Field-reversed Configuration Research Articles

Analysis of azimuthal electron current driving by rotating magnetic field in field-reversed configuration electric propulsion

Field-reversed configuration electric propulsion is an advanced space electromagnetic propulsion technology with significant application prospects but poor thrust performance. To delve into the intrinsic physical mechanisms, a model of the rotating magnetic field penetrating into the plasma and azimuthal electron current driving was developed. The simulation results show that rotating magnetic field strength, frequency, and initial seed plasma density are the key factors that exist as an optimal threshold. Specifically, the rotating magnetic field feed current (i.e., magnetic field strength) was not less than 1000 A, the rotating magnetic field frequency was ∼200–300 kHz, and the plasma density was approximately 1 × 1018 m−3 order of magnitude.

Structure Formation Through Magnetohydrodynamical Instabilities in Primordial Disks

The shear flow instabilities under the presence of magnetic fields in the primordial disk can greatly facilitate the formation of density structures that serve as seeds prior to the onset of the gravitational Jeans instability. We evaluate the effects of the Parker, magnetorotational and kinematic dynamo instabilities by comparing the properties of these instabilities. We calculate the mass spectra of coagulated density structures by the above mechanism in the radial direction for an axisymmetric magnetohydrodynamic (MHD) torus equilibrium and power density profile models. Our local three-dimensional MHD simulation indicates that the coupling of the Parker and magnetorotational instability creates spiral arms and gas blobs in an accretion disk, reinforcing the theory and model. Such a mechanism for the early structure formation may be tested in a laboratory. The recent progress in experiments involving shear flows in rotating tokamak, field reversed configuration (FRC) and laser plasmas may become a key element to advance in nonlinear studies.

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 (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) 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 B w 2 / B w 1 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.

Experimental study on the formation and evolution of unconfined counter-helicity spheromaks merging using magnetized coaxial plasma gun

The formation and evolution of unconfined counter-helicity spheromaks merging have been experimentally investigated by using a magnetized coaxial plasma gun. By comparing the time-dependent photodiode signals and plasma radiation images of counter-helicity spheromaks merging and plasma jets merging, it is found that the field-reversed configuration (FRC) plasma formed by counter-helicity spheromaks merging has a distinct contour and a long maintenance time. For plasma jets merging, the resulting plasma has no discernible contours and a shorter lifetime. In addition, it is inferred from these data that stagnation heating and magnetic reconnection events occur during the counter-helicity spheromaks merging, causing a rapid rise in plasma pressure at the merging midplane and sharp kinks in the field lines near the merger region. By changing different operating parameters and observing the impact on the merger characteristics, it is suggested that the qualitative dynamics of the FRC plasma depends on the balance between the plasma pressure and the magnetic pressure. The high discharge voltage breaks the equilibrium in the merged body, while the large gas-puffed mass just weakens the compression effect of the merged body. These results give us an intuitive understanding of the counter-helicity spheromak merger process and its dependence on discharge parameters, and also provide a distinct perspective for the optimal design of FRC.

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 gyrokinetic simulation model for 2D equilibrium potential in the scrape-off layer of a field-reversed configuration

The equilibrium potential structure in the scrape-off layer (SOL) of the field-reversed configuration (FRC) can be affected by the penetration of edge biasing applied at the divertor ends. The primary focus of the paper is to establish a formulation that accurately captures both parallel and radial variations of the two-dimensional (2D) potential in SOL. The formulation mainly describes a quasi-neutral plasma with a logical sheath boundary. A full-f gyrokinetic ion model and a massless electron model are implemented in the GTC-X code to solve for the self-consistent equilibrium potential, given fixed radial potential profiles at the boundaries. The first essential point of this 2D model lies in its ability to couple radial and parallel dynamics stemming from resistive currents and drag force on ions. The model successfully recovers the fluid force balance and continuity equations. These collisional effects on 2D potential mainly appear through the density profile changes, modifying the potential through electron pressure gradient. This means an accurate prescription of electron density and temperature profiles is important in predicting the potential structure in the FRC SOL. The Debye sheath potential and the potential profiles applied at the boundaries can be additional factors contributing to the 2D variations in SOL. This comprehensive full-f scheme holds promise for future investigations into turbulent transport in the presence of the self-consistent 2D potential together with the non-Maxwellian distributions and open boundary conditions in the FRC SOL.

