Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М
At present paper the existence of longitudinal current in plasma and time dependence of plasma density in experiments on torsatron U-3M are explained from the point of neoclassical theory. The time evolution of longitudinal current in plasma is explained by excitation of bootstrap current within int...
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Pashnev, V.K. Sorokovoy, Ed.L. 2017-01-06T13:11:36Z 2017-01-06T13:11:36Z 2008 Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М / V.K. Pashnev, Ed.L. Sorokovoy // Вопросы атомной науки и техники. — 2008. — № 6. — С. 31-33. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.55.Dy, 52.55.Hc https://nasplib.isofts.kiev.ua/handle/123456789/110804 At present paper the existence of longitudinal current in plasma and time dependence of plasma density in experiments on torsatron U-3M are explained from the point of neoclassical theory. The time evolution of longitudinal current in plasma is explained by excitation of bootstrap current within internal areas of the plasma column and by appearance of reverse-current in the external areas of plasma. The observed rise of plasma density after RF-power cut-off is explained by influence of anomalous pinch-effect. This effect is caused by the electric field, appearing due to decrease of longitudinal current in plasma after the RF-power cut-off. Приведены экспериментальные данные, связанные с возбуждением продольного тока в режиме ВЧ-нагрева плазмы в торсатроне У-3М. На основании экспериментальных данных сделан вывод, что наблюдаемый продольный ток является бутстрэп-током. На основании расчетов показано, что банановая область, где может возбуждаться бутстрэп-ток, находится вблизи оси шнура, а расчетные величины бутстрэп-тока близки к экспериментально измеренным значениям. Объяснено временное поведение тока на стадии нарастания, а также возрастание плотности плазмы после выключения ВЧ-нагрева. Наведено експериментальні дані, які пов'язані із збудженням подовжнього струму в режимі ВЧ-нагріву плазми в торсатроні У-3М. На підставі експериментальних даних зроблено висновок, що спостережуваний подовжній струм є бутстреп-струмом. На підставі розрахунків показано, що бананова область, де може збуджуватися бутстреп-струм, знаходиться поблизу вісі шнура, а розрахункові величини бутстреп-струму близькі до експериментально виміряних значень. Пояснена тимчасова поведінка струму на стадії наростання, а також зростання щільності плазми після вимкнення ВЧ-нагріву. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М Проявлення неокласичних ефектів в поведінці плазми в торсатроні У-3М Проявление неоклассических эффектов в поведении плазмы в торсатроне У-3М Article published earlier |
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| title |
Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М |
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Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М Pashnev, V.K. Sorokovoy, Ed.L. Magnetic confinement |
| title_short |
Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М |
| title_full |
Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М |
| title_fullStr |
Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М |
| title_full_unstemmed |
Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М |
| title_sort |
appearance of neoclassical effects in plasma behavior in torsatron uragan-3м |
| author |
Pashnev, V.K. Sorokovoy, Ed.L. |
| author_facet |
Pashnev, V.K. Sorokovoy, Ed.L. |
| topic |
Magnetic confinement |
| topic_facet |
Magnetic confinement |
| publishDate |
2008 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Проявлення неокласичних ефектів в поведінці плазми в торсатроні У-3М Проявление неоклассических эффектов в поведении плазмы в торсатроне У-3М |
| description |
At present paper the existence of longitudinal current in plasma and time dependence of plasma density in experiments on torsatron U-3M are explained from the point of neoclassical theory. The time evolution of longitudinal current in plasma is explained by excitation of bootstrap current within internal areas of the plasma column and by appearance of reverse-current in the external areas of plasma. The observed rise of plasma density after RF-power cut-off is explained by influence of anomalous pinch-effect. This effect is caused by the electric field, appearing due to decrease of longitudinal current in plasma after the RF-power cut-off.
