Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap
In the work using Rogowski loop, measurements of the diamagnetic current, generating in the plasma volume of the “Trimyx-3M” Galatea multipole magnetic trap under its filling by plasmoids have been carried out. These measurements are confirmed by signals from diamagnetic probes. The mean value of...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2011 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2011
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap / A.M. Bishaev, A.I. Bugrova, M.V. Kozintseva, A.S. Lipatov, V.V. Savelyev, A.S. Sigov, I.A. Tarelkin, V.A. Terekhov, A.V. Desyatskov // Вопросы атомной науки и техники. — 2011. — № 1. — С. 20-22. — Бібліогр.: 7 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859914101010989056 |
|---|---|
| author | Bishaev, A.M. Bugrova, A.I. Kozintseva, M.V. Lipatov, A.S. Savelyev, V.V. Sigov, A.S. Tarelkin, I.A. Terekhov, V.A. Desyatskov, A.V. |
| author_facet | Bishaev, A.M. Bugrova, A.I. Kozintseva, M.V. Lipatov, A.S. Savelyev, V.V. Sigov, A.S. Tarelkin, I.A. Terekhov, V.A. Desyatskov, A.V. |
| citation_txt | Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap / A.M. Bishaev, A.I. Bugrova, M.V. Kozintseva, A.S. Lipatov, V.V. Savelyev, A.S. Sigov, I.A. Tarelkin, V.A. Terekhov, A.V. Desyatskov // Вопросы атомной науки и техники. — 2011. — № 1. — С. 20-22. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | In the work using Rogowski loop, measurements of the diamagnetic current, generating in the plasma volume of the
“Trimyx-3M” Galatea multipole magnetic trap under its filling by plasmoids have been carried out. These
measurements are confirmed by signals from diamagnetic probes. The mean value of the energy in plasma volume in
the process of the trap filling by plasma and during plasma decay have been determined by the magnitude of
diamagnetic current. These measurements are carried out simultaneously with the measurement of the time dependence
of mean plasma density by microwave interferometer.
За допомогою поясу Роговського здійснено виміри діамагнітного струму, що виникає в плазмовому об’ємі мультипольної магнітної пастки-Галатеї "Трімікс-3М" при наповненні її плазмовими згустками. Ці виміри підтверджені сигналами з діамагнітних зондів. За величиною діамагнітного струму визначалася величина енергії в плазмовому об’ємі і її зміна в процесі заповнення пастки плазмою і її розпаду. Виміри проведено одночасно з вимірами за допомогою СВЧ-інтерферометра часової залежності середньої концентрації плазми.
С помощью пояса Роговского произведены измерения диамагнитного тока, возникающего в плазменном объеме мультипольной магнитной ловушки-Галатеи «Тримикс-3М» при наполнении ее плазменными сгустками. Эти измерения подтверждены сигналами с диамагнитных зондов. По величине диамагнитного тока определялась величина энергии в плазменном объеме и ее изменение в процессе заполнения ловушки плазмой и её распада. Измерения проведены одновременно с измерением с помощью СВЧ-интерферометра временной зависимости средней концентрации плазмы.
|
| first_indexed | 2025-12-07T16:04:12Z |
| format | Article |
| fulltext |
20 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2011. 1.
Series: Plasma Physics (17), p. 20-22.
INVESTIGATION OF ENERGY AND MASS BALANCE IN “TRIMYX-3M”
GALATEA MULTIPOLE MAGNETIC TRAP
A.M. Bishaev1, A.I. Bugrova1, M.V. Kozintseva1, A.S. Lipatov1, V.V. Savelyev2, A.S. Sigov1,
I.A. Tarelkin1, V.A. Terekhov1, A.V. Desyatskov1
1Moscow Institute of Radio Engineering, Electronics and Automation (Technical University),
Moscow, Russia;
2 Keldysh Institute for Applied Mathematics RAS, Moscow, Russia
E-mail: bishaev@mirea.ru, ssvvv@rambler.ru
In the work using Rogowski loop, measurements of the diamagnetic current, generating in the plasma volume of the
“Trimyx-3M” Galatea multipole magnetic trap under its filling by plasmoids have been carried out. These
measurements are confirmed by signals from diamagnetic probes. The mean value of the energy in plasma volume in
the process of the trap filling by plasma and during plasma decay have been determined by the magnitude of
diamagnetic current. These measurements are carried out simultaneously with the measurement of the time dependence
of mean plasma density by microwave interferometer.
