Influence of the ion viscosity on the current sheet formation and plasma heating
This paper deals with the problem of the ion viscosity influence on the current sheet formation and plasma heating, in the experiments performed on “Current sheet” facility (Prokhorov General Physics Institute, Russian Academy of Sciences). On the basis of magnetohydrodynamic theory one can see that...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
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irk-123456789-1091132016-11-21T03:02:48Z Influence of the ion viscosity on the current sheet formation and plasma heating Kurov, A.A. Stepanov, K.N. Фундаментальная физика плазмы This paper deals with the problem of the ion viscosity influence on the current sheet formation and plasma heating, in the experiments performed on “Current sheet” facility (Prokhorov General Physics Institute, Russian Academy of Sciences). On the basis of magnetohydrodynamic theory one can see that pressure force and viscid tension force can bring considerable contribution to the formation and heating of the current sheet plasma. The estimations obtained show that the effect of the ion viscosity is comparable with other effects which were taken into account previously. Сделаны оценки влияния ионной вязкости на нагрев и формирование токового слоя в экспериментах, проведённых на установке “Токовый слой” (Институт общей физики им. Прохорова РАН). На основе магнитогидродинамической теории показано, что сила давления и сила вязких напряжений могут играть существенную роль в формировании и нагреве токового слоя. Полученные оценки показывают, что эффект ионной вязкости сравним с другими эффектами, которые учитывались ранее. Зроблено оцінки впливу іонної в’язкості на нагрів та формування струмового шару в експериментах, проведених на установці “Струмовий шар” (Інститут загальної фізики ім. Прохорова РАН). На основі магнітогідродинамічної теорії показано, що сила тиску та сила в’язких напружень можуть відігравати істотне значення у формуванні та нагріві струмового шару. Отримані оцінки показують, що ефект іонної в’язкості порівняний з іншими ефектами, які враховувалися раніше. 2012 Article Influence of the ion viscosity on the current sheet formation and plasma heating / A.A. Kurov, K.N. Stepanov // Вопросы атомной науки и техники. — 2012. — № 6. — С. 96-98. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 51.20.+d, 52.25.-b, 52.25.Xz, 52.30.Cv http://dspace.nbuv.gov.ua/handle/123456789/109113 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Фундаментальная физика плазмы Фундаментальная физика плазмы |
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Фундаментальная физика плазмы Фундаментальная физика плазмы Kurov, A.A. Stepanov, K.N. Influence of the ion viscosity on the current sheet formation and plasma heating Вопросы атомной науки и техники |
| description |
This paper deals with the problem of the ion viscosity influence on the current sheet formation and plasma heating, in the experiments performed on “Current sheet” facility (Prokhorov General Physics Institute, Russian Academy of Sciences). On the basis of magnetohydrodynamic theory one can see that pressure force and viscid tension force can bring considerable contribution to the formation and heating of the current sheet plasma. The estimations obtained show that the effect of the ion viscosity is comparable with other effects which were taken into account previously. |
| format |
Article |
| author |
Kurov, A.A. Stepanov, K.N. |
| author_facet |
Kurov, A.A. Stepanov, K.N. |
| author_sort |
Kurov, A.A. |
| title |
Influence of the ion viscosity on the current sheet formation and plasma heating |
| title_short |
Influence of the ion viscosity on the current sheet formation and plasma heating |
| title_full |
Influence of the ion viscosity on the current sheet formation and plasma heating |
| title_fullStr |
Influence of the ion viscosity on the current sheet formation and plasma heating |
| title_full_unstemmed |
Influence of the ion viscosity on the current sheet formation and plasma heating |
| title_sort |
influence of the ion viscosity on the current sheet formation and plasma heating |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2012 |
| topic_facet |
Фундаментальная физика плазмы |
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http://dspace.nbuv.gov.ua/handle/123456789/109113 |
| citation_txt |
Influence of the ion viscosity on the current sheet formation and plasma heating / A.A. Kurov, K.N. Stepanov // Вопросы атомной науки и техники. — 2012. — № 6. — С. 96-98. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-07T22:35:10Z |
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2025-07-07T22:35:10Z |
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1837029351997046784 |
| fulltext |
96 ISSN 1562-6016. ВАНТ. 2012. №6(82)
INFLUENCE OF THE ION VISCOSITY
ON THE CURRENT SHEET FORMATION AND PLASMA HEATING
A.A. Kurov, K.N. Stepanov
National Science Center «Kharkov Institute of Physics and Technology»,
Kharkov, Ukraine
This paper deals with the problem of the ion viscosity influence on the current sheet formation and plasma heat-
ing, in the experiments performed on “Current sheet” facility (Prokhorov General Physics Institute, Russian Acad-
emy of Sciences). On the basis of magnetohydrodynamic theory one can see that pressure force and viscid tension
force can bring considerable contribution to the formation and heating of the current sheet plasma. The estimations
obtained show that the effect of the ion viscosity is comparable with other effects which were taken into account
previously.
