Magnetized dusty sheaths
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| Дата: | 2002 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Цитувати: | Magnetized dusty sheaths / Yu.I. Chutov, O.Yu. Kravchenko, S. Masuzaki, A. Sagara, R.D. Smirnov, Yu. Tomita // Вопросы атомной науки и техники. — 2002. — № 5. — С. 9-11. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-778172015-03-08T21:39:28Z Magnetized dusty sheaths Chutov, Yu. I. Kravchenko, O.Yu. Masuzaki, S. Sagara, A. Smirnov, R.D. Tomita, Yu. Magnetic confinement 2002 Article Magnetized dusty sheaths / Yu.I. Chutov, O.Yu. Kravchenko, S. Masuzaki, A. Sagara, R.D. Smirnov, Yu. Tomita // Вопросы атомной науки и техники. — 2002. — № 5. — С. 9-11. — Бібліогр.: 16 назв. — англ. 1562-6016 PACS: 52.40.Kh http://dspace.nbuv.gov.ua/handle/123456789/77817 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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English |
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Magnetic confinement Magnetic confinement |
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Magnetic confinement Magnetic confinement Chutov, Yu. I. Kravchenko, O.Yu. Masuzaki, S. Sagara, A. Smirnov, R.D. Tomita, Yu. Magnetized dusty sheaths Вопросы атомной науки и техники |
| format |
Article |
| author |
Chutov, Yu. I. Kravchenko, O.Yu. Masuzaki, S. Sagara, A. Smirnov, R.D. Tomita, Yu. |
| author_facet |
Chutov, Yu. I. Kravchenko, O.Yu. Masuzaki, S. Sagara, A. Smirnov, R.D. Tomita, Yu. |
| author_sort |
Chutov, Yu. I. |
| title |
Magnetized dusty sheaths |
| title_short |
Magnetized dusty sheaths |
| title_full |
Magnetized dusty sheaths |
| title_fullStr |
Magnetized dusty sheaths |
| title_full_unstemmed |
Magnetized dusty sheaths |
| title_sort |
magnetized dusty sheaths |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2002 |
| topic_facet |
Magnetic confinement |
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http://dspace.nbuv.gov.ua/handle/123456789/77817 |
| citation_txt |
Magnetized dusty sheaths / Yu.I. Chutov, O.Yu. Kravchenko, S. Masuzaki, A. Sagara, R.D. Smirnov, Yu. Tomita // Вопросы атомной науки и техники. — 2002. — № 5. — С. 9-11. — Бібліогр.: 16 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT chutovyui magnetizeddustysheaths AT kravchenkooyu magnetizeddustysheaths AT masuzakis magnetizeddustysheaths AT sagaraa magnetizeddustysheaths AT smirnovrd magnetizeddustysheaths AT tomitayu magnetizeddustysheaths |
| first_indexed |
2025-07-06T02:01:27Z |
| last_indexed |
2025-07-06T02:01:27Z |
| _version_ |
1836861135970631680 |
| fulltext |
MAGNETIZED DUSTY SHEATHS
Yu. I. Chutov, O.Yu. Kravchenko, S. Masuzaki*, A.Sagara*, R.D. Smirnov, Yu. Tomita*
Taras Shevchenko Kiev University, Kiev, Ukraine
*National Institute for Fusion Science, Toki, Japan
PACS: 52.40.Kh
INTRODUCTION
Magnetized sheaths exist at the material walls of fusion
devices (divertors, limiters, etc) and determine particle
and energy fluxes to the walls influencing the overall
operation of the fusion devices [1]. Investigations of the
sheaths are started long ago [2] and are prolonged
intensively now [3-5]. It was established recently that dust
particles can be created in fusion devices due to the
plasma-wall interaction [6]. Detail investigations of the
helical divertor operation and erosion/deposition at target
surfaces in LHD (Large Helical Device, NIFS, Japan)
shown that dust particles with size of 3-15 µm were
sampling in various regions of LHD [7]. It can be
expected a remarkable influence of the dust particles on
the magnetized sheaths of LHD due to a continuous
selective collection of background electrons and ions by
the dust particles. The collection can cause an essential
change of both electron and ion energy distribution
functions as well as an ion flux in sheaths so that spatial
distributions of plasma parameters in magnetized sheaths
can be essentially changed [5]. The aim of the work is the
computer simulation of magnetized dusty sheaths for
conditions close to the LHD edge plasma.
MODEL
Sheaths are investigated very often without a
consideration of presheaths due to essential differed space
and time scales of both regions. Of course, boundary
conditions at a sheath edge have to be formulated at the
investigations. However the Bohm’s boundary conditions
used in various works very often for sheaths in
collisionless plasmas are not self-consistent due to an
acceleration of ions in presheaths to the ion sound speed
from undisturbed plasma. Therefore in this work, it is
developed the relaxation model for magnetized sheaths
without special boundary conditions for the sheaths. The
model was used earlier for investigations of non-
magnetized dusty sheaths [8-10]. The model is based on a
study of a temporal evolution of one-dimensional slab
plasma, which include a sheath and a part of presheath.
