FRC History, Physics, & Recent Developments. Alan Hoffman Redmond Plasma Physics Laboratory University of Washington (ICC 2004) (May 25-28, 2004)

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1 FRC History, Physics, & Recent Developments Alan Hoffman Redmond Plasma Physics Laboratory University of Washington (ICC 24) (May 25-28, 24) 1

2 FRC Geometry r c r s B o B e x s r s /r c Compact toroid with negligible toroidal field. Axial equilibrium requires high beta: β = 1 - ½x 2 s. Flux conservation: B e = B o /(1 x s2 ). Simple radial pressure balance: p + B 2 /2µ o = B e2 /2µ o. Field null at R = r s / 2. Since generally highly elongated (prolate), usually shown with z-axis horizontal. then talk of reversing external B z field. 2

3 Outline History Achieving Field Reversal Desirable Reactor Attributes & Non-Standard Physics High Density Pulsed & Low Density Steady-State Approaches Recent Developments Using Rotating Magnetic Fields (RMF) for both formation & steady-state current drive 3

4 Attempts at Field Reversal have a Long History supra-thermal ring currents First tried at LLNL in ASTRON Program in 196s using electron beams. Next tried in Mirror Program using Tangential Neutral Beam Injection (TNBI). Finally achieved by Hans Fleishmann at Cornell using pulsed electron ring. Ion ring needed for fusion application but much more difficult. 4

5 Field Reversal in a θ-pinch plasma currents - I plasma + I coil End View I coil Theta-pinches (rapid rise of θ current in external single turn coil using high voltage capacitor bank) produced some of the first thermonuclear plasmas. Lifetime was short due flow out ends. To close-up the ends, start with some negative bias flux and reconnect with added forward flux. Some original demonstrations done in Germany and USSR, with FRC (name given by Rulon Linford) experiments started at LANL (~1978) as part of Mirror enhancement program. 5

6 Original Russian TOR (Kurtmallaev group) Developed high energy FRCs by delaying reconnection at ends and producing strong axial implosions. Program also included imploding liners 6

7 FRX/C-T at LANL Studied translation & adiabatic compression Interferogram taken on FRX-C using holography 7

8 LSX at STI Optronics s = r s rdr ρ R r s i Kinetic # of internal gyro-radii parameter 8

9 FRC Advantages & Problems Advantages Simplest possible cylindrical geometry. High β allows for low field confinement magnets. Natural divertor out ends. Advanced fuel potential. Translatability allows for separation of generation and burn. Natural geometry for space propulsion. Problems Physics very different from other toroidal configurations. Stability uncertain due to lack of strong toroidal field (reliance on kinetic and flow effects). All currents diamagnetic difficult to sustain; transport may be rapid. Amount of poloidal flux is key scaling component for compact toroids and achieving high flux is technologically difficult. 9

10 Why Continued Interest in FRCs? More (6) advantages than problems (4). Many highly favorable and unique reactor features make FRC approach worth pursuing despite physics uncertainties. Unique and extremely interesting physics. Impressive tendency of FRC to be a natural state. Order of magnitude breakthroughs in reactor design can come about if really innovative ideas are pursued. Worth pursuing as long as good ideas remain and there is still interest and excitement from researchers. Cost must be modest until justified by performance. 1

11 Most Studied Problem - Stability Side View Rotational n=2 End View Internal Tilt Ion diamagnetic rotation drives n=2 mode due to centrifugal forces. It has been stabilized by weak multipoles with B m2 /2µ o > centrifugal pressure Internal tilt is more insidious - starts out as an axial n=1 shift. Most studied mode with various ideas proposed for observed stability 11

demonstrated experimentally by Ohi at Osaka University in 1982.

