Impurities in stellarators Matt Landreman, University of Maryland The problem HDH mode & impurity hole Some recent developments Strawman research program: What can we do?
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. 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
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
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)
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
Impurity accumulation limits the density compatible with steady state operation. W7 AS measurements Radiated Burhenn et al, NF (2009) Giannone et al, PPCF (2000)
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.
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)
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
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!
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 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) 3 2 1 0-1 -2-3 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)
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
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)