Development of a field-reversed configuration device using radio frequency antennas to produce E × B for current-drive

A unique field-reversed configuration (FRC) experiment is presently being assembled at the Plasma Technology Research Institute, KFE. It is a compact small-scale FRC device, which uses a set of radio frequency (RF) antennas to produce an internal E × B that drives the electrons for current-drive, in which E is the electric field and B is the magnetic field. This is very similar to the rotating magnetic field (RMF) current-drive, where the horizontal and vertical antennas are driven 90° out of phase. For this device, the RF antennas are arranged differently than the RMF. The RF antennas, being two separate sets, are positioned inside the vacuum chamber. Each set consists of 8 coils, for a total of 16 coils, where 80~100 kHz sine and cosine waveform currents are applied. One set of coils generates a radial B-field, while the other set provides an E-field in the z-direction. As the phase changes, the E and B fields are switched by these two sets. Nevertheless, E × B propagates in the same θ-direction so that this allows the electrons to rotate around the circumference of the device. The FRC device will test wave heating by launching 2.45 GHz microwaves. Also, passive stabilizers are positioned at each end to provide extra stability while preventing tilt instability. The experiment is expected to produce its first plasma in 2025.

A numerical survey of parameters to reach ignition condition for axial compression of a large-sized field reversed configuration

Field reversed configuration (FRC) is widely considered as an ideal target plasma for magneto-inertial fusion. However, its confinement and stability, both proportional to the radius, will deteriorate inevitably during radial compression. Hence, we propose a new fusion approach based on axial compression of a large-sized FRC. The axial compression can be made by plasma jets or plasmoids converging onto the axial ends of the FRC. The parameter space that can reach the ignition condition while preserving the FRC’s overall quality is studied using a numerical model based on different FRC confinement scalings. It is found that ignition is possible for a large FRC that can be achieved with the current FRC formation techniques if compression ratio is greater than 50. A more realistic compression is to combine axial with moderate radial compression, which is also presented and calculated in this work.

Suppression of radial motion in translated field-reversed configuration plasma via global gyro-effect

Abstract The radial motion of a field-reversed configuration (FRC) during translation at supersonic/Alfvénic speed was effectively suppressed by the global gyro-effect induced by toroidal flow. In magnetohydrodynamic approximation, an FRC is inherently unstable against radial motions such as tilt and wobble. Surprisingly, the magnetic structure of the FRC remained intact even during translation at speeds exceeding the ion sonic and Alfvén speeds, despite the presence of radial motions. Optical observations were conducted on the radial motion and toroidal flow of translated FRCs under various electric boundary conditions at the device end. The implementation of end-shorting led to an increased toroidal flow rate, consequently reducing the radial displacement of the FRC during translation. This control of toroidal flow from the device’s end not only suppressed radial motion but also facilitated head-on collisions in the formation of FRCs by the collisional merging technique. The findings emphasize the significance of toroidal flow control in preserving the integrity of FRC’s simply connected geometry and enhancing its formation performance.