12 Stabilization of n=2 Rotational mode No Stabilization Octopole Stabilization First calculated experimentally by Ishimura and demonstrated experimentally by Ohi at Osaka University in Since then shown in many experiments with many external field configurations. 12

13 Growth Rate of Tilt Mode (from 3D HYM simulation) γ/γ mhd S*/E < 3.5 E = 4 E = 6 E = 12 (Elliptical) Kinetic calculations generally show reduction of tilt rate at low s, but not positive stabilization, at least in linear phase. Other effects may be important, such as strong flow, residual toroidal field, ion viscosity, Hall effects E/S* Calculations by E. V. Belova et al. 13

14 FRC Translation Demonstrates Robustness (at least at low s) Radius (cm) Axial distance (cm) Wanted to reduce n e from 5x1 21 m -3 in formation section (B e ~.5-1. T) to 5x1 19 in TCS sustainment chamber (B e ~ 5-1 mt) without significantly degrading temperature. This is made possible by non-isentropic recovery of high (~ 4 km/s) translation energy. FRC exhibits remarkable robustness in surviving violent reflections off end mirrors. 14

Disorganized Plasmoid Transitions to Preferred FRC State φ (mwb) 3. 2. 1. Rigid rotor: φ p =.

15 Disorganized Plasmoid Transitions to Preferred FRC State φ (mwb) Rigid rotor: φ p =.31x s φ Internal probe measurements Time (µsec) Internal Field (mt) Initial and Final Flux Measurements Bz 1st pass 2nd pass Rear Front Bx 3-3 Captured 2-D MHD Calculation of Reflection Process Radius (cm) 15

16 Larger θ-pinches Built to Study Stability & Confinement with Increasing s 1m 2 cm (FRX/C & FRX/C-T 4 & 6 cm dia.) TRX, FRX/B ( ) 8 cm LSX ( ) 5 m 4 cm 27 cm 8 cm 2.5 m LSX/mod ( ) TCS (2 - ) 16

17 Measured FRC Particle Confinement 1 LSX Time (µsec) 1 TRX-1 TRX-2 FRX-B FRX-C LSM LSX τ N (r s / ρ i ) 3 General τ N x s r s2 /ρ i No tilt instability seen in LSX up to s = r s /2 ρ i (cm 1/2 ) 17

18 FRC Confinement (for decaying FRC) a ~r s /4 δ s a/ρ io w = δ/ρ io l At high β flux and particle diffusion are the same phenomenon: D = η /µ o τ φ = a 2 /D = r s2 /16D : sets absolute L/R lifetime of configuration τ N = x s a 2 [1 + w/2s]/d : open field line bottleneck only slight help Measured diffusivity in theta pinches favorable to high density operation D 5/n 1/2 (1 21 m -3 ) m 2 /s 18

19 Two Major Reactor Approaches Pulsed - High Density Most historical research theta pinch formation yields high T i and n e. Range of reactor scenarios» Adiabatic compressor moving rings (oldest reactor design approach)» RACE type accelerator use TRAP type moving wave FRC acceleration» Liner compression MTF Steady State - ~1 2 m -3 Density Tangential Neutral Beam Injection (TNBI) first tried in Mirror program.» Japanese design: ARTEMIS D- 3 He reactor» FIX (FRC Injection Experiment) at Osaka U. - first to apply TNBI to translated FRC. Rotating Magnetic Field (RMF) drive adapted from rotamak research.» TCS program: using RMF to form, build up flux, and sustain current Ultimate program: combine RMF to form and drive edge to enhance particle confinement, NB to drive center. Torques balanced. 19

1r s2 (cm)b(t) τ (µs) = 3 φ p (mwb) nτ = 3 φ p (mwb)b 2 (T) 1 14 m -3 s Non Destructive Walls At B = 1 T need φ p = 3 mwb n = 1

20 High Density Pulsed Approaches (For non-sustained plasma probably need nτ ~ 1 21 m -3 s at T = 1 kev for economical reactor) Most favorable high density scaling: τ(µs) = n 1/2 (1 21 m -3 )r s2 (cm) n(1 21 m -3 ) =.1B 2 (T) φ p (mwb).1r s2 (cm)b(t) τ (µs) = 3 φ p (mwb) nτ = 3 φ p (mwb)b 2 (T) 1 14 m -3 s Non Destructive Walls At B = 1 T need φ p = 3 mwb n = 1 24 m -3 r s = 5.5 cm τ = 1 ms Inertial Confinement At B = 1 T need φ p = 3 mwb n = 1 26 m -3 r s =.2 cm τ = 1 µs (for τ = τ inertia must have high β ) 2

Low Density Steady-State Approach (For α-heated plasmas nτ can probably be less than 1 21 m -3 s but will still need several Wb flux levels) Formation Methods Theta Pinch Formation and

