FRC History, Physics, & RPPL Program

1. FRC History, Physics, & RPPL Program Redmond Plasma Physics Laboratory University of Washington Review for TV George & Sam Barisch (September 18, 2007)

2. Compact toroid with ‘non equilibrium affecting’ toroidal field. Axial equilibrium requires high beta: = 1 - ½xs2 . Flux conservation: Be = Bo/(1 – xs2) . Simple radial pressure balance: p + B2/2o = Be2/2o . Field null at R = rs/2 . Since generally highly elongated (prolate), usually shown with z-axis horizontal - then talk of ‘reversing’ external Bz field. rc Be rs Bo FRC Geometry xs rs/rc Bz(r) ne(r)

3. Promise of Very Attractive Compact Fusion Reactor Neutral beams T ~ 10 keV ne ~ 1020 m-3B ~ 1 T rs ~ 2 m p ~ 4 Wb s ~ 20

4. RMF Sustainment Antenna (1 of 2) Magnetic Nozzle Mirror Coil FRC Plasma Exhaust Specific Impulse 103 - 106 sec Direct Energy Converter External Magnetic Field Confinement and Heating Coils Ideal Propulsion Geometry(should have NASA interest) Idealized Fusion Propulsion Utilizing D-3He Fuel (quick stop at Moon or Jupiter to gas-up)

5. Advantages Simplest possible cylindrical geometry. High  allows for low field confinement magnets. Natural divertor out ends. Advanced fuel potential. Fusion reaction ions will provide much of current drive. Translatability allows for separation of generation and burn. Natural geometry for space propulsion. Problems Physics different from other toroidal configurations. (Maybe not as different as first thought.) Stability uncertain due to lack of strong toroidal field (reliance on kinetic and flow effects - perhaps). 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 has been technologically difficult. FRC Advantages & Problems

6. Outline • History – ‘Achieving Field Reversal’ • FRC Physics • Pulsed & steady-state • RPPL Program & TCS Results • Non-RMF sustained translation experiments • RMF formation & sustainment experiments • TCS-Upgrade (TCSU) • Long Term Opportunities for Significantly Better Reactor, and Extremely Versatile Plasma Physics Facility

7. HISTORY

8. Attempts at Field Reversal have a Long History – supra-thermal ring currents • First tried at LLNL in ASTRON Program in 1960s 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.

9. Theta-pinches (rapid rise of  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. Icoil Icoil + - End View Field Reversal in a -Pinch – plasma currents Iplasma 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.

10. Original Russian TOR(Kurtmallaev group ~ 1970s) Developed high energy FRCs by delaying reconnection at ends and producing strong axial implosions. Program also included imploding liners

11. FRX/C-T at LANL (~1980s) Studied translation & adiabatic compression Interferogram taken on FRX-C using holography

12. LSX at STI Optronics (1990) Kinetic # of internal gyro-radii parameter Construction: $14M over 4 years (1986-1990)

13. FRC PHYSICS

14. Ion diamagnetic rotation drives n=2 mode due to centrifugal forces. It has been stabilized by weak multipoles with Bm2/2mo > 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 Internal Tilt Side View Most Studied Problem - Stability Rotational n=2 End View

15. No Stabilization Octopole Stabilization Stabilization of n=2 Rotational mode • First calculated experimentally by Ishimura and demonstrated experimentally by Ohi at Osaka University in 1982. • Since then shown in many experiments with many external field configurations.

16. 1.0 E = 4 E = 6 E = 12 (Elliptical) 0.8 S*/E < 3.5 0.6 mhd 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1.0 / E S * Growth Rate of Tilt Mode (from 3D HYM simulation) 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. Most recent calculations show FRC can be completely stabilized by fast ion component! Calculations by E. V. Belova et al.

17. s » a/rio w = d/rio d l FRC Confinement(for decaying FRC) a ~rs/4 • At high  flux and particle diffusion are the same phenomenon: D = /o •  = a2/D = rs2/16D : sets absolute ‘L/R’ lifetime of configuration • N = xsa2[1 + w/2s]/D : open field line ‘bottleneck’ only slight help • Diffusivity inferred over very limited density range in theta pinch formed FRCs appeared favorable to high density operation (but not seen in recent high and low density experiments). • D^ ~ 5/n1/2(1021 m-3) m2/s • RMF can completely reverse particle diffusion!

