Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M
The paper presents the description of the density profile computing methods by the five-channel probing on the base of the developed program code and gives the results of model investigations.
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| Zitieren: | Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M / V.L. Ocheretenko, V.L. Berezhnyj, A.V. Prokopenko, I.B. Pinos // Вопросы атомной науки и техники. — 2008. — № 6. — С. 219-221. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-1110272017-01-08T03:03:24Z Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M Ocheretenko, V.L. Berezhnyj, V.L. Prokopenko, A.V. Pinos, I.B. Plasma diagnostics The paper presents the description of the density profile computing methods by the five-channel probing on the base of the developed program code and gives the results of model investigations. Описані методи розрахунку профілю густини при п'яти канальному зондуванні на підставі розробленого програмного коду і приведені результати модельних досліджень. Описаны методы расчета профиля плотности при пятиканальном зондировании на основании разработанного программного кода и приведены результаты модельных исследований. 2008 Article Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M / V.L. Ocheretenko, V.L. Berezhnyj, A.V. Prokopenko, I.B. Pinos // Вопросы атомной науки и техники. — 2008. — № 6. — С. 219-221. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/111027 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Plasma diagnostics Plasma diagnostics |
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Plasma diagnostics Plasma diagnostics Ocheretenko, V.L. Berezhnyj, V.L. Prokopenko, A.V. Pinos, I.B. Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M Вопросы атомной науки и техники |
| description |
The paper presents the description of the density profile computing methods by the five-channel probing on the base of the developed program code and gives the results of model investigations. |
| format |
Article |
| author |
Ocheretenko, V.L. Berezhnyj, V.L. Prokopenko, A.V. Pinos, I.B. |
| author_facet |
Ocheretenko, V.L. Berezhnyj, V.L. Prokopenko, A.V. Pinos, I.B. |
| author_sort |
Ocheretenko, V.L. |
| title |
Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M |
| title_short |
Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M |
| title_full |
Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M |
| title_fullStr |
Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M |
| title_full_unstemmed |
Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M |
| title_sort |
automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the torsatron u-2m |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2008 |
| topic_facet |
Plasma diagnostics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/111027 |
| citation_txt |
Automatization of plasma density profile analysis by the multichannel microwave interferometer measurements for the Torsatron U-2M / V.L. Ocheretenko, V.L. Berezhnyj, A.V. Prokopenko, I.B. Pinos // Вопросы атомной науки и техники. — 2008. — № 6. — С. 219-221. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| first_indexed |
2025-07-08T01:31:39Z |
| last_indexed |
2025-07-08T01:31:39Z |
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| fulltext |
AUTOMATIZATION OF PLASMA DENSITY PROFILE ANALYSIS
BY THE MULTICHANNEL MICROWAVE INTERFEROMETER
MEASUREMENTS FOR THE TORSATRON U-2M
V.L. Ocheretenko, V.L. Berezhnyj, A.V. Prokopenko, I.B. Pinos
Institute of Plasma Physics, National Science Center
“Kharkov Institute of Physics and Technology”, 61108 Kharkov, Ukraine
The paper presents the description of the density profile computing methods by the five-channel probing on the base
of the developed program code and gives the results of model investigations.
PACS: 52.55.Hc
1. INTRODUCTION
The presented complex problem was firstly
developed, both on the hardware base and at the stage of
data processing, for the torsatron U-3M with
submillimeter probing and later on for the torsatron U-2M
[1]. As a result, a program code was developed for
preliminary analysis of the density profile. Subsequently,
it was expanded in order to use the microwave diagnostic
data for plotting and analysis of the plasma density
profile.
The well-developed microwave FM-CW reflectometry
is an advanced research technique permitting to obtain
necessary data for density profile analysis [2, 3]. As the
probing waves are very sensitive to the plasma
turbulence, the reflected signals show constantly
perturbations provoking the distortion in the density
profiles obtained. The methods of multichannel
microwave interferometry enable to reduce the turbulence
effects and to simplify the density profile plotting. And
having a sufficient number of probing channels one can
obtain a high spatial resolution.
The probing channels are designed by the fan-like
array with a maximum opening of 40° and with a central
channel in the horizontal plane. The authors considered
different methods of plasma profile plotting basing on the
model for Abelian transformation with the use of
gradient-displaced ellipses.
2. THE MODEL AND METHODS
OF SIMULATION FOR PLASMA PROFILE
The development of simulation methods for
determining the plasma profile is based on the calculated
model of the plasma formation in the torsatron U-2M
composed of 11 measured magnetic surfaces [4]. On each
of these surfaces the density value is assumed to be
constant (Fig.1a, for the simplicity 5 surfaces are shown).
