Introduction to Plasma Physics and Controlled Fusion Plasma Physics - Francis F. Chen
Plasma Science & Fusion Center The Case for High Field Fusion...
Transcript of Plasma Science & Fusion Center The Case for High Field Fusion...
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1Whyte, Case for High Field Fusion, APS 2017
Plasma Science & Fusion Center
The Case �for High Field Fusion (abridged)
Dennis Whyte MIT
2017 Fusion Power Associates
Full version presented at APS-DPP 2017�available at firefusionpower.org
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2Whyte, Case for High Field Fusion, APS 2017
Case: The high magnetic field path is optimal to obtain our absolute science and energy goals
• From plasma science viewpoint there are no serious “tradeoffs” in the design of your MFE burn/energy mission, you always maximize B field strength
• Achieving high B field with electromagnets has fundamental science limits; understanding this evolving science allows us as plasma physicists how to best meet our science and energy missions
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3Whyte, Case for High Field Fusion, APS 2017
Why now?
• 15+ years since we talked about this.. many of our younger scientists don’t recall key features of debate about the “tactics” involved in achieving burning plasmas.
• And haven’t things changed meanwhile? ! In physics of plasmas, magnets, etc.! Or maybe we just have more experience & insight
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4Whyte, Case for High Field Fusion, APS 2017
Volumetric fusion power density
β ≡ pthpmagnetic
= pthB2 / 2µo
Pf ! 8 pth2
βN = β q
5ε S κ( )
Troyon limit (tokamaks)+
Pf ~ β2B4
Pf ~
βN2ε2S κ( )B4
q2
Generic
Tokamak
Troyon, Gruber Phys. Lett. 110A (1985)
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5Whyte, Case for High Field Fusion, APS 2017
Confinement: tokamak• Expressing confinement through “wind-
tunnel” dimensionless scaling laws
B τ ∝ ρ*3.1β 0ν −0.35q95
−1.4κ 2.2
ITPALuce, Petty, Cordey PPCF 50 (2008)
τ ~ R3.1B2.1
Extract R, B atFixed R/a
Petty
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6Whyte, Case for High Field Fusion, APS 2017
Energy gain at fixed �physics & shape parameters
B2
pth τ Ex = pth τ E
R2B2
R3.1B2.1
R2.7B3.5
R2.8B2.2
Generic
H98
Petty
ISS04
R2B4
R3.1B4.1
R2.7B5.5
R2.8B4.2
Target Target
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7Whyte, Case for High Field Fusion, APS 2017
High B (+ strong shaping) enables stationary pedestal with high absolute pressure
βN , Ped ≤Δψ ped
5%⎛⎝⎜
⎞⎠⎟
3/4~ Peeling-�Ballooning�StabilityLimit
βN ~
ppedpmagnetic
qε
pped ≤Δψ5%
⎛⎝⎜
⎞⎠⎟3/4 B2
q
B~5.7 T
Snyder et al NF 2011
Hughes APS 17
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8Whyte, Case for High Field Fusion, APS 2017
Issue ScalingPower density B4
Confinement (generic) R2 B2
Confinement (tokamak) R2.7 B3.5 (H98)R3.1 B2.1 (Petty)
Confinement�(stellarator)
R2.8 B2.1
Gain R2-3.1 B4-5.5
Stable pedestal/I-mode ~ βN B2
Issue ScalingDensity (tokamak) R-1 B1
Density (stellarator) β B2.5 (burning)
Heat exhaust: min. fZ R1.3 B0.9
Heat exhaust: q// B-1 (burning)
Runaway e- amp. exp (R0.28 / B0.3)
Synchrotron: runaways B2
Synchrotron:thermal ~B1.5
TAE n~B, vA~B
Am I happy or sad?
