FRC on the Path to Fusion Energy (Moderate Density Steady-State Approach)

Summary

This presentation explores the development and physics of Field Reversed Configurations (FRCs) as a path toward steady-state fusion energy. It reviews experimental history from theta-pinch formation to modern rotating magnetic field (RMF) current drive methods on devices like LSX and TCS, analyzing stability, transport scaling, and reactor concepts such as ARTEMIS.

Page 1: Title Slide

Alan Hoffman Redmond Plasma Physics Laboratory University of Washington

(FPA Meeting on Fusion Pathways to the Future) (September 27-28, 2006)

Page 2: Outline

Outline

History – ‘Achieving field reversal’, θ-pinch formation.
What is an FRC? Why are we interested?
Recent developments, particularly for steady-state.
Ultimate promise.

Page 3: Attempts at Field Reversal have a Long History

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]

Page 4: Field Reversed Configurations (FRCs)

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)

Page 5: LANL FRXC/T - (1980s)

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]

Page 6: Concerns About Stability

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]

Page 7: Large s Experiment (LSX) Built at STI to Study Extrapolation to non-Kinetic Regime – (1990)

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

Page 8: What is needed for steady-state compact toroid (CT) reactor?

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)

Page 9: Techniques for Sustaining FRCs (also enhance stability)

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.

Page 10: RMF Current Drive (dipole fields)

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.

Page 11: TCS (Translation, Confinement, Sustainment)

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.

Page 12: Partial RMF Penetration is Natural Occurrence

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)

Page 13: 2D Interchange Stability Provided by Partially Penetrated RMF

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).

Page 14: RMF also reverses radial particle diffusion & results in long particle lifetime

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.

Page 15: Also see spontaneous toroidal field development: further evidence for a minimum energy state (MES)

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.

Page 16: Plasma density depends on η_⊥

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.

Page 17: Relative current drive power also decreases with temperature

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).

Page 18: Experimental results described well by empirical ‘Chodura’ formula, dependent on v_de/v_s

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

Page 19: TCS Temperature (and Flux) Limited in Present Experiments – at least partially by impurities

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.

Page 20: TCS/upgrade Built to Reduce Impurity Level and Radiative Losses

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.).

Page 21: TCS/upgrade

TCS/upgrade

[Photograph of the TCS/upgrade experimental facility and vacuum chamber/magnet array]

Page 22: Recent Interesting Results

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]

Page 23: Recent PPPL kinetic calculations show promise of complete stability

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’]

Page 24: Summary

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]

Page 25: ARTEMIS Design (D-3He)

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]

Page 26: FRC Translation Demonstrates Robustness (at least at low s)

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]