Field-reversed Configuration Formation Research Articles

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.

Experimental study of plasma gun-assisted field-reversed configuration formation

The field-reversed configuration (FRC) is a compact toroidal plasma system related to the research of alternative fusion reactors. Improving the FRC formation, which is critical to the improvement of its overall quality, is reported in this paper by using a plasma gun to assist the pre-ionization process. For the single-translated FRC, the poloidal magnetic flux increases around 30%, accompanied by an increase in the separatrix radius and plasma density, while its translation speed is found to decrease slightly. The estimated increase in particle inventory is more than 60%. The improvement of these parameters also extends the lifetime of the FRC.

Energizing charged particles by an orbit instability in a slowly rotating magnetic field.

The stability of charged particle motion in a uniform magnetic field with an added spatially uniform transverse rotating magnetic field (RMF) is studied analytically. It is found that the stability diagram of a single particle's orbit depends critically on the chosen boundary conditions. We show that for many boundary conditions and wide regions in the parameter space, RMFs oscillating far below the cyclotron frequency can cause linear instabilities in the motion which break μ invariance and energize particles. Such energization may appear at odds with the adiabatic invariance of μ; however, adiabatic invariance is an asymptotic result and does not preclude such heating by magnetic fields oscillating at slow frequencies. This mechanism may contribute to heating in the edge plasma of field-reversed configurations (FRCs) in rotamak-FRC experiments. Furthermore, these RMF-driven instabilities may significantly enhance azimuthal current drive during the formation of FRCs in such devices.

Development of Rogowski probe for internal plasma current measurement in the collisional merging process of field-reversed configurations.

To directly detect the spatial distribution of a plasma current during the collisional merging of two field-reversed configurations (FRCs) in the FAT-CM (FRC Amplification via Translation-Collisional Merging) device, an internal current probe using Rogowski coils has been developed. An FRC is a type of magnetically confined plasma maintained by a diamagnetic plasma current flowing in the toroidal direction. Self-organized FRC formation and increased poloidal flux have been observed following the destructive perturbation during the collision in collisional merging FRC formation when two initial-plasmoids collide at a relative speed of 300-400 km/s to form one FRC. It is indicated that the toroidal plasma current is driven in those processes. In this research, an internal Rogowski probe was designed and developed to have a high-frequency response to capture a rapid change of the plasma current in a few microseconds during the collision/merging process. The FRC plasma in FAT-CM has relatively high temperature (∼100 to 200eV) and high density (∼1020 to 1021m-3). As a result, the probe was built to be as compact as possible to minimize disruption to the plasma. Because of its high melting point and low Z property, a machinable boron nitride ceramic was chosen to shield the Rogowski coils thermally and electrically from the plasma. All connections and seams were constructed such that the epoxy glue used for the probe assembly was not exposed to the plasma.

Spectroscopic observation of super-Alfvénic field-reversed configuration merging process by mixing of tracer ions.

Visualization of the collisional merging formation process of field-reversed configuration (FRC) has been attempted. In the collisional merging formation process, two initial FRC-like plasmoids are accelerated toward each other by a magnetic pressure gradient. The relative speed of the collision reaches several times the typical ion sonic speed and Alfvénic speed. The magnetic structure of the initial-FRCs is disrupted in the collision process, but the FRC-like magnetic structure is reformed in ∼30 µs after the collision. Magnetic reconnection should occur in this process; however, general theoretical models in magnetohydrodynamics approximation cannot be applied to this process because of the high-beta nature of FRC and super-Alfvénic/sonic relative speed. In this work, the spectroscopic observation of the collisional merging FRC formation was conducted to evaluate the timescale and geometry of merging. A slight amount of tracer element (e.g., helium) was mixed into one of two initial-FRCs. Mixing of the tracer did not cause serious adverse effects on the performance of the initial-FRC in the collision and merging processes. The collision and merging processes were visualized successfully and observed using a fast-framing camera with a bandpass filter. The timescale of merging and the outflow speed in the collisional merging process of FRCs were optically evaluated for the first time.

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.

Observation of self-organized FRC formation in a collisional-merging experiment

Self-organized field-reversed configuration (FRC)-like formation was observed after the super-sonic/Alfvénic collisional merging of two FRCs in the FAT-CM device at Nihon University. In this experiment, two FRCs were generated initially in two separate field-reversed theta-pinch type formation regions. Those two formation regions are coaxially connected to opposite ends of a cylindrical confinement chamber. The formed FRCs are oppositely-translated and collide in the middle of the confinement chamber at super-sonic/Alfvénic velocity. During the collision, the merged plasmoid experiences destructive disturbance and loses its fast toroidal flow and characteristic FRC property of having a field-reversed magnetic configuration to become a magnetized plasma without ordered structure. After this dynamic collision, a magnetic configuration of FRC with fast toroidal rotation is self-organized within a few tens of microseconds. This observation indicates robustness of the extremely high-beta, simple magnetic configuration.

