Impurity expulsion in an RFP plasma and the role of temperature screening S. T. A. Kumar, D. J. Den Hartog, R. M. Magee, G. Fiksel, D. Craig Department of Physics, University of Wisconsin-Madison, Madison,Wisconsin, USA
Introduction: Impurities in fusion plasma Impurity sources Plasma-wall interaction Radiative edge
Introduction: Impurities in fusion plasma Impurity sources Plasma-wall interaction Radiative edge Global observations Impurity accumulation [ n z (r) n z () = ni (r) n i () ] Z Transport generally anomalous, but close to neo-classical for high confinement modes
Introduction: Impurities in fusion plasma Impurity sources Plasma-wall interaction Radiative edge Global observations Impurity accumulation [ n z (r) n z () = ni (r) n i () ] Z Transport generally anomalous, but close to neo-classical for high confinement modes Detrimental effects Fuel dilution - reduction of fusion power Radiation loss - line radiation (edge) Bremsstrahlung (core) Radiative collapse Contribution to resistivity - shaping current density profile
Impurity sources in the Madison Symmetric Torus Aluminum wall, graphite limiters, boronization 5 cm thick aluminum wall Graphite limiters Ceramic tiles Intrinsic impurities are Al, C, O, B Recent boronization efforts
Improved confinement deuterium discharges I p 4 ka, n e 1 1 19 /m 3 Time Evolution Radial Profiles ka 5 Plasma Current ( 1 19 m -3 ) 1.2. n e 1 19 Electron Density 12 T e m -3 (ev) Gauss 25 Magnetic fluctuations Improved confinement (ev) 5 T i (C +6 )..1.2.3.4 Time(s)..2.4.6.8 1. ρ
CHarge Exchange Recombination Spectroscopy (CHERS) Perpendicular viewing chords Fiber bundle view CVI emission at 343.4 nm MST vessel a = 52 cm 5 kev H beam (2 ms pulse length) Simultaneous background measurement enables high temporal resolution (up to 1 khz) Beam Beam View φ Background View Spectrometer calibrated for radiant sensitivity
Radial profile and time evolution of C +6 density hollow profile, sharp edge gradient, expulsion from the core 8 1 16 6 1 16 Improved confinement ρ ~.2 n z (m -3 ) 4 1 16 2 1 16..2.4.6.8 1. ρ ρ ~.76.15.2.25 Time(s) Slow decay of core impurity density concurrent with slow increase at the outer region Sharp C +6 gradient consistent with T e gradient - barrier formation?
Classical impurity ion confinement Outward impurity convection Impurity transport is governed by n z t + Γ = S For PPCD plasma, Γ = n z t Radial impurity flux, Γ r = D n z r +v rn z n z r = v r D n z + Γ r D
Classical impurity ion confinement Outward impurity convection Impurity transport is governed by n z t + Γ = S τ c +6 31ms at ρ.16 41 ms at ρ.371 For PPCD plasma, Γ = n z t Radial impurity flux, Γ r = D n z r +v rn z n z r = v r D n z + Γ r D D 1.6 m 2 /s (close to classical) v r 1. m/s (Positive, Outward) For steady state, Γ r =. Impurity peaking factor (v r /D) is positive.
C +6 ions are highly collisional in MST 1. 1. Pfirsh-Schluter C +6 (ν L c )/v th 1..1 Plateau D + e δ 3/2.1 Banana.1..5 1. ρ Radial impurity flux Classical + Pfirsch-Schlüter contributions
Impurity Flux (Wenzel & Sigmar NF. 199, Hirshman & Sigmar NF. 1981) 1. Classical Γ cl = ν iρ 2 i n i 2Z [ lnpi r lnp z Z r 3 lnt ] i 2 r 2. Pfirsch-Schlüter Γ PS = q2 ν i ρ 2 i n i Z [ K ( lnni r lnn z Z r ) +H ( )] lnti r K and H depends on strength parameter (α = n z Z 2 z/n i ) and main ion collisionality. Typical values are 1 and -.5 respectively In MST, C +6 is strong, not trace (α >> m e /m d ). The momentum exchange is dominated by the i-z collisions rather than i-e friction
Equilibrium impurity density profile 1. Classical n z (r) n z () = [ ] ni (r) Z [ ] Z Ti (r) 2 1 n i () T i () n i leads to accumulation, T i leads to expulsion ( screening") 2. Total (P-S + Classical) n z (r) n z () = [ ] ni (r) Z [ ] Ti (r) γ n i () T i () γ = Z 2+4q2 HZ 2+4q 2 K
Excellent matching with experimental profile Transport dominated by classical flux 8 1 16 6 1 16 4 1 16 2 1 16 C +6 Density (m -3 ) Classical ---- Total..2.4.6.8 1. ρ 5 1.2. T i (ev) n e n i..2.4.6.8 1. ρ Impurity concentrations (Al, C, B, N, O) scaled to get Z eff () 4.5 equilibra- Temperature tion assumed n i self-consistently calculated starting from n e & impurity profiles Pfirsch-Schlüter contribution is negligible as expected Impurity profile is determined by the temperature gradient - Temperature screening effect"
Summary Radial profile of impurities is clearly hollow in the improved confinement discharges in MST Impurity expulsion from the core of the plasma is observed Radial profile well explained by classical transport : Temperature screening responsible for the hollow profile, as n i profile is flat First experimental observation of classical impurity ion confinement in the RFP