18. 1000 LSX TRX-1 General N  xsrs2/i TRX-2 Time (sec) FRX-B FRX-C 100 LSM LSX N  (rs/i)3 10 100 10 1 rs/2i (cm1/2) Measured FRC Particle Confinement in Theta-Pinch Experiments (ne = 1-51021 m-3) No tilt instability seen in LSX up to s = 4

19. Pulsed - High Density Most historical research – theta pinch formation yields high Ti and ne. 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 - ~1020 m-3 Density Tangential Neutral Beam Injection (TNBI) – first tried in Mirror program. Japanese design: ARTEMIS D-3He 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. Two Major FRC Reactor Approaches

20. High Density Pulsed Approaches(For non-sustained plasma probably need n ~ 1021m-3s at T = 10 keV for economical reactor) Using optimistic -pinch density scaling: (s) = n1/2(1021m-3)rs2(cm) n(1021m-3) = 0.1B2(T) p(mWb)  0.1rs2(cm)B(T) (s) = 3p(mWb) s = p(mWb)/rs(cm) n = 3p(mWb)B2(T) 1014 m-3s Inertial Confinement At B = 1000 T need p = 3 mWb n = 1026m-3 rs = 0.2 cm s = 15  = 10 s (requires D = 0.025m2/s) (for  = inertia must have high ) Non Destructive Wall At B = 100 T need p = 300 mWb n = 1024m-3 rs = 5.5 cm s = 55  = 1 ms (requires D = 0.2m2/s)

21. Theta Pinch Formation and Translation/Expansion (LSX limited to p ~ 10-20 mWb) (Formation power input ~ 10s of GW) Merging Spheromak Formation (slower formation – flux limits unknown) (Formation power input ~ 100 MW) Rotating Magnetic Field Formation (also current drive mechanism – no fundamental flux limit) (Formation power input ~ 1 MW) Low Density Steady-State Approach(For -heated plasmas n can probably be less than 1021 m-3s but will still need several Wb flux levels) Formation Methods

22. ‘LSX’ Lifetime Scaling Not Seen in Extended Density Range Experiments • Lower density (translated, expanded) FRCs have better lifetimes and recent high density MTF (FRX-L) FRCs have poorer lifetimes. • D  1/n is not correct over wide density range!

23. ARTEMIS Design (D-3He) -pinch translation/expansion formation TNBI flux build-up and sustainment

24. RPPL PROGRAM & TCS RESULTS

25. RPPL Program • Develop technologically simpler formation method without limits on achievable flux. • Conduct studies of basic FRC equilibrium, stability, confinement, & recycling physics in steady state environment. • Present focus is on RMF formation and sustainment, but will eventually include TNBI. • Next few years emphasis is on controlling recycling impurities and achieving high steady-state temperatures. • (Great progress already made!) • High s, and low vde/vs studies would be future focus.

26. 20 cm 1m 80 cm 5 m Previous RPPL Group Devices TRX, (1980-1986) LSX (1991) 40 cm 27 cm 80 cm 2.5 m TCS (2000 - 2005) LSX/mod (1993 - )

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

28. TCS Accomplishments • 5 years of highly fruitful experiments - numerous important journal articles. 4 PhDs graduated. • Basic theory of flux sustainment and density scaling well developed both analytically and numerically. • Many additional facets, such as RMF acting as strong stabilizer, use of odd-parity drive to maintain closed field lines, and toroidal field appearance and Minimum Energy States (MES) explored. • Main problem of low temperatures limited by radiation barriers identified. TCSU program proposed. • Collaboration started with Materials Sciences Dept.

