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Investigation of Particle Pinch in Toroidal Device Kenji Tanaka 1 1 National Institute for Fusion Science, Toki, Gifu 509-5292, Japan 2 nd Asian Pacific Transport Working Group(APTWG) Meeting May 15-18, 2012 Southwestern Institute of Physics Chengdu, China 1

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In toroidal device, particle pinch exists. Tore Supra, Hoang PRL (2003)LHD, Tanaka FST (2010) For steady state (dn/dt=0), in source free region ( <~0.8), ~0 Finite dn/dr requires particle pinch term nV 2 None zero Finite

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What is the particle pinch mechanism? A. Neoclassical effects 1. Ware Pinch Observable in some tokamak. Negligible in non inductive operation and low collisionality in tokamak and helical/stellarator Obserbable in helical /stellarator Negligible in present toakamak. 2. Collisional transport effects B. Anomalous (turbulence) effects Pinch Theory predicts ITG(ion temperature gradient turbulence), TEM (trapped electron mode turbulence) can induce inward and outward pinch. Curvature pinch Thermo diffusive pinch 3

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Outline 1.Neoclassical particle pinch in toroidal device 2.Anomalous particle pinch in toroidal device 3.Summary 4

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Outline 1.Neoclassical particle pinch in toroidal device 2.Anomalous particle pinch in toroidal device 3.Summary 5

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Neocassical Ware pinch is observable in high collsionality tokamak Inward particle pinch approaches to Ware pinch with decrease of heating power Wagner, Stroth PPCF (1993) Density peaking can be explained by D=0.1 and Ware pinch in high density H mode. Stober et al., PPCF 2002 Alactor-C mod reports zero flux balanced between Ware pinch and turbulence driven diffusion Ernst et al., POP 2004. Anomalous pinch 6

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7 In LHD, neoclassical thermo diffusion is visible in some configurations, while diffusion is anomalous. Rax is magnetic axis position, can vary magnetic ripple, curvature. K. Tanaka et al. Fusion Sci. Tech, (2010) Rax=3.5mPeaked dominant Rax=3.6m, Hollow dominant Comparison of two configurations in LHD.

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Outline 1.Neoclassical particle pinch in toroidal device 2.Anomalous particle pinch in toroidal device 3.Summary 8

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Curvature pinch is proportional to magnetic shear. Curvature pinch is NOT function of plasma gradient Curavture pinch is deduced analyticaly from Hamiltonian principle (Isichenko et al., POP 1996) and examined using experimental equiliburim data for tokamak, stellarator and helical ( Mishchenko et al., POP 2007) Usually, for normal shear dq/dr>0 (tokamak), curvature pinch is directed inwardly, and reversed shear dq/dr>0 (RS tokamak or low beta helical ) directed outwardly. Curvature pinch becomes outward for low magnetic shear s >1 (Bourdelle POP 2007) 9

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Mishchenkos model calculation with curvature pinch only do NOT account for experimental observation in JT-60U and LHD. Curvature pinch plays major role when thermo diffusion pinch is small In Tore Supra, curvature pinch is domnant at =0.3-0.6 in non inductive discharge. (Hoang et al., PRL 2004) Mishchenko JAEA, PDS report (2010), K. Tanaka et al., FST (2010) JT-60U Elmy H mode LHD Rax=3.6m 10 Assumption; pinch is only anomalous curvature pinch. EXP. Model EXP.

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Clear increase of density gradient with increase of Te gradient shows inward pinch due to thermo diffusion Vneo (Hoang et al., PRL 2004) Pinch direction can be inward and outward depends on the instability condition. Angioni PPCF (2009), NF(2010), Fable PPCF (2008) Tore Supra r/a=0.3 V neo, V curv are small 11

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Quasi linear gyrokinetic simulation shows that the largest thrermo diffusion iward pinch is obtained at ITG/TEM transition. Thermo diffusion Factor Calculated for e-ITB discharge in TCV Fable et al., PPCF 2008 Real Freq Inward Outward TEM ITG 12

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Angioni NF (2004) Density pumped and density peaking by ECRH can be account. Angioni NF (2011) L mode ECH TEM dominant H mode ECH ITG dominant r Real Freq. at k i=0.3 Normalized Density Gradient R/Ln 13

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In HL2A, density ITB was found in Ohmic discharge at ITG/TEM transition region. Xiao et al., PRL 2010 ITB ITG TEM 14

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In LHD, local density gradient was compared with zero flux condition predicted by gyrokinetic calculation in source free region. For steady state (dn/dt=0), in source free region ( <~0.9), ~0 Quasi linear particle flux QL is calculated by GK calculation. QL ~0 condition is searched scanning parameter. D n nV =0 15 Rax=3.5m Rax=3.6m

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Turbulence has a two spatial peak at core and edge. Core fluctuation propagates to e-dia. and i-dia. in lab. frame at Rax=3.5 and 3.6m respectively. Rax=3.5mRax=3.6m 16 ErxBt poloidal Rotation velocity e-dia. i-dia. Core =0.4-0.8 e-dia. dominant Core =0.4-0.8 i-dia. dominant Core =0.4-0.8 Smaller i Core =0.4-0.8 larger i Red; Te, Blue;Ti

