THE OPTIMAL TOKAMAK CONFIGURATION NEXT-STEP IMPLICATIONS

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1 THE OPTIMAL TOKAMAK CONFIGURATION NEXT-STEP IMPLICATIONS by R.D. STAMBAUGH Presented at the Burning Plasma Workshop San Diego, California *Most calculations reported herein were done by Y-R. Lin-Liu. Work supported by General Atomics Internal Funds. May 1, 2001 QTYUIOP /RDS/wj

2 ANY NEXT STEP DEVICE SHOULD BE FORWARD LOOKING AND CARRY FORWARD THE CURRENT RESEARCH ISSUES OF THE DAY Any Next Step Device Will Have a Year Research Period For its research program to remain vital over that length of time, we must design the device so that it can carry forward the most up-to-the minute research issues of today Current research issues need a future to expand into If we design the device based on the physics we are currently sure of, then, considering current research progress, we have to look carefully at whether the device once built will be able to address the issues of that future day QTYUIOP /RDS/ci

3 WHAT ARE THE CURRENT PHYSICS RESEARCH LINES THAT NEED TO BE CARRIED FORWARD? Current Research Line Improved Confinement Through Transport Barriers Understanding Transport Steady-state Through High Bootstrap Fractions Operation Above the Free Boundary Beta Limit Resolution of the Disruption Issue Profile Control for higher beta and advanced confinement Detached Divertor Solutions ELM-free Operational States Erosion and Redeposition of First Wall Materials Machine Design Feature Implied Maximization of the E B Turbulence Shearing Rate Suitable Diagnostics and Operational Flexibility 1. Ability to Handle and Maintain Equilibria with Hollow Current Profiles 2. Wall Stabilization for Higher Normalized Beta Operation Wall Stabilization Through Feedback and Plasma Rotation 1. Long Pulse, Precise Plasma Control Near Understood Stability Limits 2. Ability to Handle Disruptions 3. Mitigation of Disruptions by Massive Gas Puffs or Liquid Jets 1. Auxiliary Systems to Provide Local Control of Pressure, Current, and Rotation Profiles 2. Diagnostic Systems To Measure the Resulting Profiles Divertors Capable of Detached Operation at Densities Compatible With Steady-State Ability to realize the EDA and/or QH mode regimes High Particle Fluences to Surfaces and In-vessel Access For Inspection QTYUIOP /RDS/ci

4 WE ARE READY TO TAKE UP BURNING PLASMA AND STEADY-STATE ISSUES Alpha Issues Steady State Issues DT plasma properties Alpha confinement Alpha ash exhaust More Gain Remote maintenance Alpha driven instabilities Self-heated profiles High gain burn control High bootstrap fractions (AT) Steady-state magnets Steady-state current drive Tritium inventory Hour long pulses Fluence Resolve disruption issue Blanket development Low activation materials Tritium breeding Month long operation First electric output /RDS/wj

5 WHAT IS THE OPTIMUM TOKAMAK? Lin-Liu constructed equilibria with Bootstrap fraction 99%, fully aligned Found ballooning limit 3 A point near edge p = 0 at separatrix Wall stabilization assumed for kinks Spanned 1.5 κ A 7 β T βp = 25 ( 1 κ2 β N ( ( ( fbs = cbsβp PF β 2 T B 4 T A QTYUIOP /RDS/wj

6 THE LIMITING EQUILIBRIA HIT THE BALLOONING LIMIT AT A POINT NEAR THE EDGE α (norm. p ) β N = 8.0 κ = 4.0 RDS1.6k4 Unstable α (norm. p ) β N = 5.7 κ = 6.0 RDS1.6k6 Unstable ψn ψn /RDS/jy QTYUIOP

