Plasma Rotation and Momentum Confinement Studies at JET P.C. de Vries 1 , M.-D. Hua 2,3 ,

1 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries

Plasma Rotation and Momentum Confinement Plasma Rotation and Momentum Confinement Studies at JETStudies at JET

P.C. de Vries1, M.-D. Hua2,3,

D.C. McDonald1, M. Janvier4, M.F. Johnson1, C. Giroud1, T. Tala5, K.-D Zastrow1,

TFT rotation and momentum transport working group and JET EFDA Contributors§

1EURATOM/UKAEA Fusion Association, Culham Science Centre, OX14 3DB, Abingdon, UK2Imperial College, SW7 2BY, London, UK.

3Ecole Polytechnique, Route de Saclay, 91128, Palaiseau, France. 4Institute National Polytechnique de Grenoble, Grenoble, France.

5Association Euratom-Tekes, VTT,, P.O. Box 1000, 02044 VTT, Finland.§See Appendix of M.L. Watkins, et al., Fusion Energy 2006 (Proc. 21th Int Conf. Chengdu) IAEA (2006)


IntroductionIntroduction Rotation of Tokamak plasmas is thought to play an important role in plasma

stability and the suppression of turbulence. It is therefore important to understand the scaling of plasma rotation and momentum confinement, in order to accurately predict ITER performance.

In order to study trends and scaling of plasma rotation and momentum transport and extensive databases has been set up at JET.

This presentation will:

– present the rotation database at JET

– discuss scaling of rotation of JET plasmas

– Analysis of momentum and energy transport


Rotation Database at JETRotation Database at JET The rotation database is built up of 7 subsets, each for a distinct JET operation

scenario. There is overlap between the rotation database and existing JET databases for most of the entries.

The database contains a large number of parameters describing the plasma properties, rotation and confinement characteristics

How well defined the database is depends on the number of entries, the accuracy of each parameter and the independence of each entry or parameter.

JET scenario Entries Symbol Connecting database

ELMy H-mode 239 + 60 + H-mode confinement database [13]

Counter NBI 37

Dominant ICRH 65

Hybrid 110 Hybrid database [15]

ITB 63 ITB database [14]

Total 574


Database parametersDatabase parameters Creating a large database of means a compromise between accuracy and the

number of entries/parameters.


Parameter correlationParameter correlation Correlation between entries and parameters can compromise (regression) analysis.

For many H-mode entries:

1/ inPT

0

1

2

3

4

0 1 2 3 4|Ip| [MA]

|B|

[T]

Type I ELMy H-modeType III ELMy H-modeCounter NBIDominant ICRHHybrid ScenarioITB Scenario

0

5

10

15

20

25

0 5 10 15 20 25PIN [MW]

T

[Nm

]



Mach numbersMach numbers

Mach numbers are dimensionless parameters which enables an easy comparison between various JET scenarios and other devices.

Thermal Mach number:

Alfvén Mach number:

i

i

thth eT

mv

v

vM

oAA

B

v

v

vM

/

th

A

M

M

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.0 0.2 0.4 0.6 0.8Mth(0)

MA(0

)



Scaling of averaged rotation in JETScaling of averaged rotation in JET Regression analysis has been carried out to find the scaling of Mach numbers.

Scales with the ratio of torque and input power, inversely with q and weakly negative with ne. Off-set ?

51.073.043.049.012.0 inpeth PTBInM

36.095.012.180.008.0 inpeA PTBInM

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4T / Pin [Nm/MW]

<M

th>

Type I ELMy H-mode

Type III ELMy H-mode

Counter NBI

Dominant ICRH

Hybrid Scenario

ITB Scenario


Type I and III EMLy H-modeType I and III EMLy H-mode Average Mach number is smaller for type III ELMy H-modes compared to those

with type I ELMs.


The scaling of Mach number profile peaking has been analysed.

Positive scaling with magnetic field and an inverse scaling with the density. (The last effect could be due to off-axis torque deposition at high density.

Hollow Mach profiles for dominant ICRH and counter NBI entries.

Scaling of rotation profile peakingScaling of rotation profile peaking

06.008.037.031.0 ineMA PTBnp

11.009.040.011.0 ineMth PTBnp 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20 25 30Line integrated density [1019 m-2]

MA(0

)/<

MA>



Momentum and energy confinementMomentum and energy confinement In many devices a link between momentum and energy transport has been observed. Such a link is predicted by ITG turbulence theory from which one finds that the momentum and heat diffusivity are equal.

The database finds that the global momentum and energy confinement times scale.

However individual cases can differ significantly!

T

L

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Ekin [s]

[s

]


in

kinE P

W


Although there is a rough trend between momentum and energy confinement, individual cases can differ significantly:a Although there is a rough trend between momentum and energy confinement, individual cases can differ significantly:

The ratio of energy and momentum confinement can be: 0.5 < E/ < 1.8

The ratio scales inversely with rotation (for example <MA>)

Confinement ratio

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8<M

th>

E/


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.01 0.02 0.03 0.04 0.05 0.06<MA>

E/



Regression analysisRegression analysis Reasonable fits were obtained with fitting the energy confinement time to a non-

linear model depending on ne, Ip, BT and Pin.