MHD simulation of supersonic FRC merging corrected by non-invasive magnetic measurements

In this study, a newly developed correction method with external magnetic measurements for the magnetohydrodynamics (MHD) simulation of the collisional merging formation of a field-reversed configuration (FRC) realized the estimation of the internal structure of the FRCs without invasive internal measurements. In the collisional merging formation of FRCs, an FRC is formed via merging of two initial FRC-like plasmoids at supersonic/Alfvénic velocity. An invasive diagnostic may also interfere with the collisional merging formation process. A two-dimensional resistive MHD simulation was conducted to evaluate the global behavior and internal structure of FRCs in the collisional merging formation process without invasive measurements. This code simulated the initial formation and collisional merging processes of FRCs including discharge circuits. However, the translation velocity and the pressure of initial FRCs did not simultaneously agree with the experimental values because the magnetic pressure gradient in each formation region could not be reproduced without the artificial adjustment of the initial condition. The experimentally measured current distribution was given as the initial condition of the circuit calculation in the developed correction method. The initial FRCs were successfully translated at the translation velocity and plasma pressure in the corrected simulation, both of which were equivalent to the experiments. The properties of the merged FRCs in the experiments such as volume, total temperature, and average electron density were reproduced in the corrected simulation. The detailed radial profile of the internal magnetic field of the FRC was also measured and found to agree very well with the simulation results.

Fusion gain from cylindrical liner-driven implosions of field reversed configurations

MagLIF experiments [M.R. Gomez et al., Phys. Plasmas 22, 056306 (2015)] on Z have demonstrated the basic principles of Magneto-Inertial Fusion (MIF) for wall confined plasmas. Other MIF schemes have been proposed based on the liner implosion of closed field magnetically confined plasmas such as Field Reversed Configurations (FRCs) [T. P. Intrator et al., Phys. Plasmas 15, 042505 (2008)]. We present a semi-analytical model of liner driven FRC implosions that predicts the fusion gain of such systems. The model predicts a fusion gain near unity for an FRC imploded by a liner driven by the Z Machine. We show that FRCs could be formed and imploded at the Z facility using the AutoMag liner concept [S. A. Slutz et al., Phys. Plasmas 24, 012704 (2017)]. An initial bias magnetic field can be supplied by the external magnets used in MagLIF experiments. The reverse field is then supplied by an AutoMag liner, which has helical conducting paths imbedded in an insulating substance. Experiments [Shipley et al., Phys. Plasmas 26, 052705 (2019)] have demonstrated that AutoMag can generate magnetic fields greater than 30 Tesla inside of the liner. We have performed 2D Radiation MHD simulations of the formation and implosion of an FRC, which are in good agreement with the analytical model. The FRC formation process could be studied on small pulsed power machines delivering about 1 MA.

Formation of hot, stable, long-lived field-reversed configuration plasmas on the C-2W device

TAE Technologies’ research is devoted to producing high temperature, stable, long-lived field-reversed configuration (FRC) plasmas by neutral-beam injection (NBI) and edge biasing/control. The newly constructed C-2W experimental device (also called ‘Norman’) is the world’s largest compact-toroid (CT) device, which has several key upgrades from the preceding C-2U device such as higher input power and longer pulse duration of the NBI system as well as installation of inner divertors with upgraded electrode biasing systems. Initial C-2W experiments have successfully demonstrated a robust FRC formation and its translation into the confinement vessel through the newly installed inner divertor with adequate guide magnetic field. They also produced dramatically improved initial FRC states with higher plasma temperatures (Te ~ 250 + eV; total electron and ion temperature >1.5 keV, based on pressure balance) and more trapped flux (up to ~15 mWb, based on rigid-rotor model) inside the FRC immediately after the merger of collided two CTs in the confinement section. As for effective edge control on FRC stabilization, a number of edge biasing schemes have been tried via open field-lines, in which concentric electrodes located in both inner and outer divertors as well as end-on plasma guns are electrically biased independently. As a result of effective outer-divertor electrode biasing alone, FRC plasma is well stabilized and diamagnetism duration has reached up to ~9 ms which is equivalent to C-2U plasma duration. Magnetic field flaring/expansion in both inner and outer divertors plays an important role in creating a thermal insulation on open field-lines to reduce a loss rate of electrons, which leads to improvement of the edge and core FRC confinement properties. An experimental campaign with inner-divertor magnetic-field flaring has just commenced and early result indicates that electron temperature of the merged FRC stays relatively high and increases for a short period of time, presumably by NBI and E × B heating.

