Field-reversed Configuration Research Articles

Anatomy of a field-reversed configuration

A reconstructor tool is developed for fast computation of fully two-dimensional equilibria of field-reversed configurations (FRCs) that are consistent with routine magnetic data from experiments. This tool fosters physical interpretation of multiple FRC properties. The physics model is a rotating fluid that also captures several realistic kinetic effects. The tool allows both FRC solutions and high-β mirror solutions (no closed magnetic flux) a bifurcation, dependent on the input data. A major conclusion is that FRCs can exist only within a limited shape domain, i.e., combinations of plasma radius and length. These limitations reflect the requirement of equilibrium force balance and tearing stability. Inspection of a considerable range of experiments shows that the shape domain reflects actual operational boundaries. Working from timeline data from an experiment the tool finds the evolving two-dimensional structure plus the time histories of critical properties such as trapped flux, plasma energy, and plasma current. These timelines offer clues about underlying stability and transport properties not contained within the equilibrium model itself. Properties of traditional FRCs as well as modern, neutral-beam driven FRCs are explored, and specific experimental shots are reconstructed.

Verification of local electrostatic gyrokinetic simulation of driftwave instability in field-reversed configuration

Local linear simulations of ion temperature gradient (ITG) instabilities using a gyrokinetic particle code GKD1D have been verified by comparing with the analytic dispersion relation in the slab geometry and by benchmarking with a global gyrokinetic code GTC-X in a realistic field-reversed configuration (FRC). Results of ITG simulations using either adiabatic or kinetic electrons exhibit excellent agreements between the two codes for linear frequencies, growth rates, and mode structures. The ITG modes in the FRC scrape-off layer region are mostly dominated by the poloidal m=1 harmonic. Kinetic electrons enhance the subdominant m=2 harmonic and the even parity dominates the ITG mode structure. Kinetic electrons increase the growth rates for the low-n modes, but decrease the growth rates for the high-n modes.

Detection and prediction of a beam-driven mode in field-reversed configuration plasma with recurrent neural networks

Energetic beams excite semi-repetitive modes (‘staircase mode’) in the field-reversed configuration (FRC) plasma. We explore several neural network architectures to detect, and in some cases predict, this type of mode onset. We weigh the performance of these architectures and find that recurrent neural networks (RNNs), specifically long short-term memory (LSTM) networks, outperform all other models we examine. LSTMs can predict the onset of staircase with a lead window of 0.2 ms, which has implications for plasma longevity and is a promising direction for similar analysis in FRC devices in the future.

Electrostatic quasi-neutral formulation of global cross-separatrix particle simulation in field-reversed configuration geometry

A quasi-neutral blended drift-Lorentz particle model of the field-reversed configuration (FRC) has been developed and implemented in the particle-in-cell code named ANC. A field-aligned mesh and corresponding mesh operations are constructed for solving self-consistent electric fields in FRC geometry. Particle dynamics are described in cylindrical coordinates to allow for cross-separatrix simulation coupling the core and scrape-off layer regions of the FRC. This new model is successfully verified against analytically derived dispersion relations, and FRC turbulence is studied using the blended model for the first time.

Design of High Voltage Pulsed Power Supply for HFRC

The HUST field-reversed configuration (HFRC) is a field reversed plasma research device based on colliding and merging under design. To increase the parameters of the initial plasma formed in the theta-pinch, the theta-pinch is designed with very high parameters, namely a chamber diameter of 0.6 m, a bias magnetic field of -0.16 T, a preionization frequency of 150 kHz, and a main magnetic field of 0.6 T. To control the plasma formation and ejection, the discharge regulating accuracy for the theta-pinch is required within several microseconds. Thus, a high voltage, high current pulsed power supply with high controllability is required to satisfy the physical design. This article mainly presents the challenges and solutions in the design of the power supply system. First, 18 theta-pinch coils are used for the field generation to reduce the current on each coil, which results in design parameters of 70 kV/86 kA for the power supply. Then, a new topology with two power supply modules connected in series is adopted to feed the coil, which reduces the system voltage level and increases the operational reliability. Besides, hydrogen thyratron is adopted as the pulsed switch, and a corresponding trigger circuit based on insulated gate bipolar transistor (IGBT) is designed to ensure the precise control of the sequential discharge. Experimental tests are also performed on the thyratron and its trigger circuit, and the breakdown delay time is proven to be less than 1 μs. In conclusion, the designed power supply system can satisfy the requirements of high operation parameters and high controllability.

