Field-reversed Configuration Plasma Research Articles

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)], are compared with the Spencer’s one-dimensional (1D) theory [R. L. Spencer et al., Phys. Fluids 26, 1564 (1983)] for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio Bw2/Bw1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Enhanced plasma performance in C-2W advanced beam-driven field-reversed configuration experiments

TAE Technologies’ fifth-generation fusion device, C-2W (also called ‘Norman’), is the world’s largest compact-toroid device and has made significant progress in field-reversed configuration (FRC) plasma performance. C-2W produces record breaking, macroscopically stable, high-temperature advanced beam-driven FRC plasmas, dominated by injected fast particles and sustained in steady state, which is primarily limited by neutral-beam (NB) pulse duration. The NB power supply system has recently been upgraded to extend the pulse length from 30 ms to 40 ms, which allows for a longer plasma lifetime and thus better characterization and further enhancement of FRC performance. An active plasma control system is routinely used in C-2W to produce consistent FRC performance as well as for reliable machine operations using magnet coils, edge-biasing electrodes, gas injection and tunable-energy NBs. Google’s machine learning framework for experimental optimization has also been routinely used to enhance plasma performance. Dedicated plasma optimization experimental campaigns, particularly focused on the external magnetic field profile and NB injection (NBI) optimizations, have produced a superior FRC plasma performance; for instance, achieving a total plasma energy of ∼13 kJ, a trapped poloidal magnetic flux of ∼16 mWb (based on the rigid-rotor model) and plasma sustainment in steady state up to ∼40 ms. Furthermore, under some operating conditions, the electron temperature of FRC plasmas at a quiescent phase has successfully reached up to ∼1 keV at the peak inside the FRC separatrix for the first time. The overall FRC performance is well correlated with the NB and edge-biasing systems, where higher total plasma energy is obtained with higher NBI power and applied voltage on biasing electrodes. C-2W operations have now reached a mature level where the machine can produce hot, stable, long-lived, and repeatable plasmas in a well-controlled manner.

Refueling of field-reversed configuration core via axial plasmoids injection

This study successfully developed a refueling technique for a field-reversed configuration (FRC) via axial plasmoid injection and demonstrated it on the FAT-CM device at Nihon University. The target FRC is generated using the collisional-merging formation technique combined with conical theta-pinch formation. Plasmoids with an FRC-like configuration are coaxially injected from both ends of the FAT-CM device toward the preexisting target FRC. Postinjection, the system achieves equilibrium, resulting in increases by factors of 1.8 and 2.4 in the total inventory and plasma energy, respectively, compared to cases without injection. This method effectively accomplishes FRC refueling while preserving the intrinsic characteristics of a simply connected, axisymmetric configuration and a high beta value approaching unity. Therefore, this approach offers potential for repetitive refueling in the reactor stage having a FRC plasma core. Experimental outcomes are compared with magnetohydrodynamic simulation results. In the collisional merging process, the characteristics of the pre-collision plasmoids, such as the strong toroidal rotation and coherent FRC-like magnetic field structures of the FRC, are not preserved. Experimental environments have been constructed to investigate such unique properties of the resulting FRCs.

First spectroscopic study of HFRC plasma

An advanced spectral diagnostic system was developed to measure the electron temperature (T e), electron density (N e), and ion temperature (T i) of the Huazhong University of Science and Technology field-reversed configuration plasma. The system consists of an optic fiber spectrometer with a wide spectral band and a 670 mm focal length high throughout Czerny–Turner monochromator equipped with both a 3600 g mm−1 grating and a 2400 g mm−1 grating to measure the line spectrum. Accompanying these components is an electron-multiplying charge-coupled device camera to capture spectral data. The relative intensity of the optical fiber spectrometer was calibrated using a standard luminance source, and the wavelength calibration of the spectrometer was accomplished using a Hg/Ar lamp. This diagnostic setup was configured to measure electron density based on the Stark effect of Hγ (n = 5 → n = 2; 434.04 nm). Doppler broadening of an O III (2s22p(2P0)3p → 2s22p(2P0)3s; 375.988 nm) emission line was measured and analyzed to obtain the ion temperature, and electron temperatures were estimated from the relative strength of Hβ (n = 4 → n = 2; 486.14 nm) (Dβ) and Hγ (Dγ) spectral lines when the electron density was obtained from Stark effect measurements. The initial experimental results indicate that the highest electron temperature of the formation region was approximately 8 eV, the electron density of the colliding-and-merging region was approaching 1020 m−3, and the ion temperature reached about 40 eV.

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.