Abstract In a recent paper Kirtley and Milroy [D. Kirtley, R. Milroy, J. of Fusion Energy (2023) 42:30] discuss the Helion concept for a pulsed reactor, in which two supersonic field-reversed configurations (FRCs) merge and the resulting plasmoid is adiabatically compressed to fusion conditions. Using D-He3 as fuel this would allow for efficient electromagnetic energy conversion during the subsequent expansion phase. Essential for their very promising projections of energy gain is the assumed large temperature ratio between ions and electrons ( $$\:{T}_{i}/{T}_{e}\approx\:10$$ ) resulting initially from the supersonic plasmoid collision and the following adiabatic compression. For reactor-relevant conditions, however, the collisional ion to electron power transfer exceeds the fusion power by more than an order of magnitude at $$\:{T}_{i}$$ =100 keV (and by over two orders at $$\:{T}_{i}$$ =40 keV). Even if this exchange does not change total pressure, it rapidly erodes $$\:{T}_{i}/{T}_{e}\gg\:1$$ and causes the time-integrated fusion energy yield to fall well below values inferred from the initial, non-equilibrated state. While this does not preclude a D-He3 FRC reactor our analysis implies much tighter requirements on plasma lifetime, anomalous losses, and direct-conversion efficiency than suggested in D. Kirtley, R. Milroy, J. of Fusion Energy (2023) 42:30.

Application of the passive plates for magnetic compression device based on field-reversed configuration

Abstract In this study, we present a comprehensive stability analysis of Field-Reversed Configuration (FRC) during formation and sustainment, integrating both experimental and numerical approaches. The formation of bi-directional toroidal flow during spheromaks merging is identified as a key factor in suppressing $n=1$ toroidal mode through the stretching and advection of magnetic field lines. To substantiate experimental findings and assess the efficacy of the innovative "intermittent merging" technique in maintaining plasma stability, we develop a $3$D Hall-MHD model. This technique, involving the periodic merging of new pairs of spheromaks into the FRC, demonstrates the ability to suppress low-n toroidal modes, especially $n=1$, while driving the plasma current, thereby sustaining MHD instabilities for extended periods.

An improved understanding of field-reversed configuration (FRC) merging and stability in high acceleration and compression magnetic fields is needed to speed up the development of the pulsed fusion concept developed at Helion Energy. All previous theoretical and simulation work on FRC merging and compression was performed using two-dimensional (2D) magnetohydrodynamic (MHD) models. The results of novel 2D hybrid simulations (fluid electrons and full-orbit kinetic ions) of FRC merging and compression are presented. Results of kinetic and MHD simulations, computed using the HYM code, are compared and analyzed. In cases without axial magnetic compression, both the MHD and hybrid simulations show a high sensitivity to the initial parameters (i.e. FRC separation, velocity, normalized separatrix radius, and plasma viscosity), showing that FRCs with large elongation and separatrix radius either do not merge or merge partially, forming a doublet FRC. Application of a mirror coil field at the FRC ends with increasing strength is shown to lead to fast and complete merging of the FRCs in MHD and kinetic simulations.

Results from theory, simulation, and experiment are presented that support the concept of sub-microsecond formation and compression of centimeter-scale field-reversed configurations (FRCs) for fusion yield. Such FRCs require 10–100+ T of applied field and are intended for compression to high-energy-density conditions in solid liners on the Z-machine and future accelerators. First, MHD simulations including anomalous resistivity are presented. These simulations suggest that empirical scaling laws from the literature might be used to predict the resistive lifetime of high-field FRCs, and these lifetimes are often in excess of 1 μs. The effects of applied field shape/gradients are also explored in simulation, and an analytic prediction for FRC ejection time from the liner is verified. Second, a high-field FRC formation platform on a university-scale pulsed-power facility is detailed. The Z-discharge pre-ionization (ZPI) system is characterized and shown to have critical effects on the plasma. Fast-frame visible image sequences are presented for various gas pressure, bias field, and ZPI settings. The expected plasma dynamics can be seen in the images, with long-lived plasma annuli (possibly FRCs) produced only under the proper conditions. Optimistic conclusions are drawn, and future research directions are recommended.

