Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping
The removal efficiency of the divertor X-point sweeping regimes is considered on the base of the numerical simulation of the tungsten ion motion in the gyroorbit approximation. The dependence of the loss particle fraction from the kinetic energy and initial position is studied. The results of the an...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2008 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
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| Cite this: | Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping / A.O. