HEAT TRANSPORT EXPERIMENTS IN JET: STIFFNESS AND NON … · Profile stiffness. Profile stiffness is a known concept, based on theoretical finding that both electron and ion anomalous

ITC-12 and APFA’01, December11-14, 2001, Toki, Japan

1

HEAT TRANSPORTEXPERIMENTS IN JET:

STIFFNESS AND NON-LOCALITY

V. Parail, P. Manticaa , W. Suttropb andcontributors to the EFDA-JET

workprogramme.

EURATOM-UKAEA Fusion Association, CulhamScience Centre, Abingdon, OX14 3DB, United Kingdoma)Istituto di Fisica del Plasma, Euratom/ENEA-CNR,Milano, Italyb)Max-Plank-Institut fur Plasmaphysik, EURATOM-Association, D-85740-Garching, Germany

Outline� Fast transient phenomena in JET-

experimental observations;� Concept of turbulence non-locality;� Profile stiffness as an alternative

approach to fast transient phenomena;� Conclusions


2

I. Fast Transient Phenomena onJET- Experimental Observations

� An unusually fast heat pulse, generatedby L-H transition, has been first reportedin 1993 (S. Neudachin et al., 20th EPSConference, Lisbon, 1993)

Time (s)

JG96

.139

/6c

Pulse No: 31078

Te (

kev)

13.2 13.3 13.4 13.5

4.0

3.0

2.0

1.0

ρ = 0.33

ρ = 0.50

ρ = 0.66

ρ = 0.76ρ = 0.80

ρ = 0.60

ρ = 0.40


3

� Two unusual features of this heat pulse:

I. A very fast (sometimes beyond

experimental resolution) propagation of the

temperature rise;

II. Heat pulse amplitude does not decay

(sometimes even rise) in the core

quickly attracted attention of theoreticians

and modellers.

� Since then JET and many other

tokamaks have reported a number of

heat and cold pulses with the similar

features;

� Some tokamaks (starting from TEXT, K.

Gentle,1993) reported cold pulses which

change polarity in the core;


4

Cold pulse triggered by a shallowpellet injection

5.6 5.8 6 6.2 6.4

t [s]

ρ=0.19

ρ=0.87

51084

1

3

5

7

5.6 5.8 6 6.2 6.4

t [s]

ρ=0.12

ρ=0.91

ρ=0.28

ρ=0.36

ρ=0.45

ρ=0.64

ρ=0.84

51084

0

2

4

6

8


5

Cold pulse triggered by type-IELM

Time (s)

JG96

.139

/4c

Pulse No: 30592

11.76 11.80 11.84 11.88 11.92

Te

(kev

)

ρ = 0.50

ρ = 0.66

ρ = 0.70

ρ = 0.74

ρ = 0.81

ρ = 0.84

4.0

3.5

3.0

2.5

2.0


6

Cold pulse caused by noble gaspuffing into ELM-free H-mode

7

5

3

1

3

2

1

16.0 16.2 16.4 16.6

ρ ≈ 0.4

ρ ≈ 0.9

16.8Time (s)

Pra

d (W

att)

x10

6T

e (e

V)

x103

17.0 17.2 17.4

JG99

.126

/1c


7

Cold pulse in plasma with ITBA very recent example shows that coldpulse leads to erosion of the ITB(P.Mantica, EPS 2001)

Weak ITB can becompletely destroyedby the cold pulse

1

2

3

4

5

6

7

8

6 6.1 6.2 6.3 6.4 6.5

t (s)

ρ=0.2

ρ=0.8

51581

-1

-0.8

-0.6

-0.4

-0.2

0

0 0.2 0.4 0.6 0.8 1ρ

-1

-0.8

-0.6

-0.4

-0.2

0

0 0.2 0.4 0.6 0.8 1ρ


8

� Two unusual features of these heat

pulses:

I. A very fast (sometimes beyond

experimental resolution) propagation of

the onset of the temperature rise;

II. Heat pulse amplitude does not

decay (sometimes even rise) in the core

quickly attracted attention of

theoreticians and modellers.