21 Low Density Steady-State Approach (For α-heated plasmas nτ can probably be less than 1 21 m -3 s but will still need several Wb flux levels) Formation Methods Theta Pinch Formation and Translation/Expansion (LSX limited to φ p ~ 1-2 mwb) (Formation power input ~ 1s of GW) Merging Spheromak Formation (slower formation flux limits unknown) (Formation power input ~ 1 MW) Rotating Magnetic Field Formation (also current drive mechanism) (Formation power input ~ 1 MW) 21

22 ARTEMIS Design (D- 3 He) θ-pinch translation/expansion formation TNBI flux build-up and sustainment 22

23 Recent Work with RMF Current Drive (dipole fields) driven electron current rotating field B ω RMF antenna I z = I o cosωt RMF antenna I z = I o sinωt B z field coils Drag Electrons Along With Rotating Radial Field Must have ω ci < ω << ω ce for electrons, but not ions, to follow rotation Electrons Magnetized on Rotating Field Lines (ω ce τ >> 1) Necessary for efficient current drive Absolutely necessary for rotating field penetration 23

24 Flinders 5 l Rotamak Now at PrarieView A&M RMF flux drive pushes FRC against plasma tube wall 24

25 Schematic of TCS Confinement Coils and RFM Antennas RMF Antennas 6 4 H hg21.1.2b End Coils Main Bias Coils Mirror Coils Use of flux conserving coils yields B e = B o /(1-x s2 ) FRC will expand radially until limited by high B e Y (cm) X (cm) 2 Wall V 25

26 TCS Device RMF Antennas TCS Chamber (confinement & RMF drive) LSX/mod (formation & acceleration ) Study Formation & Sustainment of RMF driven FRCs. Either form FRCs directly using RMF alone, or translate and expand theta-pinch formed FRCs from LSX/mod. 26

Standard Model of RMF Current Drive in FRCs RMF self-consistently penetrates just far enough, r ~ (B e /µ o )/n e eωr s to maintain the diamagnetic current.

27 Standard Model of RMF Current Drive in FRCs RMF self-consistently penetrates just far enough, r ~ (B e /µ o )/n e eωr s to maintain the diamagnetic current. Poloidal flux will increase as long as the RMF torque on the electrons exceeds the torque due to electron-ion drag (resistivity) r s RMF Force ne -v ez B r T RMF = 2 2 πr l / ω s ant ( B µ ) r o T η =.5πη n e 2 ω 2 e e r 4 s l s r dφ dt p = ( T T ) 2 2πREθ( R) = B RMF η e = B o /(1-x s2 ) (n e T t ) 1/2 2 neers l s Equilibrium: n e B ω /(η ωr s2 ) 1/2 E θ = η jθ + ~ v ~ ezb r + V r B z V z B r RMF Antenna B Under Antenna Outer: Inner: FRC Ends Outer: Inner: V r RMF23.15 V Z 27

28 RMF Penetration Movies 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 28

29 RMF Sustained FRCs Significantly Different than non-sustained FRCs Magnetic Field (mt) B z n e n e B z r s r s 1 5 Density (1 18 m -3 ) Blue conventional FRC (B z only partially reversed) Red RMF driven FRC (B z fully reversed) Radius (cm) r s driven close to flux conserving wall: x s r s /r c.8. Outward radial diffusion reversed, n(r s ) [and n(r=)] very low. φ p greatly increased better thermal insulation. 29

30 Uses of RMF Current Drive Axial Magnetic Field (mt) B ext (vacuum) B int Time (msec) B ω Can form FRCs and build up flux at low powers. Edge control mechanism. B ω (vacuum) 1) Greatly increases τ N 2) May be strongly stabilizing B ext brawc brawc Collisional plasma but no sign of tilt instability Can influence performance - for long pulses have seen doubling of τ E Transition to higher performance involves 1) shallower RMF penetration, 2) lower overall resistivity, 3) spontaneous generation of some toroidal field RMF Magnitude (mt) Long Pulse Operation Without External Fueling 3

Problems with RMF Current Drive as Sole Sustainment Method Heat deposition at edge (want to operate with edge drive to avoid disturbing all flux surfaces, although Cohen-Milroy technique can mitigate

