M. Endler and M. Hirsch

Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-17491 Greifswald, Germany

1. General considerations

2. Confinement region

3. Scrape-off layer (SOL)

Observation of Turbulence in Wendelstein 7-AS

experiment

theory

theory with additional effects

ion heat transport electron heat transport

From: M. Kick et al., IAEA 1996 (Montreal), vol. II, 27

1. General Considerations

Radial heat transport in W7-AS – comparison between neoclassical theory and observation:

Reason for interest in plasma turbulence: Turbulent transport

Turbulence and Transport

T1

T0

T1 > T0

pot of boiling water fusion plasma

n, T

core edge

n1, T1 n0, T0

Twofold Motivation for Observing Plasma Turbulence

• Directly measuring the turbulent transport ( synchronised observation of ≥ 2 quantities required)

• Comparison with turbulence models, simulations, theory (aim: understanding parameters controlling turbulence; influencing turbulence)

6 cm–1

1 cm

Which structure sizes can be observed?

Doppler reflectometrymicrowave scattering

Measurement in k space:spatial band pass CO2 laser scattering

ks = 1 for 300 eV

dissipation

k [cm ]–10.1 1 10 100

[cm]60 6 0.6 0.06

Measurement with limited resolution:spatial lowpass

Mirnov probes,SX

ECEBESreflectometry

Langmuir probes (multi-tip)

drivinginstabilities

a=17cm

kin

etic

en

erg

y

Raw data and statistical analysis

raw data

Example: Langmuir probe data from the W7-AS SOL (Isat)

probability distribution function

(auto)correlation function

Topics:

• Te fluctuations

• Doppler reflectometry

• Transient events

• Turbulence and transport

• Transition edge/SOL

Topics:

• Te fluctuations

• Doppler reflectometry

• Transient events

• Turbulence and transport

• Transition edge/SOL

2. Turbulence in the W7-AS confinement region

Te fluctuations in the plasma core by ECE

decorrelate thermal fluctuations

without decorrelating Te fluctuations

Challenge: < 1 % Te/Te fluctuations are masked by

thermal fluctuations of the radiation field

~ –

by observing the same volume from two positions under sufficiently large angle (first demonstration on W7-AS)

by observing at slightly different frequencies = shifted volume (first demonstration on TEXT)^

Decorrelation of thermal fluctuations

Demonstration of the principle using an artificial source for “temperature fluctuations” but true thermal fluctuations

lines of sight of observation below/above decorrelation angle

From: S. Sattler and H.-J. Hartfuß, PPCF 35 (1993) 1285, figs. 9&10

Different features in Te fluctuations

1. broadband fluctuations (bandwidth ~ 100 kHz)2. low-frequency fluctuations (< 5 kHz)3. quasicoherent modes

From: S. Sattler et al., PRL 72 (1994) 653, fig. 2

norm

aliz

ed c

ross

-cor

rela

tion

Broadband fluctuations disappear for Te = 0

From: H.-J. Hartfuß et al., PPCF 38 (1996) A227, figs. 9&10

In a region with Te = 0, only the low-frequency feature remains

From: M. Häse et al., RSI 70 (1999) 1014, fig. 5

Correlation between n and Te

~~

Topics:

• Te fluctuations

• Doppler reflectometry

• Transient events

• Turbulence and transport

• Transition edge/SOL

2. Turbulence in the W7-AS confinement region

Doppler reflectometry – using turbulence as a tracer for poloidal rotation

corrugated and fluctuating reflecting layer

antenna

microwave signal

“ordinary” reflectometry: use of 0th diffraction order of reflected signal

From: M. Hirsch et al., PPCF 43 (2001) 1614, fig. 1

Doppler reflectometry: use of (–1)st diffraction order of reflected signal

Comparison of poloidal velocity from Doppler reflectometry and from

spectroscopic data

poloidal velocity of fluctuations

≈ poloidal velocity of impurities

≈ vEB

From: M. Hirsch et al., PPCF 43 (2001) 1614, fig. 7

Time resolution of Doppler reflectometry

From: M. Hirsch et al., PPCF 48 (2006) S155, fig. 6

4 µs resolution reveals strong and fast changes in poloidal velocity and scattered power at HL backtransition

