Chapter 1. Introduction Magnetic Fusion Technology Thomas J Dolan - PowerPoint PPT Presentation

Energy gain ratio vs. triple product 1000 Q 100 10 1 0.1 0 1 2 3 4 5 nT t , 10 21 m -3 keV-s 10 21 m -3 keV s nT t dolan 2010 36

Typical values for triple product Typical values for triple product * magnetic confinement fusion: g n ~ 10 20 m ‐ 3 , T ~ 10 keV,  ~ 1 s. * inertial confinement fusion: inertial confinement fusion: n ~ 10 29 m ‐ 3 , T ~ 10 keV,  ~ 1 ns. dolan 2010 37

Reaction Rate with Two Maxwellian Distributions r(x,t) = n 1 (x,t) n 2 (x,t) <  v> If n D = n T = ½ n, then r = ¼ n 2 <  v> r = ¼ n 2 <  v> DT Dolan 2010 38

Interactions among like particles N = n(n-1)/2 ≈ n 2 /2 if n>>1 For DD reactions r = (½)n 2 <  v> For DD reactions r = (½)n 2 <  v> Dolan 2010 39

Fusion Power Density n D = n T = ½ n P DT = ( ¼ ) n 2 <  v>W DT P DD = P f = ( ½ )n 2 [<  v> ddn W ddn + <  v> ddp W ddp ] ≈ ( ½ ) n 2 <  v> dd W dd ( ) dd dd P cat ≈ ( ½ ) n 2 <  v> dd W cat The factor of ½ avoids counting the same DD reaction twice.

Catalyzed DD fuel cycle D+D  3 He(0.82) + n(2.45) D D + 3 He  4 He(3.66) + p(14.6) 3 H  4 H (3 66) (14 6) D+D  T(1.01) + p(3.02) D+T  4 He(3.54) + n(14.05) _____________________________ Net: 6D  2n + 2p + 2( 4 He) + 43.2 MeV Each DD reaction results in consumption of 3 deuterons, yielding 21.6 MeV = 3.46x10 ‐ 12 J. dolan 2010 41

Reaction rate Parameters <  v> 1 D+T 1. D+T 2. D+ 3 He 3. D+D  H+T 4 T T 4. T+T 5. T+ 3 He 6. H+ 11 B Dolan 2010 42

Reaction Rate Parameters Reaction Rate Parameters <  v> <  v> DT , m /s <  v> <  v> DD , m /s m 3 /s m 3 /s T keV T, keV 8 5.94E-23 6.90E-25 10 1.09E-22 1.21E-24 15 2.65E-22 2.97E-24 20 4.24E-22 5.16E-24 25 5.59E-22 7.60E-24 30 6.65E-22 1.02E-23

Fusion Power Density Example: n=2x10 20 m -3 , T = 10 keV P DT = ( ¼ ) n 2 <  v>W DT DT DT P DT = ¼ (10 40 ) 1.09x10 -22 2.82x10 -12 = 7 2x10 5 W/m 3 = 0 72 MW/m 3 7.2x10 W/m 0.72 MW/m P DD = (½)n 2 [<  v> ddn W ddn + <  v> ddp W ddp ] = 0.5x10 40 [ 0.626x10 -24 5.24x10 -13 + 0.582x10 -24 6.46x10 -13 ] 0 582 10 24 6 46 10 13 ] 0 5 10 40 [ 0 626 10 24 5 24 10 13 = 0.0035 MW/m 3 P cat ≈ (½)n 2 <  v> dd W cat = (½)10 40 1.21x10 -24 3.46x10 -12 = 0.021 MW/m 3 Dolan 2010 44

Plasma Pressure p = sum of pressures of (fuel ions + electrons + impurity ions) p = n i T i + n e T e +  n z T z If n = 0 and T i ≈ T = T then If n z 0 and T i ≈ T e T, then p ≈ 2nT Example: n = 10 20 m -3 , T = 10 keV p ≈ 2x10 20 m -3 10 keV 1.602x10 -16 J/keV = 3.2x10 5 Pa = 0.32 atm