It is assumed that the collisionless quasi-neutral plasma
is uniform initially and bounded at the left by an electrode
(wall). The plasma consists of electrons with density neo
and temperatures Teo as well as hydrogen ions with a
density nio and a temperature Tio as well as motionless
spherical neutral dust particles of given radius Rd. The
dust particles are distributed close to the electrode (wall)
according to a given distribution. The magnetic field B
with a given profile along the normal with the electrode is
applied to the plasma under the angle θ with the normal.
The plasma evolution starts after a start of a collection of
background electrons and ions by the electrode (wall) and
dust particles, which are charged due to the collection.
Scattering of electrons and ions by dust particles takes
place due to a large size of dust particles.
The PIC/MCC method (1D3V model) described earlier
[11] in detail for plasmas without dust particles was
developed then [8-10] for computer simulations of the
dusty plasma evolution. The method is developed in this
work for simulations of magnetized sheaths. The
simulation region size is chosen equal to 100-500 the
Debye length so that the region exceeds essentially a
sheath size. The electrode (wall) is chosen as the left
boundary of the simulation region whereas the right
boundary is located in a presheath where the plasma is
quasi-neutral during the plasma evolution. The continuous
exchange by superparticles takes place on the right
boundary of the simulation region that has to be taken into
account at the computer simulation. In this work, the
original model of the exchange was developed which
takes into account the self-consistent change of the
electric potential as well as electron and ion energy
distribution functions on the right boundary. The
electrode (wall) collects a "superparticle" if its center
reaches the electrode (wall) surface.
The Monte Carlo technique [11] is used to describe
interactions of electrons and ions with dust particles. The
interactions include Coulomb's scattering of electrons and
ions with dust particles, as well as the electron and ion
collection by dust particles. In addition to a usual
PIC/MCC scheme, the weighting procedure is used also
for the determination of a superparticle charge part, which
is interacting with neighbour dust particles. The cross-
sections of electron and ion collection by immobile dust
particles are taken according to the Orbit Motion Limited
(OML) theory [12]. The Coulomb cross-section for
electron and ion scattering by immobile dust particles is
taken from [13].
Simulations start with an initially uniform distribution
of electrons and ions and are prolonged usually up to a
moment when the rarefaction wave reached the right
boundary of the simulation region. At this moment, the
relative change of the self-consistent electric potential in
the sheath was not exceeding about 5 % during 5 ion
plasma periods.
A possibility to simulate the evolution of the temporal
evolution of one-dimensional slab plasma without dust
particles and/or the magnetic field is foreseen for a
comparison with the investigated case of magnetized
sheaths.
Problems of Atomic Science and Technology. 2002. № 5. Series: Plasma Physics (8). P. 9-11 9
RESULTS
Simulations of 1D magnetized dusty sheaths are
carried out for plasma parameters close to ones measured
in LHD (NIFS, Japan) divertor [14] and shown in Table
1. As can be seen in the table, the plasma with the
electron density ne ~ 1012 cm-3 and about equal electron
Te ~ 25 eV and ion Ti ~ 30 eV temperatures consist of dust
particles with radius Rd ~ 2.5–15 µm. The magnetic field
Bo ~ 1 T is directed on the divertor plate under angles θ ~
40 –64o with the normal to the plate surface. Chosen
simulation parameters are enclosed in brackets in the
Table 1.
Table 1
ne,
cm-3
Te ,
eV
Ti ,
eV
B,
T
θ,
degree
Rd,
µm
~1012
(1012)
~ 25
(25)
~ 30
(25)
1 40 –64
(45)
2.5–15
(~ 3)
Corresponding values of the electron Debye length LDe,
the electron rL and ion RL, gyroradius, and its ratios are
shown in Table 2. As can be seen in Table 2, the ion
gyroradius RL, exceeds essentially the electron Debye
length LDe
Table 2
LDe , cm rL , cm
(for e)
RL, cm
(for H+)
rL /LDe RL /LDe
3.7*10 -3 1.7*10-3 0.08 0.46 21.6
Unfortunately, the density of dust particles is not
known in the LHD divertor plasma (as well as in other
fusion devices) although a surface mass density of dust
collected from LHD was measured and consists of 0.1 –
0.2 g/m2 [14]. The surface density does not allow
estimating the density of dust particle in LHD, because
the collection of dust particles is not continues due to
charge of both dust particles and collection surfaces. In
order to study an influence of dust particles on
magnetized sheaths, the density of dust particles is chosen
equal to 104 cm-3 close to the divertor plate. The density
corresponds to the number of dust particles in a Debay
cube Nd = 1, at which an influence of dust particles on
non-magnetized sheaths is essential [15].
