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Journal ArticleDOI

New signal processing technique for density profile reconstruction using reflectometry.

25 Aug 2011-Review of Scientific Instruments (American Institute of Physics)-Vol. 82, Iss: 8, pp 083502

TL;DR: This data processing technique is applied to two sets of signals coming from two different reflectometer devices used on the Tore Supra tokamak, providing a clearer separation between multiple components and improves isolation of the relevant signals.
Abstract: Reflectometry profile measurement requires an accurate determination of the plasma reflected signal. Along with a good resolution and a high signal to noise ratio of the phase measurement, adequate data analysis is required. A new data processing based on time-frequency tomographic representation is used. It provides a clearer separation between multiple components and improves isolation of the relevant signals. In this paper, this data processing technique is applied to two sets of signals coming from two different reflectometer devices used on the Tore Supra tokamak. For the standard density profile reflectometry, it improves the initialization process and its reliability, providing a more accurate profile determination in the far scrape-off layer with density measurements as low as 1016 m−1. For a second reflectometer, which provides measurements in front of a lower hybrid launcher, this method improves the separation of the relevant plasma signal from multi-reflection processes due to the proximity of the plasma.
Topics: Time-domain reflectometry (61%), Reflectometry (61%), Signal (56%), Signal processing (54%), Signal-to-noise ratio (53%)

Summary (2 min read)

Introduction

  • HAL Id: hal-00961734 https://hal.archives-ouvertes.fr/hal-00961734.
  • Submitted on 21 Mar 2014 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not.
  • New signal processing technique for density profile reconstruction using reflectometry F. Clairet, B. Ricaud, F. Briolle, S. Heuraux, C. Bottereau.
  • For a second reflectometer, which provides measurements in front of a lower hybrid launcher, this method improves the separation of the relevant plasma signal from multi-reflection processes due to the proximity of the plasma.
  • Recently, a new tool6 based on a tomographic technique in the time-frequency plane has been developed and it substantially improves the traditional Fourier analysis in separating echoes with a similar frequency but over different time domains with a great precision.

A. Definition

  • The so-called tomogram transform was first defined in the context of quantum mechanics and operator theory.
  • 10, 11 0034-6748/2011/82(8)/083502/9/$30.00 © 2011 American Institute of Physics82, 083502-1.
  • Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp.
  • A self-adjoint operator depending on a parameter θ is introduced together with its eigenfunctions: the tomogram transform performs the projection over the basis formed by these eigenvectors.
  • In consequence, this transform should be appropriate in the case of reflectometry data where chirp-like components are embedded in a complex signal, as one can see, for instance, on the spectrogram of Fig. 1.

B. Practical processing steps and implementation

  • To extract the plasma reflection from the raw signal, the tomogram analysis is done in several steps.

1. Choice of θ

  • The choice of the best θ is usually made a posteriori with the help of the tomogram plot: several projections are computed, associated to different arbitrary chosen θ .
  • 2. The 2D plot highlights the different parts embedded in the signal which can be extracted by the tomogram decomposition.
  • Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp which the separation between the different parts is the greatest is chosen for the extraction (see Sec. III).
  • 2. For identical reasons, the same robustness holds if the signal to extract is not a perfectly linear chirp but possesses a small bending.

3. Choice of sets of Cθ (X) corresponding to the plasma reflection

  • 3. Several peaks of energy are present, which are the consequence of the multi-reflections contained in the signal.
  • Using a threshold, regions with a high energy density are isolated.

4. Extracted signals

  • The reconstruction of the extracted signals is then performed according to the relation (5).
  • The action of step 3 is to clear out the projection from the multi-reflection components of the signal.
  • Then, the output of part 4 gives a temporal signal containing only the plasma reflections.
  • The phase of this time-domain signal can then be used as the input of an algorithm for reconstructing the density profile.

III. STANDARD DENSITY PROFILE REFLECTOMETRY

  • A complete set of reflectometers, covering the frequency range from 33 to 150 GHz, provides density profile measurements on TS plasma from the edge to the centre and beyond.
  • Due to the low reflection efficiency of this very low edge density plasma, part of the probing wave crosses the cut-off layer and reflects onto the back wall (Fig. 1).
  • The benefits of the tomogram are shown here as these two parts of the signal form clearly two distinct regions in the range θ ∈ [π/5, π/10].
  • These cut-off frequencies have been determined from different threshold used for the amplitude rise detection.
  • Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp.

