11065 IAEA FEC2023 Manuscript Gota

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H. GOTA et al. ENHANCED PLASMA PERFORMANCE IN C-2W ADVANCED BEAM-DRIVEN FIELD-REVERSED CONFIGURATION EXPERIMENTS H. Gota TAE Technologies, Inc. Foothill Ranch, CA, USA Email: [email protected] A. Smirnov, M.W. Binderbauer, T. Tajima, S. Putvinski, T. DeHaas, S.A. Dettrick, E. Granstedt, D.K. Gupta, S. Korepanov, R.M. Magee, T. Matsumoto, M. Nations, T. Roche, J.A. Romero, J.B. Titus, E. Trask, M. Tuszewski, P. Yushmanov, K. Zhai, and the TAE Team TAE Technologies, Inc. Foothill Ranch, CA, USA L. Schmitz University of California at Los Angeles Los Angeles, CA, USA Z. Lin University of California at Irvine Irvine, CA, USA S. Krasheninnikov University of California at San Diego San Diego, CA, USA E.A. Baltz, J.C. Platt Google LLC Mountain View, CA, USA T. Asai Nihon University Tokyo, Japan A.A. Ivanov Budker Institute of Nuclear Physics Novosibirsk, Russian Federation Abstract 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, 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 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. A dedicated plasma optimization experimental campaign, particularly focused on external magnetic field profile and NB injection optimizations, has led to produce a superior FRC plasma performance; for instance, achieving total plasma energy of ~13 kJ, trapped poloidal magnetic flux of ~16 mWb (based on rigid-rotor model), and plasma sustainment in steady-state up to 40 ms. Under some operating conditions, electron temperature of FRC plasmas has reached up to ~1 keV at the peak inside the FRC separatrix. C-2W operations have now reached to a mature level where the machine can produce hot, stable, long-lived, and repeatable plasmas in a well-controlled manner. 1

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IAEA-FEC2023/1627

INTRODUCTION TAE Technologies (TAE; formerly named Tri Alpha Energy) was spun off from University of California at Irvine and established in 1998 by the late Prof. Norman Rostoker as a fusion start-up private company, aiming for the development and steady operation of commercial fusion reactors. It 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) [1,2] as the core plasma and performing plasma heating and current drive by neutral-beam (NB) injection (NBI). While at other large fusion devices deuterium-tritium (D-T) fuel is mainly considered for use in their fusion reactor development and for steady operation, TAE’s approach is to eventually adopt advanced fuels such as hydrogen-boron (p-11B) with the ultimate aim of a safe and economical fusion reactor that does not generate neutrons in its primary fusion reaction [3,4]. 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. 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 [1,2]. The volume-averaged beta (ratio of plasma pressure to external magnetic pressure) is close to unity, 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 reactor. TAE’s current experimental device, C-2W (also called “Norman,” shown in Fig. 1), is the company’s 5th generation FRC machine and the world’s largest CT device, producing high-magnetic-flux, high-temperature, stable and long-lived FRC plasmas [5,6]. In the preceding C-2 [7,8] and C-2U [9,10] experiments, the main goals were to study aspects and demonstration of the FRC plasma sustainment by NBI and edge biasing (i.e., aiming for “long enough” milestone), and the present C-2W experiment has been primarily focused on producing high-temperature FRC regime (i.e., “hot enough” milestone) to verify the previously-emerged scaling law [10]. Over the last 3 fusion devices at TAE, the following key scientific milestones have been achieved: (a) (b) FIG. 1. (a) Illustration of TAE’s 5th generation experimental device, C-2W (a.k.a., Norman), consisting of the central confinement section surrounded by 2 inner divertors, 2 formation sections, and 2 outer divertors. Eight NB injectors (4 of 15 keV fixed-energy NBs and 4 of 15–40 keV tunable-energy NBs) are installed in the central region of the confinement vessel. Plasma guns and electrodes are mounted inside divertors. (b) Sketch of FRC magnetic topology and density contours, calculated by 2D multifluid force-balanced equilibrium code, where field-line contours are traced and plasma densities are indicated with colors.