Приведены экспериментальные данные, связанные с возбуждением продольного тока в режиме ВЧ-нагрева плазмы в торсатроне У-3М. На основании экспериментальных данных сделан вывод, что наблюдаемый продольный ток является бутстрэп-током. На основании расчетов показано, что банановая область, где может возбуждаться бутстрэп-ток, находится вблизи оси шнура, а расчетные величины бутстрэп-тока близки к экспериментально измеренным значениям. Объяснено временное поведение тока на стадии нарастания, а также возрастание плотности плазмы после выключения ВЧ-нагрева.
Наведено експериментальні дані, які пов'язані із збудженням подовжнього струму в режимі ВЧ-нагріву плазми в торсатроні У-3М. На підставі експериментальних даних зроблено висновок, що спостережуваний подовжній струм є бутстреп-струмом. На підставі розрахунків показано, що бананова область, де може збуджуватися бутстреп-струм, знаходиться поблизу вісі шнура, а розрахункові величини бутстреп-струму близькі до експериментально виміряних значень. Пояснена тимчасова поведінка струму на стадії наростання, а також зростання щільності плазми після вимкнення ВЧ-нагріву.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110804 |
| citation_txt |
Appearance of neoclassical effects in plasma behavior in torsatron Uragan-3М / V.K. Pashnev, Ed.L. Sorokovoy // Вопросы атомной науки и техники. — 2008. — № 6. — С. 31-33. — Бібліогр.: 8 назв. — англ. |
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2025-11-24T11:37:42Z |
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2025-11-24T11:37:42Z |
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| fulltext |
APPEARANCE OF NEOCLASSICAL EFFECTS
IN PLASMA BEHAVIOR IN TORSATRON URAGAN-3M
V.K. Pashnev, Ed.L. Sorokovoy
Institute of Plasma Physics, National Science Center
“Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
At present paper the existence of longitudinal current in plasma and time dependence of plasma density in
experiments on torsatron U-3M are explained from the point of neoclassical theory. The time evolution of longitudinal
current in plasma is explained by excitation of bootstrap current within internal areas of the plasma column and by
appearance of reverse-current in the external areas of plasma. The observed rise of plasma density after RF-power cut-
off is explained by influence of anomalous pinch-effect. This effect is caused by the electric field, appearing due to
decrease of longitudinal current in plasma after the RF-power cut-off.
PACS: 52.55.Dy, 52.55.Hc
INTRODUCTION
Neoclassical theory of plasma transport in toroidal
magnetic traps based on record of particle traffic in
toroidal magnetic configuration binds parameters of trap
and macroscopic parameters of plasma with transport
factors of heat and particles. Effect of this theory is
prediction of longitudinal current generation by plasma
(bootstrap-current) [1,2] and abnormal pinch effect
occurrence [1,3]. Notwithstanding the fact that there is a
difference between transport factors in predictions of
theory and experiment reaching order of two, bootstrap-
current and abnormal pinch effect observed in
experiments are described quite precisely by the theory.
This fact points out that the processes which provide real
transport of particles and heat in experiments do not
influence the distortion of distribution function caused by
plasma particles movement.
Direct attempts to measure bootstrap-current have
been carried out only on stellarators (see example [4]). It
is explained by the fact that in stellarators in order to
create magnetic configuration there is no necessity in
flow of big longitudinal current on the background of
which it should be registered. Nevertheless, in stellarators
at bootstrap-current registration one should be certain that
this current is not created by RF or HF-wave fields that
provide plasma heating. Abnormal pinch effect can be
observed in toroidal traps only at existence of longitudinal
electric current. This effect is usually used to explain the
losses of plasma particles observed in experiments on
tokamaks.
Explanation of plasma behavior (existence of
longitudinal current and temporal density behavior) from
the point of view of neoclassical theory – existence of
bootstrap-current and abnormal pinch effect – is given in
this work. Besides, in this work, great attention is given to
explain the longitudinal current behavior on the initial,
dynamic stage of the charge.
RESULTS OF THE EXPERIMENT
AND THEIR DISCUSSION
Experiments have been carried out on torsatron U-3M
[5] in the mode of RF-heating at magnetic field B ≈
7.2 kG. Hydrogen was used as working gas. Temporal
behavior of longitudinal plasma current I and other
parameters of the discharge are given in the Fig. 1.