31 Problems with RMF Current Drive as Sole Sustainment Method Heat deposition at edge (want to operate with edge drive to avoid disturbing all flux surfaces, although Cohen-Milroy technique can mitigate this). Edge current drive is highly resistive and requires relatively high power input. RMF exerts strong torque on plasma, resulting in ion spin-up which can lead to rotational instabilities (although RMF profile is also strongly stabilizing). 31

32 Tangential Neutral Beam Injection (TNBI) can Counteract RMF Torque FIX Poloidal Flux (mwb) T e (ev) with NBI with NBI TNBI can balance RMF torque, and even be used to adjust toroidal flow profile. FIX FRCs had < 1 mwb of poloidal flux which required mostly axial injection with fast ions oscillating outside separatrix r =.1 m 35 Time (µs) 32

33 True TNBI near Field Null (Need about 5 mwb of flux) Ε ic (kev) r s R =.144 φ Ai Critical orbit: ( mwb) ( ) rs m Ideal energies < E ic, but can operate with E i ~ 2E ic. p 2 1 kev (2E ic ) TNBI calculations by Ricardo Farengo to set immediate TCS/mod goals. φ p (mwb) B e (T) r s (m) T e (kev) n e (1 2 m -3 ) A i beam E i (r s ) E ic TCS/mod goals kev 5 kev Reactor MeV 2 MeV φ p ~ 2 mwb in present TCS 33

34 TCS Temperature (and Flux) Limited in Present Experiments at least partially by impurities B e (mt) n e dl (1 19 m -3 ) #9729 B ω (mt) # TIME (msec) T t (ev) p rad dl (MW/m 2 ) P abs (MW) TIME (msec) Operation at High ω = 1.62x1 6 s -1 and Low B ω Need to increase φ p from ~2 mwb flux in TCS to ~6 mwb for efficient TNBI trapping. This will happen automatically with RMF formation if temperature increases. Applying more RMF power in present device results in initially higher T t and B e, but performance drops rapidly as P rad increases. 34

35 Modifications Underway on TCS to Reduce Impurity Level and Radiative Losses End/Pumping Chamber 48 cm I.D. Transition mirror Section magnet capture magnets diagnostic ports Central Confinement Section (Quartz For RMF Drive) cp cmp magnets magnets diagnostic 8 cm ports I.D. flux rings, tantalum clad, 76 cm I.D. Transition Section fast gate coil 48 cm I.D. Original Source Section 4 cm I.D. 6 CM 8 CM 32 CM 75 CM 125 CM 75 CM 32 CM 8 CM Larger, metal input section to avoid translated FRC contact with quartz. Protective tantalum covered flux rings under quartz RMF drive section. Elimination of O-rings to allow bakeout and discharge cleaning. Combination of Ti-gettering and boronization wall conditioning. Reduction of P rad will allow examination of non-radiatively limited τ E. 35

36 Other Uses for Fusion (Most exciting to our Aero & Astro students!) Mirror Coil Direct Energy Converter RMF Sustainment Antenna (1 of 2) FRC External Magnetic Field Confinement and Heating Coils Magnetic Nozzle Plasma Exhaust Specific Impulse sec Idealized Fusion Propulsion Utilizing D- 3 He Fuel (quick stop at Moon or Jupiter to gas-up) 36

37 Summary FRCs are a simple, surprisingly robust confinement scheme. Several formation and reactor (pulsed and steady state) schemes exist. Formation and sustainment has been demonstrated by RMF. Combination of RMF and TNBI is probably best scenario for sustaining moderate density FRCs m First Wall Confinement Coils Neutral beams Blanket RMF Antenna Leads 37

38 Recommendations (highly personal) Continue pursuing RMF formation and flux build-up technique to produce low density φ p ~ 5 mwb, T e > 1 ev FRCs, suitable for TNBI addition. Expand merging spheromak formation approach with same goals in prolate geometry. Continue 3-D numerical program with the addition of strong flow and RMF. Expand funding through NASA or other agency support. 38

Calculations and Measurements of Rotating Magnetic Field Current Drive in FRCs

Calculations and Measurements of Rotating Magnetic Field Current Drive in FRCs A.L. Hoffman, R.D. Brooks, E. Crawford, H.Y. Guo, K.E. Miller, R.D. Milroy, J.T. Slough, 1) S. Tobin ) 1) Redmond Plasma Physics