Verification of a Monte Carlo binary collision model for simulating elastic and inelastic collisions in particle-in-cell simulations

We present the development and verification of a Monte Carlo binary collision model for simulating elastic and inelastic collisions in particle-in-cell simulations. We apply the corrected binary collision model originally developed for charged-particles collisions to all considered scattering channels, including Coulomb collisions, elastic neutral–neutral and charged–neutral collisions, ionization, excitation, and fusion. The model's implementation is described and verified through a series of simulations, including charged- and neutral-particle thermal equilibration, slowing of electrons in warm solid-density aluminum, collisional damping of a Langmuir wave, helium gas breakdown in an applied electric field, and thermonuclear and beam–target fusion. Then, we demonstrate the model within simulations of hydrogen plasma formation in the Princeton Field-Reversed Configuration as well as of the burning of aneutronic fusion fuel p-11B. The latter includes measurement of the fusion power density in a low-density plasma and fusion production due to the stopping of a proton ignitor beam in a compressed boron target.

Reconstruction of poloidal magnetic field profiles in field-reversed configurations with machine learning in laser-driven ion-beam trace probe

The diagnostic of poloidal magnetic field ( ) in field-reversed configuration (FRC), promising for achieving efficient plasma confinement due to its high β, is a huge challenge because is small and reverses around the core region. The laser-driven ion-beam trace probe (LITP) has been proven to diagnose the profile in FRCs recently, whereas the existing iterative reconstruction approach cannot handle the measurement errors well. In this work, the machine learning approach, a fast-growing and powerful technology in automation and control, is applied to reconstruction in FRCs based on LITP principles and it has a better performance than the previous approach. The machine learning approach achieves a more accurate reconstruction of profile when 20% detector errors are considered, 15% fluctuation is introduced and the size of the detector is remarkably reduced. Therefore, machine learning could be a powerful support for LITP diagnosis of the magnetic field in magnetic confinement fusion devices.

RF dispersion relations in FRC geometries and HHFW regime

Field reversed configurations (FRC) are characterized by a magnetic field topology, which exhibits the inversion of the external magnetic field through plasma sustained current and the subsequent presence of a null field surface. A monotonical radial decrease in the longitudinal magnetic field leads to the potential presence of harmonics of the ion cyclotron frequency of any order in the region included between the outer wall and the null field surface. What is the effective hot-plasma dispersion relation obtained through the convolution of a large ensemble of high harmonics fast waves (HHFW) confined in a finite radial region represents an open question that we attempt to address here. In particular, we discuss a combination of analytical modeling and numerical treatment, which allows us to retrieve the resulting high harmonic fast wave complex wavevector for any radial location of any FRC radial profile. Moreover, we show how the obtained hot-plasma HHFW wavevector relates to the cold-plasma solution, and how it depends on the plasma parameters.

Observation of rapid flux coalescence in merging field-reversed configurations

Rapid magnetic reconnection was experimentally observed to occur within a microsecond timescale, leading to the field-reversed configuration (FRC) comprising a single closed magnetic field structure. The compressibility of the plasma within the FRC played a crucial role in accelerating the coalescence process, making it considerably faster than the resistive process. A strong similarity between the observed experimental results and those of the coalescence of solar flare loops indicates that astrophysical phenomena and laboratory plasmas are governed by a common physics.

Accelerated kinetic model for global macro stability studies of high-beta fusion reactors

The field reversed configuration (FRC), such as studied in the C-2W experiment at TAE Technologies, is an attractive candidate for realizing a nuclear fusion reactor. In an FRC, kinetic ion effects play the majority role in macroscopic stability, which allows global stability studies to make use of fluid-kinetic hybrid (also referred to as Ohm's law) models wherein ions are treated kinetically while electrons are treated as a fluid. The development and validation of such a hybrid particle-in-cell algorithm in the Exascale Computing Project code WarpX are reported here. Implementation of this model in the WarpX framework benefits from the numerical efficiency of WarpX as well as its scalability on large HPC systems and portability to different architectures. Performance benchmarks of the new algorithm for large, 3-dimensional, full device simulations from the Perlmutter supercomputer are presented. Results of a series of FRC simulations are discussed in which the impact of two-fluid effects on the tilt-mode growth rate was studied. It was observed that, in agreement with previous Hall-MHD studies, two-fluid effects have a stabilizing impact on the tilt mode.