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H. GOTA et al. (1) robust FRC dynamic formation via CT collisional-merging technique [5,7]; (2) production of stable, high-performance FRC (HPF) and advanced beam-driven FRC plasmas with drastically improved particle and energy confinement properties via effective NBI and edge biasing [11- 13]; (3) rapid accumulation of injected fast ions where about half of the initial FRC thermal pressure is replaced by fast-ion pressure [8]; (4) FRC steady-state operations where the plasma lifetime is limited only by the energy storage onsite [6,10]; (5) demonstration of real-time feedback control on FRC shape and axial instability [14,15]; and (6) plasma heating by high-power NBI (achieving multi-keV plasma temperature), resulted in a significant plasma energy ramp-up in time [6]. This paper reviews C-2W experimental apparatus in Sec. 2. Recent FRC plasma performance enhancement through various system optimizations such as on magnetic field profile, NBI power and beam injection angle is described in Sec. 3. Finally, the paper is summarized in Sec. 4. 2. C-2W EXPERIMENTAL APPARATUS The C-2W experimental device, shown in Fig. 1(a), is the world’s largest theta-pinch CT collisional- merging system, utilizing a high-power NBI and edge-biasing system to form and sustain FRC plasmas. Figure 1(b) illustrates typical FRC magnetic flux and density contours in C-2W, obtained from a 2-D multifluid force- balanced equilibrium calculation using LReqMI code [16]. The C-2W device is ~30 m in overall length and consists of the central confinement section surrounded by 2 inner divertors, 2 field-reversed theta-pinch formation sections, and 2 outer divertors, where those 7 sections can be independently isolated in terms of their vacuum boundary by gate valves. The confinement vessel (CV) is made of Inconel and has an inner-wall radius r ~0.8 m with a thin wall whose resistive wall time is about 5 ms which allows for magnetic-field ramp up as w required during a plasma discharge. Because of the relatively short wall time of the CV, an adequately controlled external magnetic field is important and critical to FRC plasma confinement as well as for plasma ramp up. The divertor vessels are made of stainless steel and have a large internal volume to accommodate a high volumetric pumping during a plasma discharge; furthermore, each divertor has its own internal cryogenic pumping system with titanium gettering and liquid-nitrogen cooling system in place to enhance pumping capability inside divertors. The formation tubes are made of quartz, which are approximately ~3.5 m in length and ~0.6 m in diameter. The overall C-2W device accommodates an ultra-high vacuum (typical vacuum level is at in the range of high 10-10 to low 10-9 Torr) with adequately set up wall conditioning and pumping systems. C-2W magnet systems consist of confinement equilibrium (EQ) and mirror (M) coils, saddle and trim coils, in-vacuum fast-switching coils, DC formation/divertor coils, and magnetic-mirror plug coils, where the overall coil configuration is symmetrically arranged relative to the machine mid-plane (z=0). In the confinement section, as illustrated in Fig. 1(b), there are 12 main magnets arranged from the mid-plane as EQ1, EQ2, EQ3, EQ4, M1, and M2 on both north and south sides symmetrically. In the formation section there are 17 sets of pulsed-power formation coils located just outside of the quartz tube. Current waveforms of each equilibrium and mirror coils are independently controlled, which allows for an adequate and flexible control of external magnetic field profile as well as plasma shape and position. In the typical C-2W experiment, external magnetic field, B, in the confinement section is about 0.1 T and can be ramped up to ~0.3 T. Trim coils are placed z beneath each of the equilibrium coils that can also be operated independently to correct error fields as well as to perform an active feedback control [14,15]. Internal magnetic mirror plugs are installed at the entrance of the outer divertors that can produce a strong magnetic field up to ~3 T. Eight NB injectors are installed on the CV, 4 of which have a tunable beam energy (15–40 keV, ~140 A) capability and the other 4 injectors have a fixed beam energy (15 keV, ~140 A). Total NB input power (electrical power on the NB power supplies) with all 15 keV NBs is ~13 MW and can be increased up to ~20 MW by ramping beam energies. The NB power supply system has recently been upgraded to extend the pulse length from 30 ms to 40 ms. NBI angle was originally fixed at 70° relative to the machine axis, but recently changed to 57° on the 4 tunable NBs to study effects of NB injection angles. Average NB injection impact parameter is b ~20 cm (adjustable within ±3 cm; co-current injection into FRC) that enables sufficient coupling between the beams and the target FRC plasma (typical radius of ~40–45 cm). The NBs provide energetic particles with a large orbit size crossing inside and outside of the FRC separatrix that stabilize global 3

