Investigation of Particle Pinch in Toroidal Device

Kenji Tanaka1 1National Institute for Fusion Science,

Toki, Gifu 509-5292, Japan

2nd Asian Pacific Transport Working Group(APTWG) MeetingMay 15-18, 2012

Southwestern Institute of PhysicsChengdu, China

1

In toroidal device, particle pinch exists.

0

1

2

0

0.5

1.0

0 0.5 1n e(x

1019

m-

3 )

Particle Source R

ate (A.U

.)

3D DEGAS

Tore Supra, Hoang PRL (2003) LHD, Tanaka FST (2010)

Stn nV

r

nD

For steady state (dn/dt=0), in source free region (r<~0.8), G~0Finite dn/dr requires particle pinch term nV

2

None zero

Finite

What is the particle pinch mechanism?

A. Neoclassical effects1. Ware Pinch

pware BEV

Observable in some tokamak.Negligible in non inductive operation and low collisionality in tokamak and helical/stellarator

e

e

e

r

e

eeneoe T

T

D

D

T

eE

n

nDn

2

3

1

21_

Obserbable in helical /stellaratorNegligible in “present” toakamak.

2. Collisional transport effects

B. Anomalous (turbulence) effectsPinch

Theory predicts ITG(ion temperature gradient turbulence), TEM (trapped electron mode turbulence) can induce inward and outward pinch.

Curvature pinch

e

e

T

T

Thermo diffusive pinch q

q3

Outline

1.Neoclassical particle pinch in toroidal device

2.Anomalous particle pinch in toroidal device

3.Summary

4

Outline

1.Neoclassical particle pinch in toroidal device

2.Anomalous particle pinch in toroidal device

3.Summary

5

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=0.1c 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

7

10-3

10-2

10-1

100

0.1 1 10

Exp. Rax=3.5m Neo. Rax=3.5m

Exp. Rax=3.6mNeo. Rax=3.6m

D(

=0.

4 -

0.7

) (m

2 /s)

b*(=0.4 - 0.7)

Exp.

Neo.-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.1 1 10V(

=0.

4 -

0.7

) (m

/s)

b*(=0.4 - 0.7)

Inw

ard

Ou

twa

rd

Exp.

Neo.

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

e

etneo TTDV

Comparison of two configurations in LHD.

Outline

1.Neoclassical particle pinch in toroidal device

2.Anomalous particle pinch in toroidal device

3.Summary

8

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)

qq

nDqcurv

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 and strong axis shifts a>>1 (Bourdelle POP 2007) 9

Mishchenko’s 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 r=0.3-0.6 in non inductive discharge. (Hoang et al., PRL 2004)

Mishchenko JAEA, PDS report (2010), K. Tanaka et al., FST (2010)

0

1

2

0 0.5 1 n

e(x10

19m

- 3 )

JT-60U Elmy H mode LHD Rax=3.6m

10

Assumption; pinch is only anomalous curvature pinch .

EXP.

Model Model

EXP.

Clear increase of density gradient with increase of Te gradient shows inward pinch due to thermo diffusion

e

etther T

TnD

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

Vneo, Vcurv are small11

Quasi linear gyrokinetic simulation shows that the largest thrermo diffusion iward pinch is obtained at ITG/TEM transition.

Ther

mo

diffu

sion

Fac

tor

Calculated for e-ITB discharge in TCVFable et al., PPCF 2008

Real Freq

Inw

ard

Out

war

dTEMITG

12

Angioni NF (2004)

Density pumped and density peaking by ECRH can be account .

Angioni NF (2011)

Angioni NF (2011)

L mode ECHTEM dominant

H mode ECHITG dominant

wr Real Freq. at kri=0.3

Nor

mal

ized

Den

sity

Gra

dien

t R/L

n

13

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

ITB

ITG

ITG TEM

TEM

14

In LHD, local density gradient was compared with zero flux condition predicted by gyrokinetic calculation in source free region.

0

1

2

1012

1013

1014

0 0.5 1

ne S

n e(x10

19m

- 3 )

Particle Source R

ate (A.U

.)

0

1

2

1012

1013

1014

0 0.5 1

n e(x10

19m

- 3 )

Particle Source R

ate (A.U

.)

Stn nV

r

nD

For steady state (dn/dt=0), in source free region (r<~0.9), G~0Quasi linear particle flux GQL is calculated by GK calculation. GQL~0 condition is searched scanning parameter.

D n∇

D n∇

nV

nVG=0 G=0

15

Rax=3.5m Rax=3.6m

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=3.5m Rax=3.6m

16

ErxBt poloidalRotation velocity

e-dia.

e-dia.

e-dia.

e-dia.i-dia.

i-dia.

i-dia.

i-dia.