For the plasma cross-section the parabolic density
distribution
p
e L
Lxnxn
−−=
2
0 1)( (1)
was taken, where x is the number of surface in the model
of plasma formation, L and p are the parameters of profile
broadening-flattening.
2.1. THE PROFILE CALCULATION BY FAN-TYPE
CHORDS
In accordance with the applied plasma cross-section
model and five probing chords designed by the fan-like
array (Fig.1a), the program was developed for calculation
of plasma density profile. For every chord we determined
and recorded in the program the values xi for points of
chord intersection with corresponding surfaces and, also,
the point in the section center between the surfaces.
So, for chords К1, ..., К5 determined were 17, 21, 23,
21 and 17 points, respectively. For model calculations the
values of measured NL1, ..., NL5 by 5 chords for the test
profile were calculated using the graphic model with
parabolic distribution of density values on the surfaces.
The program calculation was performed by the
following procedure. The conventional profile y(x)= ne(x)
for the values of n0 = 1⋅1012 cm-3, L = 10, p = 1 is
calculated by formula (1). The x value changes within the
range from 0 to 10. Thus, we obtain 11 initial values
n1, ..., n11 for the profile model from 0 to 1⋅1012 cm-3.
Then the values y1(xi), ..., y5(xi) for 5 chord probing
channels in compliance with the calculated values n1, ...,
n11 are determined. Basing on the obtained profile values
in compliance with lengths xi for every chords, the areas
S1, …, S5, proportional to the values NL of the real profile
are calculated. The method for area calculation can be
various, e.g. simply the method of triangles or the method
with the use of smoothing splines when plotting the
profile curve.
Taking the horizontal channel K3 (Fig.1a) as a basic
one we determine the correspondence between the
obtained value of the area S3 and NL3, i.e. we obtain the
coefficient of density recalculation C = NL3 / S3.
2.2. AUTOMATIC CALCULATION ALGORITHM
Using the coefficient C we calculate for the rest four
channels the expected values nl1, nl2, nl4, nl5, for example,
nl1 = C ⋅ S1 (nl3 = NL3). By comparison of the calculated
values nl with measured ones, the error is determined.
Basing on this error the broadening-flattening parameter
profile parameters (L and p) are changed and a new
calculation is performed. After several recalculations the
optimum values nl1, ..., nl5 with a minimum error, relative
to the measured values NL of the real profile, are chosen.
The choice is carried out, for example, by the method of
least squares. Finally, using the optimum values
n1, ..., n11 the profile with N1, ..., N11 (N1 = C ⋅ n1 etc.) is
plotted.
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6. 219
Series: Plasma Physics (14), p. 219-221.
Fig.1. Arrangement of the model probing chords for microwave interferometers in the torsatron U-2M
The simulation results are presented in Fig.2. For the
test parabolic profile the error in determining the values
NL1, ..., NL5 is ~ 1%.
In the real experiment for every probing channel it is
intended to use a quadrature interferometer with the two
separate output signals S1 = A⋅cosϕ and S2 = A⋅sinϕ. The
processing and conversion program allow us to obtain the
phase values for every chord. These data are used for
determination of the current measured values NL1, ..., NL5.
With the data reception frequency of 3 MHz for the
discharge time interval of ~10 ms it is possible to obtain
near 3000 profiles.
0
0.2
0.4
0.6
0.8
1
-30 -25 -20 -15 -10 -5 0 5 10
K1
K2
K3
K4
K5
r, cm
Ne*1012 cm-3
Fig.2. Result of the calculation of the test parabolic
profile model for five probing chords К1 – К5 (Fig.1а)
2.3. USE OF THE MODEL FOR ABELIAN
TRANSFORMATION
Plasma profile plotting basing on the Abelian
transformation is often applied to the layered onion-like
structures [5]. The external chord K1 determines the
density value in the external layer (Fig.1b). The next
chord K2 intersects the external and second layers and so
on.
The above-described method was considered as a base
for plasma profile plotting in the case of five probing
chords located in the upper part of the chamber (Fig.1b).
Here the cross-section of plasma surfaces is simulated by
the five gradient-displaced ellipses. In this model for the
first channel K1 we have three intersection points – on the
left with the last surface, in the contact with the second
one and on the right. For the second chord K2 there are 5
points, for K3 -7 points and for K4 – 9 points. And, at
last, for K5 there are 11 points (with taking into account
the central point).
The simulation procedure was as follows. First we
calculated the initial test profile for 11 plasma surfaces
(similar to that in Section 2.1), named P1-11 (the analogous
profile is shown in Fig.2, curve K3). Then the calculation
results were used to determine the expected values nl1, ...,
nl5 for probing chords K1 – K5 (Fig.1b). They were used
as the initial data to calculate the profile basing on the
model for Abelian transformation which we named РА1-5.
