Impurities in stellarators

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1 Impurities in stellarators Matt Landreman, University of Maryland The problem HDH mode & impurity hole Some recent developments Strawman research program: What can we do?

2 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

3 In plasmas that are not perfectly quasisymmetric or axisymmetric, there is a robust neoclassical impurity pinch. zs zs zz c1 dns c1 qs zs 1 dts c1 qz zz z Er c2 ~ Er c1 0 species s ns dr Ts Ts dr Tz

4 In plasmas that are not perfectly quasisymmetric or axisymmetric, there is a robust neoclassical impurity pinch. zs zs zz c1 dns c1 qs zs 1 dts c1 qz zz z Er c2 ~ Er c1 0 species s ns dr Ts Ts dr Tz W7 AS data Ion root inward E r : both n i and T i drive impurities in: E r ii 1 Tdn i i c2 dti 0 ii q i ni dr c1 dr 0 t = 0.38s 0.78s 1.18s 1.48s Giannone et al, PPCF(2000) 20

5 In plasmas that are not perfectly quasisymmetric or axisymmetric, there is a robust neoclassical impurity pinch. zs zs zz c1 dns c1 qs zs 1 dts c1 qz zz z Er c2 ~ Er c1 0 species s ns dr Ts Ts dr Tz W7 AS data Ion root inward E r : both n i and T i drive impurities in: t = 0.38s 0.78s 1.18s 1.48s ii 1 Tdn i i c2 dti Er 0 ii q i ni dr c1 dr 0 Can get outward z from E r > 0 in electron root ( T e T i ), but may not be reactor relevant. 20 Giannone et al, PPCF(2000)

6 In plasmas that are not perfectly quasisymmetric or axisymmetric, there is a robust neoclassical impurity pinch. zs zs zz c1 dns c1 qs zs 1 dts c1 qz zz z Er c2 ~ Er c1 0 species s ns dr Ts Ts dr Tz W7 AS data Ion root inward E r : both n i and T i drive impurities in: ii 1 Tdn i i c2 dti Er 0 ii q i ni dr c1 dr 0 Can get outward z from E r > 0 in electron root ( T e T i ), but may not be reactor relevant. Axisymmetry and perfect quasisymmetry are different: species s zs c1 q T s s 0 Physically, you can transform away E r. All fluxes are independent of E r. Main pinch term is gone. dt/dr can give temperature screening. Do HSX/NCSX/ARIES CS have these advantages? t = 0.38s 0.78s 1.18s 1.48s Giannone et al, PPCF(2000) 20

7 Impurity accumulation limits the density compatible with steady state operation. W7 AS measurements Radiated Burhenn et al, NF (2009) Giannone et al, PPCF (2000)

8 Impurity accumulation limits the density compatible with steady state operation. W7 AS measurements Radiated Burhenn et al, NF (2009) Giannone et al, PPCF (2000) But, high n is good in edge: friction with main ions pulls impurities out.

9 High density H mode (W7 AS) Rapid puffing at start, n e > 1 2x10 20 m 3, NBI Impurity hole (LHD) NBI, ion ITB, peaked T i, low n e. E r < 0. HDH mode (3 discharges) LCFS McCormick et al, PRL (2002) Ida et al, PoP (2009)

10 Some recent developments Mikkelsen 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

11 Some recent developments Alonso et al, ISHW (2015) ExB flow can be large enough for inertia to affect n z (,):... mnb uu Tn z z z Gives flux z nu z E B Landreman et al, PoP (2014) Mollen et al, PoP (2015) SFINCS code: 1, Fokker Planck Landau collisions between any # of species, no trace approx. c C n zi 6 1 flux H in W7-X SFINCS 1/ Theory: 1/ C outward DKES + momentum correction C inward Also get flux from magnetic drifts if you break stellarator symmetry!

12 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?

13 Extra slides

14 At high n, edge impurities can be screened by friction with main ions Impurity parallel momentum: V 1 m p ZeE m V V 0.71Z T 2.6 Z T... Friction Thermal force (10 4 m/s) Friction force dominant Thermal force dominant z z z z i z 2 e 2 i t n z Friction, good Thermal force, bad High n n LCFS =5.0x10 19 m -3 Low n n LCFS =1.5x10 19 m -3 EMC3 EIRENE simulations for LHD. Kobayashi et al, NF (2013)

15 The neoclassical impurity pinch is predicted to be significant in W7 X. Impurities decrease the bootstrap current in W7 X Peaking factor a/l nz for C 6+ in W7 X r/a=0.8 Ion root Peaked (bad) r/a=0.2 Electron root Hollow (good) Mollen et al, PoP (2015) SFINCS code

16 High density H mode (W7 AS) Rapid puffing at start, n e > 1 2x10 20 m 3, NBI Impurity hole (LHD) NBI, ion ITB, peaked T i, low n e. E r < 0. HDH mode (3 discharges) LCFS n e [10 20 m 3 ] Normal confinement HDH McCormick et al, PRL (2002) r eff [cm] Ida (2009), Yoshinuma IAEA (2010)