Topics:

• Te fluctuations

• Doppler reflectometry

• Transient events

• Turbulence and transport

• Transition edge/SOL

2. Turbulence in the W7-AS confinement region

ELM-like transient transport events

• profile flattening in ECE Te signals

• in region of strong pressure gradient• causing cold pulses propagating inward on diffusive

time scale• simultaneously bursts in broadband Mirnov activity

and small-scale density fluctuations

From: S. Zoletnik et al., 32nd EPS (Tarragona, 2005) P-5.023, fig. 1

Correlation analysis:

From: M. Hirsch et al., 25th EPS (Prague, 1998) 2322, fig. 1a

Transient magnetic activity – poloidal mode structure

Magnetic activity:

• poloidal mode number related to edge rotational transform

• bursts of ~ 100 µs

See: M. Anton et al., J. Plasma Fusion Res. SERIES 1 (1998) 259

Arrangement of Mirnov coils in poloidal cross section:

From: S. Zoletnnik et al., PPCF 44 (2002) 1581, fig. 24

Correlation between magnetic and density fluctuations

Complement poloidal resolution of Mirnov coils with radial resolution of Li beam

See: S. Zoletnik et al., PoP 6 (1999) 4239, fig. 5

= r

adia

l^

correlation of Mirnov signal with various BES channels along the Li beam

Tentative model for transient transport events

After: S. Zoletnik et al., 32nd EPS (Tarragona, 2005) P-5.023

• poloidally localised event (associated with broadband

turbulence) causes radial transport of hot, dense plasma

• flattening of pressure (temperature, density) gradient

• initial poloidal gradient causes MHD oscillations with m =

1/until gradients on flux surface are balanced (after a few

ion transit times ~ 100 µs)

Topics:

• Te fluctuations

• Doppler reflectometry

• Transient events

• Turbulence and transport

• Transition edge/SOL

2. Turbulence in the W7-AS confinement region

• Is fluctuation amplitude related to transport?

• Turbulent transport cannot be measured directly in the confinement region

Turbulence and transport in the confinement region

We may still be lacking important diagnostic information (phase between quantities? small scales, e. g., ETG turbulence?)

- Sometimes, yes: ne, Te amplitude is correlated with heat

diffusivity for density variation (at fixed heating power)

~~

- Sometimes, not in the expected way: ne, Te amplitude is

anti-correlated with heat diffusivity for heating power variation (similar: for variation)

~~

Topics:

• Te fluctuations

• Doppler reflectometry

• Transient events

• Turbulence and transport

• Transition edge/SOL

2. Turbulence in the W7-AS confinement region

Density fluctuations inside and outside the last closed magnetic surface (LCMS)

• no significant radial correlation across the LCMS

• different character of density fluctuations in edge and SOLSee: S. Zoletnik et al., PoP 6 (1999) 4239, fig. 4

(from fast Li beam diagnostic)

Transport in the scrape-off layer

Definition of last closed magnetic surface (LCMS):

by a limiter by a magnetic separatrix

scrape-off layer (SOL)

B

radial transport B

transport B to the target plates

confinement region

3. Turbulence in the W7-AS scrape-off layer

Topics:

• Spatial structure of turbulence

• Phase between fluctuating quantities

• Transport

Topics:

• Spatial structure of turbulence

• Phase between fluctuating quantities

• Transport

Langmuir probe heads:

1 cm

Diagnostics – Langmuir probes

Positions of Langmuir probes in W7-AS:

Diagnostics – H fluctuation diagnostic

emissivity: ne n0 f (Te)

only weaktemperature dependence

pla

sma

lens

vacuum vesselwindow

glass fiber16

gas valve(H2/D2)

photomultipliers

filters

Raw data from the H fluctuation diagnostic (density fluctuations)

