Post on 16-Jun-2020
Impurities in stellarators
• The problem• HDH mode & impurity hole• Some recent developments• Strawman research program: What can we do?
Matt Landreman, University of Maryland
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
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
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
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
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
Impurity accumulation limits the density compatible with steady‐state operation.
W7‐AS measurements
Giannone et al, PPCF (2000)
Radiated
Burhenn et al, NF (2009)
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.
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)
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
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!
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?
Extra slides
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
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.
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)