7 J M (ka/m 2 ) R (m) P (kj/m 3 ) R (m) 2.65

8 dp/dsi (kj/m 3 /web) q Sort (si) FFPRIM SIn 1.0

9 J M (ka/m 2 ) P (kj/m 3 ) R (m) 2.65

10 dp/dsi (kj/m 3 /web) 2039 q Sort (si) FFPRIM SIn 1.0

11 ULTIMATE AT PRESSURE PROFILES WILL REQUIRE AN ITB AT LARGE RADIUS, CONSISTENT WITH MHD STABILITY AND HIGH BOOTSTRAP FRACTION Modeling indicates that increasing ITB radius and barrier width is consistent with: Higher fusion performance (larger high confinement volume) Non-optimal profile ITB radius, ρ ITB Optimal profile ITB half width ρ DIII D NATIONAL FUSION FACILITY SAN DIEGO Schematic ITB T i profiles Improved MHD stability limits MHD modeling of β N limit β N (%-m-t/ma) stable unstable ITB Radius, Ψ ITB High bootstrap fraction and improved bootstrap current alignment ARIES-AT Modeling Desired current profile T i (kev) ITB r/a

12 HIGH BOOTSTRAP FRACTION ARIES-AT SCENARIO DEMONSTRATES NEED FOR TRANSPORT CONTROL AT LARGE BOOTSTRAP FRACTION J (Zmag, KA/m 2 ) (a) AT large boostrap (I BS /I) 100% J becomes naturaly hollow (NCS) Alignment of J BS with J total requires broad pressure profile Control of J requires control of transport profiles (c) q (b) R (m) MA/m J φ R o R 0.1 Bootstrap + diamag + PS sqrt (psi) Bootstrap Diamagnetic Pfirsch-Schluter DIII D NATIONAL FUSION FACILITY SAN DIEGO 32500/TST/wj

13 THE FUTURE Advanced Tokamak stability theory points to states with very broad pressure profiles and hollow current profiles and nearly 100% bootstrap current as perhaps the ultimate potential of the Tokamak q Pressure Profile P ARIES AT A=3.3 κ=2.5 δ=0.6 β=14% β N =6 Current Profile JB B/R Kink Stability r wall /a ARIES ST A=1.6 κ=3.6 δ=0.64 β=56% β N = /rs

14 10 8 A= δ = β N κ

15 10 A=1.6 8 δ = 0.7 β N κ

16 A= δ = 0.5 β T (%) κ

17 150 A=1.6 δ = β T (%) κ

18 BetaN_vs_A BetaN K=1.5 K=2.0 K=2.5 K=3.0 K=3.5 K=4.0 K=4.5 K=5.0 K=5.5 K= A

19 OPTIMIZING Q IN A STEADY-STATE MACHINE P Q F γ P = = CD F = PCD nir( 1 fbs I n = f GR πa 2 ( κ ( γ CD βn 2 2 Bc 1 1 A fgr R( 1 fbs ( ( 2 Ra2 Bc = field at centerpost (fixed maximum from stress) A c bs f bs = c bs β p = A qcyl 20 β N Express β N (A) as β NO A α and κ as κ O A φ Optimize the function ( 1 A 2α c bs 20 ( 1 q cyl for α = 1/2; φ = 1/2 A max = 2.3 α = 1; φ = 1/2 Amax = A ( 2 β N0 A φ A 1/2 α ( QTYUIOP /RDS/wj

20 Passively Stable κ goes like 1/A A Reasonable Assumption for Feedback Stabilized κ is A Unstable Feedback Stability Broad J(r) (li=0.6) Elongation START? Peaked J(r) (li = 1.0) Passive Stability Limit Stable Feedback Stability for Peaked J(r) Unstable Stable Broad J(r) (li = 0.5) Passive Stability Limit Aspect Ratio 1) Passive stability results from A. Sykes, "Progress on Spherical Tokamaks," Plasma Phys. and Contr. Fusion 36, B93 (1994). 2) Feedback stability results for peaked profiles from R. D. Stambaugh, et. al., "Relation of Vertical Stability and Aspect Ratio in Tokamaks," Nucl. Fusion 32, 1642 (1992). 3) Feedback stability results for broad profiles from recent work by L. Lao. QTYUIOP

21 OPTIMIZING Q IN A STEADY-STATE SYSTEMS (Continued) Fit Lin-Liu's data to β N = β N0 A (a+bκ) (c + dκ + eκ 2 ) Use this β N in ratio for Q Use κ A 0.5 Q index optimizes for A = depending on the bootstrap fraction Fusion Power/Current Drive Power Index f bs ~ 90% f bs ~ 80% f bs ~ 70% A QTYUIOP /RDS/wj

