HEAT TRANSPORT
EXPERIMENTS IN JET:
STIFFNESS AND NON-LOCALITY
V. Parail, P. Manticaa , W. Suttropb andcontributors to the EFDA-JETworkprogramme.
EURATOM-UKAEA Fusion Association, Culham
Science Centre, Abingdon, OX14 3DB, United Kingdoma)
Istituto di Fisica del Plasma, Euratom/ENEA-CNR,Milano, Italyb)
Max-Plank-Institut fur Plasmaphysik, EURATOMAssociation, D-85740-Garching, Germany

Outline½ Fast transient phenomena in JETexperimental observations;½ Concept of turbulence non-locality;½ Profile stiffness as an alternative
approach to fast transient phenomena;½ Conclusions
1ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

I. Fast Transient Phenomena on
JET- Experimental Observations½An unusually fast heat pulse, generatedby L-H transition, has been first reported
in 1993 (S. Neudachin et al., 20th EPS
Conference, Lisbon, 1993)
Pulse No: 31078
4.0

ρ = 0.33

ρ = 0.40

2.0

ρ = 0.50
ρ = 0.60
ρ = 0.66

1.013.2

ρ = 0.76

ρ = 0.80
13.3

13.4

JG96.139/6c

Te (kev)

3.0

13.5

Time (s)2ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

½ Two unusual features of this heat pulse:I.

A very fast (sometimes beyond

experimental resolution) propagation of thetemperature rise;II.

Heat pulse amplitude does not decay(sometimes even rise) in the corequickly attracted attention of theoreticiansand modellers.
½ Since then JET and many othertokamaks have reported a number ofheat and cold pulses with the similarfeatures;½ Some tokamaks (starting from TEXT, K.
Gentle,1993) reported cold pulses whichchange polarity in the core;3

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Cold pulse triggered by a shallow
pellet injection

751084
ρ=0.1951084
8
ρ=0.1265ρ=0.28ρ=0.364

ρ=0.453

ρ=0.642

ρ=0.84
ρ=0.911
5.6

ρ=0.87
5.8

6
t [s]

6.2

6.4

0
5.6

5.8

6

6.2

6.4

t [s]

4

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Cold pulse triggered by type-I
ELM
Pulse No: 30592
ρ = 0.50
4.0

3.0

ρ = 0.66
ρ = 0.70

2.5
ρ = 0.74
2.0

ρ = 0.81

JG96.139/4c

Te (kev)

3.5ρ = 0.84
11.76

11.80

11.84
11.88
Time (s)11.92

5ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Cold pulse caused by noble gas
puffing into ELM-free H-mode

Te (eV) x103

7ρ ≈ 0.4

53

ρ ≈ 0.9

32

JG99.126/1c

Prad (Watt) x106

11
16.0

16.2

16.4

16.6

16.8 17.0
Time (s)

17.2

17.4

6

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Cold pulse in plasma with ITB
A very recent example shows that cold
pulse leads to erosion of the ITB(P.Mantica, EPS 2001)
8051581
ρ=0.2

7-0.2

6-0.4

5-0.6

4-0.8

3-1

2

00.2

0.4

ρ

0.6

0.8

100.2

0.4

ρ

0.6

0.8

1

ρ=0.8
106

6.1

6.2

6.3

6.4

6.5

t (s)
-0.2

Weak ITB can becompletely destroyedby the cold pulse

-0.4

-0.6

-0.8

-1

7

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

½ Two unusual features of these heatpulses:I.

A very fast (sometimes beyond

experimental resolution) propagation of
the onset of the temperature rise;II.

Heat pulse amplitude does notdecay (sometimes even rise) in the corequickly attracted attention oftheoreticians and modellers.

8ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Let us compare experimental resultswith the prediction from a simple
diffusive model with the constant χ :
012

7-0.1

8-0.2

5-0.3

4

3-0.4

000.2

0.4 ρ 0.6

7

0.8

1
1

-0.5
0

0.2

0.4

ρ

0.6

0.8

1

951084

ρ=0

ρ=0.19

8
7
56
5
4
3

3

DTmax

2
ρ=0.87
1
5.8

5.9

6

6.1
t [s]

6.26.3

ρ=1
1
0.8

0.9

1

1.1

1.2

1.3

t (s)

9ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

½ The difference in the speed of cold
pulse propagation and in the radial
profile of the cold pulse amplitude isobvious.
½ How can we explain such a fast, nondiffusive kind of cold pulse propagation?
½ Two possible explanations are being
considered by theoreticians at present:
 Non-local turbulence paradigm(streamers),
 Stiff local transport paradigm(avalanches).

Non-local turbulence.
½ Non-local turbulence as a mean of afast L-H transition in JET has been
proposed in (J.G. Cordey et al., NF1995) and implemented in an empirical
JETTO transport model (M. Erba et al.,PPCF, 1997);½ Since then the model has beensuccessfully applied to a number oftransient phenomena.
10ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

½ The physics mechanism of theturbulence non-locality originates from: Toroidal coupling of unstable vortices, Inverse non-linear cascade of unstablemodes into long wave length part of thewave spectrum;½ Both mechanisms lead to a formation oflong radially correlated structures(strimmers), which can explain fast nonlocal 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);½ JET transport model assumes that thesource of the turbulence localised near
the separatrix, so that

χ Bohm ≈ C ⋅ cs ⋅ ρi ⋅ q2 ∇TeTe sep½ Next slide shows an example of L-Htransition simulation with JET model;
11ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Pulse No: 31078
4.0

ρ = 0.33

ρ = 0.40

2.0

ρ = 0.50
ρ = 0.60
ρ = 0.66

1.013.2

ρ = 0.76

ρ = 0.80
13.3

13.4

JG96.139/6c

Te (kev)

3.013.5

Time (s)12ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Pulse No: 31078
4.0

ρ = 0.33

ρ = 0.40

2.0

ρ = 0.50
ρ = 0.60
ρ = 0.66

1.013.2

ρ = 0.76

ρ = 0.80
13.3

13.4

JG96.139/6c

Te (kev)

3.013.5

Time (s)13

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Profile stiffness.