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IAEA-FEC2023/1627 magnetohydro-dynamic (MHD) modes; they also provide a significant amount of fast-ion population and pressure inside the core, thus producing beam-driven FRC plasmas. During the plasma pressure build-up via ramping up NBI power, the external magnetic field in the CV is also increased to maintain the plasma radius, accordingly. In order to control open-field-line plasmas and to provide sufficient radial electric field for E´B shearing around the FRC separatrix, end-on coaxial plasma guns and concentric annular electrodes are installed inside of each outer divertor as illustrated in Fig. 1. The edge-biasing electrode system has a good flexibility in terms of its operations, for instance relatively high voltage (up to ~5 kV) can be applied on the electrodes and its pulse duration is longer than 40 ms (i.e., longer than NB pulse duration). Electrical potentials on those electrodes can be controlled independently by its power supplies, where an active voltage and current control has been implemented and routinely used to control and maintain reliable edge-biasing current and potential. This is a key element of reliable C-2W operations, together with magnetic field control in the CV and divertor regions, for effective edge/boundary control of FRCs via open-field-lines / scrape-off layer (SOL). The role of SOL and divertors is not only to provide a favorable boundary condition for the core FRC plasma but also to handle energy and particle exhaust from the core. C-2W is currently equipped with more than 70 operational diagnostic systems [17,18]. The diagnostics are spread out over the entirety of the machine with good coverage throughout the CV, inner/outer divertors, and formation sections. The diagnostic suite’s purpose is to measure the behavior of FRC/open-field-line plasmas throughout the machine. In C-2W the role of the open-field-line plasma has proven to be nearly as important as the core behavior. The open-field-line plasma plays a significant role in stabilizing and controlling the core plasma. As such, the distribution of measurement capability is far more widespread throughout the vessel, but the main focus is still on the core. The diagnostics deployed on C-2W are required to provide data for a very wide range of plasma parameters to follow the discharge evolution from a seed FRC to a much hotter and higher energy state. Signals and data from each diagnostic system are transferred to a data-acquisition system that acquires several 1000s channels on every C-2W shot. The raw data are post-processed into plasma parameters and then stored in a physics database for further data analysis. Some raw data, such as magnetic probe signals, get processed continuously during a plasma shot through the real-time control system for use in active feedback control of the plasma. Each C-2W shot typically generates more than 10 gigabytes of data, including analysis movies and computations; data usage has been greatly reduced by employing single-precision floating point in the final product for processed signals, while continuing to save raw signals with high precision. 3. C-2W EXPERIMENTAL RESULTS 3.1. Enhanced performance in advanced beam-driven FRC Producing a stable FRC for effective NBI is one of the most important elements to obtain a beam-driven FRC plasma state because the injected fast ions typically take ~1 ms to accumulate and develop sufficient pressure inside the FRC. This plasma state was initially obtained in C-2U via synergetic effect of edge biasing and NBI, where FRC plasma was maintained for 5+ ms [10]. In C-2W with significantly upgraded key subsystems from C-2U, as previously reported in Ref [6], FRC performance and its superior plasma state has been considerably advanced and sustained in steady state up to 30 ms (limited by NB pulse length). Furthermore, C-2W NB systems have recently been upgraded to extend its pulse length to 40 ms, at which some dedicated NB system optimization has also been conducted to further enhance FRC plasma performance; details are described in Sec. 3.3 below.

