1. Measurements of density fluctuations in magnetic confined plasmas
Laure Vermare
LPP, Ecole Polytechnique
Palaiseau, FRANCE
TORE SUPRA

2. Outline
Motivations of characterizing density fluctuations in tokamak plasmas
Reflectometry and scattering techniques
Doppler backscattering system
Example of applications

3. Principle of the magnetic fusion
Electric power production from fusion reactions :
D T He (3,56 MeV) + neutron (14,03 MeV)
Topology of nested flux surfaces
=>iso-thermal surfaces
Hot core / cold edge
toroidal magnetic
field
poloidal component
generated by a toroidal current induced in the plasma = +
helicoidal field lines
Tokamak configuration

4. Performances limited by plasma turbulence
Strong pressure gradients
 Instabilities
Turbulent system
GYRO code
La qualité de principe du confinement magnétique est cependant réduite par la turbulence. En effet, les très forts gradients de pression de température, inhérents au confinement, impliquent que le système est hors d’équilibre, et qu’il va développer des instabilités, en réaction à cette forte puissance injectée, en expulsant la chaleur du centre vers les parois.
On le voit sur cette cartographie 3D obtenue par une simulation récente, au lieu de la structure isolante en feuillets, se développent à plus ou moins grande échelle, ce que l’on peut considérer comme des cellules de convection tourbillons qui agitent le plasma dans cette direction transverse au champ magnétique: les lignes de contour représentées ici sont en effet les lignes le long duquel s’effectue l’écoulement du plasma. Il s’opère ainsi un brassage qui mélange les lignes du cœur chaudes et le bord, diminue la température et le confinement.
Radial heat transport
Prediction and control of turbulent transport

5. Instabilities over a large range of spatial scales
Drift waves – Resonances with different class of particles
Interchange type, Threshold instabilities
ITG /TEM ETG 
ki
Ion modes
Electron modes 1
T, n B
Larmor radius ion
Larmor radius e
1 mm to 1 cm
10 m to 100 m
GYRO code

6. Non-linear evolution Jupiter’s zonal flows
Streamers : convection cells allongated in the radial direction => generate an important radial transport
Flux zonaux & Geodesic Acoustic ModeS :
fluctuations of the poloidal velocity which tear apart turbulence cells
=> decrease the radial transport

7. Control mechanisms of turbulence « self generated »
Without zonal flows
=> Strong radial transport
With zonal flows
=> decrease of the radial transport
=> Collisionality is found to damp zonal flows

8. Gyrokinetic simulation from GYSELA code

9. Prediction of the performances of future devices
Using empirical laws extracted from large database of discharges in existing machines and using dimensionless approach (ITER size has been determined using extrapolation of performances trough normalized Larmor radius) but large uncertainties appear for others parameters => more precise determination of dimensionless scaling of transport and turbulence are required
Using powerful numerical simulations and theoretical models such as gyrokinetic codes : realistic ITER plasmas with all physical ingredients are impossible to compute at this time
=> simplification, approximation : electrostatic, local, adiabatic … which must be evaluated trough comparisons with experiments NOT only comparing scalar parameters such as heat transport coefficient and turbulence level but several characteristics which allow high detailed comparisons

10. Micro-wave reflectometry techniques
Which tools ?
Scattering of electromagnetic waves
Micro-wave reflectometry techniques
Antennas
receptor
Cut-off layer
N=0 reflexion F F
kfluc
kdiff ki 
emitter
-> selectivity in spatial scale
-> spatial localisation

11. Doppler system installed on Tore Supra
Measurement of the backscattered
electric field Ed (t) :
Tiltable motorized antenna
- Gaussian optics
(beam waist 40mm)
- Low diverging beam
(2.2° HPBW)
- Poloidal angle 0 to 20°
(typically 3° to 9°)
=>k : 3 to 25 cm-1
=>kri ~0.5 to 5
O mode / V-band (50-75 GHz)
r/a = 0.3 to 0.9
X mode / W-band ( GHz)
r/a = 0.5 to 1.2
kd = ki + k
backscattered kd=-ki => k=-2ki ki kd k
Selection in wavenumber :
Bragg rule 
Cut-off layer : N=0
incident wave
Doppler reflectometers are installed on several fusion devices :
- DIII-D, USA
- ASDEX Upgrade, Germany
- TJ-II, Spain …

12. Doppler reflectometer scheme
All Tore Supra & new JET reflectometers based on the same scheme
Single side band modulator
Heterodyne detection
Active quadrupler : 10 mW output
Stable source (synthesizer) 12.5 to 19 GHz
Single antenna with high directivity directional coupler
High gain (35 dB) GOLA x6 x4
Data acquisition :
12 MHz
A cos ϕ
A sin ϕ
[Hennequin et al, RSI2004]

13. Density fluctuations measurements
Tore Supra => long pulse discharges : stationary phases long enough
to scan the poloïdal angle =>k-spectrum
Steps of the probing frequency (∼200ms)

14. Frequency spectra = kv Mean perpendicular velocity
Doppler shift
= kv
Mean perpendicular velocity
of density fluctuations
Energy fluctuations
at a specific spatial scale

