Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M
Series of experiments on generation of mode with high β (up to about 1.3%) in torsatron U-3M were performed using nitrogen as working gas. The dependence of average β from input power was obtained. The average plasma radii in modes with various β were determined. The estimation of rotational trans...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M / V.K. Pashnev, P.Ya. Burchenko, A.Ye. Kulaga, A.V. Lozin, Yu.K. Mironov, A.A. Petrushenya, V.S. Romanov, D.A. Sitnikov, Ed.L. Sorokovoy, S.A. Tsybenko, N.V. Zamanov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 37-39. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-882172015-11-10T03:02:26Z Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M Pashnev, V.K. Burchenko, P.Ya. Kulaga, A.Ye. Lozin, A.V. Mironov, Yu.K. Petrushenya, A.A. Romanov, V.S. Sitnikov, D.A. Sorokovoy, Ed.L. Tsybenko, S.A. Zamanov, N.V. Магнитное удержание Series of experiments on generation of mode with high β (up to about 1.3%) in torsatron U-3M were performed using nitrogen as working gas. The dependence of average β from input power was obtained. The average plasma radii in modes with various β were determined. The estimation of rotational transformation angle was done in view of presence of the plasma in device. На торсатроні У-3М проведено серію експериментів по створенню режиму з високим β (до 1.3%) з використанням азоту в якості робочого газу. Отримано залежність середнього β від потужності, що вводиться. Було визначено середній радіус плазми в режимах з різним β. Оцінка кута обертального перетворення була зроблена з урахуванням наявності плазми в установці. На торсатроне У-3М проведена серия экспериментов по созданию режима с высоким β (до 1.3%) с использованием азота в качестве рабочего газа. Получена зависимость среднего β от вводимой мощности. Был определён средний радиус плазмы в режимах с различным β. Оценка угла врщательного преобразования была сделана с учетом наличия плазмы в установке 2009 Article Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M / V.K. Pashnev, P.Ya. Burchenko, A.Ye. Kulaga, A.V. Lozin, Yu.K. Mironov, A.A. Petrushenya, V.S. Romanov, D.A. Sitnikov, Ed.L. Sorokovoy, S.A. Tsybenko, N.V. Zamanov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 37-39. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.55.Dy, 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/88217 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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| language |
English |
| topic |
Магнитное удержание Магнитное удержание |
| spellingShingle |
Магнитное удержание Магнитное удержание Pashnev, V.K. Burchenko, P.Ya. Kulaga, A.Ye. Lozin, A.V. Mironov, Yu.K. Petrushenya, A.A. Romanov, V.S. Sitnikov, D.A. Sorokovoy, Ed.L. Tsybenko, S.A. Zamanov, N.V. Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M Вопросы атомной науки и техники |
| description |
Series of experiments on generation of mode with high β (up to about 1.3%) in torsatron U-3M were performed
using nitrogen as working gas. The dependence of average β from input power was obtained. The average plasma radii
in modes with various β were determined. The estimation of rotational transformation angle was done in view of
presence of the plasma in device. |
| format |
Article |
| author |
Pashnev, V.K. Burchenko, P.Ya. Kulaga, A.Ye. Lozin, A.V. Mironov, Yu.K. Petrushenya, A.A. Romanov, V.S. Sitnikov, D.A. Sorokovoy, Ed.L. Tsybenko, S.A. Zamanov, N.V. |
| author_facet |
Pashnev, V.K. Burchenko, P.Ya. Kulaga, A.Ye. Lozin, A.V. Mironov, Yu.K. Petrushenya, A.A. Romanov, V.S. Sitnikov, D.A. Sorokovoy, Ed.L. Tsybenko, S.A. Zamanov, N.V. |
| author_sort |
Pashnev, V.K. |
| title |
Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M |
| title_short |
Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M |
| title_full |
Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M |
| title_fullStr |
Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M |
| title_full_unstemmed |
Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M |
| title_sort |
influence of plasma with finite pressure on magnetic configuration of torsatron u-3m |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2009 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/88217 |
| citation_txt |
Influence of plasma with finite pressure on magnetic configuration of torsatron U-3M / V.K. Pashnev, P.Ya. Burchenko, A.Ye. Kulaga, A.V. Lozin, Yu.K. Mironov, A.A. Petrushenya,
V.S. Romanov, D.A. Sitnikov, Ed.L. Sorokovoy, S.A. Tsybenko, N.V. Zamanov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 37-39. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| fulltext |
INFLUENCE OF PLASMA WITH FINITE PRESSURE
ON MAGNETIC CONFIGURATION OF TORSATRON U-3M
V.K. Pashnev, P.Ya. Burchenko, A.Ye. Kulaga, A.V. Lozin, Yu.K. Mironov, A.A. Petrushenya,
V.S. Romanov, D.A. Sitnikov, Ed.L. Sorokovoy, S.A. Tsybenko, N.V. Zamanov
Institute of Plasma Physics, NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
Series of experiments on generation of mode with high β (up to about 1.3%) in torsatron U-3M were performed
using nitrogen as working gas. The dependence of average β from input power was obtained. The average plasma radii
in modes with various β were determined. The estimation of rotational transformation angle was done in view of
presence of the plasma in device.
PACS: 52.55.Dy, 52.55.Hc
INTRODUCTION
Equilibrium of plasma in toroidal helical magnetic
traps, such as tokamaks or stellartors (torsatrons), is
supported by flows of plasma currents. The expressions
for these currents can be written as [1]:
[ ] )()()( '
22
' ρραρρ P
B
B
B
BPj
+∇= , (1)
where j
– density of plasma current, P – gas-kinetic
plasma pressure on magnetic surfaces ρ , )(ρP′ –
derivative of P with respect to instant radius, B –
magnetic field induction, )(ρα – coefficient, which was
obtained from solution of the expression 0=jdiv
:
[ ] 22
1
B
B
B
B ∇∇−=∇ ρα
. (2)
The first term in expression (1) describes the current,
that flows across magnetic field lines (diamagnetic
current). The second term of (1) corresponds to the dipole
component of de-polarization current (Pfirsch-Schlueter
current). The simple form of expression for de-
polarization current can be written as follows [2,3]:
( ) ϑρ
ι
cos'2
.. P
B
cj sp −= , (3)
where ι – rotational transformation angle and ϑ –
poloidal angle. The current described by (3) flows along
the magnetic field lines and creates the additional
magnetic field, that perturbs the initial magnetic
configuration. To the first approximation, the influence of
the disturbing magnetic field on a magnetic configuration
is similar to the influence of equivalent transverse
uniform magnetic field with value of
ιβ 2≅⊥ BB . (4)
Here 28 BPπβ = . If we take into account the real
distribution of gas-kinetic plasma pressure on magnetic
surfaces, the difference between the disturbing magnetic
field and the transverse uniform magnetic field is
distinctly increased. In stellarators (torsatrons), the helical
harmonics of de-polarization current appear and influence
the variation of the rotational transformation angle.
It is well known, that the transverse magnetic field of
stellarators shifts the internal magnetic surfaces of the
magnetic configuration, disrupts the near-separatrix
magnetic surfaces and modifies the profile of the
rotational transformation angle.
The purpose of our experimental study was to obtain
the maximal value of β in torsatron U-3M, as well as to
measure the small radius of the plasma and to determine
variation of the rotational transformation angle with
increasing β.
EXPERIMENTAL RESULTS
AND DISCUSSION
The experiments in torsatron U-3M were performed in
RF-heating mode [4]. In a typical operation mode of RF-
heating the hydrogen plasma was heated by Alfven wave
at the frequency ratio ω/ωi ≈ 0.8 (ωi – ion cyclotron
frequency). In this mode β ≈ 0.03% was achieved at
magnetic field induction on axis of B0 ≈ 0.72 Т [5], where
overline means averaging over cross-section of the
plasma column. To obtain the large values of β , we
chose the RF-heating in which the plasma was heated by
fast magneto-sonic (FMS) wave using nitrogen as
working gas, at small magnetic field induction of
B0 ≈ 0.04 Т and at anode voltages of lamps of two RF-
generators U(G1) = 5…7.5 kV and U(G2) = 5…6.5 kV.
