulation (a model that treats ions as particles and electrons as fluid) is performed to analyse the propagation of waves excited in the field-reversed configuration plasma and the resulting plasma response. The current of the wave excitation antenna changes in a sine wave, and its frequency is set so that it has an ion cyclotron resonance point inside the separatrix. When the antenna current is maximum, a magnetic field with a magnitude of 40% of the external magnetic field is created on the separatrix. A toroidal magnetic field is excited in the plasma by applying waves. The observed propagation velocity of the toroidal magnetic field is comparable with the shear Alfvén wave outside the separatrix, and is on the same order within the separatrix. This result has a tendency similar to the propagation velocity outside the separatrix reported in the wave experiment in the past FIX machine. The simulation results also show that when the excited magnetic field propagates in the axial direction, the separatrix is compressed or expanded, and the high-density region of the ions formed thereby moves in the axial direction. In addition, the excited magnetic energy is rapidly decreased near the position where the velocities of the shear Alfvén wave and the ion sound wave are equal (local beta value is 0.88). It is found that the decay of the excited magnetic energy occurred at a point outside the ion cyclotron resonance point. This suggests that the compression and expansion of the plasma is caused while maintaining the quasi-equilibrium state according to the change in the external magnetic pressure.

Overview of C-2W: high temperature, steady-state beam-driven field-reversed configuration plasmas

TAE Technologies, Inc. (TAE) is pursuing an alternative approach to magnetically confined fusion, which relies on field-reversed configuration (FRC) plasmas composed of mostly energetic and well-confined particles by means of a state-of-the-art tunable energy neutral-beam (NB) injector system. TAE’s current experimental device, C-2W (also called ‘Norman’), is the world’s largest compact-toroid device and has made significant progress in FRC performance, producing record breaking, high temperature (electron temperature, T e > 500 eV; total electron and ion temperature, T tot > 3 keV) advanced beam-driven FRC plasmas, dominated by injected fast particles and sustained in steady-state for up to 30 ms, which is limited by NB pulse duration. C-2W produces significantly better FRC performance than the preceding C-2U experiment, in part due to Google’s machine-learning framework for experimental optimization, which has contributed to the discovery of a new operational regime where novel settings for the formation section and the confinement region yield consistently reproducible, hot, and stable plasmas. An active plasma control system has been developed and utilized in C-2W to produce consistent FRC performance as well as for reliable machine operations using magnets, electrodes, gas injection, and tunable NBs. The active control system has demonstrated stabilization of FRC axial instability. Overall FRC performance is well correlated with NBs and edge-biasing system, where higher total plasma energy is obtained by increasing both NB injection power and applied-voltage on biasing electrodes. C-2W divertors have demonstrated a good electron heat confinement on open-field-lines using strong magnetic mirror fields as well as expanding the magnetic field in the divertors (expansion ratio > 30); the energy lost per electron ion pair, η e ∼ 6–8, is achieved, which is close to the ideal theoretical minimum.

Main ion charge exchange recombination spectroscopy on C-2W FRC plasmas.

A main ion charge exchange recombination spectroscopy (mChERS) diagnostic has been developed to measure the velocity and temperature of the main deuterium ions in the C-2W (also called Norman) field-reversed configuration (FRC) device. A modulated diagnostic neutral beam (DNB) of hydrogen with 40 keV full energy and a nominal current of 8.5A provides the charge exchange signal. The DNB can achieve a fast modulation frequency of up to 10 kHz, a rare attribute to find on other fusion devices, which defines the time resolution of mChERS. Currently, the mChERS diagnostic provides simultaneous measurements at five spatial locations in the FRC plasma using a high-speed camera. The design and capabilities of the mChERS system are presented along with first experimental data.

Multi-point density measurement of a collisional merging formation process of FRCs.

Collisional merging formation of field-reversed configuration (FRC) plasmas at supersonic velocities was performed using the FRC amplification via translation-collisional merging device. Supersonic collisional merging formation is a novel technique to form an FRC that is long-lived compared to a conventional initial formation FRC; however, this technique requires measuring the plasma parameters at multiple points simultaneously because of the dynamic translation/merging process. Herein, we have developed a new interferometer and have observed the dynamic behavior of FRCs in the formation, translation, and merging processes simultaneously. In this study, as one of the performance evaluations of the developed simultaneous density measurement, collision/merging of FRCs have been conducted in the confinement section with and without background neutral gas. Comparing translation into deuterium gas vs translation into a vacuum environment prior to the collisional merging, we found that the background neutral particles were trapped in the merged FRC; moreover, a difference in the decay rate of the stored internal energy was observed.

Measurements of impurity ion temperature and velocity distributions via active charge-exchange recombination spectroscopy in C-2W.

In TAE Technologies' C-2W experiment, electrode biasing is utilized for boundary control of a field-reversed configuration (FRC) plasma embedded in a magnetic mirror. Understanding the underlying physics associated with FRC rotation, stabilization, and heating is crucial for improving machine performance. Impurity ion rotation and temperature are sensitive to biasing effects, and measurements of these quantities can provide insight into important plasma dynamics and overall effectiveness of the biasing system. To this end, a charge-exchange recombination spectroscopy (ChERS) diagnostic was developed and deployed to measure local impurity ion temperature and velocity in the confinement vessel of C-2W. The system utilizes a new diagnostic neutral beam (40 keV, 8.5A) and a fiber-coupled spectrometer with an image-intensified high-speed camera to measure beam-induced spectral line emission at multiple lines-of-sight. Design details and the first experimental results obtained with this new diagnostic are presented and discussed.