PACS: 52.55.–s, 52.55.He
1. INTRODUCTION
Energy confinement time and particles confinement
time in magnetic plasma traps are determined by
processes of leaving of particles (of working gas mass)
and energy from plasma volume of a trap. In a general
view, following [1] a balance of mass and energy can be
written in the form:
−
=
dt
dnI
n
pτ ;
−
=
dt
dWP
W
Eτ , (1)
where: n is a average concentration of ions in plasma, W
is total energy in plasma, I is speed of ionization, is
power incoming into plasma, τ , τ are particles and
energy confinement time in plasma, accordingly. The
presented dependences (1) show that for τ and τ
determination it is necessary to measure not only the rate
of change, but also value of concentration and energy in
plasma. If the total energy and the volume V occupied by
plasma are known, it is possible to determinate medium
pressure: p = 2W/3V = nkT, where: k – Boltzmann
constant, – average temperature in plasma. Hence is
proportional to W. On the other hand, as it follows from
the equation of magneto-hydrodynamics equilibrium
(balance of magnetic and plasma pressure) [2], is
proportional to the electric current in plasma volume. The
measurement of the toroidal magnetic flux allows to
determine the pressure in tokamaks [3] and stellarators
[4]. The magnetic flux is measuring by means of magnetic
coil [5]. The confining magnetic field is only poloidal in
magnetic plasma traps – Galatea [6] unlike tokamaks. The
toroidal current ID generating in plasma at the equilibrium
state, is caused only by plasma diamagnetism and is
proportional to average pressure. The results of
measurement of a diamagnetic current value in
multipole magnetic trap - Trimyx-3M [7] are presented in
the given work. The values of W, p have been determined
by ID. The value of τ has been determined by the
dependence of ID from time. The concentration of plasma
was measured by means of the microwave interferometer.
2. EXPERIMENT
Energy balance and mass measurement in multipole
traps and particularly in Trimyx-3M trap, is based on
following assumptions: a) p = K ID (average pressure is
proportional to the value of diamagnetic current); b) W =
3/2 (nkTV)= 3/2( ⋅V) (the relationship between plasma
energy, its concentration n, temperature k and volume
V); c) M=nmV (plasma mass is proportional to the
number of particles with mass m in plasma). The pressure
p can be determined from the next treatment. Plasma
volume V in Trimyx-3M trap has torus form of complex
cross-section with Z as the axis (as all other Galatea
traps) (Fig. 1). The outer boundary of the torus has the
form of one of the closed magnetic surface γ [7].
Fig. 1. Magnetic force lines 1 and cross-section of
plasma volume γ for Trimyx-3M trap. Arrangement of
Rogowski loop 2, magnetic probes 4, 5 and
interferometer antennas 3
If we assume that all diamagnetic current runs along
plasma boundary surface with constant current density,
then Ampere force acting on plasma surface (FA) is equal
to: FA = ID/L∫B(l)2πr(l)dl=2πID<rB> (integration along
force line from 0 to L). Then:
3
1
2
5
4
mailto:bishaev@mirea.ru
mailto:ssvvv@rambler.ru
21
V
WIK
Lr
rBI
S
Fp D
DA
3
2
=⋅=
><
><
==
γ
, (2)
where is magnetic field induction, < > - average value.
Coefficient K for the trap barrier magnetic field 0,1 T is
0,114 Pa/A. Plasma volume V in the trap measured by
electric probes [7] is 0,09 m3. The equation (2) allows to
calculate the average pressure and energy in plasma using
known value of ID. In this work the value of current ID was
measured by Rogowski loop (RL). The plasma density
was measured by microwave interferometer with λ=8 mm.
RL was installed so as trap coils do not cross loop contour
area (see Fig. 1). Therefore signal from the RL is
proportional to the time derivative from ID. Main trap coils
currents do not generate electromotive force in RL.
Diamagnetic effect generating in Trimix-3M trap was also
measured by magnetic coils of diamagnetic probes
(DMP). The arrangement of DMP and interferometer
antennas is shown in Fig. 1. As it is seen from Fig. 1
diamagnetic probes don’t cross plasma volume, unlike
RL. The signal from these probes is proportional to the
time derivative of ID and current in trap main coils.
