1. Joint European Research Doctoral Network in Fusion Science and Engineering
Edge Pedestal Profile Characteristics of H-Mode Discharges in ASDEX Upgrade
Philip Schneider
Special Thanks to
E. Wolfrum, J. Boom, B. Kurzan
and the ASDEX Upgrade Team
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

2. Why is the plasma edge so important? What is the edge pedestal?
How do we access the edge pedestal at AUG?
What is done to evaluate the data?
Which conclusion can be drawn from the analysis?
There are several questions I want to address in this talk.
First, why do we look at the plasma edge at all.
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

3. H-MODE H-Mode L-Mode Typical for H-Mode: Various models available
steeper gradients
reduced turbulent transport in the steep gradient region
Er well increased
Various models available
Most models explain gradient with turbulence reduction by ExB shear
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

4. Core Temperature Depends on Edge Temperature
W.Suttrop et al., PPCF 1997
The core plasma performance depends on the edge temperature
⇒ reaching fusion relevant temperatures in the plasma core is coupled with the edge performance
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

5. ELMs limit the Gradients possible in the Pedestal Region
Edge localized modes (ELMs) are present in “every” H-Mode discharge
Peak power load on the wall
Limit to the pressure gradient achieved at the plasma edge
⇒ understanding of ELMs is crucial
to run ITER without destroying the first wall
to predict the pedestal of ITER
Best theory for ELMs at hand ⇒ peeling-ballooning-theory
pressure-driven ballooning mode
ELM crash
More important they are a very Fusion relevant Plasma Instability.
First
current-driven peeling mode
Both instabilities depend on the edge values of Te, ne and their gradients
Connor et al. Phys. Plasmas 1998
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

6. My Work as a Physicist analyse raw data build database for measured
plasma parameters (Te, Ti, ne, …)
design and conduct
new experiments
find new
compare with existing
empirical models
Now that you have a little motivation why I look at the plasma edge
I have here a little scetch what I actually do.
Here at AUG I am in the fortunate situation to have access to the data of many different discharges.
Look at the data in DB in the right way, that means think
theory
empirical models
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

7. The H-Mode is Characterized by a Steep Gradient at the Edge
Pedestal Top
Pedestal / Edge Transport Barrier
Pedestal Width
Gradient
Pedestal Bottom
Experimentally challenging:
2 orders of magnitude in Te, Ti (10 – 103 eV)
1 order of magnitude in ne (0.5 – 10 · 1019 m-3)
small spatial scale of few cm (1.5 – 2.5 cm)
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

8. Robust Criteria Needed to Describe Pedestal
The edge pedestal is described with:
pedestal top value (Te,ped)
pedestal bottom value (Te,sep)
pedestal width (Te,ped)
maximum gradient (Te,ped)
⇒ robust criteria are needed to define these parameters for a wide range of different discharge properties
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

9. Edge Diagnostics at AUG
Li-Beam: ne
(active measurement with Li atoms)
(+) 1 kHz, sees the whole pedestal
(–) ne<9·1019m-3
ECE Radiometer: Te
(passive measurement of electron cyclotron emission)
(+) 32 kHz, whole radius
(–) shinethrough, cut-off
Thomson Scattering: Te & ne
(active measurement with laser beams)
(+) Te & ne at the same radial position
(–) Hz, sees not always the whole pedestal
Edge Charge Exchange: Ti
(active measurement with NBI heating beams)
At first we have to look were our data comes from
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

10. Equilibrium Reconstruction Increases Uncertainties
Alignment of the diagnostics is very important
calculate quantities (βp, Pe, …), which depend on several measured parameters (Te, ne, Ti, …)
Aligning these diagnostics can be done with equilibrium reconstruction
Thomson Scattering (VTS) is used for aligning Te and ne
only possible with an acceptable accuracy for few dedicated discharges
not perfect:
0 - 5mm shift between diagnostics
~ 0.25 Te,ped
⇒ pedestal definition must not be based on the equilibrium reconstruction
We have to keep this in mind for later when we look for methods to define
4mm vs. 2.16m is a very good accuracy, but not good enough for our purposes
plasma is equilibrated poloidal and toroidal on the field lines +> measure at the same position
the equilibrium is most likely not wrong the same way for all discharges
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