Advanced neutral beam injection in a field-reversed configuration plasma

Abstract A new methodology for achieving the formation and compressional heating of a Field Reversed Configuration (FRC) plasmoid has been investigated both theoretically and experimentally at the University of Washington and MSNW. This approach, based on previous FRC empirical scaling, is expected to achieve fusion gain as large as 10. For the FRC, the fusion gain, G ~ φp·Be2 where φp is the FRC poloidal flux and Be the confining axial magnetic field. G is essentially independent of the FRC radial scale making feasible a small, compact reactor. The necessary φp (> 60mWb) is achieved by employing a large formation chamber (~ 0.8m radius) combined with the requisite axial magnetic field reversal time (Eθ ~ 20kV/m) for generating a high initial temperature (Ti > 1keV) FRC. By employing the dynamic formation procedure, the FRC is accelerated to ~100-150km/s. This subsonic velocity is maintained as the FRC is translated through a series of cylindrical coils of decreasing radius but of sufficient length (> LFRC) and number (~ 10) to produce essentially an isentropic and adiabatic radial wall-compression of the equilibrium FRC. The final stage is a 12cm diameter, 3-6m long confinement and burn chamber with a vacuum field of 7-9T produced by external solenoidal coils inside the flux conserving cylinder. The vacuum field is compressed by the FRC on insertion to 35 T resulting in fusion gain conditions for the 2-5 ms transit. The large ratio of FRC to inner wall radius (0.85) substantially lowers the FRC edge pressure thereby greatly reducing both particle and thermal losses. The resulting D-T fusion yield for the 3.5MJ FRC is 20-40MJ/pulse. The final ejection and expansion of the FRC into a large, low field mirror chamber provides a mechanism for FRC energy recovery. The experimental justification and the physics basis for the entire process from formation through burn of the Compact FRC Fusion Reactor (CFR2) concept is presented.

The field reversed configuration (FRC) has been a curious case in plasma physics research in that early MHD analysis suggested FRCs should be grossly unstable, while experimental results contradicted that prediction. Later, this theory was able to resolve this contradiction by understanding that finite Larmor radius effects largely negated the MHD predictions. Similarly, previous theoretical studies of beam driven FRCs predicted that such system would be unstable to beam driven modes while, again, experimental results indicated the contradiction. In this paper, we reconcile the theoretical understanding of beam driven modes with experimental observations of stability in these systems. By self-consistently capturing fast ion generation from neutral beam injection and its impact on the plasma equilibrium, we show that low amplitude perturbations in the magnetic field, driven by betatron particles, modify the precession frequencies of the betatron particles such that the drive for compressional Alfvén waves in the thermal plasma is reduced. Finally, we are able to demonstrate, for the first time, stable beam driven FRC evolution at high S*/E in 3D kinetic simulations.

In the Norm experiment at TAE Technologies, a reversed field configuration (FRC) is formed by reversing the magnetic field of a mirror configuration using neutral beam injection. An FRC is formed and sustained in a steady state by the diamagnetic current of the thermal plasma and the azimuthal current provided by fast ions. In the present paper, we present numerical simulations of FRC formation using the Q2D code. Q2D is a code that couples 2D MHD equations with separate ion and electron temperatures, a fluid model for the neutral gas, and a 3D Monte Carlo module, which is used to calculate neutral beam injection, fast ion orbits, and their interaction with the thermal plasma and neutral fluid. We use Q2D to simulate the FRC formation and sustainment by neutral beam injection, and we study the effects of different beam injection angles, impact parameters, equilibrium magnetic fields, and neutral beam current. We analyze the different types of fast ion orbits and their contribution to the diamagnetic current. The simulations show that the fast ion current can reverse the magnetic field if the current density is sufficiently high. Equilibria with higher magnetic field require higher diamagnetic current density for FRC formation.