-1600
-1200
-800
-400
0
0
500
1000
t, ms
I,
A
I R
F,
a.
u.
0.1
0.2
0.3
0.4 nT/I, erg/(cm3*A)
0 10 20 30 40 50
0
1
2
3
n e
, 1
012
c
m
-3
Fig. 1. Temporal behavior of the discharge parameters:
IRF – current in antenna of RF-heating; I –longitudinal
plasma current; nT/I –energy-content plasma, measured
by diamagnetic loop, ratio to longitudinal current and
ne – average plasma density
As it is clear from the Fig. 1, the longitudinal plasma
current appears just after working gas breakdown and
after ~ 10 ms goes to the stationary level. Value of
energy-content plasma ratio to longitudinal current nT/I is
almost constant along the whole length of RF pulse.
From neoclassical theory, expression for density of
bootstrap-current excited on stationary stage looks as
follows:
nTrnT
rr
R
B
cjB ∝
∂
∂
≅ )(
2/1
ι . (1)
Dynamics of behavior of such current in discharge is
described by expression:
)(** tnTRIR
t
IL α=+
∂
∂ . (2)
Here L is inductance of plasma column, R* - its
resistance and α - operator that describes neoclassical
electromotive force. As it is seen from expression (2),
nT/I ratio can be constant only on condition when L = 0.
Evidently, total inductance of plasma column in not equal
to 0, therefore, we will consider that neoclassical
electromotive force appears only in limited area along
cross-section of plasma column in order to describe
plasma current behavior. Thus, at bootstrap-current
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6. 31
Series: Plasma Physics (14), p. 31-33.
excitation in the rest part of plasma column the current of
opposite sign can flow. If bootstrap-current flows in
internal areas of plasma column and the current of
opposite sign excites in external, then, we suppose that
nT(t)=nT0[1-exp(-t/ι*)], where ι*=L/R*, solution to
electro technical equation (2) looks in the following way:
I = I0[1-exp(-t/ι*)] (3)
and nT/I ratio = constant on initial dynamic stage of the
charge.
380
400
420
440
t, ms
nT
, e
rg
/c
m
3
-1360
-1320
-1280
-1240
I,
A
600
650
700
I R
F,
a.
u.
τ Ε = 2 ms
17 18 19 20 21 22 23 24 25 26 27
Fig. 2 Temporal behavior of IRF at activation of
additional power on quasi-stationary stage of the
discharge, longitudinal plasma current I and energy-
content plasma density nT
Addition of RF-power done on quasi-stationary stage
of the discharge, as it is seen from the Fig. 2, variously
influences on a temporal behavior of nT and I. It means
that on quasi-stationary stage the profile Te and ne differs
from initial stage. Reverse current, in this case, is not
excited, that is confirmed by fulfilling the condition
0
0
≅
∂
∂
→tt
I
. Solution of the equation (2) allows, in this
case, to determine ohmic resistance of plasma column [6]
0
0
2
2
*
I
t
IL
R
E
t
τ
→∂
∂
≅ . (4)
Z ≅ 2 – average charge value in the discharge has been
determined knowing the Te(r) profile distribution [7] and
conductivity.
-1
0
1
D
ν
ε h > ε t
ε h < ε t
ω Β ω t
( ε h/ε t)3/4ω Β ( ε h/ε t)3/2ω Β
Fig.3. Dependence of diffusion coefficient D from
collision rate ν for various ratio of toroidal εt=r/R and
helical εh ripple of magnetic field
According to neoclassical theory, the dependence of
diffusion coefficient D from collision rate ν is given in the
Fig. 3. Boundary value of collision rates ν=ωB=
2/3
R
r
R
VT
ι - boundary rate of “banana” area and ν=ωt=
R
VTι - boundary rate in the mode of “plateau”, where VT –
thermal velocity of plasma particles, t – angle of
rotational transformation and R – major plasma radius.