IV. REFLECTOMETRY AND LHCD LAUNCHER ARRANGEMENT

  • The edge density profile is a key parameter to address the additional power coupling efficiency.
  • The presence of a cut-off density, nco, below which the LH wave does not propagate, necessitates the ability to control the electron density in front of the LH launcher.
  • Due to the low space availability inside the LH antenna, the probing waves are emitted and received directly through open waveguides.
  • During plasma operation the first cut-off is clearly identified in Fig. 9 by a strong and abrupt amplitude rise of the reflected signal.
  • Second, the amplitude of the signal decreases dramatically (Fig. 9) in the second half of the sweep: time-frequency regions at the end of the sweep are masked in the tomographic projection due to their lack of energy.

V. CONCLUSION

  • A new data processing tool has been applied to experimental reflectometry signals to provide significant improvements for the extraction of the relevant plasma reflection from the multi-valuated component nature of reflectometry signals.
  • The tomogram provides then an efficient way of filtering out the effect of the walls surrounding the plasma.
  • The tomogram decomposition is done using a relatively simple implementation with fast algorithms.
  • The authors are planning this year to install definitively a new reflectometer in this launcher because the knowledge of the edge density is crucial for the physic of the power coupling.
  • It will be the opportunity to evaluate the tomographic method, which has given us so far the best results, and to test additional tomographic basis.

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HAL Id: hal-00961734
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Submitted on 21 Mar 2014
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New signal processing technique for density prole
reconstruction using reectometry
F. Clairet, B. Ricaud, F. Briolle, S. Heuraux, C. Bottereau
To cite this version:
F. Clairet, B. Ricaud, F. Briolle, S. Heuraux, C. Bottereau. New signal processing technique for
density prole reconstruction using reectometry. Review of Scientic Instruments, American Institute
of Physics, 2011, 82, pp.3502. �10.1063/1.3622747�. �hal-00961734�

REVIEW OF SCIENTIFIC INSTRUMENTS 82, 083502 (2011)
New signal processing technique for density profile reconstruction
using reflectometry
F. C l a i r e t ,
1
B. Ricaud,
1,2
F. Briolle,
2,3
S. Heuraux,
4
and C. Bottereau
1
1
CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
2
CPT UMR 6207, Campus de Luminy, case 907, F-13288 Marseille, France
3
CReA, BA 701, F-13306 Salon de Provence, France
4
IJL-P2M, UMR-CNRS 7198, Université Henri Poincaré, F-54506 Vandoeuvre, France
(Received 11 March 2011; accepted 14 July 2011; published online 25 August 2011)
Reflectometry profile measurement requires an accurate determination of the plasma reflected signal.
Along with a good resolution and a high signal to noise ratio of the phase measurement, adequate
data analysis is required. A new data processing based on time-frequency tomographic representation
is used. It provides a clearer separation between multiple components and improves isolation of the
relevant signals. In this paper, this data processing technique is applied to two sets of signals coming
from two different reflectometer devices used on the Tore Supra tokamak. For the standard density
profile reflectometry, it improves the initialization process and its reliability, providing a more accu-
rate profile determination in the far scrape-off layer with density measurements as low as 10
16
m
1
.
For a second reflectometer, which provides measurements in front of a lower hybrid launcher, this
method improves the separation of the relevant plasma signal from multi-reflection processes due to
the proximity of the plasma. © 2011 American Institute of Physics. [doi:10.1063/1.3622747]
I. INTRODUCTION
Reflectometry relies on the fact that as an electromag-
netic wave propagates through the plasma, its phase is shifted
due to the deviation of the local refractive index from the vac-
uum value. At a certain critical density corresponding to the
cut-off layer, in a WKB description (or under WKB assump-
tions), this refractive index goes to zero and the probing wave
is reflected. The In and Quadrature phase detection of the re-
flected wave provides a complex signal from which amplitude
and phase variation can be measured separately. The density
profiles are then reconstructed from the detected phase ac-
cording to a recursive numerical algorithm.
1
Among the tradi-
tional filtering techniques and Fourier analysis to recover the
relevant plasma echo, many signal analysis procedures have
been extensively tested most of the time to compensate for the
lack of signal and phase s crambling due to the turbulence.
24
This latter problem has been overcome over the past decade
by using fast sweep heterodyne techniques,
5
which provide
reliable and accurate phase measurements. However, reflec-
tometry signals exhibit a multi-frequency nature and the ex-
traction of the relevant plasma echo can, in some circum-
stances, appear to be delicate. As a matter of fact, the sig-
nal analysis can become problematic when multi-reflection
processes occur simultaneously. Recently, a new tool
6
based
on a tomographic technique in the time-frequency plane has
been developed and it substantially improves the traditional
Fourier analysis in separating echoes with a similar frequency
but over different time domains with a great precision. While
Fourier transform is based on the projection onto a basis of
sine and cosine functions, the tomogram transform consists
in a decomposition of the signal onto an orthonormal basis of
linear chirps. In this paper we illustrate the performance of
the tomographic analysis applied to Tore Supra (TS) reflec-
tometry signals through various examples. We first present, in
Sec. II, the theoretical aspects of the tomogram technique to
motivate its application to improve the signal extraction corre-
sponding to the first plasma reflection and to provide a better
rejection of multi-reflections. In Secs. III and IV, these two
performances of the tomographic analysis are illustrated with
two different reflectometer configurations. In Sec. III, we ap-
ply this analysis technique, to the standard density profile re-
flectometer, for the first X-mode cut-off detection. The prob-
lem that we encounter on TS is to separate the plasma scrape-
off layer echo from the back wall component. This problem
can prevent a proper density profile initialization and modify
substantially the reconstruction at the far edge. The second ex-
ample, treated in Sec. IV, corresponds to data obtained using
the same reflectometer but measuring density profiles in front
of a lower hybrid current drive (LHCD) launcher. Two waveg-
uides bring the wave directly inside the vacuum chamber at a
few millimeters from the detected plasma edge. The multi-
component nature of the signal is particularly significant as
the reflectometer antennas are very close to the plasma, which
causes secondary multi-reflections. This reflectometer was in-
stalled for a short period of time for test purposes. Such a
reflectometry configuration will occur on ITER to address at
least two specific physic studies: the plasma positioning con-
trol with a plasma position reflectometry system,
7, 8
and, the
power coupling to the plasma of additional powers such as ion
cyclotron resonance heating (ICRH) or LHCD systems where
measurements are foreseen in front of the launchers.
9
Then,
in Sec. V we discuss the advantages and limitations of this
new signal processing technique, and directions for further
research.
II. TOMOGRAM
A. Definition
The so-called tomogram transform was first defined in
the context of quantum mechanics and operator theory.
10, 11
0034-6748/2011/82(8)/083502/9/$30.00 © 2011 American Institute of Physics82, 083502-1
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp

083502-2 Clairet
et al.
Rev. Sci. Instrum. 82, 083502 (2011)
FIG. 1. (Color online) Short time window FFT analysis and instantaneous beat frequency (solid line) vs. probing frequency of a V-band reflectometer signal.
Both signals have been recorded during the same plasma at different time without (left) and with (right) additional ICRH.
A self-adjoint operator depending on a parameter θ is intro-
duced together with its eigenfunctions: the tomogram trans-
form performs the projection over the basis formed by these
eigenvectors. The properties of the operator ensure that the
eigenfunctions are θ -dependent and orthogonal for all fixed
θ. As a consequence, the signal can be projected, separated in
parts, and each part can be re-synthesized in time in a fast and
efficient way. Moreover, θ allows tuning the decomposition in
order to be adapted to the signal. It allows a better separation
of the different parts.
In the framework of Tore Supra reflectometry, the tomo-
gram associated to the operator (θ)ofRef.12 is used. It
is the association of two parts, one related to time, the other
related to frequency and a parameter θ [π/2/2]. The
parameter θ allows to pass from the time representation of the
signal (θ = 0) to the frequency one (θ = π/2) via intermedi-
ate representations. The operator (θ)is
(θ) = cos θt + i sin θ
d
dt
,
where t and d/dt are, respectively, the t-multiplication oper-
ator and the derivative operator. Its eigenfunctions ψ
θ
X
, i.e.,
defined by (θ )ψ
θ
X
= X ψ
θ
X
,where X corresponds to an eigen-
value of the operator (θ ), form an orthogonal basis. The re-
flectometry signals are of finite time-length T and the ψ
θ
X
on
the domain [0,T] have the following expressions:
ψ
θ
X
(t) =
1
T
exp
i
1
2tanθ
t
2
X
sin θ
t