The value of β was determined based on
measurements of magnetic diagnostics sensors
(diamagnetic loop and saddle coil) [6]. The variation of
the toroidal magnetic flux measured by the diamagnetic
loop in a “current less” plasma can be expressed:
P
B
adP
B
a
0
22
00
2 48 πρρπ =−=∆ Φ ∫ . (5)
The variation of the poloidal magnetic flux measured
by the saddle coil, looks like
ρρ
ι
ρπ dP
B
A
a
2
0
'
0
)(4
∫−=∆ Ψ , (6)
where A – coefficient, which is connected with
geometrical size of the test coil.
From (5) one can see, that value of average gas-kinetic
plasma pressure P can be easily determined with
accuracy of the size of plasma column. The correlation
between variation of the poloidal magnetic flux measured
by the saddle coil and plasma pressure is more
complicated. However, in case of homogeneous
distribution of the rotational transformation angle over the
cross-section of the plasma column and when we set a
distribution of the plasma pressure in the form of
−=
m
a
PP ρ10 , the expression, which describes the
variation of the poloidal magnetic flux, can be written as
2
0
4 aP
B
A
ι
π−=∆ Ψ . (7)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2009. № 1. 37
Series: Plasma Physics (15), p. 37-39.
It is obvious, that in case of homogeneous or weakly
unhomogeneous distribution of the rotational transformation
angle ι over the cross-section of the plasma column, the
simultaneous measurements of diamagnetic loop and saddle
coil allow us to determine the value of ι .
The radiance of neutral atoms of nitrogen is sensitive to
the profile of electron temperature and to the plasma density
on the boundary of the plasma column. Therefore, the cross-
section size of the plasma column was estimated from the
profile of the chord distribution of spectral line radiance of
neutral nitrogen NI (λ = 4109Ǻ), which was scanned over
the vertical plane. To achieve the sufficient accuracy of
measurements, the plasma radiation was obtained from
plasma volume with vertical size of less then 1 mm.
Figure 1 shows the time dependence of the average
chord density of electrons and the variation of the
poloidal magnetic flux ∆ψ measured by the saddle coil in
the causes, when one (G1, t≥7 ms) or two (G1+G2,
t ≥ 24 ms) RF-generators were switched on. It can be
seen, when the second RF-generator (G2, t ≥ 24 ms) was
switched on, that plasma density and energy content of
plasma, which is interconnected with flux variation ∆ψ,
were raised. The fronts of these signals are strongly
overextended because we used additional HF-filtrations to
reduce the high frequency inducings.
0 10 20 30 40 50
0
100
200
300
0 10 20 30 40 50
0
1
2
3
t, ms
GI GI+GII
Ψ
, a
.u
.
n e
, 1
012
c
m
-3
Fig.1. Time dependence of average chord density of
electrons and variation of poloidal magnetic flux ∆ψ
measured by saddle coil
Reliable diamagnetic measurements were obtained only
during the operation of RF-generator G1 (t=7…24ms),
because when RF-generator G2 was switched on, the
level of high frequency inducings were increased strongly
and, as a result the operation of electron integrators, was
distorted. On the basis of simultaneously measurements
by diamagnetic loop and saddle coil at maximal RF-
power of generator G1 and under the assumption of
uniform distribution of ι over the cross-section of the
plasma column, the value of ι ≈ 0.4 was obtained.
As it is clear from expressions (5) and (7), β can be
determined on the basis of magnetic measurements, if we
know the average radius a of the plasma column. To
determine a, at first, the chord distribution of spectral
line radiance of neutral nitrogen NI (λ = 4109Ǻ) was
obtained using optical measurements (see Fig. 2). Then,
we determined a from comparison of chord distribution of
spectral line radiance of neutral nitrogen and location of
calculated magnetic surfaces. Thus, during the operation
of RF-generator G1, the average radius of the plasma
column was equal to a = 9 cm. When generators G1 and
G2 were switched on simultaneously, a = 8 cm.