The trap filling by plasma has been carried out by
plasmoids generated by plasma gun [7]. Plasmoid, having
passed through the outer magnetic barrier into zero
magnetic field region, fills the trap. The dependences ID
and n from time are determined by the process of energy
and mass leaving from the trap. Oscillogram of signals
from RL and DMP are represented in Fig. 2. These signals
integrated on time are represented in Fig. 3. The start of
signals in Figs. 2 and 3 corresponds to the moment of
plasma gun firing.
Fig. 2. Oscillogram of signals from RL and DMP
Fig. 3. Signals from RL and DMP integrated on time
These data are evidance of the diamagnetic current is
generated in plasma. Ampere force, directed into the
plasma volume, arises under the interaction of this current
with the magnetic field of the trap. Changing of the
direction of the trap magnetic field to the opposite one has
leaded to the change of the diamagnetic current direction.
It is seen from Fig. 3 that RL and DMP signals change
identically because of both of them are proportional to the
change of ID in time. The dependences (t) and W(t) have
been determined using data from Fig. 3 for RL and
equation (2). The temperature has been determined by the
concentration and pressure values. Ionization speed I has
been calculated in assumption of the Maxwell
distribution.
The measurement of dependences of ID(t) for different
values of magnetic field barrier at the Trimyx-3M trap
has been carried out in this work. The results of these
measurements are shown in Fig. 4.
Fig. 4. Averaged dependences of diamagnetic current for
different values of magnetic field barrier of Trimyx-3M
trap
Dependences are obtained by RL signals averaging for
5 – 10 shots of plasma gun under the same magnetic
field. The obtained dependences show the following: the
increase of current ID starts at 35 µs after voltage feeding
onto plasma gun. During the next 35…40 µs ID increases.
Then ID begins to decrease. This behavior of ID shows
that the process of plasma trap filling is finished at
70…80 µs. Since 300th µs ID became too insignificant for
measurement carrying out. The energy confinement time
has been determined by the rate of the decrease of the
diamagnetic current. For the given trap the value of P is
equal zero in formula (1). Values of plasma pressure in
the trap for the different barrier values of magnetic field
at 77th µs and at 202nd µs have been calculated by data of
Fig. 4 and equation (2). This dependence is shown in
Fig. 5.
0
2
4
6
0 0.05 0.1 0.15
B,T
<P
>,
Pa
Fig. 5. Plasma pressure for different values of magnetic
field barrier of Trimix-3M trap: - 77µs, - 202µs
It is seen, that just after trap filling by plasma (77th µs)
pressure is approximately the same for all values of
magnetic field. This fact points out that parameters of
plasmoid having penetrated through the barrier do not
depend from magnetic field. The dependence ) at
202nd µs shows the improvement of energy confinement
under the increase of magnetic field value. This
conclusion is confirmed by results of calculation of τ
and τ , which are shown in Fig. 6. The time τ has been
determined by equation (1) and by the dependence n(t)
measured by interferometer. The estimation of value kT
by simultaneous measurement of and n gives value of
15...25 eV.
22
0
50
100
150
200
250
300
350
0 0.05 0.1 0.15
B,
τE
an
d
τp
, µ
s
Tp
TE
Fig. 6. Dependence of τ and τ from barrier value of
magnetic field of Trimix-3M trap
CONCLUSIONS
The carried out researches have shown:
1. It is possible to measure value of the total diamagnetic
current generating in plasma volume in Galatea multipole
magnetic traps with the help of a Rogowski loop.
2. Simultaneous measurement of value of a diamagnetic
current and average concentration of plasma allows to
determine the energy and mass balance in a trap and also
plasma temperature.
ACKNOWLEDGEMENTS
The work has been carried out in the frames of
realization of FPP “Research and research-educational
personnel of innovational Russia” for 2009-2013 on the
state contract #P957.
REFERENCES
1. E.I. Kuznetsov, D.A. Sheglov. Methods of diagnostics
of high-temperature plasma. Moscow: “Atomizdat”,
1974, p.101-125 (in Russian).
2. M.V. Gavrikov, and V.V. Savelyev. Equilibrium
Configurations of Plasma in The Approximation of
Twu-fluid Magnetohydrodynamics with Ele tron
Inertia Taken intu Account // Journal of Mathematical
Sciences. 2009, v.163, N1, p. 1-47.
3. S.J. Lukjanov, N.G. Kowalsky. Hot plasma and
controlled thermonuclear fusion. Moscow: “MIFI”,
1999, p. 313-324 (in Russian).