15. Mean velocity of fluctuations, plasma velocity profile
Fluctuations are used as tracers of plasma movement
Shear of velocity of the plasma has interesting effect on
transport by reducing the size of the vortices
By changing the probing frequency
=> access to the radial profile of plasma velocity
[Hennequin et al, Nuc Fus 2006]
[E. Trier et al., Nuc Fus., 2008]

16. Scattering position and wave-number from ray tracing
(F, q)  (r,k) from ray tracing
±0.05
S(k)
Beam Tracing using density profiles
from fast sweep reflectometry
[Honoré et al, Nuc Fus 2006]

17. Shape of k-spectrum on Tore Supra
-> identification of driving mechanisms : ionic /electronic transport, role of small scales
-> qualifies the impact of interaction between scales (NL process) on saturated levels (is the k spectrum shape universal?)
Example of
ICRH discharge (#45511)
@ r/a = 0.8  0.08
Ps(a.u.)
[L. Vermare et al, CRAS 2011]

18. Shape of k-spectrum on Tore Supra
Example of a ICRH discharge r/a = 0.8  0.08
Ps(a.u.)
Fair agreement for all cases with the model taking into account
Interactions between disparate scales (drift-waves-zonal flows)
[O. Gürcan et al, PRL09, PPCF10]

19. Dedicated experiments on the effect of collisionality
Dimensionless parameters well matched !
Similarity principle
Scan en *
n constant
Motivations of Tore Supra experiments :
Combine dimensionless scans and turbulence measurements
Reach the lowest collisionality accessible on Tore Supra
to observe a possible transition (ITG-TEM)
Check this effect of collisionality on the k-spectrum

20. * dependence of spectrum shape
Decreasing collisionality affect only the quasli-linear
part of the spectrum :
spectrum more peaked at low *
no clear impact in the transfer region
In contrast with effect expected from zonal flows damped by collisions !

21. Perpendicular velocity evolution with k
v (k) = I VExB + V(k) I
Vdia / k
x103 V
(m/s)
Vion
high * :
dia (k)k
with
>1
Ve-
<1
low * :
dia (k)k
- mixed turbulence ?
[L. Vermare et al, PoP2011]

22. First observation of GAMs on Tore Supra
Geodesic Acoustics Modes are detected from the observation of coherent oscillations of the perpendicular velocity of density fluctuations measured.
Observed on several machines for long time, and using DS in AUG [G. Conway, PPCF05, PPCF08,PRL11] and DIIID [L. Schmitz, RSI08] …
These oscillations are located at the edge of the plasma,
maximal around r/a=0.95 but still detectable up to r/a=0.75
L. Vermare, submitted to NF

23. New Doppler system with vertical line of sight
Motivations :
Characterisation of long-range correlations
of density fluctuations and of their using
correlation between equatorial
and vertical reflectometers
(toroidal + poloidal)
Access to Geodesic Acoustic Modes (GAMs)
in vertical line of sight (poloidal structure m=1)
One channel identical to the equatorial Doppler system
O-mode polarisation, V-band
Tiltable antenna with Gaussian optics
Synchronise acquisition
L. Vermare
TTG 09, IRW 09

24. Location on the machine
TOP VIEW
OF TORE SUPRA Q1 Q2 Q3 Q4 Q5 Q6
Equatorial system
DIFDOP
Vertical system
DREVE
120°

25. Adaptating radial position and wavenumber
Same cut-off (O-mode) but poloidal angle
will depend on the Shafranov shift :
r/a = 0.87
2k= 8.78 cm-1
x (cm) radial
O-mode
F=60GHz
=-88°
DREVE
z (cm) vertical
r/a = 0.87
2k= 8.55 cm-1
z (cm) vertical
O-mode
F=60GHz
=6.5°
DIFDOP
x (cm) radial

26. Correlation between both systems
During the 2011 experimental campaign …
Temporal correlation function
of velocity fluctuations between DIFDOP & DREVE
Spectrum of velocity fluctuations
Correct level of correlation and no delay between both locations
=> coherent with GAMS observation

27. Summary
Scattering and reflectometry techniques largely used in fusion community to diagnose density fluctuations
Doppler backscattering system technique gives access to several turbulence characteristics : plasma velocity, repartition of spatial scales, dispersion relation, flow oscillation such GAMs which allow high detailed comparison between simulations and experiments
It is a versatile tool, which can be adapted for different purposes : diagnose small scales, correlation …
Apparatus compact, lightweight and portable
=> DREVE on TCV (Lausanne)
Development of powerful and complementary diagnostics is essential to improve our knowledge in turbulence & transport issues

28. Thanks ! Tore Supra’s team
Institut de Recherche sur la Fusion Contrôlée
CEA/DSM, Cadarache
R. Sabot
F. Clairet
C. Bourdelle
X. Garbet
C. Bottereau
J-C. Giaccalone
D. Molina
F. Leroux
L. Ducobu
B. Soler
Laboratoire de Physique des Plasmas
Ecole Polytechnique, Palaiseau
P. Hennequin
O. Gürcan
C. Honoré
E. Trier
V. Berionni
Association Euratom-