11. Definitions of Tanh- and 2Line-Fit
ped-width
2Line-fit
(+) good reproduction of pedestal top and gradients
(o) pedestal bottom predefined
(+) Te,bot = Te,sep = 100eV
A. Kallenbach et al., JoNM 2005
(-) ne,bot ?
(-) not good for modeling
ped-top
offset
height
shift on r-axis
width
ped-width
ped-bottom
Tanh-fit
(+) yields width without further assumptions
(+) smooth function for modeling
(-) symmetric function – data is not always symmetric
(-) fit to pedestal is influenced by data in the SOL
There are two methods: most common tanh
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

12. Both Tanh- and 2Line-Fit can be good
Te,ped [keV]
0.43±0.02
0.45±0.04
Te,ped [cm]
2.1±0.1
1.7±0.3
Te,ped [keV/m]
-23±10
-21±4
tanh
line
ne,ped
[1019m-3]
6.5±0.3
6.7±0.4
ne,ped [cm]
2.1±0.2
1.8±0.2
ne,ped
[1019m-4]
-311
-307
Te: s
ne: s
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

13. Tanh-fit is Strongly Influenced by Data Outside Pedestal
TANH is a symmetric function <--> the data is often not symmetric
⇒ tanh is combined with polynomials outside the pedestal
this cannot always compensate for asymmetry in the data
⇒ tanh-fit can lead to “wrong” results for the pedestal
Boundary conditions always influence tanh -> more scatter
line fit
tanh
line
ne,ped
8.5 · 1019m-3
8.0
ne,ped
2.8 cm
1.6
ne,ped
-330 · 1019m-4
-380
This will not be a problem for – I would say two thirds of the discharges – however it can lead to wrong …
If I would now start over and begin to determine the paramaters via daumen*Pi, I would loose the objective criterion I was looking for.
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

14. LINE Fit Reproduces Pedestal Width Better Than TANH Fit
Pedestal width measured with
LINE Fit
Te,ped  [1.5,2.3] cm
ne,ped  [1.4,2.1] cm
TANH Fit
Te,ped  [1.2,2.9] cm
ne,ped  [1.2,2.6] cm
⇒ LINE Fit yields less scatter in measurements of discharges with the same properties
here: Ip=1.0MA, Bt=-2.5T, Pheat=6.5MW, constant gas fuelling and plasma shape
Since the pedestal top values are pretty accurate, this is also true for gradients
one could think, that these are rather small deviations, however, if one wants to analyse a whole bunch of these data statistically every improvement in resolution is needed. Especially since we search for effects, which are normally not that pronounced
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

15. Te Increases with Pheat
Pedestal top:
Te increases with Pheat
Te decreases with ne at constant Pheat
A small simple example, what I do with my database that should visualize that it is not always obvious
⇒ very important to distinguish between various dependencies,
here Te(Pheat,ne,…)
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

16. Increasing the Density does not Increase the Pressure
constant Ip=1.0MA, Bt=-2.5T, Pheat=8.5MW, shape
variing gas fuelling level
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

17. Summary and Outlook
Any systematical comparison between the pedestal of different discharges has to be independent of the equilibrium
The fit with two straight lines has advantages over the tanh fit concerning the reproduction of pedestal widths and gradients
(scatter reduced by a factor of ~2)
Feed the database
Do better filtering
Include more measurements of the pedestal
especially Ti and vtor
Compare with scalings found at other machines
e.g. ped  √βp (P. Snyder 2009)
Modeling = test data against theory
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

18. peeling & ballooning ballooning mode: peeling mode: pressure driven
ballooning stability parameter:
peeling mode:
edge current driven
bootstrap current:
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

19. Different Equilibria Result in Radial Shifts of the Data
24163: t = s during Raus-scan
ECE measured frequencies
FPP, EQI, EQH
R, z p
FPP is routinely used, EQH needs large amounts of
radial shift due to different equilibria of up to 4mm (~0.2 Te,ped)
shape is preserved
⇒ pedestal definition must not be based on the equilibrium or p
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

20. Li-beam optics, passive He II: Er Reflectometry: ne (HFS, LFS), ne
New edge CXRS: Ti
Thomson scattering:
ne, Te
ECE: Te
Li-beam:
ne, Ti, ni, ne
Li-beam optics, passive He II: Er
Reflectometry:
ne (HFS, LFS), ne
Doppler Reflectometry: ~
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

21. Understand physics by looking at many discharges -> DB
obvious dependencies
heating vs. Te top
fuelling vs. ne top
delta Te vs. heating
delta felm vs elmtype in same Raus-scan
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics

22. Phase in Raus-Scan Does Not Influence the Pedestal width
Philip Schneider - JERDNiFSaE - Edge Pedestal Profile Characteristics