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Impurities in stellarators
• The problem• HDH mode & impurity hole• Some recent developments• Strawman research program: What can we do?
Matt Landreman, University of Maryland
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In stellarators, like in tokamaks,‐ Core impurities radiate energy.‐ Core impurities dilute fuel.‐ Need to extract He ash.+ Edge impurities mitigate divertor heat flux.
Unlike tokamaks,‐ Strong neoclassical impurity pinch (usually).‐ Impurities can limit density.‐ Lower reactor T more line radiation.? Different divertor configurations.? Different (drifts vs centrifugal.)
Complicated interaction: 1. PSI, 2. SOL, 3. core
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In plasmas that are not perfectly quasisymmetric or axisymmetric, there is a robust neoclassical impurity pinch.
1 1 12 1
species
1 ~ 0zs zs zz
s s szs zzz r r
s zs
z
s s
c dn c q dT cE c E cn dr T T T
qdr
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In plasmas that are not perfectly quasisymmetric or axisymmetric, there is a robust neoclassical impurity pinch.
• Ion‐root inward Er : both ni and Tidrive impurities in:
Giannone et al, PPCF(2000)
t = 0.38s0.78s1.18s1.48s
W7‐AS data
1 1 12 1
species
1 ~ 0zs zs zz
s s szs zzz r r
s zs
z
s s
c dn c q dT cE c E cn dr T T T
qdr
2
1
1 0ii
i i ir ii
i i
T dn c dTEq n dr c dr
0
20
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In plasmas that are not perfectly quasisymmetric or axisymmetric, there is a robust neoclassical impurity pinch.
• Ion‐root inward Er : both ni and Tidrive impurities in:
Giannone et al, PPCF(2000)
t = 0.38s0.78s1.18s1.48s
W7‐AS data
1 1 12 1
species
1 ~ 0zs zs zz
s s szs zzz r r
s zs
z
s s
c dn c q dT cE c E cn dr T T T
qdr
2
1
1 0ii
i i ir ii
i i
T dn c dTEq n dr c dr
0• Can get outward z from Er > 0 in electron root
(|Te| |Ti|), but may not be reactor‐relevant. 20
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In plasmas that are not perfectly quasisymmetric or axisymmetric, there is a robust neoclassical impurity pinch.
• Physically, you can transform away Er.• All fluxes are independent of Er. Main pinch term is gone.• dT/dr can give temperature screening.
• Ion‐root inward Er : both ni and Tidrive impurities in:
Do HSX/NCSX/ARIES‐CS have these advantages?
1
species
0zs
s
ss
c qT
Giannone et al, PPCF(2000)
t = 0.38s0.78s1.18s1.48s
W7‐AS data
1 1 12 1
species
1 ~ 0zs zs zz
s s szs zzz r r
s zs
z
s s
c dn c q dT cE c E cn dr T T T
qdr
2
1
1 0ii
i i ir ii
i i
T dn c dTEq n dr c dr
0• Can get outward z from Er > 0 in electron root
(|Te| |Ti|), but may not be reactor‐relevant.
Axisymmetry and perfect quasisymmetry are different:
20
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Impurity accumulation limits the density compatible with steady‐state operation.
W7‐AS measurements
Giannone et al, PPCF (2000)
Radiated
Burhenn et al, NF (2009)
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Impurity accumulation limits the density compatible with steady‐state operation.
W7‐AS measurements
Giannone et al, PPCF (2000)
Radiated
Burhenn et al, NF (2009)
But, high n is good in edge:|| friction with main ions pulls impurities out.
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High‐density H mode(W7‐AS)
Impurity hole (LHD)
Ida et al, PoP (2009)
NBI, ion ITB, peaked Ti, low ne. Er < 0.
Rapid puffing at start, ne> 1‐2x1020 m‐3, NBI
LCFS
McCormick et al, PRL (2002)
HDH mode(3 discharges)
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Some recent developmentsMikkelsen et al, PoP (2014)Gyrokinetic calculations show inward C flux contrary to experiment.
Garcia‐Regana et al, arXiv (2015)EUTERPE code: usually‐neglected 1 terms can affect LHD neoclassical impurity flux.
LHD impurity hole: GS2 quasilinear impurity flux
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Some recent developmentsLandreman et al, PoP (2014)Mollen et al, PoP (2015) SFINCS code: 1, Fokker‐Planck‐Landau collisions between any # of species, no trace approx.
SFINCS
DKES + momentum correction
1 /
Theory:
61 flux in W7-Xzi
Hc C n
1 /
Cou
tward
Cinward
Alonso et al, ISHW (2015)ExB flow can be large enough for inertia to affect nz(,):
|| ...z z zm n T n b u u
z zn u E×BGives flux
Also get flux from magnetic drifts if you break stellarator symmetry!
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Strawman research program: What can we do?
• Study the transition from symmetry to non‐symmetry. Are HSX, NCSX, ARIES‐CS symmetric enough to realize advantages of QH/QA? (HSX experiments?)
• Can 1 be manipulated to give an outward flux?
• Modeling to leverage US XICS investments in LHD & W7X.
• More impurity studies with gyrokinetic codes.
• Target divertor or edge features in stellopt? (What quantity exactly should be targeted?)
• Core stellopt targets: High gyrokinetic particle flux? Neoclassical temperature screening coefficient?
• Other ideas?
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Extra slides
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At high n, edge impurities can be screened by || friction with main ions
3 12 0 -1 -2 -3Friction – Thermal force (104 m/s)
Friction force
dominant
Thermal force
dominant
EMC3‐EIRENE simulations for LHD. Kobayashi et al, NF (2013)
Impurity parallel momentum:
|| 2 2|| || || || || ||
1 0.71 2.6 ...zz z z i z e i
z
Vm p ZeE m V V Z T Z Tt n
Low nnLCFS=1.5x1019 m-3
High nnLCFS=5.0x1019 m-3
Thermal force, badFriction, good
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r/a=0.8Ion root
r/a=0.2Electron root
Mollen et al, PoP (2015) SFINCS code
Peaked
(bad)
Hollow
(goo
d)
“Peaking factor” a/LnZfor C6+ in W7‐X
Impurities decrease the bootstrap current in W7‐X
The neoclassical impurity pinchis predicted to be significant in W7‐X.
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High‐density H mode(W7‐AS)
Impurity hole (LHD)
Ida (2009), Yoshinuma IAEA (2010)
NBI, ion ITB, peaked Ti, low ne. Er < 0.
Rapid puffing at start, ne> 1‐2x1020 m‐3, NBI
LCFS
McCormick et al, PRL (2002)
reff [cm]
n e[102
0m
‐3]
HDH
Normalconfinement
HDH mode(3 discharges)