Nuclear Fusion Nucl. Fusion 61 (2021) 106039 (19pp) https://doi.org/10.1088/1741-4326/ac2521 Overview of C-2W: high temperature, steady-state beam-driven field-reversed configuration plasmas H. Gota, M.W. Binderbauer, T. Tajima, A. Smirnov, S. Putvinski, M. Tuszewski, S.A. Dettrick, D.K. Gupta, S. Korepanov, R.M. Magee, J. Park, T. Roche, J.A. Romero, E. Trask, X. Yang, P. Yushmanov, K. Zhai, T. DeHaas, M.E. Griswold, S. Gupta, S. Abramov, A. Alexander, I. Allfrey, R. Andow, B. Barnett, M. Beall, N.G. Bolte, E. Bomgardner, A. Bondarenko, F. Ceccherini, L. Chao, R. Clary, A. Cooper, C. Deng, A. Dunaevsky, P. Feng, C. Finucane, D. Fluegge, L. Galeotti, S. Galkin, K. Galvin, E.M. Granstedt, K. Hubbard, I. Isakov, M. Kaur, J.S. Kinley, A. Korepanov, S. Krause, C.K. Lau, A. Lednev, H. Leinweber, J. Leuenberger, D. Lieurance, D. Madura, J. Margo, D. Marshall, R. Marshall, T. Matsumoto, V. Matvienko, M. Meekins, W. Melian, R. Mendoza, R. Michel, Y. Mok, M. Morehouse, R. Morris, L. Morton, M. Nations, A. Necas, S. Nicks, G. Nwoke, M. Onofri, A. Ottaviano, R. Page, E. Parke, K. Phung, G. Player, I. Sato, T.M. Schindler, J.H. Schroeder, D. Sheftman, A. Sibley, A. Siddiq, M. Signorelli, M. Slepchenkov, R.J. Smith, G. Snitchler, V. Sokolov, Y. Song, L.C. Steinhauer, V. Stylianou, J. Sweeney, J.B. Titus, A. Tkachev, M. Tobin, J. Ufnal, T. Valentine, A.D. Van Drie, J. Ward, C. Weixel, C. White, M. Wollenberg, S. Ziaei, the TAE Team, L. Schmitz, Z. Lin, A.A. Ivanov, T. Asai, E.A. Baltz, M. Dikovsky, W.D. Heavlin, S. Geraedts, I. Langmore, P.C. Norgaard, R. Von Behren, T. Madams, A. Kast and J.C. Platt 1 TAE Technologies, Inc., Foothill Ranch, CA, United States of America 2 University of California at Los Angeles, Los Angeles, CA, United States of America 3 University of California at Irvine, Irvine, CA, United States of America 4 Budker Institute of Nuclear Physics, Novosibirsk, Russia 5 Nihon University, Tokyo, Japan 6 Google LLC, Mountain View, CA, United States of America Abstract TAE Technologies, Inc. (TAE) is pursuing an alternative approach to magnetically confined fusion, which relies on field-reversed configuration (FRC) plasmas composed of mostly energetic and well-confined particles by means of a state-of-the-art tunable energy neutral-beam (NB) injector system. TAE’s current experimental device, C-2W (also called ‘Norman’), is the world’s largest compact-toroid device and has made significant progress in FRC performance, producing record breaking, high temperature (electron temperature, Te > 500 eV; total electron and ion temperature, Ttot > 3 keV) advanced beam-driven FRC plasmas, dominated by injected fast particles and sustained in steady-state for up to 30 ms, which is limited by NB pulse duration. C-2W produces significantly better FRC performance than the preceding C-2U experiment, in part due to Google’s machine-learning framework for experimental optimization, which has contributed to the discovery of a new operational regime where novel settings for the formation section and the confinement region yield consistently reproducible, hot, and stable plasmas. An active plasma control system has been developed and utilized in C-2W to produce consistent FRC performance as well as for reliable machine operations using magnets, electrodes, gas injection, and tunable NBs. The active control system has demonstrated stabilization of FRC axial instability. Overall FRC performance is well correlated with NBs and edge-biasing system, where higher total plasma energy is obtained by increasing both NB injection power and applied-voltage on biasing electrodes. C-2W divertors have demonstrated a good electron heat confinement on open-field-lines using strong magnetic mirror fields as well as expanding the magnetic field in the divertors (expansion ratio > 30); the energy lost per electron ion pair, ηe ∼ 6–8, is achieved, which is close to the ideal theoretical minimum. TAE Technologies, Inc. (TAE; formerly named Tri Alpha Energy) was established in 1998 as a fusion start-up private company, located in Southern California, aiming for the development and steady operation of commercial fusion reactors, and is currently one of the world’s largest privately-funded fusion research companies. TAE’s concept of a