Momentum Transport Studies at JET by Peter de Vries

1 Plasma Rotation and Momentum Transport Studies at JET – by Peter de Vries – ITPA Meeting 24-27 April 2005

Momentum Transport Studies at JETMomentum Transport Studies at JET

by

Peter de Vries

H.C.M. Knoops4, K.M. Rantamäki2, C. Giroud1,

E. Asp3, G. Corrigan1, A. Eriksson3, M. de Greef4, I. Jenkins1, P. Mantica5, H. Nordman3,

P. Strand3, T. Tala2, J. Weiland3, K.-D Zastrow1 and JET EFDA Contributors§

1EURATOM/UKAEA Fusion Association, Culham Science Centre, Oxon. OX14 3DB, UK.2VTT Technical Research Centre of Finland, EURATOM-Tekes, Espoo, Finland.

3Chalmers University of Technology, EURATOM/VR Association, Göteborg, Sweden.4Eindhoven University of Technology, Dept. of Applied Physics, Eindhoven, The Netherlands.

5Istituto di fisica del plasma, Associazione Euratom-ENEA-CNR, Milan, Italy.§See Appendix of J.Pamela et al., Fusion Energy 2004 (Proc. 20th Int Conf. Vilamoura) IAEA, Vienna (2004)


Outline

Plasma Rotation and Momentum Transport at JET

– Introduction

– Rotation and ion temperature Ti profiles» Relationship between v (or ) and Ti profiles

» Gradient lengths of v (or ) and Ti profiles

» Mach number of JET plasmas

– Momentum and ion heat transport» Torque and power deposition profiles

» Local momentum and ion heat i diffusivities

» The ratio of momentum and ion heat diffusivity (Prandtl number)

– Global momentum confinement

– Conclusions (and further work)


Introduction

Coupling of momentum and ion energy confinement

– Theory» Viscosity and heat diffusion are coupled in turbulent fluids (Prandtl)

» ITG turbulence theory for Tokamak plasmas predicts that = i

– Experimental observations» Many devices report profile consistency: v(r) Ti(r)

» Many devices have shown that E

– Experimental study of momentum and ion heat transport» Profile analysis: v(r) (or ) Ti(r)

» Momentum confinement data-base» Global confinement / Scaling

» Local transport properties and i

» Determine Prandtl number: Pr = / i ieffiii TnQ

effS


Rotation and temperature profiles

CXRS determines the rotation and ion temperature profile» In case of profile consistency (r) / Ti(r) cnst

» Ratio for 7 CXRS channels (omit 2 outer most channels)» Statistics for all 2000-2003 pulses» No consistency is found for high density H-mode JET discharges

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30

Ratio of angular rotation and ion temperature [rad/eVs]

Nu

mb

er

of

dis

ch

arg

es

#1

#2

#3

#4

#5

#6

#7

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30

Ratio of angular rotation and temperature [rad/eVs]

Nu

mb

er

of

dis

ch

arg

es

#1

#2

#3

#4

#5

#6

#7

H-mode

OS/ITB



Behaviour of v(r) Ti(r) during L to H-mode transition



Behaviour of v(r) Ti(r) during an ITB formation» Complication with the determination of v(r) in the presence of an ITB.

M increases at ITB formation


Mach numbers of JET plasmas

Mach number» Definition:

» Because (r) / Ti(r) cnst: M scales with Ti (higher Ti larger M)

T

v

e

m

v

vM

therm

kin

T

v

e

m

v

vM

therm

kin

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

PNBI/PTOT

Cen

tral

Mac

h n

um

ber

ITB

Type I H-modeType III H-mode


Gradient Lengths

Relationship between R/Lv and R/LT:» For H-mode discharges only: R/LT > R/Lv flatter v(r)

» Similar observation in ASDEX*

» More relevant for momentum transport: R/L

* D. Nishijimi, et al., Plasma Phys. Control. Fusion 47 (2005) 89

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

R/Lv

R/L

T

Rho=0.2-0.4

Rho=0.4-0.6

Rho=0.6-0.8

effS


Transport studies in H-modes at JET

Discharge selection» Steady state (part of confinement database)

» Predominantly NBI heated discharges (PICRH 0-0.2 PNBI)

» ELMy H-mode with high density n > 11020 m-2

» ITG dominated: Te=Ti and flat density profile (R/Ln< 2)

» Some discharges at ITG threshold (R/LT 5) show Ti profile stiffness

Transport properties» Profiles are averaged over a time interval (0.2-0.4s)» Properties determined in the gradient region: 0.3<<0.7

