1. Radial propagation of Type-I ELMs on JET
W.Fundamenski, W.Sailer
ITPA, St.Petersburg
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

2. Radial propagation of Type-I ELMs on JET, W.Fundamenski
Outer B-coil
Inner B-coil
LM11
LM12
LM14
LM15
LM18
LM19
LM21, 22
Soft X-ray
Vertical D
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

3. Radial extent of the SOL density (/t = 0)
|| G|| +  G = 0
G|| = nv||  D||||n
G = nv  Dn
|| diffusion: tD ~ L||2/D||
|| convection: tv ~ L||/Mcs
net || transport: t|| = min (tD , tv) ~ tv
 diffusion: ln,D ~ (Dt||)1/2
 convection: ln,v ~ vt||
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

4. Radial extent of the SOL energy (/t = 0)
|| q|| + q = 0, a = {i,e}
q|| = ½(mv2+ 5T)nv||  nc||||T
q = ½(mv2+ 5T)nv  ncT
|| conduction: tc ~ L||2/c|| , c||e >> c||i
|| convection: tv ~ L||/Mcs
net || transport: t|| = min (tD , 5/2tc)
 conduction: lq,c ~ (ct||)1/2
 convection: lq,v ~ vt||
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

5. Experimental observation of exponential decay
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

6. RCP probe + ELMs: MkIIGB, 45490
Type-I ELMs with 8 MW interact with probe upto limiter radius
No ELMs observed beyond 20 mm into the limiter shadow
Consistent with ~ 4 cm decay length
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

7. Transient evolution of SOL density (/t  0)
n/t + || G|| +  G = 0
|| G|| = nv||  D||||n  n /t||
G = nv  Dn
 dn/dt = 0, d/dt = /t + v/r  /r (D/r) + 1/ t||,
Greens function is a convected, gaussian wave-packet
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

8. Slow diffusion (A=1, v=1, D=0.1)
no || loss (t|| = 1000)
slow diffusion (D= 0.1)
strong || loss (t|| = 1)
slow diffusion (D= 0.1)
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

9. Moderate diffusion (A=1, v=1, D=1)
no || loss (t|| = 1000)
mod. diffusion (D= 1)
strong || loss (t|| = 1)
mod. diffusion (D= 1)
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

10. Strong diffusion (A=1, v=1, D=10)
no || loss (t|| = 1000)
strong diffusion (D= 10)
strong || loss (t|| = 1)
strong diffusion (D= 10)
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

11. Characteristic times in the SOL
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

12. Kinetic estimates of || losses
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

13. Kinetic estimates of || losses
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

14. Plasmoid (blob) model of ELM propagation: I
(Krasheninnikov,2001)
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

15. Plasmoid (blob) model of ELM propagation: II
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

16. Radial propagation of Type-I ELMs on JET, W.Fundamenski
Core
SOLdiv
SOLlim D
Im(t)
tELM
tm= ta + Dta-m v
In(t)
Dta-m
t||
tn= ta + Dta-n
Dta-n
Da(t)
ta = tELM + t||
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

17. Slow (10 kHz) vs. Fast (250 kHz) signals
Daslow
Dafast
I22fast
I22slow
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

18. Fast ELM signals: B-coils, soft X-ray, Da
Dafast
Daslow
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

19. Typical discharge: 12 MW, 2.5 MA/2.4 T
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

20. Typical ELM seen by LM probes
Davertical
Inmeasured
Inohmic
Vsupply
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

21. detail: definition of times & delays
DtaFWHM
tarise
tapeak
tnrise
tnpeak
DtnFWHM
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

22. I  D0.780.03 r1/2 exp{(8.50.5)r}, r-rlim < 0.3 m
Amplitude analysis:
I  D0.780.03 r1/2 exp{(8.50.5)r}, r-rlim < 0.3 m
I  D0.920.04 r1/2 exp{(22.81.0)r}, r-rlim < 0.1 m
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

23. Radial propagation of Type-I ELMs on JET, W.Fundamenski
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

24. ELM Temperature estimate
Fitting for peak ELM values, yields Te ~ 25 eV
Same for all LM probes
The ELM electrons are cold at the plates !!! (at least for high clearance JET discharges with r - rsep > 10 cm)
What about the ions ? They are probably hot !
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

25. Temporal analysis: rise time delays
rise < || rise ~ L|| / cs ~ msec
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

26. Temporal analysis: peak time delays
from the slope, v ~ 950  200 m/s
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

27. Temporal analysis: FWHM widths
 ~ 0.18 ms ~ 0.16 m, D ~ 500  100 m2/s
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

28. SOL density drop vs. lim/sol discontinuity
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

29. SOL velocity variation vs. lim/sol discontinuity
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

30. ELM energy flux to the limiters: I
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

31. ELM radial velocities: summary
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

32. Plasmoid model vs. measured velocities
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

33. Predicted plasmoid size
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

34. Radial propagation of Type-I ELMs on JET, W.Fundamenski
Extrapolation to ITER
gives v0 ~ 1.0 km/s, 0 ~ 11 cm
<v/cs> / (v/cs)ped ~
Hence, need rlim > cm for < few % energy to wall
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

35. Inner limiter probes: MkIIA ~ 38000
Type-I ELMs with up to 15 MW; 3 inner probes
Have not yet analysed data, but initial examination indicates that...
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski

36. Inner probe amplitudes smaller & broader:
Outer
Inner
16/11/2018
Radial propagation of Type-I ELMs on JET, W.Fundamenski