PACS: 51.20.+d, 52.25.-b, 52.25.Xz, 52.30.Cv
INTRODUCTION
The experimental investigation of phenomenons in
two-dimensional current sheet (Fig. 1), which was gen-
erated by means of fast magnetoacoustic waves in the
zero line zone, were carried out in Prokhorov General
Physics Institute, Russian Academy of Sciences [1-4].
Fig. 1. Cross section of the “Current Sheet” device [1]:
1 – vacuum chamber; 2 – conductors to produce quad-
rupole magnetic field with the null line which is com-
bined with the vacuum chamber axis (Bx0=hy, By0=hx,
Bz0=0); 3 – current sheet (2Δy~0.6 cm, 2Δx~6…7 cm);
arrows at layer's surface show position and orientation
of the magnetic probes; 4 – the central area where
plasma radiation is registered
The alternating electrical current in plasma ( )tJ z
was directed along the zero line of the magnetic field. It
was driven by activating pulse voltage between two
electrodes (Fig. 2). These electrodes were inserted in
plasma from the sides of the chamber end faces
( ) ( ) t
0z etJ=tJ δω −sin .
Fig. 2 Alternating electrical current in plasma from
Ref. [1]
The start phase of current sheet formation
(Δt~1 mcs) is considered. In this phase the temperature
of Ar+ ions comes up to 80 eV (Fig. 3) and plasma den-
sity increases from initial 1014…1015 to 1016 cm-3 [1].
Fig. 3 Measured temperature of ions Ar+ (9)
and C++ (10) from Ref. [1]
The magnetic field component, which is tangential
to sheet's surface, shows considerable increasing in the
interval t=0.5…1.0 mcs. When x=0 and y=0.6 cm,
Bx=5 kG and Bx/Bx0~3.6; going away from zero line, the
Bx-component shows the decreasing. At first it dimin-
ishes smoothly to 3 kG by x=2 cm and then much more
sharply. There is simultaneous decreasing of perpen-
dicular, relative to sheet, By-component relatively its
initial value of By0 [1].
AN ANALYSIS OF VISCOSITY
INFLUENCE ON THE CURRENT SHEET
FORMATION AND HEATING
The evaluations for a region near the zero line are
carried out at Δt~1 mcs, Bx~5 kG, Ti~80 eV, Te~10 eV,
n~1016 cm-3.
The estimation of Ampere force value which is re-
sponsible for plasma acceleration, allows to establish
the velocity of Y-motion
,cmdyn
BB
c
Bj
=f 3xxxz
y /10~
y24
~ 6
Δπ
t, mcs
Jz, kA
Ti, eV
t, mcs
ISSN 1562-6016. ВАНТ. 2012. №6(82) 97
./101.6~~ 6 scm
nm
tf
v
ii
y
y ⋅
Δ
The force due to pressure gradient and Ampere force
have the same order-of-magnitude
./102.1~
y2
~ 6 3ii
pressurey cmdyn
Tn
y
p=f ⋅
Δ∂
∂
−
The estimation of the viscosity force was obtained
taking into account a significant distinction between
sheet's thickness and its width Δy/Δx~1/10
y
f yy
viscy ∂
∂
−≈
π
,
where tensor of viscid tension, which takes into account
the effects of finite Larmor radius is equal [5]:
,W+W+WWW= yy
i
yy
i
yy
i
yy
i
yy
i
yy 4433221100 ηηηηηπ −−−
and values of η depend on parameter ξ=ωciτi~1.3, where
ωci~1.2·106 s-1, τi~1.1·10-6 s:
iii
i Tn= τη 0.960 ,
2.3316.1216
2.235/24
24
2
1 ++
+Tn= iii
i
ξξ
ξτη .
The terms with W2yy, W3yy, W4yy are negligible since By
and Bz components are small as compared with tangen-
tial to layer surface component Bx,
,
v
3
1~v3
v3
vv
3
v
)13(
v
)13(
3
1W
y
y222
0
yy
hh
x
hh
xy
hh
y
h
x
hh
z
zy
z
zx
yx
yx
y
x
xyyy
∂
∂
⎥
⎦
⎤
∂
∂
+
+
∂
∂
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂
+
∂
∂
+
⎢
⎣
⎡
+
∂
∂
−+
∂
∂
−⎟
⎠
⎞
⎜
⎝
⎛ −≈
,
v
~v)1(v)1(
vv)1(
v
)1(v)(W
y22
2
y22222
1
yy
hhh
x
hhh
xy
hhh
y
h
x
hhh
z
yzy
z
yzx
yx
yyx
y
x
zyxyy
∂
∂
∂
∂
−−
∂
∂
++
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂
+
∂
∂
−−
−
∂
∂
−+
∂
∂
−≈
where BBh /
rr
= , 1~xh , 1<<yh , 1<<zh .