Fig. 4 shows spatial distribution of values of U-3M
magnetic field ripple due to helical harmonics εh and
toroidicity εt. It is clear that εt>εh is in the bigger part of
plasma column.
Fig. 5, based on the well-known distribution Te(r) [7],
n(r) [8] and assuming that Z = 2 along the whole cross-
section of the pinch, distribution of collision ratio ve is
given, and boundaries of banana ωB and super-banana
areas ωB(εh/εt)3/4 for electrons. It is clear that electronic
component of plasma in the range of 0.18<r/a<0.68 lies in
banana area by parameters. Accuracy of determination of
plasma parameters, and Z value mainly, does not allow to
state the possibility of plasma existence in super-banana
area. At the same time, the presence of bootstrap-current
itself indicates occurrence of considerable part of plasma
in banana area. Bootstrap-current can flow in the range of
0.18<r/a<0.68 that is pointed by vertical dotted line in
Figs. 4 and 5. The obtained data allows to calculate the
value of bootstrap-current that makes IB ≈ 2 kА. The
calculated value of bootstrap-current differs not very
much from the measured in the experiment I ≈ 1.6 kА.
0 0.2 0.4 0.6 0.8 1
0
0.04
0.08
0.12
0.16
0.2
r/a
ε h
ε t
ε t, ε h
Fig. 4. Distribution of toroidal εt and helical εh of
magnetic field ripples along the cross-section of plasma
column in torsatron U-3M
0 0.2 0.4 0.6 0.8 1
0.0E+000
4.0E+004
8.0E+004
1.2E+005
ν e
ω B
ω B(ε h/ε t)
3/4
r/a
ν , s-1
Fig. 5. Distribution of collision rate of ve electrons,
boundary particles of banana area ωB and super-banana
area ωB(εh/εt)3/4 along the cross-section of plasma column
If to pay attention to temporal behavior of density in the
discussed discharge (see Fig. 1) it is clear that after
switching off of RF-pulse the density increases. This
problem has caused surprise to researchers since 1985. The
assumption, confirmed by many experimental facts, that
RF-field shields inflow of working gas into confinement
area causing ionization of working gas outside the
confinement volume in the area of divertor magnetic field
lines, was stated in this work [7]. Apparently, that after RF-
pulse is switched off the additional flow of neutral
hydrogen gets to confinement area and, being ionized there,
leads to increase of density. Nevertheless, it is not the only
32
one explanation of phenomenon. If to examine carefully
the process after RF-pulse was switched off you can see
that increase of density starts with decrease of current and
finishes in the moment of its conversion into zero. It is
clearly seen in the Fig. 6.
45 50 55
0
1
2
3
0
400
800
1200
1600
t, ms
I, A
n e
, 1
012
c
m
-3
Fig. 6. Temporal behavior of average plasma density ne
and to longitudinal current I when RF-power
is switched off
Evidently, that electrical field will appear after RF-
field is switched off due to current decay
≈
∂
∂=
t
IL
R
E
π2
1 4*10-3 V/cm (5)
Under influence of this field for plasma which is in
“banana” area on collision rate (according to fig. 5 this
area 0.18<r/a<0.68) the abnormal pinch effect [1] should
appear and it will lead to drift of plasma inward with
velocity
≈=
B
R
r
Ecvdr
ι 103 cm/s (6)
Value of drift velocity is comparable to diffusion flow
which should lead to increase of density in the moment of
current decay. Fig. 7 shows dependence of maximal
increase value of plasma density Δne after RF-power is
switched off and normed on density value before
switching off of RF-power depending upon velocity of
current decay tI ∂∂ / for various meanings of power
supplied to RF-antenna (W ≈ 70−150 kW) and working
gas pressures (0,6*10-5−1*10-5 torr).
0 2 4 6
0
0.2
0.4
0.6
0.8
1
dI/dt * 10-5, A/sec
∆n
e/n
e
Fig. 7. Dependence of density increase value Δne/ne from
velocity of longitudinal current tI ∂∂ / after RF-power is
switched off
It is clear that increase of density linearly depends on
decay velocity of longitudinal current, i.e., from the value
of appearing electric field that determines velocity of
abnormal plasma pinching.