½ Profile stiffness is a known concept,
based on theoretical finding that bothelectron and ion anomalous transport
increases rapidly when some plasma∇Ti
in case of ITG) exceed
parameters (Ticertain limit (F. Romanelli, F. Zonca, PF1993; A. Dimits et. Al., PP 2000);½ Generally, transport coefficient with aprofile stiffness has the following form:
2 ∇Ti ∇Ti
ρresi ⋅ VTi
×−a ⋅χi = χi +C TRTi crit  i ∇Ti ∇Ti
−H TTi crit  i2ρresi ⋅ VTi½ Usually χ i << C, thereforeR
14

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japantransport changes rapidly in the region

∇Ti
∇Ti
≈
;
Ti
Ti crit12106

LLNLGKFit to LLNLGKU. Col GK
1994 IFS/PPPL
1997 PPPL GFL
1998 PPPL GFL
Sydora GK

42Weiland QL-ITG
005R/LTclin R/LTexpt

1015

JG01.337-1c

χiLn/ρi2vti

820R/LTi

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

15

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

The figure allows concluding:½ Temperature profile keeps the same
shape in case when heating power
exceeds critical level;½ Core temperature depends on theedge temperature rather than on thelevel of transport;½ Cold pulse can propagate rapidly (likeavalanche) with the characteristic χ2
ρ∇Ti
HPi ⋅ VTi
χi ≅ C>> χ iPBa⋅R
Ti crit16

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan½ Profile stiffness is a recognised
concept, which has been found inpractically every tokamak;
0.06

q e,⊥ [MW/m2 ]JET
ICRH + NBI heatingρ = 0.4
0.04

0.02

0.00
01234

∇T / T [1/m]½ The question is whether this concept
can explain all experimentally observed
fast transient phenomena, or we stillneed a non-local transport on the top;17

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Profile stiffness vs. non-locality½ Before going to a detailed comparisonof two concepts, let us look at somerecent result of cold pulse modellingwhich uses stiff transport models(J. Kinsey, 2000-01)½ Three theory based transport models(MMM-95, IFS/PPPL and GLF-23) havebeen used to simulate the same recent
cold pulse from JET;
751084
ρ=0.1951084
8
ρ=0.126

5

ρ=0.28ρ=0.364

ρ=0.453

ρ=0.642

ρ=0.84
ρ=0.911
5.6

ρ=0.875.8

6t [s]

6.2

6.4

0
5.6

5.8

6

6.2

6.4

t [s]

18

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

78IFS/PPPL

ρ=0.
7

ρ=0.

6

655443322
ρ=0.76

ρ=0.7651084 IFS-PPPL
1651084 IFS-PPPL
16.1

6t [s]

77GLF 23

ρ=0.

6544332MMM-95

ρ=0.

6516.1t [s]

26t [s]ρ=0.8

ρ=0.851084 GLF2351084 GLF23

6.1

166.1
t [s]

7766

ρ=0.

ρ=0.
554433221

6

ρ=0.8

ρ=0.851084 MM9551084 MM95

6.1t [s]1

66.1t [s]ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

19

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?”½ Stiff models should have a problem
reproducing L-H transition (theperturbation should actually reducetransport rather than increase it);
½ It will be difficult to reproduce
experimentally observed asymmetry inpropagation of the cold pulse, triggeredat the edge and in the core;
χcp
χst20

1000

JG96.139/13c

χeff (m2 / sec)

30

10203040

ω (Hz)JET, 199420

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

½ Very fast cold pulse propagation
requires extremely high level of stiffness,
which has only a limited support from thetheory;

Conclusions½ Fast transient phenomena found on
JET and other tokamaks make a big
impact on a theory of plasma turbulence.
½ It led to a development of a non-local
approach to plasma turbulence(streamers) as well as to a developmentof stiff local transport models(avalanches);½ A single theoretical model able toreproduce all experimentally observed
phenomena (both steady state andtransient) has yet to be found;½ Most probably such a model will be a
combination of stiff transport withelements of non-locality in it.
21

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

Pulse No: 31341
5.2

R = 3.0m

5.0
3.6

R = 3.4m

3.4
3.2

2.8
2.6
2.4
2.2
2.0
R = 3.7m
1.8
11.48

11.50

11.52

11.54

JG96.292/3c

Te (keV)

3.0

11.56

Time (s)22

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan30 ρ i

51554

51554
ρ =0.2

6

5.7

5.8

5.5

5.6

5.3
4.8

5.4
4.9

ρ =0.3

ρ =0.33

4.6

4.7

4.4

4.5

4.2
3.84.33.4

ρ =0.4

ρ =0.44

3.6

3.2

3.4

3

3.2
3.1

2.8

ρ =0.53

ρ =0.57

2.9

2.8

2.7

2.6

2.5
2.5

2.4
2.3

ρ =0.69ρ =0.6
2.3

2.1

2.1

1.9

1.9
2.1

1.7
2.1

ρ =0.76ρ =0.7
1.9

1.9

1.7

1.7

1.5
1.8

1.5
1.8

ρ =0.8ρ =0.84

1.6

1.6

1.4

1.4
1.2

ρ =0.22

5.9

1.2

47.4

47.5

47.6

t [s]

47.7

47.4

47.5

47.6

t [s]

47.7

47.8

47.8

23

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan

24

ITC-12 and APFA’01, December
11-14, 2001, Toki, Japan