300 400 500 600 700
0
40
80
120
160
200 GI
GI+GII
mm
I N
I(4
10
9
A)
, a
.u
.
o
Fig.2. The chord distribution of spectral line radiance of
neutral nitrogen NI (λ = 4109Ǻ) over the vertical plane of
the plasma column
During the operation of RF-generator G1 at minimal RF
power, β ≈ 0.45% was obtained from diamagnetic
measurements (in this case a = 9 cm). If we assume, that
profile of ι is uniform and ι ≈ 0.4, then the value of
equivalent transverse magnetic field, which is connected
with the presence of plasma with β ≈ 0.45%, will be
equal to ιβ 2≅⊥ BB ≈ 0.56%. In the described
experiments at β = 0 the value of the transverse magnetic
field was equal to BB⊥ = 1.25%. Therefore, the total
equivalent transverse magnetic field at the presence of
plasma will be equal to BB⊥ = 1.25 + 0.56 = 1.81%.
The previous results of investigations of magnetic
configuration of U-3M [7] confirm our assumptions. As it
can be seen from these results (see Fig. 3), at
%81.1≈⊥ BB the distribution of rotational
transformation angle ι is approximately uniform over
cross-section of the plasma column and ι equals to about
0.4. When we used this profile of ι in calculations of
plasma pressure P on the basis of independent
measurements of diamagnetic loop and saddle coil, the
obtained values of P were close to each other. This
confirms validity of choice of uniform profile of ι = 0.4.
0 2 4 6 8 10 12 14
0
0.1
0.2
0.3
0.4
0.5
0.6
1.0%
1.5%
1.82%
2.0%
ι 3.5%
r, cm
_
Fig.3. The calculated radial profiles of the rotational
transformation angle ι at various BB⊥ : 1%, 1.5%,
1.82% [7], 2.0%, 3.5% [8]
Fig. 4 shows the dependences of the average radius a
of the last magnetic surface on the value of BB⊥ , which
were obtained during investigations of magnetic
configuration of U-3M (dotted line) and from numeric
calculations (solid line). It can be seen, that a = 9 cm
obtained from optical measurements at β ≈ 0.45 is some
less, than one at BB⊥ =1.81 % in both causes in Fig. 4.
38
-2 -1 0 1 2
5
7
9
11
13
15
B⊥ /B0, %
r, cm
_
Fig.4. The calculated (solid line) [7] and measured
(dotted line) average radius a of the last magnetic surface
as a function of BB⊥
It can be seen from Fig. 3 that the rotational transformation
angle of ι ≈ 0.60 is maximal near magnetic axis at
%5.3≅⊥ BB and than ι weakly drops towards the edge of
the confinement region. It is obvious, that the value of ι must
be approximately in the range of 0.4<ι <0.6 at values of
transverse magnetic field of %5.31.81 << ⊥ BB , which
corresponds to our experimental conditions. If we assume that
uniform profile of ι , the maximal value of β of about
∼maxβ 1.3% at <ι > = 0.5 (1.11 << maxβ 1.625% at 0.4<ι
<0.6) can be obtained from (6) when a = 8 cm (generators G1
and G2 were switched on simultaneously). In this case the
value of total equivalent transverse magnetic field will lie in
the range of %28.3175.2 << ⊥ BB . According to tendency
of calculated curve in Fig. 4 (solid line) a < 6.5 cm at
%28.3175.2 << ⊥ BB . But the optical measurements give
a = 8 cm. Therefore, these results allow us to conclude that
disruption of magnetic configuration of U-3M at maximal
values of β , which have been achieved in our experiments,
occurs slowly than it results from calculated curve in Fig. 4.
In [7] the results of measurements of magnetic configuration
of U-3M also give values of a, which are higher, than the
calculated curve. They are close to values of a obtained from
optical measurements at maximal value of β .