. (1)
The associated eigenvalue takes discrete values,
X =
2π sin θ
T
n, (2)
where n is an integer. The tomogram transform M of a signal
u is defined by
M
u
(X) =|C
θ
(X)|
2
, (3)
where C
θ
(X) is the scalar product:
C
θ
(X) =
1
T
T
0
u(t)ψ
θ
X
(t)dt. (4)
Remark that this transform represents an energy den-
sity and for θ = 0 the tomogram is just
|
u(t)
|
2
, whereas for
θ = π/2, it is the density of the Fourier transform
|
U (ω)
|
2
.
The general theory of self-adjoint operators gives the re-
synthesis of the signal via the following relation:
u(t) =
X
C
θ
(X)ψ
θ
X
(t). (5)
In fact, each ψ
θ
X
is a linear chirp with phase derivative
φ
(t) =−
1
tan θ
t +
X
sin θ
= 2π (st + f
0
).
If plotted in the time-frequency domain, ψ
θ
X
is a ridge
of slope s = (2π tan θ)
1
and initial frequency (at t = 0)
f
0
= X/2π sin θ .
Thus, the tomogram transform can be seen as the projec-
tion on a basis of linear chirps. In consequence, this transform
should be appropriate in the case of reflectometry data where
chirp-like components are embedded in a complex signal, as
one can see, for instance, on the spectrogram of Fig. 1.
B. Practical processing steps and implementation
To extract the plasma reflection from the raw signal, the
tomogram analysis is done in several steps.
1. Choice of
θ
The selection of θ is not straightforward and depends on
the signal. As explained in Sec. II A, each ψ
θ
X
is a linear chirp
with phase derivative: φ
(t) = st + f
0
. Let us assume that the
signal to extract is a linear chirp with slope a and initial fre-
quency b:ifs is taken equal to a, the tomogram decompo-
sition will give the maximum of its efficiency since all the
chirp energy will be concentrated on one peak situated at f
0
= b. This would correspond to the orthogonal projection on
ψ
θ
X
with θ = arctan(1/2aπ ) and X = 2π sin θ . The choice
of the best θ is usually made a posteriori with the help of the
tomogram plot: several projections are computed, associated
to different arbitrary chosen θ . Then a comparison of the re-
sults is done by plotting the values of the function of two vari-
ables M
u
. In the present study, for a more intuitive approach,
we have adopted the chirp point of view and we plot M
u
with
respect to θ and f
0
; an example is shown in Fig. 2. The 2D plot
highlights the different parts embedded in the signal which
can be extracted by the tomogram decomposition. The θ for
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp

083502-3 Clairet
et al.
Rev. Sci. Instrum. 82, 083502 (2011)
FIG. 2. (Color online) Tomograms of the ohmic (left) and ICRH (right) signals. The dashed line represents the parameter chosen for the projection at θ
= π/5.
which the separation between the different parts is the great-
est is chosen for the extraction (see Sec. III). It is important
to notice that the choice of the angle is robust, meaning that
a small change of θ will lead to a small change of the energy
pattern. This can be seen on the tomograms plotted in Fig. 2.
For identical reasons, the same robustness holds if the signal
to extract is not a perfectly linear chirp but possesses a small
bending.
2. Computation of the signal projections
C
θ
(X): The reflectometry signal is discrete and con-
tains N = 2000 points per run of length T = 20 μs.
The sampling frequency is F
s
= N / T = 100 MHz.
The relation (4) is here the discrete sum: C
θ
(X)
=
N
n=1
u(
n
F
s
)
1
T
exp(i
1
2tanθ
n
2
F
2
s
)exp(i
X
sin θ
n
F
s
). This quan-
tity can be calculated using a fast Fourier transform (FFT)
algorithm (when N is a power of 2), as one can remark that
the above equation is the discrete Fourier transform of the
function s(
n
F
s
)exp(i
1
2tanθ
n
2
F
2
s
)
1
T
.
3. Choice of sets of C
θ
(
X
)
corresponding to the
plasma reflection
For a given θ, the energy density is calculated and plot-
ted in Fig. 3. Several peaks of energy are present, which are
the consequence of the multi-reflections contained in the sig-
nal. Using a threshold, regions with a high energy density
are isolated. The set of frequencies f
0
corresponding to the
plasma reflections is extracted. This gives the set S of ele-
ments X = f
0
2π sin θ , which will be used for the signal re-
construction.
4. Extracted signals
The reconstruction of the extracted signals is then per-
formed according to the relation (5). For the plasma reflec-
tions, the sum is hence over the values of X belonging to S.
The action of step 3 is to clear out the projection from the
multi-reflection components of the signal. Then, the output of
part 4 gives a temporal signal containing only the plasma re-
flections. The phase of t his time-domain signal can then be
used as the input of an algorithm for reconstructing the den-
sity profile.
III. STANDARD DENSITY PROFILE REFLECTOMETRY
A complete set of reflectometers, covering the fre-
quency range from 33 to 150 GHz, provides density profile
measurements on TS plasma from the edge to the centre
and beyond.
13, 14
For normal operation, the reflectometer
antennas are located in a dedicated porthole outside the
θ
θ
θ
θ
FIG. 3. (Color online) Slices of the tomogram at θ = π/5 for the ohmic signal (left) and the ICRH signal (right). Three components are present in the signal
and correspond, respectively, to the quartz window, the plasma, and the back wall echoes.
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp

083502-4 Clairet
et al.
Rev. Sci. Instrum. 82, 083502 (2011)
FIG. 4. (Color online) Spectrograms of the plasma signals separated by the tomographic analysis for ohmic and ICRH conditions (the solid lines correspond to
a calculation from the instantaneous phase derivative).
vacuum vessel behind a quartz window. X-mode polarisation
can provide an accurate initialization of the density profile as
long as the magnetic field profile is known. The detection of
the first cut-off frequency, which equals the electron cyclotron
frequency at zero density, provides the starting position of
the radial density profile. According the TS specificities
(plasma size, magnetic field aspect ratio, etc.) during routine
operation, the profile initialization is mainly performed with
the V-band reflectometer signal, which is treated here. The
reflectometer signal frequency, also called the beat frequency
(F
b
), is related to the time derivative of the phase, such
that
F
b
=
1
2π
∂φ
t
.
The beat frequency can be determined either at a given
point using the phase derivative at this point (the instanta-
neous beat frequency used to calculate the density profiles)
or from sliding FFT which, in this case, realises an average
over the time window analysis. Despite this averaging, the
advantage of the FFT analysis is to conveniently provide a
full picture of every signal components. In the following,
several spectrograms are shown and are all constructed from
the 2000 points signal by using short-term Fourier transform
with windows of 100 points and a step of 10 points. Zero
padding has been done using 1900 points to increase the
smoothness of Fig. 1. Moreover, to make the different com-
ponents visible even when the signal amplitude is low, the
signal energy has been normalized to one for each window.
The scrape-off layer (SOL) region is characterized by
outboard plasma with very low density (10
17
m
3
). Due to
the low reflection efficiency of this very low edge density
plasma, part of the probing wave crosses the cut-off layer and
reflects onto the back wall (Fig. 1). Unfortunately, the fre-
quency discrimination of these two echoes with traditional fil-
tering techniques appears to be somewhat difficult due to their
closeness in frequency. Figure 1 shows two different plasma
edge behaviours according the experimental scenarios: under
ohmic condition and with additional heating during the same
plasma discharge.
Evidences of different plasma boundary conditions be-
tween the two plasma phases are observed. During the ohmic
phase, the first plasma cut-off frequency occurs around 70
GHz, while during the additional heating phase the cut-off
appears above 60 GHz. In this latter case, additional plasma
is created in the periphery probably due to some extra power
deposition at the edge and/or because of the enhanced particle
transport. When this edge plasma starts reflecting the wave, it
does not screen totally the back wall because of its low den-
sity. The beat frequency increases continuously from 10 to
20 MHz with the probing wave frequency. A change in the
reflection behaviour appears above 68 GHz where the beat
FIG. 5. (Color online) Reflected signal amplitude comparison using tomography analysis (dashed line) and band-pass filter 5-19 MHz (solid line), for ohmic
(left), and ICRH (right).
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp

Figures (14)
Citations
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Journal ArticleDOI
TL;DR: The frequency modulated continuous wave reflectometer was developed for the first time on the HL-2A tokamak and the density profile behavior of a fast plasma event is presented and it demonstrates the capability of the reflectometer.
Abstract: The frequency modulated continuous wave reflectometer was developed for the first time on the HL-2A tokamak. The system utilizes a voltage controlled oscillator and an active multiplier for broadband coverage and detects as heterodyne mode. Three reflectometers have been installed and operated in extraordinary mode polarization on HL-2A to measure density profiles at low field side, covering the Q-band (33–50 GHz), V-band (50–75 GHz), and W-band (75–110 GHz). For density profile reconstruction from the phase shift of the probing wave, a corrected phase unwrapping method is introduced in this article. The effectiveness of the method is demonstrated. The density profile behavior of a fast plasma event is presented and it demonstrates the capability of the reflectometer. These diagnostics will be contributed to the routine density profile measurements and the plasma physics study on HL-2A.