However, this model did not give satisfactory results for the momentum confinement time

– This suggests again a difference between the energy and momentum confinement

The best results were found when rotation or torque information was added to both models:

The regression analysis on the global energy and momentum confinement times suffered from a coupling between torque and power. This coupling was especially strong for the H-mode only subset of the data.

11602.044.006.013.006.056.002.037.0 1 AinpeE MPBIn

22603.072.010.013.003.079.003.038.0 1 Ainpe MPBIn


Although there is a rough trend between momentum and energy confinement, individual cases can differ significantly

The effective momentum diffusivity was found to be smaller than the heat diffusivity in the core of the plasma (0.2< <0.7). Pr<1.

Difference between core and edge confinement?

DifferencesDifferences

0.01

0.10

1.00

10.00

100.00

0.01 0.10 1.00 10.00 100.00ci [m

2/s]

c [m

2 /s]

Type I ELMy H-mode

Type III ELMy H-modeCounter NBI

Dominant ICRH

Hybrid Scenario

ITB Scenario


Core and edge confinementCore and edge confinement The core and edge/pedestal confinement times for momentum and energy can be compared.

The pedestal energy and momentum are less accurately determined than the total values, which are given by the integration of profiles.

Works for JET but Ill-defined?

pedE

coreE

in

pedcore

in

kin

E P

WW

P

W

pedcorepedcore

T

LL

T

L

Wped

Lped

Wcore

Lcore

Ene

rgy

or m

omen

tum

den

sity

r

nped Tped

lped

plasmapedped

eplasmapedped VRmnVlL 95.095.0 2

plasmapede

pedi

ped VnTW 95.03


Momentum pedestalMomentum pedestal The pedestal momentum scales with the pedestal energy.

– For H-mode entries only one finds: [kg m2 s-1, MJ]

– For most H-mode entries:

22.167.0

pedped WL

1/ inPT

0.01

0.10

1.00

10.00

0.01 0.10 1.00 10.00Wped [MJ]

Lpe

d [k

g m

2 s-2

]

Type I ELMy H-mode


Dominant ICRH

Counter NBI

Hybrid scenario

ITB scenario


Core and edge confinementCore and edge confinement The core and edge confinement of energy and momentum differ. The edge/pedestal momentum confinement is smaller than that of the energy! For many H-mode cases the core momentum confinement is better than that of the energy. High density counter NBI discharges were an exception.

pedestal/edge core

0.0

0.1

0.2

0.3

0.0 0.1 0.2 0.3E

ped [s]

p

ed [

s]

Type I ELMy H-modeType III ELMy H-modeDominant ICRHCounter NBIHybrid ScenarioITB Scenario

0.0

0.1

0.2

0.3

0.0 0.1 0.2 0.3E

core [s]

co

re[s

] Type I ELMy H-mode


Dominant ICRH

Counter NBI

Hybrid Scenario

ITB Scenario


Type I and III EMLy H-modeType I and III EMLy H-mode Average Mach number is smaller for type III ELMy H-modes compared to those with type I ELMs

The difference is caused by a degraded pedestal momentum confinement.

E(type I)=180ms

E(type III)=160ms

drop of 12%

(type I)=120ms

(type III)=85ms

drop of 30%

ped(type I)=83ms

ped(type III)=49ms

drop of 40%

core=36ms

unchanged


Scaling of core confinementScaling of core confinement The ratio of total energy and momentum confinement decreased with M

– The ratio of the pedestal energy and momentum confinement did not depend on M– But the core ratio did:

The core momentum confinement may be affected by an inward pinch1,2.[1] A.G. Peeters, Phys. Rev. Lett. 98 (2007) 265003 [2] T. Tala, et al., Plasma Phys. Control. Fusion (2007)

0.0

0.5

1.0

1.5

2.0

2.5

0.00 0.20 0.40 0.60 0.80

<Mth>

Eco

re /

core

Type I ELMy H-mode

Type III ELMy H-modeDominant ICRH

Counter NBI

Hybrid Scenario

ITB Scenario


Conclusions (1) Conclusions (1) A extensive database has been built at JET to study the scaling of plasma rotation

and momentum transport.

Thermal and Alfvén Mach numbers proved to be useful (dimensionless) parameters to compare rotation properties between various JET scenarios.

General scalings for the thermal and Alfvén Mach number in predominantly NBI heated JET discharges have been found.

The peaking factor of the Mach number or plasma rotation profile may be affected by the NBI torque deposition profile.

– Information related to the torque deposition profile is relevant to understand the scaling of rotation and momentum transport.


Conclusions (2)Conclusions (2) The global momentum and energy confinement times are not identical in JET

plasmas and can differ substantially in individual discharges (> factor 2).

The scaling of both energy and momentum confinement times was found to depend on the rotation (i.e. Alfvén Mach number).

The confinement of momentum by the pedestal was found to be worse than its energy confinement.

The core momentum confinement for many H-mode discharges was often found to be better than that of the core energy confinement.

The core momentum confinement could be improved compared to the energy confinement by the presence of an inward non-diffusive transport (pinch).

TF Ripple …

Documents

Plasma Rotation and Momentum Confinement Studies at JET P.C. de Vries 1 , M.-D. Hua 2,3 ,