FRC on the Path to Fusion Energy (Moderate Density Steady-State Approach) Alan Hoffman Redmond Plasma Physics Laboratory University of Washington (FPA Meeting on Fusion Pathways to the Future) (September 27-28, 2006) Outline - History – ‘Achieving field reversal’, θ-pinch formation. - What is an FRC? Why are we interested? - Recent developments, particularly for steady-state. - Ultimate promise. Attempts at Field Reversal have a Long History – supra-thermal ring currents - ASTRON & Reversed Field Mirrors at LLNL in the 1960s. - Achieved with pulsed electron rings; ion rings being pursued. [Diagram showing Neutral Beams injection forming ring currents in magnetic field lines] Field Reversed Configurations (FRCs) (plasma currents producing field reversal) - Compact toroid with ‘negligible’ toroidal field - 0.5 < ⟨β⟩ < 1.0 - Simple cylindrical geometry – natural divertor. - Low magnetic fields – inexpensive reactors & experiments. - Low field region – kinetic physics applies. - High voltage θ-pinch formation – best for pulsed approach. Equations: x_s ≡ r_s / r_c ⟨β⟩ = 1 - 1/2 x_s^2 B_e = B_o / (1 - x_s^2) LANL FRXC/T - (1980s) - FRCs extremely robust – survive dynamic translation, reflection, & capture. - Translated FRCs develop moderate toroidal fields. - Evidence of high β minimum energy state in more recent TCS experiments. - Pulsed plasmas with only ~100s of µsec lifetimes. [Images: LANL FRXC/T apparatus and interferogram taken on FRX-C using holographic interferometry] Concerns About Stability - 2-D interchange type instabilities, driven by plasma rotation, have been stabilized by weak multipoles with B_m^2 / 2µ_o > centrifugal pressure - Internal tilt is more insidious – kinetic effects are important. [Diagrams: Interchange end view, Tilt side view, and stability plot of γ/γ_mhd vs E/S* showing typical kinetic calculations by E. V. Belova et al. indicating stability for S*/E < 3.5] Large s Experiment (LSX) Built at STI to Study Extrapolation to non-Kinetic Regime – (1990). Kinetic # of internal gyro-radii parameter: s = ∫ (r_R to r_s) (r dr) / (r_s ρ_i) Stable FRCs formed with s up to ~ 4, n ~ 10^21 m^-3, nτ ~ 10^18 m^-3 s T_i up to 2 keV, T_e up to 0.5 keV τ_φ ≈ τ_N, τ_E ≈ 1/2 τ_N Scaling: LSX: τ_N ∝ (r_s / √ρ_i)^3 General: τ_N ∝ x_s r_s^2 / ρ_i What is needed for steady-state compact toroid (CT) reactor? - Ideal n_e ~ 1-2×10^20 m^-3, T_e = T_i ~ 10 keV, B_e ~ 1-1.5T - Continued stability up to s ~ 20-30 - Sufficient energy confinement - nτ_E > 10^20 m^-3 s. - Reactor relevant formation methodology - Efficient sustainment of cross-field diamagnetic current I_θ – η_⊥ is anomalous. – It is actually the poloidal flux which must be sustained; (I_θ = 2B_e / µ_o simply due to diamagnetism) Techniques for Sustaining FRCs (also enhance stability) - Tangential Neutral Beam Injection (TNBI) – Kinetic ions should be stabilizing (low s particles). – Studied in Japan and proposed by PPPL & UW. No current experiments. - Rotating Magnetic Fields (RMF) can drive electrons in same manner as induction motor. (Also formation technique.) – Provides stabilizing inward radial force – Developed in Australia and adopted by UW. Recently demonstrated in TCS. - Key parameter is anomalous cross field resistivity, η_⊥, since it determines current drive (or flux sustainment) power requirements. – All transport may be related to this parameter. RMF Current Drive (dipole fields) - Simple loop antennas with ~10-200 kHz RF phased 