29. Sampling of Important Papers • Detailed examination of translated and RMF generated plasmoids to show self-organization into high- state. • H.Y. Guo, et. al., “Flux conversion and evidence of relaxation in a high- plasma formed by high-speed injection into a mirror confinement structure”, PRL 92, 245001 (2004). • H.Y. Guo, et. al., “Evidence of relaxation and spontaneous transition to a high-confinement state in high- steady-state plasmas formed by RMF”, PRL 97 235002 (2006). • Extensive development of RMF current drive theory for flux confined FRCs. • A.L. Hoffman, “RMF current drive of FRCs subject to equilibrium constraints”, NF 40, 1423 (2000). • R.D. Milroy, “An MHD model of RMF current drive in an FRC”, POP 7, 4135 (2000). • H.Y. Guo, et. al., “Formation and steady-state maintenance of FRCs using RMF current drive”, POP 9, 185 (2002). • A.L. Hoffman, et. al., “Resistivity scaling of RMF current drive in FRCs”, NF 43, 1091 (2003). • R.D. Milroy, et. al., “Edge-driven RMF current drive of FRCs”, POP 11, 633 (2004). • H.Y. Guo, et. al., “Sustainment of elongated FRCs with localized RMF current drive”, POP 11, 1087 (2004). • A.L. Hoffman, et. al., “Principal physics of RMF current drive of FRC", POP 13, 012507 (2006).

30. Additional Important Papers • Long term FRC sustainment demonstrated with spontaneous toroidal field development leading to enhanced performance. • A.L. Hoffman, et. al., “Long pulse FRC sustainment with enhanced edge driven RMF current drive”, NF 45, 176 (2005). • Interchange mode stabilization with implications well beyond FRCs. • H.Y. Guo, et. al., “Stabilization of interchange modes by RMF”, PRL 94, 185001 (2005). • Use of anti-symmetric RMF to eliminate FRC field line opening. • S.A. Cohen & R.D. Milroy, “Maintaining the closed magnetic field line topology of an FRC with the addition of static transverse magnetic fields”, POP 7, 2539 (2000). • H.Y. Guo, et. al., “Observations of improved confinement of FRCs sustained by anti-symmetric RMF”, POP 12, 062507 (2005). • Ti coating experiments to identify scrape-off layer flow and recycling impurity sources. • G.C. Vlases, “TCS edge studies final technical report”, RPPL-UW (2005).

31. Non-RMF Driven FRC Translation Experiments

32. FRC Translation Demonstrates Robustness (at least at low s) Radius (cm) Axial distance (cm) Used to reduce ne from5x1021 m-3in formation section(Be~ 0.5-1.0 T)to5x1019in TCS sustainment chamber(Be ~ 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.

33. 60 B B Initial and Final Flux Measurements z x Rear 30 0 Front 1st pass -30 60 30 Internal Field (mT) 0 2nd pass -30 60 30 0 Captured -30 0 10 20 30 0 10 20 30 Radius (cm) Disorganized Plasmoid Transitions to Preferred FRC State 3.0 2.0 1.0 0 Rigid rotor: p = 0.31xs  (mWb) Internal probe measurements 0 5 0 100 150 200 250 Time (sec) 2-D MHD Calculation of Reflection Process

34. Low Density Lifetimes Considerably Exceed Values Inferred from High Density Scaling Translated FRC Lifetime Measurements

35. Due to high Elongation & small Aspect Ratio actually have safety factor above unity and significant field shear even with low B/Bz . FRC will be high  as long as B << Bz . 60 (a) B z 30 B q B (mT) 0 rs -30 0 0.1 0.2 0.3 r (m) 3 (b) 2 q 1 hg2005.st-frc.05 0 0 0.25 0.50 0.75 1.00 Y Translated FRC q Profile • Amount of shear satisfies cylindrical Suydam criterion based on centrifugal force. (Other than lack of center column, B profile appears very much like ST)

36. Rotating Magnetic Field Current Drive

37. driven electron current rotating field Bw RMF antenna Iz = Iocoswt RMF antenna Iz = Iosinwt Bz field coils RMF Current Drive • ‘Drag’ Electrons Along With Rotating Radial Field • Must have wci < w << wce for electrons, but not ions, to follow rotation • Electrons Magnetized on Rotating Field Lines (wcet >> 1) • Necessary for efficient current drive • Absolutely necessary for rotating field penetration

38. Flinders 50  Rotamak Now at PrairieView A&M RMF flux drive pushes FRC against plasma tube wall

39. H 60 40 20 0 -20 -40 -60 RMF Antennas Y (cm) V Wall hg2001.1.2b Mirror Coils End Coils Main Bias Coils 0 -60 -40 -20 20 40 60 X (cm) Schematic of TCS Confinement Coils and RFM Antennas Induced axial oscillation of electrons, vez, combined with RMF radial component, Br, produces azimuthal drive, Fe. Flux conserving wall is key!