22 10 BetaN vs A Symbols are Calculations Lines are Fits BetaN K=1.5 K=1.5 K=2.0 K=2.0 K=2.5 K=2.5 K=3.0 K=3.0 K=3.5 K=3.5 K=4.0 K=4.0 K=4.5 K=4.5 K=5.0 K=5.0 K=5.5 K=5.5 K=6.0 K= A

23 BetaN vs A Using Limiting Kappa (A), (SQRT(1/A)) Best Fit is BetaN (A) = 9.9 A Kappa BetaN Fit A

24 OPTIMUM ASPECT RATIO ST IS 1.5 Optimize P FUSION P CENTERPOST as Stambaugh et al., Fusion Technology 33, 1 (1998) P F P C at constant bootstrap fraction is ( (1 + κ 2 4 A 1 ) β N A ( 2 Use κ A 1/2 and β N A 1/2 Optimum of ( A 1 A 6 ( 2 is A = 1.5 QTYUIOP /RDS/wj

25 SC AND NC TEST REACTORS (T-peak at 20 kev, f bs = 90%, and S n =0.25, S t = 0.25) Direct $M SC Test k=1.5 SC Test k=2 SC Test k=3 0.5 GWf GWf 0.1 GWf 0.5 GWf 0.2 GWf GWf 0.5 GWf 0.2 GWf 0.1 GWf Aspect Ratio Aspect Ratio SC Test k=1.5 NC Test k= Aspect Ratio NC Test k=3 Direct $M GWf 0.2 GWf 0.1 GWf GWf 0.2 GWf 0.1 GWf GWf 0.2 GWf 0.1 GWf Aspect Ratio Aspect Ratio Aspect Ratio 18th IAEA Fusion Energy Conference, Sorrento, Italy 2000 GA Wong 2000 QTYUIOP jy

26 SC AND NC POWER REACTORS (T-peak at 20keV, fbs=90%, and Sn=0.25, St=0.25) 200 SC Power k=1.5 SC Power k=2 2 GWe 1 GWe 1 GWe GWe 200 SC Power k=3 0.5 GWe 0.5 GWe COE, mill/kwh Aspect Ratio Aspect Ratio GWe Aspect Ratio 1 GWe 2 GWe COE, mill/kwh NC Power k= GWe 2 GWe 1 GWe NC Power k=2 0.5 GWe 1 GWe 2 GWe NC Power k=3 0.5 GWe 1 GWe 2 GWe Aspect Ratio GA Wong Aspect Ratio 18th IAEA Fusion Energy Conference, Sorrento, Italy Aspect Ratio QTYUIOP jy

27 093 01/RDS/df QTYUIOP

28 TF center bore Vacuum vessel TF coil (upper leg) 1 m 0 m TF coil (outer leg) Superconducting PF coil set Test blanket module Blanket shield Superconducting PF coil set /RDS/df QTYUIOP

29 Plasma vacuum vessel + plasma-facing first wall Water-cooled copper (double wall, water cooled) divertor coil (1 of 4, with radiation-resistant insulation) LHe-cooled NbTi superconducting PF Coil (1 of 6, T = 4.5 K) Port Shield Tangential Access Port (NBI, 2 azimuthal locations) Port Shield Breeding Blanket and Nuclear Shield Breeding Blanket and Nuclear Shield TF Coil Centerpost I = 16.3 MA 0 Plasma I = 13 MA Breeding Blanket and Nuclear Shield Blanket Test Module or port-mounted H/CD or diagnostic system module (10 azimuthal locations) Breeding Blanket and Nuclear Shield TF coil vertical leg (12 azinuthal locations) 7.0 m TF coil radial leg: 1 = 1.35 MA (12 azimuthal locations, upper + lower) 9.5 m Demountable joints (upper and lower) /RDS/df QTYUIOP

30 Hot Cell (north) TF rectifier cabinets TF rectifier cabinets Test blanket module TF feeder TF feeder Compartmentalized TF rectifier cabinet option NBI Radial TF feeder option Hot Cell (south) /RDS/df QTYUIOP