Formation of field-reversed configuration using an in-vessel odd-parity rotating magnetic field antenna in a linear device.

A Field-Reversed Configuration (FRC) is formed by an in-vessel odd-parity rotating magnetic field (RMF) antenna in a tandem mirror device, Keda mirror with axisymmetricity. The 40-cm diameter antenna is fed independently by four IGBT-based power units with an output current of 1500 A each at 84 kHz, and their phases are adjustable to launch odd or even parity RMFs. A medium-sized washer gun is utilized to generate a highly ionized seed hydrogen plasma. Driven by RMF, the resultant FRC is formed with a separatrix radius of ∼17 cm, external field of ∼50 G, and trapped poloidal flux of ∼0.15 mWb. The formation process of FRCs is evidenced by the measurement of an array of internal two-dimensional probes; a comparison with the rigid rotor model is presented in this paper. In addition, substantial toroidal electron current is found to be driven, despite the partial RMF penetration. Moreover, the dependence of the driven current on the antenna current is reported and is found to be consistent with the RMF current driving model.

Field-reversed configuration formed by in-vessel θ-pinch in a tandem mirror device.

We describe a field reversed configuration (FRC) experiment featuring in-vessel θ-pinch coils and open-field-line plasmas confined in a tandem mirror. Two FRCs, formed near the west and the east mirror throats of a central cell, are ejected toward the mid-plane for colliding and merging. Each FRC consists of four groups of pulsed power supplies and four groups of coils, having diameters 35, 35, 40, and 45 cm. The rise time of the main reversal field is 7.15 μs, and the maximum voltage is 40 kV with total currents of 416 kA, corresponding to a magnetic field of 1690 G. The total capacitive stored energy is 115.2 kJ. A fast pulse gas injection system was designed and tested to inject neutral gas into the FRC formation region with controlled directions. The successful installation of the θ-pinch coils inside the vacuum vessel offers greater freedom for diagnostics and control instruments as well as preserving magnetic tandem mirror configuration. The magnetic field reversal is confirmed by internal magnetic field measurements. The plasma temperature, density, and lifetime are, respectively, ∼100 eV, ∼3.0 × 1018 m-3, and ∼300 μs for the current operating conditions.

Formation of Field Reversed Configuration (FRC) on the Yingguang-I device

As a hybrid approach to realizing fusion energy, Magnetized Target Fusion (MTF) based on the Field Reversed Configuration (FRC), which has the plasma density and confinement time in the range between magnetic and inertial confinement fusion, has been recently widely pursued around the world. To investigate the formation and confinement of the FRC plasma injector for MTF, the Yingguang-I, which is an FRC test device and contains a multi-bank program-discharged pulsed power sub-system, was constructed at the Institute of Fluid Physics (IFP), China. This paper presents the pulsed power components and their parameters of the device in detail, then gives a brief description of progress in experiments of FRC formation. Experimental results of the pulsed power sub-system show that the peak current/magnetic field of 110 kA/0.3 T, 10 kA/1.2 T and 1.7 MA/3.4 T were achieved in the bias, mirror and θ-pinch circuits with quarter cycle of 80 μs, 700 μs and 3.8 μs respectively. The induced electric field in the neutral gas was greater than 0.25 kV/cm when the ionization bank was charged to 70 kV. With H2 gas of 8 Pa, the plasma target of density 1016 cm−3, separatrix radius 4 cm, half-length 17 cm, equilibrium temperature 200 eV and lifetime 3 μs (approximately the half pulse width of the reversed field) have been obtained through the θ-pinch method when the bias, mirror, ionization and θ-pinch banks were charged to 5 kV, 5 kV, 55 kV and ±45 kV respectively. The images from the high-speed end-on framing camera demonstrate the formation processes of FRC and some features agree well with the results with the two-dimension magneto hydrodynamics code (2D-MHD).