Imploding Liner Compression of a Field-Reversed Configuration With Diffusional Losses

Compression of a magnetized plasma in the form of a field-reversed configuration (FRC) to megagauss magnetic field levels by implosion of a surrounding cylindrical liner of liquid metal must address the need for implosion times sufficiently short compared with various loss times from the FRC. This issue is examined in the context of FRCs with high elongation, which may allow stability. Implosion times comparable to the initial value of loss time for magnetic flux, scaling energy, and particle loss times appear adequate to achieve large gains in plasma energy and temperature during compression. With loss based on neoclassical transport, liners at feasible drive pressures and initial diameters of tens of centimeters should be satisfactory for useful compressions of FRCs. In the dimensionless analyses presented, the product of liner speed and initial plasma radius indicates the importance of high initial temperature (~500–800 eV) to reduce the size and cost at allowable drive pressures for the stabilized liner implosion.

Generalized radial profile of field-reversed configurations based on symmetrical properties

Field-reversed configurations (FRC) exhibit several remarkable symmetrical properties. In the idealized FRC, Bz at the geometric axis and separatrix are of the same value but have opposite signature. The total poloidal flux at the inner field-lines (geometric axis to the O-point) is equal to that of the outer field-lines (O-point to the separatrix), which perfectly cancels out so that there remains zero flux at the separatrix. With these properties, a semi-analytical model of the radial profile is constructed. The symmetric (SYM) model begins with an analytical description of the current density profile j θ(r) having symmetric features. The model then takes into account of finite current at the separatrix that brings in asymmetric features. It is the combination of these two attributes, which determine the radial profile for the SYM model. This gives a generalized description that is applicable to a wide range of FRC settings for peaked and hollow current density profiles. Comparisons are made with the well-known rigid rotor (RR), two-point equilibrium (2PE), and Cobb et al model for two cases: (1) FRC behaves more symmetrically for conditions when Bz at the geometric axis (Bs) is almost equal to Be, and (2) asymmetric when Bs is lower than Be. A possible equilibrium profile for high performance FRCs at Be = 0.5 T is also presented.

Optimization of the Pulsed High-Field Coil in a Magnetic Trap Type Plasma Compression Device

A new field reversed configuration (FRC) device is under design at the Huazhong University of Science and Technology. The FRC plasma is formed by collision merging, and then magnetically compressed to increase plasma parameters. A FRC plasma with an interface radius of 0.3 m and a lifetime of 500 μs is expected. Theoretical calculation proposed that the magnetic field in the compression chamber which having diameter of 1 m and total length of 6 m should rapidly rise to 2 T within 100 μs and then keep rising to 3 T in the following 2 ms. The design scheme of pulsed compression coils is presented in this paper. The compression coil system consists of 18 coils. The maximum magnetic field of the coil in the magnetic mirror area reaches 9 T. The current in the compression coil changes rapidly, up to 2 MA/100 μs. The effect of eddy currents in the coil on magnetic field, electromagnetic force and capacitor bank pulsed power supply are analyzed.

Small-scale fusion tackles energy, space applications

Efforts are underway to exploit a strategy that could generate fusion with relative ease. On July 14, 2015, nine years and five billion kilometers after liftoff, NASA’s New Horizons spacecraft passed the dwarf planet Pluto and its outsized moon Charon at almost 14 kilometers per second—roughly 20 times faster than a rifle bullet. Samuel Cohen and his team hope to beat the standard timetable for fusion by about a decade using a reactor—initially for rocket propulsion—that’s a fraction of the size and cost of the huge tokamak devices. Cohen’s design takes advantage of the phenomenon of field reversed configuration (FRC), in which a dense mass of ionized plasma holds itself together. Image credit: Princeton Plasma Physics Laboratory. The images and data that New Horizons painstakingly radioed back to Earth in the weeks that followed revealed a pair of worlds that were far more varied and geologically active than anyone had thought possible. The revelations were breathtaking—and yet tinged with melancholy, because New Horizons was almost certain to be both the first and the last spacecraft to visit this fascinating world in our lifetimes. Unless, that is, Samuel Cohen succeeds with the offbeat fusion reactor that he’s developing at the Princeton Plasma Physics Laboratory in New Jersey. Cohen’s current prototype is a clear plastic cylinder that sits in the middle of his lab amidst a dense mass of cables, magnets, and power supplies, emitting a violet pulse of light every two seconds like a two-meter-long strobe light. “We’re only using hydrogen right now,” Cohen explains, referring to the ionized plasma inside the tube that’s emitting the flashes. So there are no actual fusion reactions taking place; that’s not in his research plan until the mid-2020s, when he hopes to be working with a more advanced prototype at least three times larger …