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H. GOTA et al. FIG. 2. Time evolutions of excluded-flux radius (r ), trapped poloidal magnetic flux (f), averaged electron density Df p inside FRC separatrix (n), and total energy of FRC (E ) for recent C-2W shot 143348 (red), compared with previously e tot reported good shot 114534 (green) [6]. In recent C-2W experiments, adequately controlled external magnetic-field profiles throughout the machine and proper gas injection/fueling have led to more effective edge biasing from electrodes to globally stabilize FRC plasma. This allows improvements in the efficiency of NB-to-FRC coupling as well as accumulation of more fast ions inside the FRC; therefore, more plasma heating and current drive are obtained. Due to the synergistic effect of efficient edge biasing and NB injection as well as by dedicated plasma and machine optimization efforts in C-2W, FRC plasma state has significantly advanced to a much higher level than the previously reported good FRC condition (e.g., shot #114534, also seen in Fig. 9 of Ref. [6]) as shown in Fig. 2. Note that for simplicity and performance comparison at a quiescent phase in 2 different shots, initial FRC formation phase (t < 5 ms) is not shown in the figure. Some highlights and key features of the recent enhanced plasma performance (for instance in shot #143348) are as follows: (i) excluded-flux radius of FRC is maintained at ~0.45–0.5 m until NB termination at t ~ 40 ms, while FRC length and volume can be increased and controlled by external magnetic-field reshaping during a shot in either feedforward or feedback control mode as designed [14,15]; (ii) estimated trapped poloidal flux f (based on rigid-rotor model [1]) is significantly increased up to p ~16 mWb at an equilibrium phase, indicating the effect of NB current drive; (iii) plasma density (i.e., internal plasma pressure) goes up by 50–100% during a shot depending on field shaping and particle fueling scheme, which is also indicative of injected fast-ions accumulation; (iv) as a result of the internal pressure increase, plasma energy also goes up significantly; and (v) based on an equilibrium reconstruction, fast-ion pressure is comparable to or greater than thermal plasma pressure at a quiescent phase. In this particular shot #143348, the external magnetic field profile in the confinement section was reshaped during t = 4–24 ms, after which it stayed constant until the end of the discharge; some details of the magnetic-field reshaping are described in the following Sec. 3.2. Under some operating conditions, electron temperature T of FRC plasmas has reached up to e ~1 keV at the peak and >0.75 keV averaged inside the FRC separatrix, measured by mid-plane Thomson scattering system; an example of such a high-temperature FRC plasma state is shown in Fig. 3. FRC performance is well correlated with both NB injection and edge biasing from electrodes. Figure 4(a) shows plasma total energy E (at peak value of each shot) as functions of NB’s injected power (estimated with tot the actual neutral-beam current) and edge-biasing electrode voltage for ensembled C-2W shots in the recent experimental campaign. As can be clearly seen, higher E is obtained with higher NB injection power and tot biasing voltage on electrodes, which indicates the importance of those systems to produce high-energy FRC 5

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IAEA-FEC2023/1627 FIG. 3. Time evolutions of excluded-flux radius (top) and maximum and averaged electron temperature inside FRC separatrix (bottom) in shot 122588, measured by mid-plane Thomson scattering system. (a) (b) FIG. 4. (a) Plasma total energy (at peak value) as functions of NB injection power (total injected neutral power from 8 NB injector systems) and edge-biasing electrode voltage for ensembled recent C-2W shots at a quiescent phase. (b) Comparison of E as a function of NBI power between recent shots (red circles) and the previously reported tot ensembled data (blue triangles; data from Fig. 21 of Ref. [6]), where bias-electrode operating conditions were similar in both cases. plasma conditions. E is estimated by integration of one-dimensional pressure reconstruction along the tot geometrical axis (z-axis), where the 1-D reconstruction corresponds to paraxial approximation (highly elongated plasma) with the assumption of sharp boundary between plasma and surrounding magnetic field. Figure 4(b) shows a comparison of E as a function of NBI power between recent shots (red circles) and the previously tot reported ensemble of shots (blue triangles; data from Fig. 21 of Ref. [6]); note that biasing-electrode operating conditions in both cases were similar to each other. The figure clearly shows that E in the recent campaign is tot at much higher level (>50% higher) overall as compared to the old C-2W campaign, achieving E ~13 kJ with tot high NBI power. At TAE, besides some specific and physics-focused experiments in C-2W, some dedicated system and plasma optimization campaign has been routinely conducted from time to time with hardware/configuration changes and upgrades; e.g., optimizations focused on magnets, NB injection, biasing electrodes, and gas injection systems independently, or optimizing various systems together). In the following sub-sections, two optimization campaigns focused on magnetic-field profile and the NB system are described.