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Comparison of linear growth rate and real frequency Larger and smaller | r| at Rax=3.5m peaked density profile Peaked profile is governed by increase of TEM contributions. 17

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Comparison of quasilinear particle flux showed qualitative agreements with experimental observation. =0 condition is peaked gradient for Rax=3.5m and hollowed gradient for Rax=3.6m This is consistent with experimental observations. However, neo, NBI, should be included for the precise argument. Temperature ratio, normalized Te and Ti gradient, collisionality are fixed at experimental value. 18

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Interchange type turbulence induce inward pinch in dipole field. Z.Yoshida, H. Saitoh et al., PRL(2010)See Saitoh A04 Similar obsevration in LDX, 2010 Boxer et al., Nature Phys. Levitated super conducting coil produce simple dipole field. No toroidal field, magnetic hill in whole region Interchange becomes unstable. 19

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Are there any common mechanism between RT-1, LDX and LHD magnetic hill dominant configuration of Rax=3.5m? Rax=3.5 of LHD 1. Peaked density profile 2. Magnetic hill dominant in whole region. 3. MHD study shows interchange is very strong. While 4. GK shows main turbulence is ITG, EXP suggests TEM. My concern 1.Does magnetic hill help density peaking ( Most of density profile in LHD is hollow in low collisionality regime.) 2.Turbulence level is proportional to collisionality. Is this resistive nature unlikely fot ITG/TEM? Discussion is underway with Jay Kesner of LDX group. 20

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Outline 1.Neoclassical particle pinch in toroidal device 2.Anomalous particle pinch in toroidal device 3.Summary 21

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Summary 1.Neoclassical pinch in observable in high collisionality tokmaka as an Ware pinch and low collsionality setellarator/helical as a neoclassical thermo diffusion. 2.Anomalous pinch is observable in tokamak, stellarator /helical and dipole filed devices 3.Curvature pinch is clearly obserbable in toakmak. Its role depends on plasma condition. 4.Anomalous thermo diffusion changes direction depending on the instability condition. 5.Recent results in tokamak is converging to that the largest inward pinch is obtained in ITG/TEM transition regime. 6.LHD results may follow this story as well. 7.Magnetic hill introduce density peaking as well via interchange instability. 22

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Supplement 23

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Remained issues 1.Present gyrokinetic study is limited at particular location ( ~0.5). How about other location? Are there no mans land *in particle transport? 2.Present gyrokinetic analysis is linear and quasi linear analysis. Does any non linear effects (zonal flow, mode coupling) change results significantly?Some publication says there are no significant modification (Angioni NF2010 etc). 3.Particle transport analysis in L-H transition and ITB formation will be important. 4.Linkages with other pinch (heat pinch and momentum pinch or residual stress) will be important as well. 5.RMP effects on particle transport is now hot topic. * No mans land is area where gyrokinetic simulation cannot account for experimental observation. DIII-D results shows >0.6 is no mans land. 24

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Density peaking factor increases with decrease of eff in tokamak C. Angioni PPCF 2009 eff = ei / DE DE Curvature Drift frequency ITG Increase of sdensitty peaking factor was observed at eff <1. Turbulence driven pinch Neoclasical Ware pinch This is favorable prediction for ITER. Fusion power becomes30 % higher than expected values (Hoang IFEC2004). 25

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Similar b * dependence with tokamak at Rax=3.5m of LHD opposite b * dependence at Rax=3.6m of LHD 26 H.Takenaga NF (2008) Magnetic ripple JT-60U << LHD Rax=3.5m ~LHD Rax=3.6m Magnetic Curvature JT-60U (well) LHD Rax=3.5m (Larger hill) LHD Rax=3.6m (Smaller hill) Rax; Magnetic axis position

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27 Scan of magnetic ripple shows strong variation of density profile in LHD. Stronger ripple cause hollow density profile Plateau D neo * h H.Takenaga NF (2008) 1/ Exp. region

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28 Separation of curvature pinch and thermo diffusion pinch from gyrokinetic analysis (Fable et al., PPCF2008 ) For =0, Input (Ln,Lt ) for different three k, then, estimate, Ak, Bk anc Ck. Then C T and C p are estimated. Search (Ln and Lt) till input agree with output.

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29 Plot between –grad N e /N e vs –grad T e /T e gives direction and ratio of curvature pinch and themodiffusion pinch (Hoang PRL 2004) =0 <0.3 ITG dominant <0.6 TEM dominant Ct in, Cq out Ct out, Cq in The plot is set of discharges. Te/Ti>2

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In tokamak, density profile are mostly peaked, while in helical system, it changes from pealed one to followed one due to the plasma parameter and magnetic configurations. Takenaga, Tanaka, Muraoka et al., NF (2008) JT-60U Elmy H mode Density scan LHD Rax =3.6m Power scan The effect of beam fueling is negligible in the both device, thus, the difference density profiles are due to the difference of the particle transport 30

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31 In LHD, 10 cm difference of magnetic axis results in significant difference of the particle transport due to the difference of magnetic properties. Rax=3.5m Tokamak like peaked density profile. Smaller magnetic ripple. Larger bad curvature. Rax=3.6m Helical particular hollowed profile. Larger magnetic ripple, Smaller bad curvature.

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