44 citations


Journal ArticleDOI
01 Jan 2017-Nuclear Fusion
Abstract: In-depth experimental characterisation of spontaneous shear flow patterning into a so-called staircase—named after its planetary analogue—is shown in magnetised plasma turbulence, using ultrafast-sweeping reflectometry in the Tore Supra tokamak. Staircase signatures are found in a large variety of L-mode plasma conditions. Sensitivity to the dominant source of free energy is highlighted for the first time. A connection between staircase shear layer permeability and deviation from gyro-Bohm confinement scaling is strongly suggested, opening new routes to understanding confinement in drift-wave turbulence.

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Abstract: Development of efficient tools for the representation of large datasets is a precondition for the study of dynamics on networks. Generalizations of the Fourier transform on graphs have been constructed through projections on the eigenvectors of graph matrices. By exploring mappings of the spectrum of these matrices we show how to construct more general transforms, in particular wavelet-like transforms on graphs. For time-series, tomograms, a generalization of the Radon transforms to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presence of noise. Here the notion of tomogram is also extended to signals on arbitrary graphs.

13 citations


Journal ArticleDOI
TL;DR: Improved accuracy and stability of the reconstruction method, functions more complex than the linear are evaluated here to describe the refractive index shape in each integration step, which speed up the reconstruction algorithm and enable real-time monitoring of faster density profile evolution.
Abstract: The reconstruction method published by Bottollier-Curtet and Ichtchenko in 1987 has been the standard method of density profile reconstruction for X-mode reflectometry ever since, with only minor revision. Envisaging improved accuracy and stability of the reconstruction method, functions more complex than the linear are evaluated here to describe the refractive index shape in each integration step. The stability and accuracy obtained when using parabolic and fixed or adaptative fractional power functions are compared to the previous method and tested against spurious events and phase noise. The developed relation from the plasma parameters to the best integration shapes allows for the optimization of the reconstruction for any profile shape. In addition, the density profiles can be reconstructed using less probing frequencies without accuracy loss, which speed up the reconstruction algorithm and enable real-time monitoring of faster density profile evolution.

11 citations


Dissertation
09 Dec 2013-
Abstract: Le transport radial des particules dans les tokamaks constitue une des questions les plus cruciales pour la communaute de la fusion par con finement magnetique. En eff et, d'une part la puissance de fusion est proportionnelle au carre de la pression, d'autre part l'accumulation d'impuretes lourdes dans le coeur du plasma conduit a d'importantes pertes par rayonnement qui peuvent fi nir par causer un e ffondrement radiatif du plasma. Les dent de scie et la redistribution periodique de la temperature et de la densite de coeur qui lui est associee peuvent a ffecter signifi cativement le transport radial des electrons et des impuretes. Dans cette these, nous presentons des simulations numeriques de dents de scie utilisant un code tridimensionnel non lineaire de magnetohydrodynamique appele XTOR-2F, a n d'etudier le transport de particules pendant les dents de scie. Nous montrons que le code est capable de reproduire les structures fines de densite observees apres le crash de la dent de scie avec le diagnostic de refl ectometrie a balayage rapide sur les tokamaks Tore Supra et JET. La presence de ces structures implique la possibilite que le crash de dent de scie ne soit pas aussi effi cace que prevu pour evacuer les impuretes du coeur du plasma. Cependant, en appliquant le code aux impuretes, nous montrons que finalement le taux de redistribution est quantitativement similaire a ce qui est prevu par le modele de Kadomtsev, un resultat inattendu a priori. Nous concluons que la dent de scie est e fficace pour evacuer les impuretes du coeur du plasma.