😀
😀
😀
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😀😀
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🤔
😀
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😀😀
🤔
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9Whyte, Case for High Field Fusion, APS 2017
Issue ScalingPower density B4
Confinement (generic) R2 B2
Confinement (tokamak) R2.7 B3.5 (H98)R3.1 B2.1 (Petty)
Confinement�(stellarator)
R2.8 B2.1
Gain R2-3.1 B4-5.5
Stable pedestal ~ βN B2
Issue ScalingDensity (tokamak) R-1 B1
Density (stellarator) β B2.5 (burning)
Heat exhaust: min. fZ R1.3 B0.9
Heat exhaust: q// B-1 (burning)
Runaway e- amp. exp (R0.28 / B0.3)
Synchrotron: runaways B2
Synchrotron:thermal ~B1.5
TAE n~B, vA~B
Am I happy or sad? I’m happier than before
😀
😀
😀
😀
😀
😀😀
😀
🤔
🤔
😀
😀
😀
😀
19982008
2005
2010
2010-17
2005-17
2016
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10Whyte, Case for High Field Fusion, APS 2017
Electromagnets & Tokamak plasmas: same physics
Ampere’s law
Force balance
Ohmic heating
∇x!B = µ0
!j
∇p =!j ×!B
P =η j 2
B ~ j
pmagnet ~ B2
Pmagnet ~ B2
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11Whyte, Case for High Field Fusion, APS 2017
As in toroidal plasma physics, aspect ratio is a critical and complex optimization
x ≡ ab
M = 2x +13(1− x)
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12Whyte, Case for High Field Fusion, APS 2017
Simple toroidal “solenoid” to explore limits �R=4 m, A=4, B0=Bmax/2
B =µ0 jZ∫ πR dR
2π R
Bmax = 0.3π jMA/m2
x ≡ ab= 23
M = 2.3 σ max[MPa]! M
Bmax2
2µo
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13Whyte, Case for High Field Fusion, APS 2017
LN-cooled copper + steel for stress loading�Pulsed due to lack of active cooling
Bmax~22 TB0~11 T
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14Whyte, Case for High Field Fusion, APS 2017
Superconductors: zero resistivity, but a restricted operating space in T, j and B
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15Whyte, Case for High Field Fusion, APS 2017
Superconductors: critical current, �at fixed T, depends on SC type and B
JcJc, 0
= BB0
⎛⎝⎜
⎞⎠⎟
−α
Jc0 B0 αNb-Ti 103 5 3Nb3-Sn 103 10 3
Fixed T
T~4 K, B>B0
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16Whyte, Case for High Field Fusion, APS 2017
Nb-Sn superconductors: �B limited by critical current at T~ 4K
Bmax~12 TBmax~7 T
50% SS22% cool25% Cu3 % SC
Coil Cross-section
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17Whyte, Case for High Field Fusion, APS 2017
NAS study: Cryogenic Cu could study burning plasma science at 25x smaller volume than Nb3Sn
FIRE ITERB (T) 10 5.3R (m) 2.14 6.2
Q 10 10τ / τCR > 1 > 1
Vp (m3) 30 800
pthτ E ~ R2.7B5.5
Volume ~ R3~ 1/B5
25x
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18Whyte, Case for High Field Fusion, APS 2017
Tactics? High-B, compact was known to have ~10-fold performance to cost ca. 1990 but pulsed
Compact Tokamak �Ignition ConceptsJ. WillisJ. Fusion Energy 1989
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19Whyte, Case for High Field Fusion, APS 2017
High-Temperature (HTS) REBCO superconductors
JcJc, 0
= BB0
⎛⎝⎜
⎞⎠⎟
−α
Jc0 B0 αNb-Ti 103 5 3Nb3-Sn 103 10 3REBCO 2.5x103 5 0.6
T~4 K, B>B0
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20Whyte, Case for High Field Fusion, APS 2017
With HTS magnets, stress is the only limit " multiple design choices to achieve Bmax > 20T
Bmax~23TB0 ~ 9.2 T
σmax ~700 MPa
ARCB. Sorbom et al� FED 2015
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21Whyte, Case for High Field Fusion, APS 2017
HTS magnets clearly change the tactical landscape for magnetic fusion
J. Willis J. Fusion Energy 1989
# Diversification
# Risk distribution
# Speed
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22Whyte, Case for High Field Fusion, APS 2017
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23Whyte, Case for High Field Fusion, APS 2017
Density: tokamak
n ≤ nGr =I pπa2
∝S κ( )q
BR
JET 9
Empirical Greenwald density�is a disruptive limit in tokamaks
De Vries, et al. Nucl. Fusion 49 (2009)
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24Whyte, Case for High Field Fusion, APS 2017
Power exhaust: tokamak divertor Solutions
q// ∝ PSOL B / R λq// ∝ ε ρpol ~1/ Bpoloidal
divertortargets
scra
pe-o
ff la
yer
radiatingdivertorplasma
λq//
PSOL
Prad ~ ndiv2 fz F Te( )
ndiv ~ ncore2
ncore ∝
S κ( )ε
BR
fZ ~ B0.9R1.3
Required impurityFraction to Detach1
2M.L. Reinke. Nucl. Fusion 57 (2017) 1Goldston et al PPCF 2017, APS17
cZ ∝PSOLBp fGr
2
Required impurityFraction to DissipatePsol in H-mode2