31 A B C D E FDF Base Case and Net Electric! OK Blanket OK Blanket OK Blanket OK Blanket No Wall Stabilization Cases 10 cm No Wall Stabilization Inboard BetaN down fbs 0.5 fbs 0.7 Turn up B A aspect ratio a plasma minor radius m Ro plasma major radius m κ plasma elongation Rhole Hole Size m Jc centerpost current density MA/m framp induct ramp frac Pf fusion power MW Pc power dissipated MW Pinternal power to run plant MW Qplant gain for whole plant Qplasma Pfusion/Paux Pnetelec net electric power MW Pn/Awall Neutron Power at Blanket MW/m BetaT toroidal beta BetaN normalized beta mt/ma fbs bootstrap fraction Pcd current drive power MW Ip plasma current MA Bo field on axis T Bc field at conductor T Ti(0) Ion Temperature kev Te(0) Electron Temperature kev n(0) Electron Density E20/m nbar/ngr Ratio to Greenwald Limit Zeff W Stored Energy in Plasma MJ Pheat Total Heating Power MW TauE TauE sec H H factor over 89P L-mode

32 A H I J ST FDF Base Case and Net Electric! Q=4, Blanket OK Blanket Driven VNS Low BetaN Cases 10 cm Cases at BetaN 4.15 Inboard BetaN lower fbs 0.7 Get to H=2 A aspect ratio a plasma minor radius m Ro plasma major radius m κ plasma elongation Rhole Hole Size m Jc centerpost current density MA/m framp induct ramp frac Pf fusion power MW Pc power dissipated MW Pinternal power to run plant MW Qplant gain for whole plant Qplasma Pfusion/Paux Pnetelec net electric power MW Pn/Awall Neutron Power at Blanket MW/m BetaT toroidal beta BetaN normalized beta mt/ma fbs bootstrap fraction Pcd current drive power MW Ip plasma current MA Bo field on axis T Bc field at conductor T Ti(0) Ion Temperature kev Te(0) Electron Temperature kev n(0) Electron Density E20/m nbar/ngr Ratio to Greenwald Limit Zeff W Stored Energy in Plasma MJ Pheat Total Heating Power MW TauE TauE sec H H factor over 89P L-mode VH Tau over 0.85 ELM Free

33 A F G ST FDF Base Case and Net Electric! ~OK Blanket Really High Low BT Cases 10 cm Beta Inboard Low BT fbs=0.5 A aspect ratio a plasma minor radius m Ro plasma major radius m κ plasma elongation Rhole Hole Size m Jc centerpost current density MA/m framp induct ramp frac Pf fusion power MW Pc power dissipated MW Pinternal power to run plant MW Qplant gain for whole plant Qplasma Pfusion/Paux Pnetelec net electric power MW Pn/Awall Neutron Power at Blanket MW/m BetaT toroidal beta BetaN normalized beta mt/ma fbs bootstrap fraction Pcd current drive power MW Ip plasma current MA Bo field on axis T Bc field at conductor T Ti(0) Ion Temperature kev Te(0) Electron Temperature kev n(0) Electron Density E20/m nbar/ngr Ratio to Greenwald Limit Zeff W Stored Energy in Plasma MJ Pheat Total Heating Power MW TauE TauE sec H H factor over 89P L-mode VH Tau over 0.85 ELM Free

34 300 ITER-FEAT ITER-FDR Neutron Wall Loading (MW/m 2 ) FIRE Plant Electrical Power Input (MWe) H F(1.7 T) H F B B I I J(VNS) J(VNS) D D C (f bs = 0.5) E(3.5 T) Power input data G(1.7 T) E(3.5 T) G(1.7 T) C (f bs = 0.5) Plasma gain data Electrical breakeven Fusion Power (MWth) A A Normalized Beta: β N = 8.3 β N = 5.5 β N = 4.2 blue symbols: P in red symbols: Q Plasma Gain (Q) /RDS/df QTYUIOP

35 FUSION DEVELOPMENT FACILITY Steady progress through sequenced objectives PHASES D-D PHYSICS DT PHYSICS BLANKET DEVELOPMENT TRITIUM SELF SUFFICIENCY FUSION POWER (MW) ELECTRIC POWER (MW) ~ DUTY CYCLE 0.4% 0.4% 0.4% 10% 100% 60 SECOND PULSES 60 SEC 5 MIN. ~ WEEK LONG RUNS STEADY-STATE NEUTRON WALL LOAD (MW/m 2 ) TRITIUM PER YEAR BURNED (kg) PRODUCED [NET] (kg) ~ [0.4] [4] /RDS/df QTYUIOP

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