10 citations


References
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Journal ArticleDOI
22 Nov 1999-Physics Letters A
Abstract: The characterization of non-stationary signals requires joint time and frequency information. However, time ( t ) and frequency ( ω ) being non-commuting variables there cannot be a joint probability density in the ( t , ω ) plane and the time-frequency distributions, that have been proposed, have difficult interpretation problems arising from negative or complex values and spurious components. As an alternative, time-frequency information may be obtained by looking at the marginal distributions along rotated directions in the ( t , ω ) plane. The rigorous probability interpretation of the marginal distributions avoids all interpretation ambiguities. Applications to signal analysis and signal detection are discussed as well as an extension of the method to other pairs of non-commuting variables.

124 citations


Journal ArticleDOI
Abstract: A general framework is presented which unifies the treatment of wavelet-like, quasidistribution and tomographic transforms. Explicit formulae relating the three types of transforms are obtained. The case of transforms associated with the symplectic and affine groups is treated in some detail. Special emphasis is given to the properties of the scale–time and scale–frequency tomograms. Tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector.

89 citations


Journal ArticleDOI
Abstract: The use of an ordinary mode reflectometer has already proved to be a good means for determining the density profile of a plasma, but the fact that this mode reflects where its frequency equals the local plasma frequency restricts its use to the region of the density gradient. The extraordinary mode reflectometry investigated here permits the observation of the scrape‐off layer as well as the near‐axis region and in certain conditions also the high magnetic field side of the density profile. It is also shown that this mode requires a range of frequency sweep for measuring a given density profile smaller than the ordinary mode. On the Petula‐B tokamak, the density profile has been measured in 200 μs, its evolution when applying the lower hybrid current drive could be also followed. Since the measurement is particularly sensitive near the reflection point of the wave, it could be used to determine precisely the position of magnetic islands and the fluctuation amplitudes. In addition, the access and place occupied in the vacuum chamber being very small, this diagnostic should be compatible with reactor conditions.

78 citations


Journal ArticleDOI
01 Nov 1992-Nuclear Fusion
Abstract: The TORE SUPRA lower hybrid current drive experiments (8 MW/3.7 GHz) use large phased waveguide arrays, four rows of 32 active waveguides and two passive waveguides for each of the two grills, to couple the waves to the plasma. These launchers are based on the 'multijunction' principle which allows them to be quite compact and is therefore attractive for the design of efficient multi-megawatt antennas in NET/ITER. Extensive coupling measurements have been performed in order to study the radiofrequency (RF) characteristics of the plasma loaded antennas. Measurements of the plasma scattering coefficients of the antennas show good agreement with those obtained from the linear coupling theory (SWAN code). Global reflection coefficients of a few per cent have been measured in a large range of edge plasma densities (0.3 × 1018 m-3 ≤ neg ≤ 1.4 × 1018 m-3) or antenna positions (0.02-0.05 m from the plasma edge) and up to a maximum injected RF power density of 45 MW/m2. When the plasma is pushed against the inner wall of the chamber, the reflection coefficient is found to remain low up to distances of the order of 0.10 m

58 citations


Journal ArticleDOI
G. Vayakis, C.I. Walker1, F. Clairet2, Roland Sabot2  +18 moreInstitutions (5)
24 Aug 2006-Nuclear Fusion
Abstract: Reflectometry with wavelengths in the centimetre to millimetre-wave range will be used in ITER to measure the density profile in the main plasma and divertor regions and to measure the plasma position and shape in order to provide a reference for the magnetic diagnostics in long pulses. In addition, it is expected to provide key information for the measurement of density fluctuations. A set of reflectometers to meet the relevant ITER measurement requirements has been included in its present outline as part of the ITER design since 2001 and is being adapted to the present ITER baseline and to accommodate progress with reflectometry techniques and measurement capabilities. It comprises low and high field side (HFS and LFS, respectively) ordinary (O-) mode systems for the measurement of the density profile in the gradient regions, a LFS extraordinary (X-) mode system for the detailed study of the edge profile, an HFS X-mode system operating in the left hand cutoff to measure the core profile, a dedicated O-mode system for plasma-wall gap measurement and a multi-band, multiple line of sight O-mode system to measure divertor density profiles. This paper describes the evolution of the design, in particular some recent improvements in the engineering implementation and improvements aimed at enhancing the measurement capability. It concludes with a brief assessment of the likely measurement performance against the ITER measurement requirements for the parameters of interest and the overall confidence that the technique will be implanted on ITER.

56 citations


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