Who will save the tokamak – Harry Potter, Arnold Schwarzenegger,
Shaquille O’Neal or Donald Trump?
J. P. Freidberg, F. Mangiarotti, J. Minervini MIT Plasma Science and Fusion Center
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Why does the tokamak need saving?
• Standard tokamak does not scale to a reactor
• Design determined by nuclear physics and
engineering constraints
• Minimal plasma physics enters the design
• But, the plasma physics is incompatible with the
engineering design
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Design a reactor and prove this!
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Goal – Minimize the Cost
• Total cost = Capital + Operating + Fuel ≈ Capital
• Capital = Fixed + Nuclear island
• Fixed =
• Nuclear Island =
• Cost/Watt =
• Minimize
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I IK V
F EK P
IF I
E
VK KP
+
220
0
2( )( ) (1 )( )( )
( ) /
IB B
E E
B
RV a b a b a a b c a b cP P
a b R
π ε κ κ ε κ
ε
= + + − + − + + + +
= +
Design Goals Quantity Symbol
Minor radius of the plasma Major radius of the plasma
Thickness of the blanket/shield and first wall Thickness of the magnets Plasma temperature Plasma density Plasma pressure Energy confinement time Magnetic field at Normalized plasma pressure
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a0R
b
cTnp
Eτ
0R R= 0Bβ
Engineering and Nuclear Physics Constraints
Quantity Symbol Limiting Value
Electric power output 1000 MW
Maximum neutron wall loading 4 MW/m^2 Maximum magnetic field at the coil 13 T Maximum mechanical stress on the magnet: Total = 650 MPa, Tensile = 500 MPa
500 MPa
Maximum superconducting coil overall current density
25 MA/m^2
Thermal conversion efficiency 0.4
Maximum RF recirculating power fraction 0.1 Wall to absorbed RF power conversion efficiency 0.4 Temperature at 14 keV
Fast neutron slowing down cross section in Li-7 2 barns Slow neutron breeding cross section in Li-6 950 barns at 0.025 eV
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.
EPWP
maxBmaxσ
maxJ
Tη
RPf
RFη
sdσ
0bσ
2max[ / ]v Tσ T
The Design – No Plasma Physics Required
• Elongation: Good for cost, good for plasma physics Limited by engineering, limited by plasma physics • Blanket/shield: limited by nuclear cross sections • Wall loading: relation between and :
• Coil thickness: relation between and
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1.7κ =
1.2b m=
0 R a1/2
0 2 2
1 2 1 14 1
n E
F T W
E PRE P a aπ η κ
= +
c a
1/2 1/22 20
20 0
0 max 0 0 max
2(1 ) (1 ) (1 )
21 ln
2 1
J B B M B J
BM J
B
c c c R
B BR J
σ ε ε α ε α
εα αµ σ ε µ
= + = − − − − − − −
+= = −
W nP A P=
Minimize with respect to a • Set
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/I EV P0 max(1 )BB Bε= −
Quantity Symbol max 13B =
Cost function ( 3m /MW ) /I EV P 0.79
Magnetic field at 0R R= (T) 0B 5.7
Elongation κ 1.7
Blanket thickness (m) b 1.2
Minor radius (m) a 1.49
Total magnet thickness (m) c 0.65
Major radius (m) 0R 4.8
Aspect ratio 0 /R a 3.2
Plasma volume ( 3m ) PV 357
Engineering DEMANDS on the Plasma Physics
• Profiles: • Temperature: Maximize
• Pressure:
• Beta: • Density: • Energy confinement time:
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2/v Tσ 14T keV=
22 7.3
16T F
E T F
vEP P p d p atmTσηη= = → =∫ r
020
25.6%
pBµβ = =
2 2 3/2 2 1/22 (1 ) 2.5 (1 ) 1.5 (1 )T T p p n nρ ρ ρ= − = − = −
20 32 1.35 10p nT n m−= → = ×
3 3 1.0 sec2 2
PE
E E
V pP pdα τ
τ τ= = → =∫ r
Plasma Current and Bootstrap Fraction • Requires engineering and plasma physics • The current from empirical scaling ( ):
• Kink safety factor:
• LH current drive:
• Bootstrap fraction:
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0.93 1.39 0.58 0.78 0.41 0.15 0.190
0.690.145 sec 17.5EI R a n B A
H I MAPα
κτ = → =
1H =
2 20
*0 0
2 1 1.472
a Bq
R Iπ κµ
+= =
40CD RF RF RF RP EP P f P MWη η= = =
nn
1/2 1/22 20
2 2 2
1.2 1 1 2.0pe peCD LHCD CD
CD e e
R nII MA
Pω ω ωη
ω
= ≈ ≈ + + − → = Ω Ω
1 0.89CDB
If
I= − =
How well does the plasma shape-up? • Greenwald density limit:
• Troyon beta limit:
• Kink safety factor limit:
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2 1.35 2.51GIn naπ
< ≡ → <
0
2.8% 5.6 5.8 T N NI
aBβ β β β< ≡ = → <
2 20
*0 0
2 12 2 1.52K
a Bq q
R Iπ κµ
+≈ < = → <
The Maximum Bootstrap Fraction • The maximum bootstrap fraction:
• The problem:
Plasma needs too much current for ignition
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1/2 3/2 2 1/2
1/2 1/20 0
1 1 (1 )( ) 2.44 0.055 6.8ˆB
r p n T pJR B n r T r a R Bθ θ
ρ ρρ ∂ ∂ − = − + = ∂ ∂
0
( ) 1 (1 ) 1( )ˆ/ 2 1
xB x ebI a e
αθ
θ α
ρ α α αρµ π ρ α
+ − − −= = − −
5/2 5/4 5/2 2 1/21
1/2 2 00 0
(1 )268BNC
I a pf dI R I bθ
κ ρ ρ ρµ
−= =
∫
0.89 0.39B NCf f< → <
Is there a simple way out? • Forget about minimizing • Is there any value of a that satisfies all constraints?
No!
• The standard tokamak does not scale to a reactor! 13
/I EV P
The Harry Potter Solution
• Keeps fixed
• Raise H
• Lowers the required I
• Lowers the achievable n
• Lowers the achievable
• Success requires
YES?
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/I EV P
β
1 1.42.8 3.4
Robust, disruption free operationN N
H Hβ β= → == → =
Plasma Physics Strategy - Magic
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The Arnold Schwarzenegger Solution • Raise
• Improves plasma physics
• Raises
• Forget optimization
• Set as a constraint
• Success requires
YES! 16
maxB
/I EV P
B NCf f=
max max13 17.5HTS already exist (YBCO)
/ 0.79 / 1.27 I E I E
B T B T
V P V P
= → =
= → =
Engineering Strategy – Strong B
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The Shaquille O’Neal Solution • Raise
• Keep standard
• Forget optimization
• Set as a constraint
• A larger plant
• about the same • Success requires
YES!
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EP
max, ,NH Bβ
B NCf f=
/I EV P
1000 1530/ 0.79 / 0.90
E E
I E I E
P MW P MWV P V P= → =
= → =
Utility Risk – Large Power Plant
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The Donald Trump Solution • Lower • Keep standard • Forget optimization • Set as a constraint • A large, expensive plant • Much larger • Success requires
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WP
max, ,NH Bβ
B NCf f=
/I EV P
2 24 / 2.1 // 0.79 / 1.83
W w
I E I E
P MW m P MW mV P V P
= → == → = YES!
Utility Risk – Large $/W
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What if the tokamak doesn’t work? There is always the stellarator
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