A system for analyzing equilibria with fully kinetic ions is developed, aimed at understanding ion end-loss rates in field-reversed configurations. The method builds upon the constants of motion in energy-momentum phase space. Four provinces in phase space are identified. These appear as trapping bands in the momentum index, which will be defined. The trapping bands are magnetic, mirror, electric-drift, and untrapped (chaotic). The first three have excellent trapping ability. The electric-drift trap is apparently new. How trapping is affected by ion energy, mirror ratio, and electrical biasing (a new trapping effect) is investigated. The results appear to be consistent with the experimental inferences of surprisingly good axial confinement of the scrape-off layer outside the separatrix of field-reversed configurations.

We report evidence of successful generation of field-reversed configuration plasmas by neutral beam injection. This is achieved by trapping the steady-state beams in an initial seed plasma, hence providing a direct source of toroidally directed energetic ion current and increase plasma density and temperature until plasma and magnetic pressures become comparable. Magnetic flux trapping occurs gradually, and the change in topology from open field line to fully a formed field-reversed configuration is complete within ~ 10 ms. Field reversal is first established using a traditional metric and complemented by advanced reconstruction algorithms of the magnetic topology and plasma pressure profiles; observations of characteristic changes to fast-ion orbits inferred from magnetic fluctuations; and an experimentally validated model of field reversal by neutral beam injection. These results establish a field-reversed configuration formation method which may offer technological and economic advantages on a path to a future fusion energy system.

The field-reversed configuration (FRC), a compact toroidal plasmoid, has a range of potential applications, particularly in nuclear fusion, space propulsion, and plasma research. Various formation methods have been developed to create the magnetic topology required for stable plasma confinement. Here, we propose and investigate a novel formation method using a plasma gun as the plasma source and a DC background magnetic field as the bias field. This approach reduces the device's dependence on high-voltage pulse power supplies for FRC formation and enhances magnetic flux retention. In our experiments, we observed the splitting of elongated FRCs. Specifically, FRCs with an elongation greater than 1.7 and low trapped magnetic flux—a central-to-external magnetic field ratio below 0.6—tended to split during translation. This study demonstrates a new technical scheme for FRC formation, and the experimental results may contribute to the FRC optimization and stability control during translation and compression.

The field-reversed configuration (FRC) plasma thruster driven by rotating magnetic field (RMF), abbreviated as the RMF-FRC thruster, is a new type of electric propulsion technology that is expected to accelerate the deep space exploration. An experimental prototype, including diagnostic devices, was designed and constructed based on the principles of the RMF-FRC thruster, with an RMF frequency of 210 kHz and a maximum peak current of 2 kA. Under the rated operating conditions, the initial plasma density was measured to be 5 × 1017 m−3, and increased to 2.2 × 1019 m−3 after the action of RMF. The coupling efficiency of RMF was about 53%, and the plasma current reached 1.9 kA. The axial magnetic field changed in reverse by 155 Gauss, successfully reversing the bias magnetic field of 60 Gauss, which verifies the formation of FRC plasma. After optimization research, it was found that when the bias magnetic field is 100 Gauss, the axial magnetic field reverse variation caused by FRC is the highest at 164 Gauss. The experimental results are discussed and strategies are proposed to improve the performance of the prototype.

Abstract In this paper, we use hybrid simulation to elucidate the plasma heating mechanism due to waves excited in Field-Reversed Configuration (FRC) plasma. The plasma parameters are a separatrix radius of 0.16 m and a separatrix length of 1.16 m (x-point position is z = ± 0.57 m). The wave excitation antenna consists of two loop antennas with a radius of 0.3 m and is placed at a position of z = ± 0.5 m. The current waveform of the antenna is a sine wave with a maximum current value of 30 kA and a frequency of 160 kHz. The simulation results showed that the excited waves caused compression/expansion of the plasma, and at the same time, the temperature of the plasma increased or decreased at the compressed/expanded position. When waves are applied, a 23% increase in the volume-averaged ion temperature in the separatrix is observed compared to the case without waves applied. On the other hand, no increase in electron temperature is observed. For the electron fluid, the adiabatic condition is well established, and temperature changes are observed as the plasma compressed and expanded. On the other hand, for ions, kinetic energy perpendicular to the magnetic field lines increases during compression, and part of this energy is transferred to the energy of the parallel component by collisionless pitch angle scattering, resulting in heating due to the so-called magnetic pumping.