magnetically-confined fusion reactor is based on utilizing a field-reversed configuration (FRC) as the core plasma and performing plasma heating and current drive for steady operation by neutral beam (NB) injection (NBI). While at other large fusion devices D-T fuel is mainly considered for use in fusion reactor development and for steady operation, TAE’s approach is to eventually adopt advanced fuels such as p-11B (possibly D-3He as well) with the ultimate aim of a safe and economical fusion reactor that does not generate neutrons in its primary fusion reaction. This approach also has many technological advantages that make it easier to design, construct and operate the reactor because there is little to no concern about neutron induced damage on the reactor. However, the conditions for fusion reactions/burning plasmas are more difficult and challenging than those for D-T reactions. Therefore, achieving the fusion condition with the realization of steady-state operation is our key project at TAE. An FRC is a high-beta compact toroid (CT), solely consisting of poloidal axisymmetric magnetic field inside closed-field lines formed by the toroidal self-current, where its separatrix is surrounded by open-field lines. The volume-averaged beta (ratio of plasma pressure to external magnetic pressure) is close to 100%, so FRCs can be compact and highly magnetically efficient thus economically attractive as a fusion reactor plasma. Furthermore, because the closed-magnetic-field line structure exists independently of the open-magnetic-field lines outside the separatrix, FRCs can be easily translated in the axial direction. A direct energy conversion can also be utilized by using natural divertors at both ends of the device. TAE’s current experimental device, C-2W (also called ‘Norman’, shown in figure 1), is the company’s fifth generation FRC device and the world’s largest theta-pinch, CT collisional-merging system. It forms high-magnetic-flux, high-temperature, stable and long-lived FRC plasmas. In the preceding FRC experiments, C-2 and C-2U, the primary goals were to study aspects and demonstration of the FRC plasma sustainment by NBI and edge biasing, and their key results and accomplishments were as follows: robust FRC formation via CT collisional-merging technique; production of high-performance FRC (HPF) plasmas with drastically improved particle and energy confinement properties; rapid accumulation of injected fast ions where about half of the initial FRC thermal pressure was replaced by fast-ion pressure; FRC lifetime and global plasma stability scaled strongly with synergetic effect of NBI power and edge biasing, where under the optimum C-2U operating condition FRC was sustained for 5+ ms and its configuration lifetime extended up to 10 ms via ∼10 MW NBI. In the current C-2W device several key subsystems were upgraded from C-2U, such as: higher NBI power (up to ∼20 MW) with a tunable beam energy capability (15–40 keV) during a plasma shot, where NB pulse duration has also been extended up to 30 ms; upgraded edge-biasing electrode systems in both inner and outer divertors, allowing for higher biasing voltage (up to ∼5 kV) and longer pulse operation (>30 ms); increased overall stored energy in the FRC formation pulsed-power system to produce better target FRCs for effective NBI heating and current drive; and fast external equilibrium/mirror-coil current ramp-up capability for plasma ramp-up and position/shape control, where additionally-installed trim/saddle coils can be used for active feedback plasma control. C-2W has also enhanced overall diagnostic suite in both confinement and divertor regions to investigate and characterize core FRC plasma performance as well as open-field-line plasmas. In fact, as illustrated in figure 1(b), FRC plasma is surrounded by a large volume of open-field-line plasma that is confined by strong magnetic-mirror fields (so called ‘mirror’ plasma). Therefore, understanding and improvement of open-field-line/mirror plasma characteristics are critical to the further advancement of core FRC plasma performance on C-2W. Main goals of the C-2W experimental program are as follows: (a) demonstrate plasma ramp-up by NB heating and current drive; (b) achieve high plasma temperature up to ∼3 keV by improving edge and divertor plasma performance to increase high electron temperature both at the plasma edge and inside the core; (c) develop plasma control on the time scale significantly longer than L/R vessel-wall time and plasma confinement times, and demonstrate controllable plasma ramp-up; and (d) explore a wide range of plasma parameters such as plasma temperature, magnetic field and plasma size to confirm the previously obtained energy confinement scaling. 