Optimization and feedback control of the C-2W Field Reversed configuration J.A. Romero for the TAE Team TAE Technologies, Inc. FEC. 2023 Acknowledgments D. Madura, C. Finucane, S. Galkin, H. Phung, S. Putvinski, T. Roche, G. Snitcher, E. Trask and the TAE Team Executive summary • C-2W holds a high beta FRC plasma in an easily accessible linear device • Plasma is elongated to improve performance, resulting in axial instability • Feedback control stabilizes and sustains the long plasma in steady state C-2W sustains a high temperature plasma in steady state • FRC with closed field lines inside a mirror-confined SOL (No toroidal field) • FRC plasma current is sustained using NB injection • Plasma rotation controlled using end biasing • Density sustained using gas injection • Magnetic feedback control stabilizes and sustains a long plasma in steady state [Diagram showing machine layout from S. Outer Divertor, S. Formation, S. Inner Divertor, Confinement, N. Inner Divertor, N. Formation, to N. Outer Divertor, highlighting electrodes, NB injection, magnets, scrape-off layer, FRC, separatrix, and plasma guns]. TAE’s concept is ideally suited for p-B11 fusion • Weak magnetic field in the region of high temperature minimizes synchrotron radiation • Fast particles with large orbits lead to small pressure gradients in the closed field region • End biassing can be used to control turbulence at the SOL via rotational shear • Linear, unrestricted divertors can be made as large as required to handle power exhaust • Linear magnet arrangement eases design, construction and maintenance • High beta leads to compact devices, with moderate external field requirements. • O-point: Max pressure, B=0 C-2W is the world largest compact toroid device Components: • Confinement vessel: skin time < 3 ms • Plasma gun and biasing electrodes: high voltage & long pulse capability • Inner divertors: high vacuum pumping • Formation sections: ~15 mWb trapped flux • Neutral beams: ~21 MW, ~30 ms • Outer divertors: high vacuum pumping • Magnet system: field ramp & active control Typical parameter ranges: • External Field (T): ~0.1–0.3 • FRC radius (m): ~0.35–0.55 • FRC length (m): ~1.5–3.5 • ne (m⁻³): ~1 – 6 × 10¹⁹ • Ttot = Ti + Te (keV): > 3 • NBI power (MW): ~ 10–21 (tunable) • End Biasing (MW): ~ 3–12 • Beta %: 80-90 • Flat-top (ms): ~ 45 (PSU Lim.) Real-Time Control system overview Control: • Electrodes • Magnets • Tunable NBI • Gas fueling Control Flow Architecture: • Reference Waveforms & Real time Diagnostics -> Main Control -> Magnet Control, Electrode Control, NBI Energy Control, Gas Control Hardware Architecture (Based on SpeedGoat hardware): • Magnetic Sensors -> Analogue Integrators -> SG DACQ (2.5 MHz via Aurora / LAN) • SG Compute (166 kHz) & SG Supervisor (Labview Component) connected to Main machine control and Data storage • NI aurora cards: Magnet PSU control (8 kHz Equilibrium field, 18 kHz radial field), Electrode PSU control, Gas valve control, Plasma heating control (NBI) A main control objective is to stabilize position instability Overcome density limit -> Elongate plasma -> leads to position instability FRC requires axial position control: • High Ne requires high elongation (tilt mode) • Elongated plasmas are axially unstable • Radial field controls axial position Similar problem found in Tokamaks: • High Ne requires high Ip (Greenwald) • High Ip requires high elongation (q95 >> 2) • Elongated plasmas are vertically unstable • Radial field controls vertical position Control designed to operate with external magnets Control oriented model used during C-2W design: • Induction due to plasma movements: M_{i,j} İ_j - I_P (∂M_{p,j}/∂z) ż = -R_j I_j + V_j • Force exerted by magnets and passive elements: m z̈ = -k_z z - I_P ∑_{j=1}^N (∂M_{p,j}/∂z) I_j Cast into state space form E ẋ = A x + V: • x = [ż z I_1 ... I_N]^T • E and A matrices incorporate inertia, equilibrium 'push out' force (-k_z), and inductive/resistive couplings. Vessel time determines maximum instability drive kz: • Vessel time ~ Growth time ~ 5 ms • Corresponds with k_z ~ 1 kN/m @ 1 MA • E⁻¹ A gives eigenvalues; τ_max ~ τ_cv defines the control system design point and ideal wall limit. Axial instability characterized experimentally "U" shape to "W" shape transitions: • Forces plasma elongation • Causes axial instability Cause - effect verified with changing transition time: • Measured R_Δψ (m) and Z_0 (m) demonstrating that transition timing directly dictates the onset of axial displacement and instability. Radial field used to control plasma position • Mid-plane symmetric TRIM coil currents excited in opposite directions • Resulting radial field can be used to control plasma position • Experiment with axially stable plasma shows correlated coil currents and corresponding position displacement response Z0(m). Plasma position is controlled routinely Experimental run 135155: • Plasma radius controlled in feedforward (R ~ 0.35-0.45 m) • Plasma length increases with W-shape well (L ~ 2-3 m) • W-shape well increased to elongate plasma (Well ~ 50 G) • Axial instability is feedback stabilized, |z| < 2 cm • Control applies voltage pulses to radial field system (V pulses between -40V and +40V) Conclusion • The Field Reversed Configuration - once believed to be able to operate only in pulse mode – can now be controlled and operated continuously, as required for a high-power density fusion reactor plasma core References P-B11 feasibility: • S.V. Putvinski et al., Nucl. Fusion 59 076018 (2019) C-2W project: • H. Gota et al., Nucl. Fusion 61, 106039 (2021) Turbulence reduction in SOL: • L. Schmitz, Nat. Commun. 7, 13860 (2016) Intershot optimization: • E. A. Baltz et al., Scientific Reports 7, 6425 (2017) Control system: • J. Romero. Patent US PCT/US2016/061730 Additional info at TAE research library: https://tae.com/research-library