Inductive probe measurements in a rotating magnetic field thruster

The induced magnetic field during acceleration in a pulsed rotating magnetic field (RMF) thruster is experimentally investigated. A two-axis Bdot probe is employed to characterize the time-resolved evolution of the fields in a 5 kW-class test article. This device is operated at an average power of 4 kW with an RMF frequency of 415 kHz, pulse widths of 125 µs, and a repetition rate of 155 Hz. Plasma currents induced in the thruster are shown to reach 2500 A and to have sufficient magnitude to form a field-reversed configuration plasmoid. The Lorentz force resulting from the induced magnetic field contributes ∼25% of measured thrust at this operating condition. Of this Lorentz thrust, ∼58% is due to plasma current interaction with the steady applied bias field, while the remainder is caused by interaction with secondary induced currents in nearby structural elements. This structure force is predicted to scale quadratically with plasma current magnitude. These results are discussed in the context of the historically low performance of these devices and strategies for improving their operation are presented.

Laboratory study of the PFRC-2's initial plasma densification stages

Initial plasma densification by odd-parity rotating magnetic fields (RMFo) applied to the linear magnetized Princeton field-reversed configuration (PFRC-2) device with fill gases at pressures near 1 mTorr proceeds through two phases: a slow one, characterized by a rise time τslow∼100μs, followed by a fast one, characterized by τfast∼10μs. The transition from slow to fast occurs at a line-integral-averaged electron density, tne, near 2×1011 cm−3, independent of magnetic field. Over most of the range of experimental parameters investigated, as the PFRC-2 axial magnetic field strength was increased, RMFo power decreased, gas fill pressure lowered, or lower atomic mass unit (AMU) fill gas used, the duration of the slow phase lengthened from 50 μs to longer than 10 ms after the RMFo power began. The post-fast-phase maximum ne increases with the fill-gas AMU, exceeding 5 × 1013 cm−3 for Ar. The slow phase is consistent with atomic physics processes and field-parallel sound-speed losses. The fast phase may be explained by improved axial confinement, possibly augmented by radial or axial contraction of the plasma. Another possible explanation, a large increase in electron temperature, is inconsistent with x-ray emission. The ne behavior is discussed in relation to the E to H transition.

Fundamental Scaling of Adiabatic Compression of Field Reversed Configuration Thermonuclear Fusion Plasmas

Field Reversed Configuration (FRC) plasmas are plasma devices that have demonstrated that through magnetic compression they can be heated to thermonuclear fusion conditions in the parameter space of an energy-producing generator Kirtley et al. (IEEE Symposium on Fusion Engineering, 2021). Of particular interest, FRCs are high-beta, in that the plasma particle kinetic energy is in balance with an externally applied magnetic field at all stages of operation. The following work will show that a cylindrical approximation for the energy and particle distribution within an FRC can, within 11%, match the fusion performance results of both full Magnetohydrodynamic (MHD) simulations as well as all robust, modern theoretical spatial and energy distribution models. Further, by using the simplified cylindrical model, detailed fusion reaction, radiation, and energy transport equations are now numerically-tractable and can be modelled over a wide parameter space. In the second section of this work, a detailed numerical model will be presented with the key theoretical performance of the compression of high-beta fusion plasmas in both deuterium–tritium (D–T) and deuterium–helium-3 (D–He-3) fuels. As will be shown, a high-beta D–He-3 plasma outperforms a low-beta D–T fuel and can theoretically yield a net-positive fusion generator.

Visible-Light Imaging of the Super-Alfvénic/Sonic Collisional Merging Process of Field-Reversed Configurations with a Contrast Medium-Mixed Plasmoid

Visible-Light Imaging of the Super-Alfvénic/Sonic Collisional Merging Process of Field-Reversed Configurations with a Contrast Medium-Mixed Plasmoid