Core r=0.4-0.8e-dia. dominant

Core r=0.4-0.8i-dia. dominant

Core r=0.4-0.8Smaller hi

Core r=0.4-0.8larger hi

Red; Te, Blue;Ti

Comparison of linear growth rate and real frequency

Larger g and smaller |wr| at Rax=3.5m peaked density profilePeaked profile is governed by increase of TEM contributions.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

Rax=3.5m Peaked Density Profile Rax=3.6m, Hollowed Density Profile

r/8(V

Ti/R

)

ki

Negative r indicates i-dia. direction.

r/8

e-d

ia.

i-d

ia.

r/8

17

Comparison of quasilinear particle flux showed qualitative agreements with experimental observation.

G=0　 condition is peaked gradient for Rax=3.5m and hollowed gradient for Rax=3.6m →This is consistent with experimental observations. However, Gneo, GNBI, should be included for the precise argument.

-2 10-2

0

2 10-2

-3 -2 -1 0 1 2 3

Rax=3.5m Peaked Density Profile in EXP.

Rax=3.6m Hollowed Density Profile in EXP.

-1/n dn/dr

/ 2 (A

.U.)

Rax=3.6m EXP.

Rax=3.5m EXP.

PeakedHollowed

Inw

ard

Ou

twar

dZero Flux

Temperature ratio, normalized Te and Ti gradient, collisionality are fixed at experimental value.

18

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

Are there any common mechanism between RT-1 , LDX and LHD magnetic hill dominant configuration of Rax=3.5m?

Rax=3.5 of LHD1. Peaked density profile2. Magnetic hill dominant in whole region.3. MHD study shows interchange is very strong.While4. GK shows main turbulence is ITG, EXP suggests TEM.

My concern1. 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?

0

1

2

1012

1013

1014

0 0.5 1

n e(x10

19m

- 3 )

Source

01020304050607080

0.1 1Normalized Collisionality

*b =0.4-0.7

Flu

ctu

atio

n L

evel

nti

lde/

n

at

=0.

4-0.

7 (A

.U.)

Discussion is underway with Jay Kesner of LDX group.20

Outline

1.Neoclassical particle pinch in toroidal device

2.Anomalous particle pinch in toroidal device

3.Summary

21

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

Supplement

23

Remained issues

1. Present gyrokinetic study is limited at particular location (r~0.5). How about other location? Are there no man’s 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 man’s land is area where gyrokinetic simulation cannot account for experimental observation. DIII-D results shows r>0.6 is no man’s land. 24

Density peaking factor increases with decrease of neff in tokamak

C. Angioni PPCF 2009

neff=nei/wDE

wDE； Curvature Drift frequency ∝ gITG

Increase of sdensitty peaking factor was observed at neff<1.

Turbulence driven pinch

Neoclasical Ware pinch

This is favorable prediction for ITER. Fusion power becomes30 % higher than expected values (Hoang IFEC2004). 25

0.8

1

1.2

1.4

1.6

1.8

10-1 100

LHD Rax=3.5m

LHD Rax=3.6m

JT-60U Elmy H mode

b =0.5

Den

sity

Pea

king

Fac

tor

n e(0.2

)/<

n e>

Similar nb* dependence with tokamak at Rax=3.5m of LHD opposite

nb* 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

27

0.6

0.8

1

1.2

1.4

1.6

10-1 100 101 102

Rax

=3.5m Rax

=3.6m Rax

=3.75m Rax

=3.9m

h

* at =0.5

n e(0.2

)/(n

e>

Peaky

Hollow

Larger RippleSmaller Ripple

1/ Plateau

Position along Field Line

Mag

neti

c F

ield

h_eff Scan factor 5

t)]/(v/[ T

2/3,

* qRv effheh

Scan of magnetic ripple shows strong variation of density profile in LHD. Stronger ripple cause hollow density profile

PlateauDne

o

n*h

1* h

H.Takenaga NF (2008)

1/n

Exp. region

28

Separation of curvature pinch and thermo diffusion pinch from gyrokinetic analysis (Fable et al., PPCF2008 )

For G=0,

Input (Ln,Lt ) for different three k, then, estimate, Ak, Bk anc Ck.Then CT and Cp are estimated.Search (Ln and Lt) till input agree with output.

29

Plot between　– grad Ne/Ne vs –grad Te/Te gives direction and ratio of curvature pinch and themodiffusion pinch (Hoang PRL

2004)

G=0r<0.3

ITG dominant.3<r<0.6

TEM dominant

Ct in, Cq out Ct out, Cq in

The plot is set of discharges. Te/Ti>2

0

1

2

1011

1012

1013

1014

1015

1MW2.7MW8.5MWn e(x

1019

m-

3 )

Particle Source R

ate (A.U

.)0

1

2

3

4

5

Low densityHigh Density

n e(1019

m-

3 )

0

1

2

3

4

5

0 0.5 1

Te(k

eV)

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 =3.6mPower 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

0

1

2

3

0 0.5 1

Te(k

eV)

31

0

1

2

Rax=3.5m Rax=3.6m

0 0.5 1

n e(1019

m-

3 )

0

1

2

3

0 0.5 1T

e(keV

)

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.