Magnetic mirror end-plugged by field-reversed configurations formed via rotating magnetic fields

A novel magnetic mirror concept with field-reversed configurations (FRCs) formed via rotating magnetic fields (RMFs) serving as end plugs is proposed to improve the mirror's axial confinement. Single-particle orbit calculations suggest that the FRCs in the end plugs can reflect ions back into the central cell if their parallel speeds are not so fast that they can overcome the magnetic field gradient force from the X-point of the FRC to the midplane outside of the FRC. However, this effect is limited and is no different from that of adding a weak mirror cell to the central cell. When the inward Hall electric field generated by the RMFs is considered, an additional Lorentz force emerges that pushes the incoming ions back to the central mirror, thereby dramatically improving the confinement. The Lorentz force is related to the azimuthal drift speed times the radial component of the magnetic field. By surveying the particle phase space of the speeds, we find that this Lorentz force can reflect back or trap >90% of ions escaping from the central mirror given a sufficient Hall electric field in the RMF region. Finally, preliminary experimental results from the Keda Mirror with AXisymmetricity RMF/FRC are reported and show that with the RMFs on, the axial mirror confinement can increase by a factor of ∼1.4 on average.

Soft X-Ray Measurement on the Collisional Merging Process in a Field-Reversed Configuration

Soft X-Ray Measurement on the Collisional Merging Process in a Field-Reversed Configuration

Reconnection heating experiments and simulations for torus plasma merging start-up

A series of merging experiments, TS-3 (TS-3U), TS-4, MAST and ST-40, made clear the promising characteristics of reconnection heating during merging formation of a high-beta spherical tokamak (ST), spheromak and field-reversed configuration (FRC). We developed the MW-class (<30 MW in TS-3U) ion heating using magnetic reconnection of torus plasma merging. Both the merging experiments and particle-in-cell (PIC) simulations (and also partly solar observation) agree on, (i) ion heating of the reconnection in its downstream, (ii) negative potential formation in the downstream for accelerating ions and (iii) low dependence of ion heating on the guide (toroidal) field Bg. An important finding is that the reconnection heating energy depends on the reconnecting magnetic field Brec but has little dependence on Bg in the tokamak operation region with the safety factor at the magnetic axis q0 > 2. The plasmoid/current sheet ejection promotes ion heating in the high-q region, weakening the Bg dependence of ion heating. Since the reconnection accelerated ions up to 70% of the Alfven speed of Brec, the ion temperature Ti increment (and the reconnection heating energy) scales with Brec squared under the constant plasma density. This promising reconnection heating does not depend on plasma size, as long as the reconnection time is shorter than the plasma confinement time. This scaling law extended over 1.2 keV suggests that the merging start-up may realize the burning plasma temperature Ti > 10 keV by increasing Brec. The merging/reconnection heating can explore a new direct route to burning plasma regimes without using any additional heating, such as neutral beam injection (NBI). This scaling leads us to new reconnection heating experiments for direct access to burning plasma regimes: ST-40 at Tokamak Energy and TS-3U at the University of Tokyo.

Translation speed measurements of hydrogen, helium, and argon field-reversed configurations in the central cell of a KMAX mirror device

A series of experimental results of field-reversed configurations (FRCs) on a KMAX (Keda Mirror with AXisymmetricity) tandem mirror machine are reported. Single-side FRC translation processes with three different gas species were measured by avalanche photodiodes. Consistent with the theoretical prediction, the measured FRC speeds were inversely proportional to the square root of the ion mass. However, the speeds of the hydrogen FRC increased even in a uniform magnetic field region while the speeds of the helium and argon FRCs decreased. Possible mechanisms are discussed. The speed of the second pass due to the reflection of the mirror fields was found to be ∼1/3 of the first pass speed. The internal magnetic fields were measured for a colliding-merging argon FRC, and the results show that, even for very slow-moving FRCs, merging can occur.