9

Let us compare experimental resultswith the prediction from a simplediffusive model with the constant χ :

0

4

8

12

1

3

5

7

0 0.2 0.4 0.6 0.8 1ρ-0.5

-0.4

-0.3

-0.2

-0.1

0

0 0.2 0.4 0.6 0.8 1ρ

1

2

3

4

5

6

7

8

9

0.8 0.9 1 1.1 1.2 1.3

t (s)

ρ=0

ρ=1

DTmax

1

3

5

7

5.8 5.9 6 6.1 6.2 6.3

51084

t [s]

ρ=0.19

ρ=0.87


10

� The difference in the speed of coldpulse propagation and in the radialprofile of the cold pulse amplitude isobvious.

� How can we explain such a fast, non-diffusive kind of cold pulse propagation?

� Two possible explanations are beingconsidered by theoreticians at present:

� Non-local turbulence paradigm(streamers),� Stiff local transport paradigm

(avalanches).

Non-local turbulence.� Non-local turbulence as a mean of a

fast L-H transition in JET has beenproposed in (J.G. Cordey et al., NF1995) and implemented in an empiricalJETTO transport model (M. Erba et al.,PPCF, 1997);

� Since then the model has beensuccessfully applied to a number oftransient phenomena.


11

� The physics mechanism of theturbulence non-locality originates from:

� Toroidal coupling of unstable vortices,� Inverse non-linear cascade of unstable

modes into long wave length part of thewave spectrum;

� Both mechanisms lead to a formation oflong radially correlated structures(strimmers), which can explain fast non-local change in transport coefficientsduring transient phenomena (F.Romanelli, F. Zonca, PF, 1993; V. Parailet al., NF 1997; Y. Kishimoto et. al.,IAEA, 1998; K. Itoh, S.-I. Itoh, 2001);

� JET transport model assumes that thesource of the turbulence localised nearthe separatrix, so that

sepe

eisBohm T

TqcC

∇⋅⋅⋅≈ 2ρχ

� Next slide shows an example of L-Htransition simulation with JET model;


12

Time (s)

JG96

.139

/6c

Pulse No: 31078

Te (

kev)

13.2 13.3 13.4 13.5

4.0

3.0

2.0

1.0

ρ = 0.33

ρ = 0.50

ρ = 0.66

ρ = 0.76ρ = 0.80

ρ = 0.60

ρ = 0.40


13

Time (s)

JG96

.139

/6c

Pulse No: 31078

Te

(kev

)

13.2 13.3 13.4 13.5

4.0

3.0

2.0

1.0

ρ = 0.33

ρ = 0.50

ρ = 0.66

ρ = 0.76ρ = 0.80

ρ = 0.60

ρ = 0.40


14

Profile stiffness.� Profile stiffness is a known concept,

based on theoretical finding that bothelectron and ion anomalous transportincreases rapidly when some plasma

parameters (i

i

T

T∇in case of ITG) exceed

certain limit (F. Romanelli, F. Zonca, PF1993; A. Dimits et. Al., PP 2000);

� Generally, transport coefficient with aprofile stiffness has the following form:

∇−∇

×

∇−∇⋅⋅+=

criti

i

i

i

criti

i

i

iTiiresii

T

T

T

TH

T

T

T

Ta

R

VC

2ρχχ

� Usually R

VC Tiires

i⋅<<

2ρχ , therefore


15

transport changes rapidly in the region

criti

i

i

i

T

T

T

T ∇≈∇;

A.Dimits et al., Phys. Plas., 2000

10

12

8

6

4

2

00 5 10 15 20

χ iL n/

ρi2 v

ti

JG01

.337

-1c

R/LTclinR/LTexpt

R/LTi

LLNLGK

Fit to LLNLGK

U. Col GK

1994 IFS/PPPL

1997 PPPL GFL

1998 PPPL GFL

Sydora GK

Weiland QL-ITG


16

The figure allows concluding:

� Temperature profile keeps the sameshape in case when heating powerexceeds critical level;

� Core temperature depends on theedge temperature rather than on thelevel of transport;

� Cold pulse can propagate rapidly (likeavalanche) with the characteristic χ

PBi

criti

iTiiHPi T

Ta

R

VC χρχ >>∇⋅⋅≅

2


17

� Profile stiffness is a recognisedconcept, which has been found inpractically every tokamak;

0 1 2 3 40.00

0.02

0.04

0.06

q

[M

W/m

]e,

⊥2

∇ T / T [1/m]