2.1. C-2W experimental apparatus overview 2.1.1. C-2W machine and vacuum vessel: The C-2W experimental device is the world’s largest theta-pinch CT collisional-merging system, utilizing high-power NBI and edge-biasing systems to form and sustain FRC plasmas. The C-2W device has ∼30 m in overall length and consists of the central confinement section surrounded by 2 inner divertors, 2 field-reversed theta-pinch (FRTP) formation sections, and 2 outer divertors, where those 7 sections can be independently isolated in terms of their vacuum boundary by large gate valves. The CV is made of Inconel and has an inner-wall radius rw ∼ 0.8 m with a thin wall whose resistive wall time is about 2–3 ms. The divertor vessels are made of stainless steel and have a large internal volume (∼15 m3 per divertor). Each divertor has its own internal cryogenic pumping system with titanium gettering and liquid-nitrogen cooling system, where the pumping speed is ∼2000 m3 s−1 per divertor. The formation tubes are made of quartz, approximately ∼3.5 m in length and ∼0.6 m in diameter. 2.1.2. Magnet systems: C-2W magnets consist of confinement equilibrium and mirror coils, saddle and trim coils, in-vacuum fast-switching coils, DC formation/divertor coils, and magnetic-mirror plug coils. In the typical C-2W experiment, external axial magnetic field, Bz, in the confinement section is about 0.1 T and can be ramped up to ∼0.3 T. Trim coils beneath each equilibrium coil are operated independently to correct error fields and perform active feedback control. Saddle coils provide active or passive plasma position control. In-vacuum fast-switching coils provide guide magnetic fields during FRC translation and flare fields quickly. Magnetic mirror plugs produce fields up to ∼1 T. 2.1.3. Pulsed-power systems: An initial FRC plasma is generated by dynamic FRTP formation technique with pulsed-power systems in the formation sections (17 sets of formation-coil straps per side). Pulsed-power systems consist of Bias modules (Bz ∼ −0.1 T), main-reversal (MR) modules (Bz ∼ 0.3–0.4 T; risetime ∼ 4 μs), and rotating magnetic field (RMF) modules for pre-ionization. Total stored energy exceeds 2 MJ at typical operating conditions. Two FRCs collide with relative speed up to ∼1000 km/s and merge into a single FRC. 2.1.4. Neutral beams: Eight NB injectors are installed in the central region of the CV: 4 with tunable beam energy (15–40 keV) and 4 with fixed 15 keV beam energy. Total input power is ∼13 MW (at 15 keV) up to ∼20 MW with beam ramping, with pulse duration up to 30 ms. Nominal ion current per source is ∼130 A, focal length ∼3.5 m, divergence ∼0.04 rad, and injection angle 70° (variable from 65°–75°). 2.1.5. Edge-biasing systems: To control open-field-line plasmas and provide radial electric field for E × B shearing, GDT-type coaxial plasma guns and concentric annular electrodes are installed in outer and inner divertors. Negatively-biased electrodes create an inward radial electric field (Er < 0) that propagates to the SOL, producing azimuthal flow that counters FRC spin-up in the ion diamagnetic direction and suppresses the n = 2 rotational instability, while line-tying reduces n = 1 wobble motion. 2.1.6. Particle-fueling systems: Fueling systems on C-2W include multi-pulsed CT injectors (injecting ∼10^19 particles per pulse at up to ∼100 km/s), cryogenic pellet injection (0.5–1.0 × 10^19 particles per pellet at 0.2–0.5 km/s), and gas injection systems for edge density and SOL control. 2.2. Plasma diagnostic suite: C-2W operates 62 diagnostic systems (out of 72 planned) spanning shape/position, temperature/density, fluctuations/radiation, and fast ions/neutrals. Systems include magnetic probe arrays, Thomson scattering (core and jet), FIR interferometry/polarimetry, millimeter/micrometer-wave interferometers, Doppler backscattering (DBS), bolometer arrays, impurity-ion and main-ion ChERS, fast-imaging cameras, and fusion product detectors. 