The field-reversed configuration (FRC) amplification via a translation–collisional merging device was used to conduct experiments where two initial FRC-like plasmoids produced by the field-reversed theta pinch method were translated and accelerated to supersonic/Alfvénic velocities before being subjected to collisional merging. The temporal evolution of the toroidal flow was measured throughout each experimental phase. The plasmoids initially rotated in the ion paramagnetic direction relative to the open-field region and subsequently spun up in the diamagnetic direction. The toroidal angular momentum of the plasmoids was conserved during the translation and acceleration phases but not during the collisional merging process. As the reversed magnetic field reformed, a toroidal flow formed in the paramagnetic direction and then accelerated in the diamagnetic direction. This behavior appears to be a unique feature of collisional merging and cannot be solely explained by the coherent magnetic field connection between the two initial plasmoids. This paper discusses the temporal evolution of the toroidal flow and the implications for the collisional merging process.

Abstract The two-dimensional (2D) separatrix shaping plays a crucial role in the confinement of the field-reversed configuration (FRC), and the magnetic coils serve as an effective means for its control. In this work we develop a weighted matching method to obtain an MHD equilibrium that accurately corresponds to the shape of target separatrix. By iteratively calculating the coil currents, the plasma current, and the equilibrium magnetic flux, the equilibrium separatrix progressively converges towards the desired shape. The coil currents are determined through a matching method, and the NIMEQ code is employed to compute the FRC equilibrium with a rigid rotor model of plasma distribution. This approach enables the adaption of the equilibrium separatrix into any desired shape, thus offering a potential scheme for the design and control of the 2D shaping of FRC plasma.

The general concept of the magnetic reconnection converter (MRC) is considered, based on the cyclic combination of two physical processes: 1) controlled turbulence using super-linear Richardson diffusion and/or self-generated/self-sustaining physical processes increases the stochasticity of the magnetic field (MF) in a limited volume of plasma and, accordingly, the global helicity H through the processes of twisting, writhing, and linking of the MF flow tubes to the level of a local maximum (optimally global), which is determined by the plasma parameters, boundary conditions, magnetic tension of the field lines, etc. At this stage of the MF turbulent pumping, the β of plasma will decrease to the minimum possible value with a corresponding increasing in the accumulated "topological" MF energy; 2) upon reaching the local (if possible global) maximum of MF stochasticity, turbulent magnetic reconnection (TMR) occurs in the plasma, which reduces the state of the local (if possible global) maximum of MF stochasticity and increases the kinetic stochasticity of plasma particles, accelerating and heating them, which is used in direct converters of electrical power. At this stage of turbulent discharge, the β of plasma will increasing to the maximum possible value with a corresponding increasing in its kinetic and thermal energy; 3) when the kinetic stochasticity of plasma particles subsequently decreases and reaches a local minimum, the control system repeats the MF turbulent pumping in the plasma and the cycles are repeated. Practically, the basis of the MRC can be the fusion scheme of two anti-spiral spheromaks, the helicity of which is increased in a cycle with the help of controlled turbulence before their fusion and the creation of a field-reversed configuration (FRC) to increase the efficiency of the annihilation of their toroidal and poloidal magnetic fields into kinetic and thermal energy of plasma particles with its subsequent direct transformation into electrical power for industrial use or single-volume plasma (spheromak) with changing beta at turbulent pumping/discharge phases of the working cycle.

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.

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.

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.