The dependences of β on input power W are shown in
Fig. 5. In this figure we assumed that input power W is
proportional to square of anode voltage of generator lamp. It
can be seen that dependences of β are linear in all range of
input power W. This indicates that in our experiments the
limited value of β is not achieved.
0.5
1
1.5
W, arb. u.
0.2 0.4 0.6 0.8 1.0
G1=5-7.5 kV
G1=5-7.5 kV + G2=5-6.5 kV
β,
%_
Fig.5. The dependence of β on input power W
CONCLUSIONS
In this study, we have investigated the influence of plasma
on magnetic configuration of torsatron U-3M. During the
experiments the maximal value of β of about maxβ ∼ 1.3%
was obtained using nitrogen as working gas and at magnetic
field induction on axis of B0 ≈ 0.04 Т. It is shown, that the
limited value of β was not achieved. With β increasing
from 0 up to maximal value, which have been achieved in
experiments, the average radius a of the plasma column was
decreased from a = 12 cm up to a = 8 cm, respectively. The
presence of plasma in the device changes the rotational
transformation angle analogously to the action of uniform
transverse magnetic field created by compensating coils.
REFERENCES
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2. J.M. Greene, J.L. Johnson and K.E. Weimer // Plasma Phys.
1966, v. 8, p. 145.
3. M.I. Mihailov// Physics of Plasma. 1980, v. 6, p. 45.
4. A.I. Lysoivan, V.E. Moiseenko, V.V. Plyusnin et al // Fusion
Engineering and Design. 1995, v. 26, p. 185.
5. V.K. Pashnev, P.Ya. Burchenko, E.D. Volkov et al.
// Problems of Atomic Science and Technology. Series “Plasma
Physics” (14), 2008, N6, p. 28.
6. V.K. Pashnev, V.V. Nemov // Nuclear Fusion, v. 33, 1993,
p. 435.
7. G.G. Lesnyakov, E.D. Volkov, A.V. Georgievskij et al
//Nucl. Fusion. 1992, v. 32, p. 2157.
8. A.V. Georgievskij et al. Investigation of magnetic
configuration of modernized torsatron Uragan-3M // VANT (3).
Moscow, 1990.
Article received 10.10.08
ИЗУЧЕНИЕ ВОЗДЕЙСТВИЯ ПЛАЗМЫ КОНЕЧНОГО ДАВЛЕНИЯ
НА МАГНИТНУЮ КОНФИГУРАЦИЮ ТОРСАТРОНА У-3М
В.К. Пашнев, П.Я. Бурченко, А.Е. Кулага, А.В. Лозин, Ю.К. Миронов, А.А. Петрушеня, В.С. Романов, Д.А. Ситников,
Э.Л. Сороковой, С.А. Цыбенко, Н.В. Заманов
На торсатроне У-3М проведена серия экспериментов по созданию режима с высоким β (до 1.3%) с
использованием азота в качестве рабочего газа. Получена зависимость среднего β от вводимой мощности. Был
определён средний радиус плазмы в режимах с различным β. Оценка угла врщательного преобразования была
сделана с учетом наличия плазмы в установке.
ВИВЧЕННЯ ДІЇ ПЛАЗМИ КІНЦЕВОГО ТИСКУ НА МАГНІТНУ КОНФІГУРАЦІЮ ТОРСАТРОНА У-3М
В.К. Пашнєв, П.Я. Бурченко, А.Є. Кулага, О.В. Лозін, Ю.К. Міронов, А.А. Петрушеня, В.С. Романов, Д.А. Ситников,
Е.Л. Сороковий, С.А. Цибенко, Н.В. Заманов
На торсатроні У-3М проведено серію експериментів по створенню режиму з високим β (до 1.3%) з
використанням азоту в якості робочого газу. Отримано залежність середнього β від потужності, що вводиться.
Було визначено середній радіус плазми в режимах з різним β. Оцінка кута обертального перетворення була
зроблена з урахуванням наявності плазми в установці.
39
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