Development of a Langmuir probe array for radial potential profile measurement in the collisional merging formation FRC.

The radial electric field in a field-reversed configuration (FRC) plasma plays an important role in the global stability and confinement properties. Herein, we developed a new Langmuir probe array named "Skewered probe" employed in measuring the radial potential profile in the collisional merging formation of an FRC in the FAT-CM (FRC Amplification via Translation - Collisional Merging) device. Because an FRC has a strong toroidal flow, the skewered probe consists of alternately skewered ring electrodes and ceramic beads on a thin stainless-steel tube to neutralize the effect of plasma flow. The developed array has nine electrodes, one every 2cm from r = 9-25cm, and it measures the FRC boundary in the case when the radius of the excluded flux ranges from 10 to 20cm. The skewered probe also has one additional electrode that measures the potential near the chamber wall as a reference for the other electrodes. The radial potential profile of the FRC formed by the collisional merging method in the FAT-CM device was measured using the probe, and the results showed that the region of negative potential gradually changed to a positive potential after merging the FRCs. It was also shown that a strong outward electric field is formed near the separatrix at n = 2 rotational instability.

A novel technique for in situ calibration of the C-2W electromagnetic neutral particle analyzer utilizing machine learning.

In TAE Technologies' current experimental device, C-2W, neutral beam injection creates a large fast ion population that sustains a field-reversed configuration (FRC) plasma. Diagnosis of these fast ions is therefore critical for understanding the behavior of the FRC. Neutral Particle Analyzers (NPAs) are used to measure the energy spectrum of fast ions that charge exchange on background or beam neutrals and are lost from the plasma. To ensure correct diagnosis of the fast ion population, a calibration check of the NPAs was performed. A novel, generally applicable method for an in situ relative calibration of diagnostics on an unknown source with a small dataset was developed. The method utilizes a machine learning technique, Generalized Additive Models (GAMs), to reconstruct the diagnostic source distribution, and Stochastic Gradient Descent (SGD) to determine the NPA channel calibration factors. The results on both synthetic and experimental datasets are presented.

Automated signal classification in the C-2W fusion experiment.

In TAE Technologies' current experimental fusion device, C-2W (also called "Norman"), record breaking, advanced beam-driven field-reversed configuration plasmas are produced and sustained in steady state utilizing variable-energy neutral beams, expander divertors, end-bias electrodes, and an active plasma control system. With a rapid shot-pace and an extensive number of data channels, the amount of data generated necessitates automated signal processing. To this end, a machine learning algorithm consisting of a multi-layered neural network as well as other data processing software has been designed for signal feature identification, allowing for accurate and fast signal classification, anomalous condition detection, and providing for signal pre-processing. With a small set of training data, the neural network can be "bootstrapped" to provide a robust classification system while minimizing human oversight. An example using data from the theta pinch plasma formation pulsed power system is presented. With an overall accuracy of ∼97%-having classified more than 5 × 106 pulsed power signals-the classification scheme is more than sufficient to fine-tune machine set points. However, this technique can be used for near-real-time preprocessing of any plasma physics signal and has wide ranging application in fusion experiments for the varied data produced by plasma diagnostics.

MHD mode identification by higher order singular value decomposition of C-2W Mirnov probe data.

The C-2W device (also known as "Norman") at TAE Technologies has proven successful at generating stable, long-lived field-reversed configuration (FRC) plasmas with record temperatures. The largest Mirnov probe array in C-2W measures three components of the magnetic field just inside the vessel wall at 64 locations distributed approximately evenly in the cylindrical vessel's azimuthal and axial dimensions. This nearly rectangular array of probes creates a unique opportunity to apply higher order singular value decomposition (HOSVD) to efficiently analyze the external magnetic field data for the purposes of reconstructing the magnetohydrodynamic mode structures in the FRC. In the first application of this method for this purpose, HOSVD is shown to quickly and effectively detect and separate toroidal modes while indicating longitudinal dependence of mode phases and amplitudes, enhancing the coherence and utility of the vast quantity of data produced by this array. Analysis of the data from the entire array at once via HOSVD proves not only computationally more efficient than methods that separately analyze groups of probes at different axial locations but also leads to improved mode resolution at axial locations where these modes are weaker.

Comprehensive imaging of C-2W plasmas: Instruments and applications.

The C-2W device ("Norman") [Gota et al., Nucl. Fusion 59, 112009 (2019)] has produced and sustained beam-driven field-reversed configuration (FRC) plasmas embedded in a magnetic mirror geometry using neutral beams and end-bias electrodes located in expander divertors. Several discrete vessels comprise this device, and many imaging instruments are required in order to view the plasma throughout. To meet this need, a suite of spatially and radiometrically calibrated, high-speed camera systems have been deployed. Besides global visualization of the plasma evolution and macro-stability, this imaging suite has been used in a variety of applications. One example application is a tomographic reconstruction of passive impurity emission. Calculation of the magnetic field in the equilibrium vessel is complicated by eddy currents in conducting structures and internal currents in the high-β FRC plasma. In addition, thus far non-perturbative measurements of internal field have not been available. The tomographic reconstruction of O4+ impurity emission enables an independent visualization of the plasma geometry, serving as a check on magnetic modeling and indirect evidence for field reversal within the FRC. A second application uses the cameras to view the Balmer-α emission throughout the plasma in order to estimate the ionization rate in each region. These rates can then be incorporated into particle balance calculations and a circuit model for currents from the end-bias electrodes. Finally, arcing on the electrode surfaces is identified through automated image processing of carefully selected spectral line emission.