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H. GOTA et al. 3.2. Magnetic field topology/profile optimization Both formation and sustainment / ramp-up of the FRC system are critically dependent on the topology of the externally applied magnetic field. This includes the shape of CV magnetic field, mirror ratios, formation section background field, and field flaring in the divertors. As the dynamics of the system change during a shot, the magnetic field must also be reshaped to properly provide the magnetic confinement required. This dynamical process starts before any plasma is generated and continues after the shot comes to an end. There are several stages in the process: initial field configuration, target establishment configuration, and steady-state configuration (rarely a static case in terms of external magnetic field). Since the initial field configuration stage was previously reported in Ref. [5], this paper only focuses on the target establishment and steady-state configuration stages, particularly in the confinement section. Once the FRC plasma is well established in the CV and NB current drive is sustaining the diamagnetic current, plasma pressure inside the FRC can increase. To contain the increase in pressure while keeping the size constant, the magnetic field structure can be modified in a couple of ways. First, the magnitude of the magnetic field is increased at the mid-plane; on its own this will only arrest the expansion of the FRC in the radial direction. Second, the length of the plasma can be increased; to accomplish this, magnet currents near the end of the CV are decreased. Figure 5(a) shows sample waveforms of the equilibrium magnet/coil current (EQ1-4) in the confinement section, where a pair of EQ1 magnets is located near the machine mid-plane and the other pairs are spread out axially as illustrated in Fig. 1. In this particular shot, magnet/coil currents during t = 3−20 ms are adjusted to produce external magnetic field profiles such as “U-shaped” profile early in time for target FRC establishment and then modified to “W-shaped” profile later in time for steady-state operations, as depicted in Fig. 5(b). By doing such a dynamic coil-current adjustment and magnetic-field reshaping, the generated and confined FRC plasma becomes highly elongated axially in the CV. Note that this type of dynamic coil-current waveforms was obtained through some dedicated experimental campaign with the Google’s Optometrist Algorithm [19] to achieve high stored energy (e.g., thermal energy E and total energy E ) of FRC plasma as th tot well as to enhance plasma performance in general. As an example of this magnetic-field reshaping (from U- shaped to W-shaped field profile) and plasma length control, Fig. 6 shows time evolution of E as a function of tot FRC length during the field reshaping. Data is from typical plasma discharges (under similar operating conditions but 5 non-repeated shots), and their parameters are at t = 5, 15 ms and when maximum E is tot obtained in each shot (typically t > 20 ms). It clearly shows that the total plasma energy is effectively increased as FRC plasma gets elongated axially via magnetic-field reshaping. As the plasma gets longer it becomes axially unstable. However, with the use of active feedback control the plasma can be affected to remain centered in the CV (or at any desired z-location) [6,14,15]. By reading and (a) (b) FIG. 5. (a) Equilibrium magnets (EQ1-4) coil current time evolution, only showing t=0–30 ms time window for simplicity. (b) External axial magnetic field and excluded-flux radius axial profile at t7.5 ms (blue dashed lines) and t~17.5 ms (red solid lines), where reshaping axial magnetic field profile from U-shaped to W-shaped as well as elongated FRC length can be clearly seen. 7

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IAEA-FEC2023/1627 FIG. 6. Time evolution of total energy as a function of FRC length during magnetic-field reshaping (from U-shaped to W-shaped field profile). Data is from typical plasma discharges (similar operating conditions but 5 non-repeated shots) whose time stamps are at t = 5, 15 ms and when maximum E is obtained in each shot (typically t > 20 ms). tot interpreting plasma diagnostics during a shot, the feedback system is capable of affecting the length, shape, location, density, and overall stability of the plasma by changing various magnet currents, controlling edge- biasing electrode voltage/current, varying energies of the tunable NBs, and modifying gas fueling rates. By specifying a desired plasma condition before the shot, the control system will read several data streams during the shot and make adjustments to actuators to achieve the desired plasma condition. 