Optimum Temperature p = 2nT  n = p/2T p = 2nT  n = p/2T P DT = ( ¼ ) n 2 <  v>W DT = ( ¼ ) (p/2T) 2 <  v>W DT At a given pressure what T maximizes P At a given pressure, what T maximizes P DT ? ? <  v> (10 -22 m 3 /s) <  v>/T 2 T , keV 5 5 0.129 0.129 0.0052 0.0052 8 0.594 0.0093 10 1.09 0.0109 15 2.65 0.0118 20 4.24 0.0106 25 25 5.59 5 59 0 0089 0.0089 30 6.65 0.0074 35 7.45 0.0061 40 8.03 0.0050

Reactor Power Balance Reactor Power Balance dolan 2010 47

Toroidal coordinate system Toroidal coordinate system dolan 2010 48

Definitions of a, b, c Definitions of a, b, c minimize V bsc = 2  Ro  [(a+b+c) 2 – a 2 ] dolan 2010 49

Estimation of required b, c Estimation of required b, c Tritium breeding ratio > 1 and  b  b ~ 1.2 m Coil shielding factor 10 ‐ 6 10 6 C il hi ldi f 1 2 magnet coil stress < 300 MPa, and coil volume minimized  c ≈ 0.25(a+b)  c ≈ 0 25(a+b) coil volume minimized (Freidberg, 2007) dolan 2010 50

Optimization of R, a V = 2  R o  a 2 S = 2  R o 2  a Neutron wall power flux : P w = 0.8 (fusion power density)V/S < 4 MW/m 2 0 8 (fusion power density)V/S < 4 MW/m 2 P Electrical power P E = 1.2  e (fusion power density)V 1.2  e (fusion power density)V P E V bc /P E = 2  R o  [(a+b+c) 2 – a 2 ] / (3SP w  e /2) Minimizing this ratio  a = (5/3)b = 2.0 m, c = (a+b)/4 = 0.8 m If P w = 4 MW/m 2 , and P E = 1000 MWe, then R o = 0.04 P E /aP w ≈ 5 m (Freidberg, 2007) dolan 2010 51

Determination of reactor parameters Determination of reactor parameters  b ~ 1.2 m Nuclear cross sections  c (a+b)/4  c (a+b)/4 B B max and stress limit and stress limit  a 2 m Cost optimization  R o Electrical power & neutron wall loading 5 m  p  p Fusion power & volume Fusion power & volume  optimum T Maximization of fusion power density  required value of  High ‐ Q or ignition  required value of   Plasma pressure and B (Freidberg, 2007) dolan 2010 52

What Experiments Are Underway?

http://www.iterbelgium.be/en/system/files/upload/n___Fusion_research_in_Belgium_ ‐ _R__Weynants.pdf dolan 2010 54

Culham Laboratory Joint European Tokamak (JET) UK U

Tokamak Fusion Test Reactor (TFTR)

Large tokamaks D III -D JT-60 JET Location Location 1.66 3.4 2.96 R m 0.67 1 0.96 a m 2 2 2.2 4.2 4 2 4 4 B T B, T 3 5 6 current I , MA 6 4 -- ECH, MW 5 10 12 ICH, MW 20 40 24 NBI, MW -- 8 8 7 7 LH, MW LH MW  > 12% long pulses ~ 28 s P(DT) = Achievements equivalent Q > 1. 15 MW being upgraded b i d d B Be walls ll dolan 2010 57

Plasma Shapes R/a = “Aspect Ratio” R/a Aspect Ratio a a R R Compact Ordinary Spherical Stellarator Stellarator Tokamak Tokamak Tokamak Tokamak R/a ~ 6 R/a ~ 4 R/a ~ 1.4

MegAmpere Spherical Tokamak (MAST) --------  R = 0.85 m

National Spherical Torus Experiment (NSTX) (NSTX)  = (plasma pressure) / (magnetic field pressure) ~ 0.3

Simulation of IRE in ST National Institute of Fusion Science, Japan Growth of helical perturbation

Globus-M Globus M a=0 24 m a 0.24 m R=0.37 m Ioffe Institute, St. Petersburg, Russia B t = 0.35 T I I  = 0.25 MA 0 25 MA (future 0.5 MA) V  = 4V  Pulse ~ 60 ms (future 200 ms)

Experimento Tokamak Esférico (ETE) Brazilian National Space Science Institute, INPE

Assembly of SUNIST

Website “All the world’s tokamaks” http://www toodlepip com/tokamak/ http://www.toodlepip.com/tokamak/

Stellarators Stellarators Conventional stellarator Conventional stellarator torsatron or heliotron torsatron or heliotron dolan 2010 66