40. Formation of FRC Inside Flux Conserver Compresses Initial Bias Flux Be Bo rc Add RMF rs R xsrs/rc • RMF forces produce flux and generates FRC. • Use of flux conserving coils yields Be = Bo/(1-xs2). • FRC will expand radially until limited by high Be. p  (xs/2)1.3R2Be. • Compressed bias field keeps FRC off wall.

41. 200 Be Pulse: 3569 100 0 -100 Bint -200 40 Wall r 20 0 nem 2 1 0 40 Ttot 20 0 10 Iant 3 2 0 Pabs 1 -10 0 alhaps2001.4a 0 500 1000 1500 2000 2500 3000 Time m ( s) FRC formed by RMF alone Up to 60 kAof current is driven by RMF, and maintained in steady state for the entire duration of RMF. Operating space: Ttot:20 ~ 100 eV ne:0.5 ~ 4 1019 m-3 Be:5 ~ 20 mT B:1 ~ 6 mT

42. p greatly increased – better thermal insulation. rs driven close to flux conserving wall: xs rs/rc  0.8 . Outward radial diffusion reversed, ne(rs) [and ne(0)] very low. 10 10 ne 5 5 Density (1018m-3) Magnetic Field (mT) 0 0 Bz -5 rs -10 0 5 10 15 20 Radius (cm) rs ne Bz RMF Sustained FRCs Significantly Different than non-Sustained FRCs Blue – conventional FRC Bz only partially reversed ne(rs) fairly high Red – RMF driven FRC Bz fully reversed ne(rs) very low

43. RPPL Development of RMF Current Drive Theory for FRCs

44. 1  = I/Isynch =40  0 0 20 40 60 Previous Static Calculations based on Fixed Density and Resistivity • Calculations for stationary plasma based on RMF drive and penetration parameters. Non-linear penetration, with no penetration beyond simple skin depth  until  exceeds , and then full penetration. • Penetration occurs due to near synchronous rotation of electrons, e  ,  =  - e very small.

45. RMF Force ne-vezBr rs * MHD Model of RMF Current Drive in FRCs • The RMF parameters and underlying plasma resistivity determine ne. • The temperature is determined independently by power balance. • The penetration distance * adjusts automatically dependent on  and is less than rs for  < 1. (RMF drive ceases if  > 1)

46. RMF Antenna B V Under AntennaOuter: Inner: FRC Ends Outer: Inner: r V Z RMF2003.15 Torque Based Model Accounts for Resistive Torque Everywhere Plasma flow can distribute the RMF drive forces throughout the FRC, both radially and longitudinally. An FRCs length is determined by particle and energy balance.

47. RMF Penetration Movies Vacuum calculation in lab frame of reference Plasma measurement in RMF frame of reference Plasma calculation in RMF frame of reference, with uniform resistivity. (Calculation starts from already formed FRC)

48. fe fd f Experimental measurement of internal probe (aligned at 45) frequency content for f = 258 kHz. Edge Driven Mode (due to very non-uniform resistivity profile) Calculation based on  = 30 + 1000/(1+e(a-r)/) -m, with a = 35 cm,  = 1 cm. Inner structure rotates at e and tearing and oscillating torque occurs at d =  - e.

49. RPPL RMF Current Drive Experiments

50. The plasma density is seen to be proportional to B, independent of other factors. 120 12 Be (mT) Tt (eV) 80 8 40 4 0 0.6 pradd (MW/m2) 6 0.4 4 ned (1018m-3) 2 The magnetic field is proportional to Tt1/2. The initial temperature is high before recycling brings in impurities and radiative energy losses dominate. Higher fields and currents are accommodated without increases in B or Pabs. 0.2 0 0 3 2.0 Pabs (MW) 1.5 #9729 2 B (mT) 1.0 #9751 1 0.5 0 0 0 0.4 1.6 0.8 1.2 0 0.4 1.6 0.8 1.2 TIME (msec) TIME (msec) Illustration of Impurity Radiation Limiting Temperature in TCS Operation at High  = 1.62x106 s-1 and Low B