who will save the tokamak – harry potter, arnold schwarzenegger, shaquille o’neal or donald...
TRANSCRIPT
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Who will save the tokamak – Harry Potter, Arnold Schwarzenegger,
Shaquille O’Neal or Donald Trump?
J. P. Freidberg, F. Mangiarotti, J. MinerviniMIT Plasma Science and Fusion Center
PPPL Jan. 20 , 2015
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Why does the tokamak need saving?
• Standard tokamak does not scale to a reactor
• Design determined almost entirely by
nuclear physics and engineering constraints
• One piece of plasma physics enters the design –
empirical
• The plasma physics is not up to the task
E
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How can I prove this?
• Design a tokamak reactor from an engineering view
• Use only plasma physics
• Obtain reasonable values for all engineering parameters
• Obtain reasonable values for all plasma parameters
• More important – give a non-plasma physics reason for choosing
each parameter
• Test design against known tokamak operational limits
• The design FAILS
E
4
The approach• Use simple models
• No pretense of high precision
• Show there is one possible show stopper
• Discuss 4 strategies to solve the problem
• Many of you are aware of the key results
• How we get there is what is interesting
• Let the design begin
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Goals of the designQuantity Symbol
Minor radius of the plasma
Major radius of the plasma
Elongation
Thickness of the blanket region
Thickness of the TF magnets
Average plasma temperature
Average plasma pressure
Average plasma density
Energy confinement time
Magnetic field at
Normalized plasma pressure
Plasma current
Bootstrap fraction
0R R
a
c
b
0R
0BE
npT
Bf
I
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Nuclear Physics Constraints
• Neutron slowing down:
• Tritium breeding:
• D-T Fusion:
2 barnssd
1/2( / )
960 barns
0.025 eV
BR B T
B
T
E E
E
2
max/ at 14 keVv T T
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Engineering constraints 1
Steady state ignited reactor
• Electric power out:
• Neutron wall loading:
• Recirculating power fraction:
• Thermal conversion efficiency:
1000 MWEP
24 MW/mWP
0.4T
0.1RPf
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Engineering constraints 2
Superconducting niobium-tin magnets
• Maximum field at the coil:
• Maximum mechanical stress:
• Maximum current density:
• Wall to RF conversion efficiency:
maxB 13 T
max 600 MPa
0.4T
2max 20 MA/mJ
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Analysis strategy• Use the constraints to express all parameters in
terms of
• Define a reference case:
• No justification for reference case – just an example
• Examine design as a function of
• Show no value of works: identify show-stopper• Examine 4 possible solutions
a
0 / 4R a
a
a
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Ellipticity
• Not very controversial• Good for plasma physics: increased and • Good for engineering: lower • But there are limits• Plasma limit – vertical instabilities• Engineering limit – feedback control design• We choose
Icost
1.7
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Focus on the Blanket• Blanket thickness from nuclear physics constraints
• Use conservation of mass and energy
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0 6
(0) 14.1 MeV 1 / 0.1 m
(0) 1 / 0.003 m at 0.025 eV
S Li SS
BR Li BRBR
dE EE N
dx
dN
dx
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Blanket (cont.)
• Calculate to reduce neutron flux to
• Add some shield, first wall, and vacuum chamber, improve optimization
• We choose 1.2 mb
0ln 1 ln 0.9 S Bb
x
1/2
710B FB
S T
EE
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Neutron Wall LoadingRelation between R0 and a
• Wall loading relation
1/222
0
14.1
22.4
1 4
2
n W
n En F
F T
P P S
E PP P
E
S R a
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Solve for R0
• Solution
• Reference case:• Then
1/22
0 2
1 1 1 7.14 2
n E
F T W
E PR
E P a a
0 / 4R a
01.3 m 5.3 ma R
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Magnetic field at R = R0
• A good approximation:
• Then
• For the reference case
00
RB B
R
0 max0
(1 ) 0.14 ( )B B
a bB B a a b
R
0 6.8 TB
0.47B
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TF Coil DesignRelation between c and a
• Coil thickness = structure + superconductor
• Structure - Magnet forces
• Tensile forces
• Centering forces
• Overturning forces
• Overturning forces small - neglect
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Tensile force balance• Tensile forces
• Solve for the tensile stress
2 20 0
0
2 2 20
0
1 ln
1
(1 ) (1 )
/ stress thickness tensile e s
2
str s
BZ
B
T
Z
T T T B B M
M M
M
T
T
F B R
F A R
c
F
c R
F
20
0
ln[(1 ) / (1 )]2 (2 2 )
B BT
M B M
B
ZF
TF TF
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Centering force balance• Centering forces
• Solve for the compression stress
20 0
0
20 0
0
2 ( )
2 2
2 ( )
2 2 2 ( ) compression stress
R in out
inB M
o
R
utB M
C C C c M
C
C
F F F
B a b RF
B a b RF
F A c
F
a
F
b
20
0
2(2 2 ) 1
BC
M B M B
B
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Stress thickness
• Tresca Stress = Maximum stress
• Solve for stress thickness
maxT C
2 1/2
20
0 max
0
2 11 ln
1 2 1
1 [(1 ) ] 0.39 mM
BM
B
B B
B
B
M
B
c R
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SC current density thickness• How much SC is needed to carry TF current?