2.3. Advanced optometrist algorithm: Machine-learning optimization developed with Google optimizes high-dimensional parameters using human expert feedback on 'better' or 'worse' shot performance. Meta-parameters (MPs) describe complex subsystems. The Optometrist Algorithm with Logistic Regression (OALR) fits logistic regression across shot history with linear and quadratic terms to guide search trajectories. Optimizing formation trigger timings of the 17 FRTP coils resulted in a 200%–300% extension in plasma lifetime, leading to ∼30 ms steady discharges. 2.4. Active feedback plasma control systems: C-2W employs a distributed digital control system based on Speedgoat modules and FPGA implementations to execute real-time magnetic (100 kHz / 10 μs latency) and kinetic controls. It regulates equilibrium currents to act as a dynamic flux conserver and controls trim coils to stabilize axial shift instability. 3.1. Steady-state advanced beam-driven FRC: C-2W achieves steady-state beam-driven FRC plasmas sustained for up to 30 ms (limited only by NB pulse duration). Compared to C-2U, trapped poloidal flux φp increases significantly (e.g. from ∼4 mWb at 1 ms to ∼10 mWb at 15 ms), plasma radius is maintained via magnetic field ramping, and temperatures continuously rise. 3.2. Characteristics of FRC stability and fluctuation: - Magnetic fluctuation: Stable beam-driven FRCs display a hollow density profile with peak density near the excluded-flux radius rΔφ. MHD magnetic fluctuations δB/Bz remain below 0.005. - Density fluctuation: Four-channel Doppler backscattering measurements show near-exponential wavenumber spectra in the SOL, but significantly suppressed, flat low-k turbulence inside the FRC core due to large thermal ion Larmor radii and short connection lengths. - Rotation and velocity shear: ChERS and DBS confirm that applied negative bias drives an inward radial electric field and electron diamagnetic E × B rotation (vE×B ~ 5.5–7.5 × 10^4 m/s). Velocity shearing rates ωE×B ≈ 4.2 × 10^5 rad/s exceed turbulence decorrelation rates, suppressing ion-scale fluctuations by 25%–30%. - Bayesian plasma reconstruction: Multi-instrument time-linked Bayesian inference reconstructs 2D density structures and low-n mode evolution across 200 μs bursts. - Axial instability control: Real-time feedback regulation of trim coil currents maintains FRC axial position within ±5 cm over the 30 ms discharge. 3.3. High temperature and energy state: - Electron temperature reaches Te > 500 eV and total temperature Ttot > 3 keV. - Interpretative equilibrium reconstructions reveal that fast-ion pressure dominates the core, exceeding background thermal plasma pressure by up to an order of magnitude. - Plasma total energy Etot scales strongly with increasing NBI power and biasing electrode voltage. - Open-field-line electron heat loss in divertors achieves ηe ≈ 6–8 (energy lost per electron-ion pair), approaching the ideal theoretical minimum (5–6) and vastly improved over C-2U (ηe ≈ 30), supported by an ambipolar potential of ∼4–5 Te. 4. Summary: The C-2W device is now reliably operational, producing stable, high temperature (Te > 500 eV, Ttot > 3 keV), steady-state beam-driven FRCs up to 30 ms (limited by NB pulse length). Google’s advanced optometrist algorithm and in-house active plasma control systems are routinely used in C-2W to produce superior FRC performance as well as for reliable machine operations. FRC performance is well correlated with NBs and edge-biasing system, where higher total plasma energy is obtained by increasing both NBI power and electrode-biasing voltage. C-2W divertors with strong magnetic mirror fields have demonstrated a good electron heat confinement on open-field-lines, achieving the energy lost per electron ion pair, ηe ∼ 6–8, which is close to the ideal theoretical minimum. Acknowledgments & References: Key citations include works on FRC physics by Tuszewski (1988), Steinhauer (2011), Binderbauer et al (2010, 2015, 2016), Gota et al (2017, 2019), and machine-learning applications by Baltz et al (2017) and Dikovsky et al (2021).