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.

Simulation on the compressed field-reversed configuration with alpha particle self-heating

Study on the compression of field-reversed configuration (FRC) by a magnetic-driven solid liner is carried out based on a one-dimensional code. In the investigation, plasma self-heating effect by alpha particles is taken into account. Numerical results show that the self-heating of alpha particles to DT plasma mainly occurs in the vicinity of O-point of the FRC target. The plasma ignition region is divided into two parts: the low-density ignition region near the central axis and the high-density ignition region in the O-point area. Before FRC plasma target expansion, the energy of alpha particles is well confined nearby the O-point by compressed magnetics. The DT plasma volume burning exists in a short time (approximately 0.1 µs) after a maximum convergence ratio of solid liner and the compressed strong magnetic field degrades the propagation of FRC plasma burning.

Cross-separatrix simulations of turbulent transport in the field-reversed configuration

Recent local simulations of the field-reversed configuration (FRC) have reported drift-wave stability in the core and instability in the scrape-off layer (SOL). However, experimental measurements indicate the existence of fluctuations in both FRC core and SOL, with much lower amplitude fluctuations measured in the core. With the updated cross-separatrix capabilities of the simulation code used in this paper, nonlinear turbulence simulations find that linear instabilities grow in the SOL, generating fluctuations which spread from SOL to core. After saturation of the linear instabilities, a balance of the inward spread and local damping in the core is achieved. The steady state toroidal wavenumber spectrum shows lower amplitude core fluctuations and larger SOL fluctuations with amplitude decreasing towards shorter wavelengths, which are consistent with experimental measurements.

Collisional merging formation of a field-reversed configuration in the FAT-CM device

Collisional merging formation of field-reversed configurations (FRCs) at super Alfvénic velocity have been successfully initiated in the FAT-CM device at Nihon University. It is experimentally evidenced that the quiescent FRC profile is formed in a self-organizational manner after distructive disturbances by the super Alfvénic collision of two translated magnetized plasmoids. A drastic increase of the excluded flux compared to the field-reversed theta-pinch formation section has also been observed. This formation process has an important role in realizing an FRC based high-beta reactor core to capture high-energy beam ions, and it has been clearly observed by magnetic diagnostics of excluded flux and internal probe array. The experimental results are compared with two-dimensional magnetohydrodynamic (MHD) simulation results computed for the typical conditions of the FAT-CM experiments. Collisional merging of the two separately translated FRCs causes a conversion of the kinetic energy to mostly thermal ion energy, which contrasts with the spheromak merging dominated by magnetic energy in an MHD manner, resulting in an increase of the ion pressure and polodal flux that drastically expands the FRC volume.

Global simulation of ion temperature gradient instabilities in a field-reversed configuration

We investigate the global properties of drift waves in the beam driven field-reversed configuration (FRC), the C2-U device, in which the central FRC and its scrape-off layer (SOL) plasma are connected with the formation sections and divertors. The ion temperature gradient modes are globally connected and unstable across these regions, while they are linearly stable inside the FRC separatrix. The unstable global drift waves in the SOL show an axially varying structure that is less intense near the central FRC region and the mirror throat areas, while being more robust in the bad curvature formation exit areas.

Hybrid Simulation Study on Anisotropic Response of Ions to a Low-Frequency Wave in a Field-Reversed Configuration

Using a hybrid simulation code, we studied the application of low-frequency wave to a field-reversed configuration plasma. The wave application antenna was arranged to sandwich the separatrix, and the antenna current was varied sinusoidally with a maximum of 30 kA and a frequency of 80 kHz. The simulation revealed that when the ion pressure is regarded as a tensor, the parallel ion temperature estimated from the axial velocity distribution near the midplane exceeds the perpendicular temperature. That is, the plasma ions respond anisotropically to a low-frequency wave.

Collisional Merging of Field-Reversed Configurations in the FAT-CM Device Form Targets for the Excitation of Low-Frequency Waves

Collisional Merging of Field-Reversed Configurations in the FAT-CM Device Form Targets for the Excitation of Low-Frequency Waves