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

1

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

2

Design a reactor and prove this!

3

Goal – Minimize the Cost

• Total cost = Capital + Operating + Fuel ≈ Capital

• Capital = Fixed + Nuclear island

• Fixed =

• Nuclear Island =

• Cost/Watt =

• Minimize

4

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

5

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

6

.

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

7

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

8

/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:

9

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:

10

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

12

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?

14

/I EV P

β

1 1.42.8 3.4

Robust, disruption free operationN N

H Hβ β= → == → =

Plasma Physics Strategy - Magic

15

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

17

The Shaquille O’Neal Solution • Raise

• Keep standard

• Forget optimization

• Set as a constraint

• A larger plant

• about the same • Success requires

YES!

18

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

19

The Donald Trump Solution • Lower • Keep standard • Forget optimization • Set as a constraint • A large, expensive plant • Much larger • Success requires

20

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

21

What if the tokamak doesn’t work? There is always the stellarator

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