4. V.K. Pashnev. Application of Magnetic Diagnostics to
Determine Basic Energy Characteristics of Plasma //
Problems of Atomic Science and Technology. Series
“Plasma Physics” (14). 2008, N 6, p. 225-226.
5. I.H. Hutchinson. Principles of plasma diagnostics /
Cambridge: “University Press”. 1990, p. 10 – 16.
6. A.I. Morozov, V.V. Savel’ev. On Galateas – magnetic
traps with plasma-embedded conductors//Physics-
Uspekhi. 1998, v.41, N11, p.1049-1089.
7. A.I. Morozov, A.I. Bugrova, et al. Injection of Plasma
into the Trimyx Galathea // Plasma Physics Reports.
2006, v. 32, N 3, p.171-182.
Article received 30.10.10
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| id | nasplib_isofts_kiev_ua-123456789-90610 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:04:12Z |
| publishDate | 2011 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Bishaev, A.M. Bugrova, A.I. Kozintseva, M.V. Lipatov, A.S. Savelyev, V.V. Sigov, A.S. Tarelkin, I.A. Terekhov, V.A. Desyatskov, A.V. 2015-12-28T20:19:54Z 2015-12-28T20:19:54Z 2011 Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap / A.M. Bishaev, A.I. Bugrova, M.V. Kozintseva, A.S. Lipatov, V.V. Savelyev, A.S. Sigov, I.A. Tarelkin, V.A. Terekhov, A.V. Desyatskov // Вопросы атомной науки и техники. — 2011. — № 1. — С. 20-22. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.55.–s, 52.55.He https://nasplib.isofts.kiev.ua/handle/123456789/90610 In the work using Rogowski loop, measurements of the diamagnetic current, generating in the plasma volume of the “Trimyx-3M” Galatea multipole magnetic trap under its filling by plasmoids have been carried out. These measurements are confirmed by signals from diamagnetic probes. The mean value of the energy in plasma volume in the process of the trap filling by plasma and during plasma decay have been determined by the magnitude of diamagnetic current. These measurements are carried out simultaneously with the measurement of the time dependence of mean plasma density by microwave interferometer. За допомогою поясу Роговського здійснено виміри діамагнітного струму, що виникає в плазмовому об’ємі мультипольної магнітної пастки-Галатеї "Трімікс-3М" при наповненні її плазмовими згустками. Ці виміри підтверджені сигналами з діамагнітних зондів. За величиною діамагнітного струму визначалася величина енергії в плазмовому об’ємі і її зміна в процесі заповнення пастки плазмою і її розпаду. Виміри проведено одночасно з вимірами за допомогою СВЧ-інтерферометра часової залежності середньої концентрації плазми. С помощью пояса Роговского произведены измерения диамагнитного тока, возникающего в плазменном объеме мультипольной магнитной ловушки-Галатеи «Тримикс-3М» при наполнении ее плазменными сгустками. Эти измерения подтверждены сигналами с диамагнитных зондов. По величине диамагнитного тока определялась величина энергии в плазменном объеме и ее изменение в процессе заполнения ловушки плазмой и её распада. Измерения проведены одновременно с измерением с помощью СВЧ-интерферометра временной зависимости средней концентрации плазмы. The work has been carried out in the frames of realization of FPP “Research and research-educational personnel of innovational Russia” for 2009-2013 on the state contract #P957. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Магнитное удержание Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap Дослідження балансу енергії і маси в мультипольній магнітній пастці-Галатеї "Трімікс-3М" Исследование баланса энергии и массы в мультипольной магнитной ловушке-Галатее «Тримикс-3М» Article published earlier |
| spellingShingle | Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap Bishaev, A.M. Bugrova, A.I. Kozintseva, M.V. Lipatov, A.S. Savelyev, V.V. Sigov, A.S. Tarelkin, I.A. Terekhov, V.A. Desyatskov, A.V. Магнитное удержание |
| title | Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap |
| title_alt | Дослідження балансу енергії і маси в мультипольній магнітній пастці-Галатеї "Трімікс-3М" Исследование баланса энергии и массы в мультипольной магнитной ловушке-Галатее «Тримикс-3М» |
| title_full | Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap |
| title_fullStr | Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap |
| title_full_unstemmed | Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap |
| title_short | Investigation of energy and mass balance “Trimyx-3M” Galatea multipole magnetic trap |
| title_sort | investigation of energy and mass balance “trimyx-3m” galatea multipole magnetic trap |
| topic | Магнитное удержание |
| topic_facet | Магнитное удержание |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/90610 |
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