» Careful mapping and profile fit for T and (or v)

» NBI Torque and heat sources determined from PENCIL » Interpretative JETTO calculations

LR

LRTn

Q

STii

ii /

/

i

effiii TnQ effS

XRX

XRLR X ln/


Gradient Lengths

Normalised inverse gradient lengths» R/LT < R/L (Remember R/LT > R/Lv)

» Ion temperature profile stiffness observed (R/LT 5) larger ieff

» However, no threshold found for the velocity / momentum density profile

LR

LRTn

Q

STii

ii /

/

Increasing

17.0/

/

LR

LR T

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

R/L

R/L

T


NBI energy and momentum deposition

Different NBI energy and torque deposition differ» A smaller fraction is transferred to the ions at higher density (or lower T)» More NBI energy to the ions, less to the electrons, in the core» Torque deposition is more off-axis than NBI ion heat deposition

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

0.0 0.2 0.4 0.6 0.8 1.0

Po

wer

[M

W/m

3 ] an

d t

orq

ue

[N/m

2 ] d

epo

siti

on NBI ion power dep.

NBI electron power dep.

NBI torque dep.

#62458 nelint=8.26 1019 m-2

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.2 0.4 0.6 0.8 1.0

Po

we

r [M

W/m

3 ] a

nd

to

rqu

e [

N/m

2 ] d

ep

osi

tio

n

NBI ion power dep.NBI electron power dep.NBI torque dep.

#57865 nelint=25.1 1019m-2


Energy and momentum deposition Different NBI energy and torque deposition differ

» A smaller fraction is transferred to the ions at higher density (or lower T)» More NBI energy to the ions, less to the electrons, in the core» Torque deposition is more off-axis than NBI ion heat deposition» ICRH heat deposition on-axis for these discharges

Ratio of normalised sources» Less torque and a larger ion heat flux

Ratio of normalised gradients » Limited ion temperature gradient

LR

LRTn

Q

STii

ii /

/

38.021.0 ii

i

Tn

Q

S

LR

LR T

/

/17.0


Diffusivities and Prandtl numbers

Effective diffusivities (0.3<<0.7)» Effective diffusivities: include convective transport

» Analysis with ‘Weiland-model’ with = c i best match c = 0.2

» Trends in Prandtl number: smaller for ITG dominated discharges

35.018.0 i

rP

0.01

0.10

1.00

10.00

0.1 1.0 10.0

Ion heat diffusivity [m2/s]

Mo

men

tum

dif

fusi

vity

[m

2 /s]

Prandtl = 0.2


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Energy confinement time [s]

Mo

me

ntu

m c

on

fin

eme

nt

tim

e [

s]

Global Confinement

Ratio of energy and momentum times» Analysis of all 2000-2004 discharges (PNBI>6MW, IP>2MA, ‘steady state’)

» At high density: E and at low density: < E

» Global Prandtl number ratio of ion energy and momentum confinement

T

P

WE

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 5 10 15 20 25 30

Line integrated denisty [1019 m-2]

Ra

tio

of

en

erg

y a

nd

mo

me

ntu

m c

on

fin

em

en

t ti

me

s

All = L-mode, OS/ITB, Hybrid, H-mode


Global ion confinement Ion energy confinement time

» Momentum confinement time scales with ion energy confinement time» Confinement time is a global parameter /and diffusivity a local parameter

» Effective diffusivities depends on local profile gradients: R/LT < R/L

» Edge confinement (Pedestal: momentum confinement worse ?)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Ion and Total energy confinement time [s]

Mo

men

tum

co

nfi

nem

ent

tim

e [s

]

T

P

WE

ion

ionionE

P

W

ion

E

irP


Conclusions

Plasma Rotation and Momentum Confinement– Rotation and temperature profiles

» Profile consistency between v and Ti breaks down at high density

» At high density: ion heat deposition (NBI+ICRH) more on-axis.

» Profile stiffness for Ti but no threshold for the v profile

– Torque and heat deposition» At high density: torque deposition (by NBI) in JET is off-axis » But the ion heat deposition (NBI/ICRH) peaks on axis

– Global confinement» At high(er) densities: E but at low density < E

» Momentum confinement time scales with ion energy confinement time !

– Momentum diffusivities for JET H-mode discharges» The effective Momentum diffusivity scaled with the ion heat diffusivity

» But Prandtl numbers significantly less than unity: Pr = / i = 0.18-0.35

» Eventhough ionE

» Off-axis momentum source sustained a significant gradient pinch ?» The edge Prandtl number is expected to be above unity

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Momentum Transport Studies at JET by Peter de Vries