• Solve for
2 2
0 0max
2
0
0
0
[(1 ) (1 ) ]
2
/
J
J B B J
J J
B
A Rc R
RI J A
Jc
2 1/2
x
0
0
0 0 ma
1 [(1 ) ] 0
2
.58 mJ
J
B B Jc R
BR J
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Total coil thickness
• Total = sum of tensile plus centering
• For the reference case
M Jc c c
0.97 mc
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Plasma temperature
• Assume
• Fusion power density
• Choose to maximize
e iT T T
22
1( )
16p n
vS E E p
T
T 2/T
v T
14 keVT
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Plasma pressure
• Thermal power must produce desired output power
• Simple “vanilla” profiles
2216
T FE
vEp d P
T
r
20
2 1/2
2 3/2
2 (1 ) cos
1.5 (1 ) sin
2.5 (1 )
T T R R a
n n Z a
p p
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Plasma Pressure (cont.)
• Cross section
• Volume element
• Solve for
• For the reference case
4
0
exp (ln )mmv k T
2 204d a R d r
p1/2
2
12 2 1/220
0
64 8.8 atm
25 (1 )E
T F
P Tp
E R a av d
7.6 atmp
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Plasma density
• Density from
• For the reference case
2p nT
20 31/2
5 1.7 (10 )
12p
n mT a
20 31.4 10 mn
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Energy confinement time
• Ignited operation: alpha power = thermal conduction losses
• Solve for
• For the reference case
32 E
P pd r
E2 2 1/2
03 0.8F TE
E
ER a p a
E P
0.94 secE
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The plasma current• Here is where plasma physics enters
• Empirical ELMy H-mode scaling
• Solve for the current
• For the reference case
0.93 1.39 0.58 0.78 0.41 0.15 0.190
0.690.145 secE
I R a n B AH
P
0.741.08 1.63
1.08 1.49 0.62 0.84 0.44 0.16 0.20 0.160 0 0
7.9812E E
F T
E P aI MA
H R a n B A E B
14 MAI
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The kink safety factor
• From the definition
• For the reference case
2 21.37 1.160
* 00 0
2 10.11
2a B
q a BR I
* 1.6q
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Bootstrap fraction
• From recirculating power fraction and CD efficiency
• Assume Lower Hybrid current drive – outside launch
• Recirculating power fraction
• Electrical conversion efficiency
(0.1) 100 MWR RF EF RP EP P PP
(0.5)(0.8) 40 MWCD R CD RFF RF PP P P
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Bootstrap fraction (cont.)• Current drive
• For the reference case
• The bootstrap fraction
1/2 1/22 2
2 2
20 0
( ) 1 1
2 ( )
1
0 8
.
.
2
pe pe LHm
e e
CD CDCD C
LH m
D
m
P PI
R n R n
n
n
2.3 MACDI
1 0.84CDB
If
I
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Two additional figures of merit• Cost:
• Reference case
• Heat flux:
• Reference case
2 20
0
2
Volume of materialElectric power
( )(
ou
)
4 (2 2 2 )[(
tput
1 ) 2 ]
B
I B TF
E E
TF
V R
V V V
a b a b a
V c R a b
P P
c a b c
3/ 1.0 /I EV P m MW
0
0 02 2 SOL
LP B PQ
R a R
500 MW-T/mQ
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How well does the plasma shape up?