LHD coils LHD coils dolan 2010 67

LHD helical coils LHD helical coils dolan 2010 68

l Large Helical Toki, Japan H li Device, L

Wendelstein 7 ‐ X coils Wendelstein 7 X coils dolan 2010 70

W7X Stellarator

W7X Modular Coil

Large stellarators LHD, Japan LHD Japan W 7-X Germany W 7 X, Germany Location 3.5-3.9 5.5 R, m , 0.6 0.53 a, m 2 - 3 3 B, T 2 50 modular coils number of helical coils 2 2 10 10 ECH, MW ECH MW 15 5 NBI, MW 3 3 3 3 ICRH, MW ICRH MW > 10 3 s at low n 1800 pulse length, s nT  nT  4 4x10 19 4.4x10 under construction under construction m -3 keV-s m keV-s dolan 2010 73

National Compact Stellarator Experiment (NCSX)

Potential advantages of stellarators over tokamaks No disruptions Current free operation  slower heat loss Current free operation  slower heat loss Plasma current drive not required  lower input power, higher Q dolan 2010 75

Alternative confinement concepts Reversed field pinches (RFP) spheromaks spheromaks field reversed configurations (RFC) magnetized target fusion (MTF) tandem mirrors rotating plasmas rotating plasmas internal rings dolan 2010 76

Alternative Concepts

Reversed Field Pinch (RFP) “Taylor Minimum Energy State”  o J =  x B = k B Dynamo turbulence adjusts magnetic field components.

Spheromaks 1. Magnetic field 3. Apply high voltage 2. Puff hydrogen V 4. Plasma acceleration 5. Plasma expansion 6. Sustained spheromak Sustained Spheromak Physics Experiment (SSPX) p y p ( ) a ~ 0.22 m,  ~ 5%, B ~ 0.25 T, T e ~ 200 eV for several ms.

Field Reversed Configurations (FRC) Separation Coils p Fluxcores EF Coils F Coils .19m Coaxial Gun .19m m 1.8m Coaxial Gun Torus Coils OH Coil 1.8m Y. Ono, U. of Tokyo TS-4 U of Tokyo: R ~ 0 5 m R/a ~ 1 2-1 9 B ~ 0 4 T I ~ 300 kA . TS 4, U. of Tokyo: R 0.5 m, R/a 1.2 1.9, B 0.4 T, I 300 kA .

Merging Two Spheromaks t F to Form an FRC FRC Y. Ono, U. of Tokyo , y

Repetitively Merging Spheromaks Shield Plug Over Vacuum Pumps Feedback Coils Vacuum Pump (4 total) Plasma Core (Ceramic Rotors) Plasma Sheath Plasma Sheath CT Formation S/C Coil (8 total) & Push Coils Separatrix 1.2 m Blanket Central Core with Pumping Coaxial Accel. Vacuum Pump (2 total) Inductive Accel. Region Twisted T i t d First Wall Tubes Divertor Plates and C-X Neutrals Pumping Channel Structure Hollow 0 5 Conducting SPHACTIV Section Away From Pumps R. BOURQUE 12/98 Core meters

Magnetized Target Fusion (MTF) Plasma Achieved n < 8x10 16 cm -3 , T ~ 300 eV, B ~ 3 T,  ~ 10  s.  J. M. Tacetti et al., RSI 74 (2003) 4314-4232.

Magnetized Target Fusion (MTF) W = 5 MJ

Magnetized Target Fusion (MTF)

Magnetic Mirrors

Inertial Confinement Fusion (ICF)

Compression Methods

National Ignition Facility – 192 beams

Plasma around Target Sphere

High Gain ICF Targets F Frozen DT fuel DT f l can be compressed to very high density. y g y TaCHO pusher stops x-rays and stops x rays and hot electrons to prevent preheating fuel.

NIF Target Chamber Interior

Laser MegaJoule (LMJ), France 240 beams, 1.8 MJ, 600 TW operation 2010

Osaka University Laser Room Osaka University Laser Room

ICF Problems

ICF Problems

Diode ‐ Pumped Solid State Lasers (DPSSL) Cooled by He gas flowing at Mach 0.1

Diode ‐ Pumped Solid State Lasers (DPSSL) M Mercury Laser: Yb:S-FAP slabs  20 J per pulse L Yb S FAP l b  20 J l Goal: 100 J 10 ns 10 Hz 10% efficiency Goal: 100 J, 10 ns, 10 Hz, 10% efficiency