3.3. Neutral beam optimization Reliable operation of the NBI systems is critical to plasma performance on C-2W. The NBI systems include four static energy beams (15 keV, ~140 A) and four tunable energy beams (15−40 keV, ~140 A), injected 20 degrees off magnetic normal. The eight NBI systems generally operate at the designed specification, but small modifications to beam parameters can lead to greater plasma performance. Three of these beam- related parameters are the injected beam current, I , the beam energy, E , and beam impact parameter, b. inj NB A strong correlation has been found between I and total stored energy within the plasma E . In this inj tot context, I is defined as NB current minus losses from the vacuum duct and reionization. Following the inj relationship between beam current and beam size described by the Child-Langmuir law [20], each NBI system generally operates at a specific current to minimize beam size, limiting losses to the vacuum duct. This is called the nominal beam current, I , and is monitored shot-to-shot by multiple diagnostics. The time-integrated nominal injected beam power and horizontal position is measured at the entrance port of each beam via a wire calorimeter [21]. The vertical position and beam shine-through are inferred measurements made by an array of secondary electron emission detectors located in the beam dump [22]. The NBI systems are optimized by manipulating the beam neutralization gas pressure, beam position, and ion source perveance. The optimization of injected beam current is thoroughly outlined in Ref. [23]. As mentioned above, I is directly correlated to increased plasma performance on C-2W. As total inj injected beam current increases, the stored energy within the plasma increases, as illustrated in Fig. 7(a). The data points and error bars are the average and standard deviation of the upper 20% of stored energy values during plasma optimization campaign with beam energy at 15 keV. Furthermore, an increase in I can be inj attained by increasing the injected currents past their nominal values, as suggested by experiments on Joint European Torus (JET) [24]. For a small increase in ion current, up to 10% of the total current, I increases inj despite the increased loss to the vacuum duct due to the beam size increase. It is seen in Fig. 7(a) that in the regime where I > I , a non-linear increase in E occurs. The gains in current are finite, however, as losses inj nominal tot accumulate in the vacuum duct, a plasma can form, and beam stoppage will occur. There are a couple of mechanism that can lead to the non-linearity. The increased fueling from NBI could increase plasma density, which would lead to better beam capture. Also, the increases in current would lead to

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H. GOTA et al. an increase in fast ion current, and thus, an increase in fast ion pressure. Beam shine-through for the data set in Fig. 7(a) is 15 ± 5% independent of I value, so it is not the case that beam capture is increasing. What does inj occur, however, is that the applied magnetic fields from the equilibrium coil set are able to be increased without affecting plasma stability. This suggests that the increase in beam current is leading to an increase in fast ion pressure, which can then be balanced by external pressure from the magnetic field. The change in applied magnetic field, measured at the CV wall as external magnetic field, B , can be seen in Fig. 7(b); tunable beam ext energy E = 15 keV case. By increasing the injected beam current, C-2W can operate at higher external tunable magnetic field. In addition to beam current, beam energy plays a role in fast ion pressure as well. The dependence of B ext on E and I is also shown in Fig. 7(b). The data points and error bars are the average and standard tunable inj deviation of the upper 50% of stored energy values during the experimental campaign. As mentioned above, for E = 15 keV case, there is a nonlinear effect above the nominal current, as shown in Fig. 7(a). As the tunable tunable energy is increased to E ∼25 keV, B increases with I , as well. The optimal magnetic field is higher for tunable ext inj both E ~25 keV and ~30 keV ensembles when compared with the E = 15 keV data for the same tunable tunable injected beam current. This suggests that the fast ion pressure is increasing with both I and E , enabling inj tunable higher compression by the external magnetic fields, and thus, larger stored energies. This shows favorable (a) (b) FIG. 7. (a) The dependence of plasma stored energy E on injected neutral beam current I normalized by the tot inj nominal beam current I , where the data points represent the average of the top 10% highest performing shots, nominal and the error bars reflect the standard deviation. (b) The dependence of magnetic field measured at the CV wall (B ) ext at the point of maximum total stored energy with respect to I normalized by I . The data points represent the inj nominal average of the top 50% highest performing shots and the error bars reflect the standard deviation. FIG. 8. Trapped poloidal flux ϕ as a function of effective beam impact parameter b . p eff 9