Individual “fluctuation events” are propagating in poloidal direction

lifetime: several 10 µspoloidal correlation length: 1–5 cmpoloidal velocity: O(100)–O(1000) m/s

time

poloidal position

500 µs

9 c

m

Frequency spectrum

(floating potential data)

Auto power density spectrum

arb.

uni

ts

103

104

105

106

107

0 200 400 600 800f [kHz]

10 100f [kHz]

same, double logarithmic

From: J. Bleuel et al., NJoP 4 (2002) 38, fig. 5

Poloidal-temporal correlation function

d [

cm]

3

2

1

0

1

2

320 10 0 10 20

[µs]

1.0

0.8

0.6

0.4

0.2

0.0

0.2

grey

sca

le

(floating potential data)

Correlation/coherency || B

fl data from SOL, 6.3 m probe tip separation || B, torus outboard side

cross correlation cross coherency

From: J. Bleuel et al., NJoP 4 (2002) 38, figs. 20&22

Correlation || B in W7-AS – comparison of poloidal-temporal correlation functions

Correlation function between single probe tip and the tips of the poloidal array displaced by 6 m || B (at radial position of maximum correlation)

Correlation function between the tips of the poloidal array

From: J. Bleuel et al., NJoP 4 (2002) 38, fig. 21

Radial-poloidal correlation function – obtained from the angular array

(floating potential data)

5 different time lags:

radial separation dr [cm]

From: J. Bleuel et al., NJoP 4 (2002) 38, fig. 11

polo

idal

sep

arat

ion

d [

cm]

Comparison with spatial structure from model calculations

3D simulation of ITG/drift wave turbulence, Te fluctuations

at fixed time:

From: B. Scott, Phys. Plasmas 7 (2000) 1845–1856

Topics:

• Spatial structure of turbulence

• Phase between fluctuating quantities

• Transport

3. Turbulence in the W7-AS scrape-off layer

Particles:

Energy (for each species):

Transport due to “electrostatic” turbulence

Correlation and phase between different fluctuating quantities

Correlation between floating potential and ion saturation current:

Typically, a phase of /2.../3 between these quantities is observed, maximising transport, if fl fluctuations are considered equivalent to pl fluctuations

From: J. Bleuel et al., NJoP 4 (2002) 38, fig. 8

p0

Phases between n and in interchange instability

r

B

p

Target plate

j ≠ 0 due to curvature

j||

E vExB

fl

Isat

fl

Phase between n, Te and pl fluctuations

n - Te

n - pl

Te - pl

From: M. Schubert, PhD thesis, Greifswald (2005), figs. 5.24&25 (accessible through http://edoc.mpg.de/)

Isat - fl

Modelling of SOL turbulence

• The observed phases are consistent with a drift-interchange type of turbulence

• The impact of the target plate boundary conditions has not yet been fully explored

• The changes of the phases in radial direction are not yet understood in detail

Topics:

• Spatial structure of turbulence

• Phase between fluctuating quantities

• Transport

3. Turbulence in the W7-AS scrape-off layer

Fluctuation-induced radial energy transport

From: M. Schubert, PhD thesis, Greifswald (2005), fig. 5.33 (accessible through http://edoc.mpg.de/)

Observed: (6.6 ± 1.5) kW/m2

Expected from global energy balance: 24 kW/m2

(assuming homogeneous transport across LCMS, taking into account local flux expansion)

Summary

• improving knowledge about relations between different quantities

• capability to observe directly the turblence-induced transport

• qualitative agreement with transport to be expected from global confinement

Confinement region:

• Progress to be expected from improvement of diagnostic capabilities

SOL:

• detailed knowledge of spatial structure of turbulence

Tentative outlook

Confinement region:

• high temporal & spatial resolution required problem of intensity – could progress in lasers help?

• combine several methods to obtain information on different quantities, or complementary information on one quantity

SOL:

• improve advanced methods (fast sweeping of electrostatic probes?) and perform parameter studies

• continue detailed comparison with theory and modelling

• “turbulence engineering” by suitable shaping of targets or by active methods?