220
At the first stage, the profile P1-11 by formula (1) with
the parameters L = 10, p = 1 was calculated.
Unfortunately, for this profile we did not succeed in
plotting the maximally corresponding profile РА1-5 (with
changing the parameters L = 4 − 5, p = 0.4 − 3) because
of a great error, from 20% to 70% over the channels.
0
0.2
0.4
0.6
0.8
1
-30 -25 -20 -15 -10 -5 0 5 10
r, cm
1
2
Ne*1012 cm-3
Fig.3
0
0.2
0.4
0.6
0.8
1
-30 -25 -20 -15 -10 -5 0 5 10
r, cm
1
2
Ne*1012 cm-3
Fig.4
At the second stage of calculations it has been
established that the best correspondence between the
initial profile P1-11 and the calculated profile РА1-5 can be
obtained by plotting P1-11 with the parameter p = 2.3
(Fig.3, curve 1). In this case for the profile PA1-5 (with the
parameters L = 5, p = 0.62, Fig.3, curve 2) the maximum
error in determination of the values nl1, ..., nl5 was near
9%. In the profile center the density decrease by ~14% is
obtained.
At the third stage we introduced into formula (1) the
additional coefficient of profile correction np:
p
pe L
Lxnnxn
−−+=
2
0 1)( , (2)
that permitted to decrease the error in the calculation of
the values nl1, ..., nl5. So, for the profile РА1-5 (with the
parameters np = 0.15⋅n0, L = 5, p = 1.18, Fig.4, curve 2)
the maximum error in the calculated values nl1, ..., nl5 was
2%. Thus, in the central profile part the density values
became lower (by 5 − 15 %) due to the additional density
increase at the extremity.
3. CONCLUSION
Reasoning from the calculation results, the following
is deduced. Using the model with a sufficient number of
surfaces (11 and more), the plasma profile can be
reconstructed with a high accuracy (to several percents).
For the case of simulation with the use of 5 gradient-
displaced ellipses the value of error depends on the
calculation method and can be within 5 − 20 %.
REFERENCES
1. V.L. Berezhniy, V.I. Kononenko, V.L.Ocheretenko,
V.A. Maslov, V.A. Svich, A.N. Topkov // Fizika
Plazmy (20). 1994, №1, p. 12-14 (in Russian).
2. L. Zeng, G. Wang, E.J. Doyle, T.L. Rhodes,
W.A. Peebles and Q. Peng // Nucl. Fusion. 2006,
v. 46, p. 677-684.
3. P. Varela, M.E. Manso, A. Silva, the CFN Team and
the ASDEX Upgrade Team // Nucl. Fusion. 2006,
v. 46, p. 693-707.
4. G.G. Lesnyakov, D.P. Pogozhev, Yu.K. Kuznetsov,
N.T. Besedin, E.D. Volkov, O.S. Pavlichenko // 23rd
European Physical Society Conference on Controlled
Fusion and Plasma Physics. Kiev, Ukraine, 24-28
June 1996. Contributed Papers. Part II, p. 547.
5. A.T. Ramsey and M. Diesso // Rev. Sci. Instrum.
1999, v. 70, №1, Part II, p. 380-383.
Article received2 22.09.08.
АВТОМАТИЗАЦИЯ АНАЛИЗА ПРОФИЛЯ ПЛОТНОСТИ ПЛАЗМЫ ПО ИЗМЕРЕНИЯМ
МНОГОКАНАЛЬНЫМ СВЧ ИНТЕРФЕРОМЕТРОМ ДЛЯ ТОРСАТРОНА У-2М
В.Л. Очеретенко, В.Л. Бережный, А.В. Прокопенко, И.Б. Пинос
Описаны методы расчета профиля плотности при пятиканальном зондировании на основании
разработанного программного кода и приведены результаты модельных исследований.
АВТОМАТИЗАЦІЯ АНАЛІЗУ ПРОФІЛЮ ГУСТИНИ ПЛАЗМИ ПО ВИМІРЮВАННЯХ
БАГАТОКАНАЛЬНИМ НВЧ ІНТЕРФЕРОМЕТРОМ ДЛЯ ТОРСАТРОНА У-2М
В.Л. Очеретенко, В.Л. Бережний, А.В. Прокопенко, І.Б. Пінос
Описані методи розрахунку профілю густини при п'яти канальному зондуванні на підставі розробленого
програмного коду і приведені результати модельних досліджень.
221
Institute of Plasma Physics, National Science Center
“Kharkov Institute of Physics and Technology”, 61108 Kharkov, Ukraine
REFERENCES
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