Typical results of computer simulations are shown in
Fig.1–3 where the spatial coordinate x is divided by the
initial Debye length λd = (kTe /4πnoe2)1/2 and the time t is
multiplied by the initial ion plasma frequency ωi0 = (4π
noe2/M)1/2. The figures consist of spatial-temporal
distributions of plasma parameters, which evolve due to a
collection of electrons and ions by the electrode (wall)
and dust particles. Some figures consists of spatial
distributions of the dust particle number Nd in a Debye
cube in order to mark out the dusty region and to make
clearer understanding spatial distributions of other
parameters. The results are shown at a condition that the
number Nd of dust particles in a Debye cube is constant at
x < xo = 16 and equal to Ndo = 1. The number Nd
decreases according to Nd = Ndo exp(-(x- xo)2 /w2 ) at xo <x
<x1 where w = 6λd. Dust particles absent at x > x1 = 28.
The profile of the magnetic field B is given by B = Bo
exp(-x2 / a2 ) where a = 100λd .
Obtained results show that disturbance of ion and
electron densities is formed close to the electrode (wall)
-4
-2
0 50 100
tω io
φ w/φ 0
-0.5
0.0
0.5
50 100
tω io
φ r/φ 0
φ r/φ 0
Fig.1. The evolution of boundary potentials.
Fig.2. Spatial distributions of the electric field E divided by
the characteristic potential E
o
= kT
e
/λ
D
.
-0.5
0.0
50 100
E/E0
Bo= 1 T, Ndo=0
Bo= 1 T, Ndo=1
x/λd
initially due to the ion collection. The disturbance transits
continuously in the undisturbed plasma so that the
disturbance wave propagates in the dusty region initially
and than penetrates into plasma without dust particles
converting into a rarefaction wave. The evolution of
boundary potentials divided by the characteristic potential
φo = kTe/e accompanied the wave transit is shown in Fig.
1. As can be seen in Fig. 1, the electrode (wall) potential
φw changes initially very quickly and the potential is
oscillating then. The potential φr on the right boundary is
oscillating also but it remarkable changes only after an
arrival of the rarefaction wave to the boundary.
Simulations show that a ratio of oscillation amplitude to a
mean boundary potential is growing with an increase of
the magnetic field and its angle with the normal to the
electrode (wall) surface.
Spatial distributions of the electric field E divided by
the characteristic electric field Eo = kTe/λD is shown in
Fig. 2 after an establishment of boundary potentials by
solid and dashed line for magnetized sheaths in cases with
and without dust particles, respectively. As can be seen in
Fig.2, dust particles decrease the electric field in the
sheath and create an additional electric field close to a
boundary of dust particles like to a sheath in an oblique
magnetic field investigated earlier [16]. As simulations
show, the increase of the magnetic field or its angle with
the normal to the electrode surface causes the decrease of
the electric field in the magnetized sheaths.
The established dust particle charge nd qd divided by
the initial ion charge no e is shown in Fig. 3 for conditions
of Fig. 2. As can be seen in Fig. 3, there is not an essential
difference between both cases.
CONCLUSION
The PIC/MC computer simulation of magnetized dusty
sheaths is carried out by using an evolution of one-
dimensional slab plasma for conditions close to the LHD
divertor plasma consisting of dust particles with size of 3-
15 mm. Obtained results show the existence of
oscillations of a self-consistent potential in magnetized
dusty sheaths including boundary potentials. The role of
the oscillations is growing at the increase of the magnetic
field and its angle with the normal to the electrode
surface. Dust particles weaken magnetized sheaths and
create additional sheaths close to a boundary of dust
particles. The magnetic field does not influence on the
dust particle charge.
ACKNOWLEDGMENT
One of the authors (Yu.I. Chutov) thanks the Heiwa-
Nakajima Foundation for a support of his stay at NIFS
where the paper was completed.
REFERENCES
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-0.5
0.0
50 100
Bo=0, Nd=1
Bo=1, Nd=1
x/λ d
ndqd/n0e
Fig.3.The established dust particle charge n
d
q
d
divided
by the initial ion charge n
o
e.
16. Yu. I. Chutov, O.Yu. Kravchenko, V.S. Yakovetsky
Sheaths with dust particles in an oblique magnetic
field // J. Plasma and Fusion Research. SERIES.
2000. V.3, p.558-561.
Taras Shevchenko Kiev University, Kiev, Ukraine
INTRODUCTION
MODEL
RESULTS
CONCLUSION
ACKNOWLEDGMENT
REFERENCES
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