The adopted assumptions allow us to get an estima-
tion for the tensor of viscid tension and viscosity force
at ξ~1.3
y
v
++
+)(+Tn= y
iiiyy ∂
∂
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
2.3316.1216
2.235/24
3
0.96
24
2
ξξ
ξτπ ,
( )
./103~
y2
0.45
~
~0.45
6
2
3yiii
y
iiiviscy
cmdyn
vTn
y
v
Tn
y
=f
⋅
Δ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂
∂
∂
τ
τ
An evaluation of ions heating velocity was obtained
by means of entropy production [5] dQ / dt = Ti dSi / dt
( )
./101.3~
y2
0.12
~
~
92
1
12
2
2
1
0
2
serg
vTn
i+
y
v
=
dt
dQ
yiii
i
yvisc
⋅
Δ
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂
τ
η
η
Thereby an estimation of heating time was obtained
and this value coincides with measured one by the order
of magnitude
s6
viscosity 101.5~ −⋅τ .
Both, the ions mean free path and Larmor radius
have the same order of magnitude. Also, characteristic
distance 2Δy of plasma parameters change has this or-
der of value.
cmv=l Tiipath free 0.15~τ ,
/ ~1Li Ti ci= v cmρ ω ,
6/ 1.4 10 /Ti i iv = T m cm s≈ ⋅ .
CONCLUSIONS
The research of ion viscosity influence on the forma-
tion and heating of current sheet in a X-line magnetic
configuration in terms of equations of multicomponent
magnetic hydrodynamics was carried out. An analysis
of the magnetic fields data which is received on CS-2D
device, allows to reveal that besides Ampere force,
which takes part in the current sheet formation and
plasma acceleration, essential role can take force of
plasma pressure and viscid stress force. These two
forces become equal to Ampere force by order of mag-
nitude after a lapse of time.
Such estimations show that viscid friction force is
responsible for the heating of plasma ion component
(Ar+ ions) and heating time of these ions has order of
magnitude of measured heating time.
The calculated time of ion-to-ion collisions coin-
cides by order of magnitude with typical time of the
sheet macroscopic parameters changing. Mean free
path, Larmor radius of the ions and typical distance
have the same order, when such macroscopic sheet pa-
rameters like density, temperature, magnetic field com-
ponent and current density across the magnetic field
change their values. In this case the magnetohydrody-
namic description of current sheet dynamics can not be
used and carried out estimations is valid only by order
of magnitude and point on considerable role of the dis-
sipative processes of the viscosity upon the formation of
a current sheet.
98 ISSN 1562-6016. ВАНТ. 2012. №6(82)
REFERENCES
1. S.Yu. Bogdanov, G.V. Dreiden, N.P. Kyrie,
I.I. Komissarova, V.S. Markov, G.V. Ostrovskaya,
Yu.I. Ostrovskiy, V.N. Phylippov, A.G. Frank,
A.Z. Khodzhaev, and E.N. Shedova // Fizika Plazmy.
1992, v. 18, p. 1269 (in Russian).
2. G.S. Voronov, N.P. Kyrie, V.S. Markov,
G.V. Ostrovskaya, A.G. Frank. Spectroscopic meas-
urements of the electron and ion temperatures and effec-
tive ion charge in current sheets formed in two- and
three-dimensional magnetic configurations // Plasma
Physics Reports. 2008, v. 34, №12, p. 999-1015.
3. A.G. Frank, S.N. Satunin. Dynamics of the structure
of electric currents and electrodynamic forces in current
sheets // Plasma Physics Reports. 2011, v. 37, №10,
p. 829-847.
4. Anna G. Frank, Sergey G. Bugrov, and Vladimir S.
Markov. Hall currents in a current sheet: Structure and
dynamics // Phys. Plasmas. 2008, v. 15, p. 092102.
5. S.I. Braginskij. Voprosy teorii plazmy / ed.
M.A. Leontovich. Moscow: “Gosatomizdat”, 1963, v. 1,
p. 183-272 (in Russian).
Article received 19.09.12
ВЛИЯНИЕ ИОННОЙ ВЯЗКОСТИ НА ФОРМИРОВАНИЕ И НАГРЕВ ТОКОВОГО СЛОЯ
А.А. Куров, К.Н. Степанов
Сделаны оценки влияния ионной вязкости на нагрев и формирование токового слоя в экспериментах,
проведённых на установке “Токовый слой” (Институт общей физики им. Прохорова РАН). На основе магни-
тогидродинамической теории показано, что сила давления и сила вязких напряжений могут играть сущест-
венную роль в формировании и нагреве токового слоя. Полученные оценки показывают, что эффект ионной
вязкости сравним с другими эффектами, которые учитывались ранее.
ВПЛИВ ІОННОЇ В’ЯЗКОСТІ НА ФОРМУВАННЯ ТА НАГРІВ СТРУМОВОГО ШАРУ
О.О. Куров, К.М. Степанов
Зроблено оцінки впливу іонної в’язкості на нагрів та формування струмового шару в експериментах,
проведених на установці “Струмовий шар” (Інститут загальної фізики ім. Прохорова РАН). На основі магні-
тогідродинамічної теорії показано, що сила тиску та сила в’язких напружень можуть відігравати істотне зна-
чення у формуванні та нагріві струмового шару. Отримані оцінки показують, що ефект іонної в’язкості по-
рівняний з іншими ефектами, які враховувалися раніше.
|