JET

ICRH + NBI heating

ρ = 0.4

� The question is whether this conceptcan explain all experimentally observedfast transient phenomena, or we stillneed a non-local transport on the top;


18

Profile stiffness vs. non-locality� Before going to a detailed comparison

of two concepts, let us look at somerecent result of cold pulse modellingwhich uses stiff transport models

(J. Kinsey, 2000-01)

� Three theory based transport models(MMM-95, IFS/PPPL and GLF-23) havebeen used to simulate the same recentcold pulse from JET;

5.6 5.8 6 6.2 6.4

t [s]

ρ=0.19

ρ=0.87

51084

1

3

5

7

5.6 5.8 6 6.2 6.4

t [s]

ρ=0.12

ρ=0.91

ρ=0.28

ρ=0.36

ρ=0.45

ρ=0.64

ρ=0.84

51084

0

2

4

6

8


19

IFS/PPPL

GLF 23

MMM-95

1

2

3

4

5

6

7

6 6.1

t [s]

ρ=0.

ρ=0.76

51084 IFS-PPPL1

2

3

4

5

6

7

8

6 6.1

t [s]

ρ=0.

ρ=0.76

51084 IFS-PPPL

1

2

3

4

5

6

7

6 6.1

t [s]

ρ=0.

ρ=0.8

51084 GLF231

2

3

4

5

6

7

6 6.1t [s]

ρ=0.

ρ=0.8

51084 GLF23

1

2

3

4

5

6

7

6 6.1

t [s]

ρ=0.

ρ=0.8

51084 MM951

2

3

4

5

6

7

6 6.1

t [s]

ρ=0.

ρ=0.8

51084 MM95


20

Now we can try to answer the question:“Can we explain all fast transientphenomena by a stiff local transport orwe still need a non-local transport?”

� Stiff models should have a problemreproducing L-H transition (theperturbation should actually reducetransport rather than increase it);

� It will be difficult to reproduceexperimentally observed asymmetry inpropagation of the cold pulse, triggeredat the edge and in the core;

ω (Hz)

χ eff (

m2

/ sec

)

JG96

.139

/13c

00

10

20

30

10 20 30 40

χst

χcp

JET, 1994


21

� Very fast cold pulse propagationrequires extremely high level of stiffness,which has only a limited support from thetheory;

Conclusions

� Fast transient phenomena found onJET and other tokamaks make a bigimpact on a theory of plasma turbulence.

� It led to a development of a non-localapproach to plasma turbulence(streamers) as well as to a developmentof stiff local transport models(avalanches);

� A single theoretical model able toreproduce all experimentally observedphenomena (both steady state andtransient) has yet to be found;

� Most probably such a model will be acombination of stiff transport withelements of non-locality in it.


22

3.4

3.6

5.0

5.2

3.2

3.0

2.8

2.6

2.4

2.2

2.0

1.811.48 11.50 11.52 11.54 11.56

Time (s)

Te

(keV

)

JG96

.292

/3c

R = 3.7m

R = 3.4m

R = 3.0m

Pulse No: 31341


23

5.4

5.6

5.8

6 ρ =0.2

51554

4.3

4.5

4.7

4.9 ρ =0.3

2.8

3

3.2

3.4 ρ =0.4

2.4

2.6

2.8

3 ρ =0.5

1.7

1.9

2.1

2.3 ρ =0.6

1.5

1.7

1.9

2.1 ρ =0.7

1.2

1.4

1.6

1.8

47.4 47.5 47.6 47.7 47.8

ρ =0.8

t [s]

5.3

5.5

5.7

5.9 ρ =0.22

51554

4.2

4.4

4.6

4.8 ρ =0.33

3.2

3.4

3.6

3.8 ρ =0.44

2.5

2.7

2.9

3.1 ρ =0.57

1.9

2.1

2.3

2.5 ρ =0.69

1.5

1.7

1.9

2.1 ρ =0.76

1.2

1.4

1.6

1.8

47.4 47.5 47.6 47.7 47.8

ρ =0.84

t [s]

ρ30 i


24

Documents

HEAT TRANSPORT EXPERIMENTS IN JET: STIFFNESS AND NON … · Profile stiffness. Profile stiffness is a known concept, based on theoretical finding that both electron and ion anomalous