• Test the plasma against 4 plasma limits
• Greenwald density limit
• Troyon beta limit
• Kink safety factor limit
• Achievable bootstrap fraction
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Bootstrap fraction limit• The maximum bootstrap fraction:
• Model for the total
1/2
0
3/2 2 1/2
1/4 1/2 1/20
1 1( ) 2.44 0.055
(1 )6.8
B
r p n TJ
R B n r T r
pa R B
B
1/20
4/9
( )( )
/ 2
1 (1 ) 1 2.53
1
x
Bb
I a
x ex
e
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Bootstrap fraction limit (cont.)• The neoclassical bootstrap fraction
• The bootstrap limit
• For the reference case
5/2 5/4 5/2 2 1/21
1/2 2 00 0
(1 )268B
NC
I a pf d
I R I b
B NCff
0.84 0.44
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The basic problem
• Too much current is needed for ignition• Yes but we assumed that• Maybe there is a better value for ?• Let’s see!• Plot
• All must simultaneously be less than 1 for success
0 / 4R a a
*
/ vs. / vs. /q vs. / vs.
G
T
K
B NC
n n aa
q aff a
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What should we do about it?
Four possible solutions
• The Harry Potter solution
• The Arnold Schwarzenegger solution
• The Shaquille O’Neal solution
• The Donald Trump solution
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The Harry Potter SolutionAdvanced Plasma Physics
• Raise , set to fix
• Lowers the required I
• Lowers the achievable n
• Lowers the achievable
• Still violates limit
• Success requires
1 1.3 (ACT1 = 1.65)2.8 3.6 (ACT1 = 4.7)
Robust, disruption free operationN N
H H
B NCff aH
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The Arnold Schwarzenegger SolutionAdvanced Magnet Technology
• Raise , set to fix
• Improves plasma physics
• Raises
• Success requires
maxB
/I EV P
max max13 17.6HTS already exist (YBCO)This is a game changer
B T B T
B NCff a
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Engineering Strategy – Strong B
0
0
0
*
3
12.4 T0.97 m7.4 m
/ 7.77.6 MA1.5 %
q 20.69
/ 1.87 m /MWQ 660 MW-T/m
B
I E
BaRR aI
f
V P
max 17.6 TB
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The Shaquille O’Neal SolutionEconomy of Scale
• Raise , set to fix
• Keep standard
• Economy of scale benefits
• Leads to a larger plant
• About the same• Success requires
EP
max, ,NH B
1000 1530Improved grid capacity
E EP MW P MW
B NCff a
/I EV P
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Utility Risk – Large Power Plant
0
0
0
*
3
8.5 T1.44 m7.7 m
/ 5.311.2 MA
2.5 %q 2
0.70
/ 1.2 m /MWQ 670 MW-T/m
B
I E
BaRR aI
f
V P
1550 MWEP
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The Donald Trump SolutionEasier Engineering
• Lower , set to fix• Keep standard• Eases engineering• A large, expensive plant • Much larger • Success requires
WP
max, ,NH B
/I EV P
2 24 MW/m 2.1MW/mA big wallet
W wP P
B NCff aa
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Economic Risk – Large $/W
3
0
0
0
*
/ 2.6 m /MWQ 370 MW-T/m
9.7 T1.35 m10.7 m
/ 7.58.5 MA1.5 %
q 20.66
I E
B
V P
BaRR aI
f
22.1 MW/mWP
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Our opinion
• Donald Trump: Not attractive economically
• Shaquille O’Neal: Not attractive utility-wise
• Harry Potter: May work, but risky if only option
• Arnold Schwarzenegger: Best new hope
because of game changing technology
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Some observations
• Some say plasma physics is done – we should focus on engineering
• We do not agree!• Do not know how to make a steady state tokamak at
high• No solution yet for heat load problem – not primarily
a materials problem, but a divertor problem• Designs tend towards larger• Plasma performance improves at high
0, ,n T B
0 0/ ,R a B
0B
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The US Fusion Program
• What elements should be included?
• How well are they supported on a scale of 10?
• Advanced tokamak physics 8
• Steady state high performance plasma 6
• Stellarator research 3
• Advanced magnet technology 1
• Fusion-fission hybrids 1