CONCLUSIONS
The work presents experimental data related to
longitudinal current excitation in RF-heating mode of
plasma in U-3M. The available experimental data allows
to consider the observed current to be a bootstrap-current.
Calculations based on available data of plasma parameters
showed that banana area, where bootstrap-current can be
excited, is near the column axis. Calculations of
bootstrap-current value are close to experimentally
measured meanings of current.
It is shown that temporal current behavior on the stage
of increase is similar to nT behavior which is explained by
excitation of bootstrap-current in internal areas of plasma
column and presence of reverse current in external areas
of plasma.
Increase of density when RF-heating is switched off
can be explained by appearance of abnormal pinch-effect
due to electric field that emerges at plasma current decay.
REFERENCES
1. A.A. Galeev, R.Z. Sagdeev. Voprosy teorii plazmy
(Problems of Plasma Theory)/ed by M.A. Leontovich.
Moscow: “Atomizdat”, 1973, v. 7, p.205 (in Russian).
2. R.J. Bickerton, J.W. Coтnor, J.B. Taylor// Nature Phys.
Science.1971, v. 229, p. 10.
3. A.A. Ware // Phys. Rev. Lett. 1970, v. 25, p. 15.
4. Yu.V. Gutarev, N.I. Nazarov, V.K. Pashnev, et al.
Observation of a bootstrap current in the Uragan-3
torsatron // JETP Lett. 1987, v. 46, p. 69.
5. A.I. Lysoivan, V.E. Moiseenko, V.V. Plyusnin, et
al// Fusion Engineering and Design. 1995, v. 26, p. 185.
6. 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. 225-227.
7. V.K. Pashnev, P.Ya. Burchenko, E.D. Volkov, et. al.
Energy confinement in the torsatron Uragan-3M during
the RF-heating mode // Problems of Atomic Science and
Technology. Series “Plasma Physics” (14). 2008, N 6,
p. 28-30.
8. V.L Berezhnyj, V.S. Voitsenya, M.P. Vasil'ev et
al // Fizika plazmy. 1990, v. 15, p. 523 (in Russian).
Article received 10.10.08
ПРОЯВЛЕНИЕ НЕОКЛАССИЧЕСКИХ ЭФФЕКТОВ В ПОВЕДЕНИИ ПЛАЗМЫ В ТОРСАТРОНЕ У-3М
В.К. Пашнев, Э.Л. Сороковой
Приведены экспериментальные данные, связанные с возбуждением продольного тока в режиме ВЧ-нагрева плазмы в
торсатроне У-3М. На основании экспериментальных данных сделан вывод, что наблюдаемый продольный ток является
бутстрэп-током. На основании расчетов показано, что банановая область, где может возбуждаться бутстрэп-ток, находится
вблизи оси шнура, а расчетные величины бутстрэп-тока близки к экспериментально измеренным значениям. Объяснено
временное поведение тока на стадии нарастания, а также возрастание плотности плазмы после выключения ВЧ-нагрева.
ПРОЯВЛЕННЯ НЕОКЛАСИЧНИХ ЕФЕКТІВ В ПОВЕДІНЦІ ПЛАЗМИ В ТОРСАТРОНІ У-3М
В.К. Пашнєв, Е.Л. Сороковий
Наведено експериментальні дані, які пов'язані із збудженням подовжнього струму в режимі ВЧ-нагріву плазми в торсатроні
У-3М. На підставі експериментальних даних зроблено висновок, що спостережуваний подовжній струм є бутстреп-струмом. На
підставі розрахунків показано, що бананова область, де може збуджуватися бутстреп-струм, знаходиться поблизу вісі шнура, а
розрахункові величини бутстреп-струму близькі до експериментально виміряних значень. Пояснена тимчасова поведінка струму
на стадії наростання, а також зростання щільності плазми після вимкнення ВЧ-нагріву.
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