90° apart - ‘Drag’ electrons along with rotating radial field Antenna configuration: RMF antenna: I_z = I_o cos(ωt) RMF antenna: I_z = I_o sin(ωt) Includes B_z field coils, driven electron current, and rotating field B_ω. TCS (Translation, Confinement, Sustainment) Layout: - LSX/mod (formation & ‘acceleration’) - TCS Chamber (confinement & RMF drive) - RMF Antennas Primarily interested in FRC formation & sustainment by RMF alone. Partial RMF Penetration is Natural Occurrence - Vacuum calculation in lab frame of reference - Plasma calculation in RMF frame of reference. (Calculation needs to start from already formed FRC) - Plasma measurement in RMF frame of reference Torque formula: T_RMF = (2π r_s^2 B_ω^2 / µ_o) * (δ* / r_s) 2D Interchange Stability Provided by Partially Penetrated RMF - Calculations show strong restoring forces to rotationally driven interchange instabilities, such as the ubiquitous rotating n=2. - Observation of stabilizing effect on rotational n=2 instability when RMF antennas extend over central region (comparing 0.05-m gap shot #13709 vs 0.35-m gap shot #13863). RMF also reverses radial particle diffusion & results in long particle lifetime - Nominal ‘τ_N’ extended by at least factor of 10. - ‘Steady-state’ sustainment due to recycling with pulse length only limited by RMF power supply. - Collisional plasma but no sign of tilt instability shown in magnetic field measurements up to 10 ms. Also see spontaneous toroidal field development: further evidence for a minimum energy state (MES) - Internal field profiles before transition (Shot 12968 – 2.63 ms, Shot 12964 – 2.5 ms) and after transition (Shot 12964 – 4.1 ms, Shot 12968 – 5.22 ms). - Temporal development of B_e and B_tor demonstrating spontaneous generation of toroidal magnetic field. Plasma density depends on η_⊥ Resistive Torque: T_η ∝ η_⊥ n_e^(3/2) T_t^(1/2) r_s^2 Resistivity scaling: η_⊥ ~ 50 / (n_m^(1/2) (10^19 m^-3)) µΩ-m Same as seen in high density θ-pinch formed decaying FRCs. Peak density formula: n_m = 0.044 { B_ω (δ*/r_s)^(1/2) / (r_s ω_r^(1/2)) }^(4/3) - Also see rapid reductions in η_⊥ with increasing temperature. - (In calculations with constant η_⊥, n_m decreases with T_t, while experimentally it increases). - Observed dependencies are characteristic of η_⊥ decreasing with v_de/v_sound, as seen in all empirical scaling, and supported by recent two-fluid numerical calculations. Relative current drive power also decreases with temperature Effective ‘η_⊥p’ plotted vs (B_e / B_ω)^2 ~ T_t: Plot of P_abs / [6.8π (2B_e / µ_o)^2 l_s] (µΩ-m) showing marked decrease as (B_e / B_ω)^2 increases across frequencies 114 kHz, 152 kHz, and 258 kHz (projecting to ~10,000 in reactor). Experimental results described well by empirical ‘Chodura’ formula, dependent on v_de/v_s. Chodura formula: η_Chod = [1050 / n_e^(1/2) (10^19 m^-3)] * (1 - e^(-v_de / v_ti)) µΩ-m Provided best numerical match to formation and translation experiments. Strong v_de/v_s scaling supported by recent numerical calculations (Non-linear 2-fluid calculations of instabilities in a Z-pinch by Loverich & Shumlak for various v_de/v_s). Projected v_de/v_s ratios: - TCS: n_e = 0.2 × 10^20 m^-3, T_t = 0.05 keV, B_e = 0.02 T, r_s = 0.4 m, f_ω = 100 kHz, v_de/v_s = 4 - TCSU (goals): n_e = 0.3 × 10^20 m^-3, T_t = 0.3 keV, B_e = 0.06 T, r_s = 0.35 m, f_ω = 100 kHz, v_de/v_s = 1.5 - Reactor: n_e = 1.0 × 10^20 m^-3, T_t = 25 keV, B_e = 1.0 T, r_s = 2.5 m, f_ω = 10 kHz, v_de/v_s = 0.1 TCS Temperature (and Flux) Limited in Present Experiments – at least partially by impurities Operation at High ω = 1.62×10^6 s^-1 and Low B_ω with symmetric RMF current drive & θ-pinch vacuum technology. Experimental traces shown for shots #9729 and #9751 comparing B_e, ∫n_e dl, T_t, ∫P_rad dl, B_ω, and P_abs over time. TCS/upgrade Built to Reduce Impurity Level and Radiative Losses - Larger, metal input section to avoid translated FRC contact with quartz. - Protective tantalum covered flux rings under quartz RMF drive section. - Elimination of Viton “O-rings” to allow bakeout and discharge cleaning. - Ti-gettering or siliconization wall conditioning. Machine schematic details sections: End/Pumping Chamber (48 cm I.D.), Transition Section (48 cm I.D.), Central Confinement Section / Quartz For RMF Drive (80 cm I.D. with tantalum clad flux rings 76 cm I.D.), Transition Section (48 cm I.D.), and Original Source Section (40 cm I.D.). TCS/upgrade [Photograph of the TCS/upgrade experimental facility and vacuum chamber/magnet array] Recent Interesting Results - Anti-symmetric RMF (originally proposed theoretically) results in completely closed field lines and, hopefully, good thermal confinement. [Plots showing RMF antenna current phasing, closed field line contours for (a) and (b), and time traces comparing anti-parallel (#13904) vs parallel (#13709) operation for B_e, ∫n dl, ∫P_r dt, and P_abs] Recent PPPL kinetic calculations show promise of complete stability HYM simulations for oblate FRCs (E~1) with a close-fitting conducting shell and energetic beam ion stabilization: - Linearly stable with respect to the n=1 tilt mode and the n=2 modes - Residual instabilities saturate nonlinearly at small amplitudes - Configuration remains MHD stable, if current is sustained. [Plots of |V_n|^2 vs tω_ci for n=1 and n=2 modes comparing 'no stabilization', 'conducting shell', and 'conducting shell & ion beam'] Summary - FRCs are a simple, surprisingly robust confinement scheme. - Unique plasma configuration: – Ideal reactor attributes (high β, simple geometry with natural divertor, advanced fuel potential). – Interesting plasma studies of η_⊥ and high-β MES in simple geometry. - Formation and sustainment has been demonstrated by RMF. - RMF with TNBI could provide stability and efficient current drive. - η_⊥ scaling with v_de/v_s is favorable for reactor. - If TCSU is successful, the next step would be a larger device, including TNBI, with lower v_de/v_s. - RMF current drive is simple, robust, and now relatively inexpensive! [Diagram: Reactor cross-section showing 13.5 m length, First Wall, Blanket, Confinement Coils, RMF Antenna Leads, and Neutral beams] ARTEMIS Design (D-³He) - θ-pinch translation/expansion formation - TNBI flux build-up and sustainment [Cutaway technical diagram illustrating Turbo Molecular Pump, TW DEC, Cusp DEC, Pinch Coil, NBI, Formation Section, Burning Section, Modulator, Decelerator, and Direct Energy Converter] FRC Translation Demonstrates Robustness (at least at low s) - Wanted to reduce n_e from 5×10^21 m^-3 in formation section (B_e ~ 0.5-1.0 T) to 5×10^19 in TCS sustainment chamber (B_e ~ 50-100 mT) without significantly degrading temperature. - This is made possible by non-isentropic recovery of high (~ 400 km/s) translation energy. - FRC exhibits remarkable robustness in surviving violent reflections off end mirrors. [Graph of Radius vs Axial distance for Shot 5167 at 0.0 µsec]