Improved Confinement of C-2 Field-Reversed Configuration Plasmas

C-2 is a unique, large compact-toroid (CT) device at Tri Alpha Energy that produces field-reversed configuration (FRC) plasmas by colliding and merging oppositely directed CTs. Significant progress has recently been made on C-2, achieving ~5 ms stable plasmas with a dramatic improvement in confinement, far beyond the prediction from the conventional FRC scaling. This stable, long-lived FRC plasma state is called the high-performance FRC (HPF) regime. The key approaches to achieve the HPF regime are as follows: (i) dynamic FRC formation by collision/merging of super-Alfvénic CTs, (ii) effective control of stability and transport by end-on plasma guns and neutral-beam (NB) injection, and (iii) active wall conditioning using titanium and lithium gettering systems. Moreover, further improvement in FRC confinement has been obtained with improved open-field-line plasma properties such as a lower fluctuation level, reduced transport rates in radial/axial directions, and lower background neutral density as well as recycling. This open-field-line plasma improvement, mainly obtained by higher magnetic fields in the formation and mirror-plug sections, allows for better NB coupling to the core-FRC plasma. In the recent HPF regime there is a sufficiently large fast-ion population that appears to improve FRC confinement properties as well as stability; the FRC particle and global energy confinement times both increased by ~30% and ~80%, respectively, compared to that of the previously obtained HPF regime.

Plasma-gun-assisted field-reversed configuration formation in a conical θ-pinch

Injection of plasma via an annular array of coaxial plasma guns during the pre-ionization phase of field-reversed configuration (FRC) formation is shown to catalyze the bulk ionization of a neutral gas prefill in the presence of a strong axial magnetic field and change the character of outward flux flow during field-reversal from a convective process to a much slower resistive diffusion process. This approach has been found to significantly improve FRC formation in a conical θ-pinch, resulting in a ∼350% increase in trapped flux at typical operating conditions, an expansion of accessible formation parameter space to lower densities and higher temperatures, and a reduction or elimination of several deleterious effects associated with the pre-ionization phase.

Measurement of Magnetic Fluctuation during Formation of Field-reversed Configuration by Counter-helicity Plasma Merging

Measurement of Magnetic Fluctuation during Formation of Field-reversed Configuration by Counter-helicity Plasma Merging

FRC Based Fusion Neutron Source for Materials Evaluation

An intense neutron source capable of generating the characteristic flux of a fusion reactor (1-4 MW/m2) is an essential element for adequate reactor materials assessment. Based on recent experimental results involving the magneto-kinetic compression of the Field Reversed Configuration (FRC), it is believed that such a fusion based neutron source can be rapidly developed at low cost. The ability to provide a fusion plasma with the necessary radiation intensity is afforded by the considerable increase in fusion neutron yield that occurs concurrently with the large reduction in reacting plasma volume from the straightforward magnetic flux compression of an FRC plasmoid. Pulsed formation and flux compression of FRCs in a prototype device operating at 4 Hz would yield a neutron power fluence at the wall of 1 MW/m2 from a fusion plasma volume of a half liter. This is roughly a factor 106 smaller than a reactor-scale fusion plasma such as ITER, thereby dramatically reducing the cost and time for the evaluation of materials for fusion application. The required magnetic compression field and energy per pulse is less than 16 T and 100 kJ respectively.

Particle-in-Cell Modeling of Field Reversed Configuration Formation by Odd-parity Rotating Magnetic Fields

We describe kinetic electromagnetic particle-in-cell simulation of a field reversed configuration with rotating magnetic fields (RMF). The energy-conserving algorithm calculates RMF penetration, gas breakdown and field reversal for the odd-parity RMF, PFRC device. An advanced simulation technique is being developed that preserves charged particle orbits for large time steps. These techniques are being developed to model future devices.

Extended magnetohydrodynamic simulations of field reversed configuration formation and sustainment with rotating magnetic field current drive

Three-dimensional simulations of field reversed configuration (FRC) formation and sustainment with rotating magnetic field (RMF) current drive have been performed with the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. The Hall term is a zeroth order effect with strong coupling between Fourier components, and recent enhancements to the NIMROD preconditioner allow much larger time steps than was previously possible. Boundary conditions to capture the effects of a finite length RMF antenna have been added, and simulations of FRC formation from a uniform background plasma have been performed with parameters relevant to the translation, confinement, and sustainment-upgrade experiment at the University of Washington [H. Y. Guo, A. L. Hoffman, and R. D. Milroy, Phys. Plasmas 14, 112502 (2007)]. The effects of both even-parity and odd-parity antennas have been investigated, and there is no evidence of a disruptive instability for either antenna type. It has been found that RMF effects extend considerably beyond the ends of the antenna, and that a large n=0 Bθ can develop in the open-field line region, producing a back torque opposing the RMF.