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IAEA-FEC2023/1627 scaling with NBI power. Lastly, the beams are normally aimed at b ~0.2 m radially, which can be changed without a vent up to a couple of degrees; this translates to a ±3 cm variation from the nominal b. As part of NBI study and optimization, a set of scans of different magnetic field configurations and effective beam impact parameters b , eff defined as the current-weighted average beam impact parameter, was conducted. Figure 8 shows, as one particular example, the dependence of trapped poloidal flux ϕ on effective beam impact parameter b under W- p eff shaped magnetic field configuration with B in the range of 0.7−0.84 kG (scanned over low magnetic field ext region). It is found that increasing the beam impact parameter yields an increase in trapped poloidal flux ϕ , but p it is actually independent of B amplitude. The same trend and characteristics were observed in U-shaped ext magnetic field configuration case. The increase in ϕ from b suggests an increase in NB current drive. As a p eff side note, one might think that B should be correlated to ϕ . We have also observed that B correlates to the ext p ext volume of the plasma, which negates any increase to ϕ from increasing B . p ext 4. SUMMARY C-2W NB system was recently upgraded to extend its pulse length from 30 ms to 40 ms, which allowed for longer steady-state operations as well as to enhance FRC plasma performance. In addition, Google’s advanced Optometrist Algorithm and in-house plasma control systems were used in C-2W to further enhance the performance as well as for reliable machine operations. Dedicated system/plasma optimization campaign, particularly focused on external magnetic field profile and NB injection optimizations, led to a superior FRC plasma performance; for instance, achieving total plasma energy of ~13 kJ and trapped poloidal magnetic flux of ~16 mWb. The plasma performance was well correlated with the injected beam current and power as well as with FRC length. Under some operating conditions, electron temperature of FRC plasmas reached up to ~1 keV at the peak inside the separatrix. C-2W operations have now reached to a mature level where the machine can produce hot, stable, long-lived, and repeatable plasmas in a well-controlled manner. ACKNOWLEDGEMENTS The authors wish to thank the entire TAE Team for their dedicated work and effort to the C-2W project, as well as to thank external collaborators including Google and our shareholders who made this exciting fusion research possible at TAE. REFERENCES [1] TUSZEWSKI, M., “Field reversed configurations,” Nucl. Fusion 28, 2033 (1988). [2] STEINHAUER, L.C., “Review of field-reversed configurations,” Phys. Plasmas 18, 070501 (2011). [3] ROSTOKER, N., et al., “Colliding beam fusion reactor,” Science 278, 1419 (1997). [4] PUTVINSKI, S.V., et al., “Fusion reactivity of the pB11 plasma revisited,” Nucl. Fusion 59, 076018 (2019). [5] GOTA, H., et al., “Formation of hot, stable, long-lived field-reversed configuration plasmas on the C-2W device,” Nucl. Fusion 59, 112009 (2019). [6] GOTA, H., et al., “Overview of C-2W: high temperature, steady-state beam-driven field-reversed configuration plasmas,” Nucl. Fusion 61, 106039 (2021). [7] BINDERBAUER, M.W., et al., “Dynamic formation of a hot field reversed configuration with improved confinement by supersonic merging of two colliding high-β compact toroids,” Phys. Rev. Lett. 105, 045003 (2010). [8] BINDERBAUER, M.W., et al., “A high performance field- reversed configuration,” Phys. Plasmas 22, 056110 (2015). [9] BINDERBAUER, M.W., et al., “Recent breakthroughs on C-2U: Norman’s legacy,” AIP Conf. Proc. 1721, 030003 (2016). [10] GOTA, H., et al., “Achievement of field-reversed configuration plasma sustainment via 10 MW neutral-beam injection on the C-2U device,” Nucl. Fusion 57, 116021 (2017). [11] TUSZEWSKI, M., et al., “Field reversed configuration confinement enhancement through edge biasing and neutral beam injection,” Phys. Rev. Lett. 108, 255008 (2012).

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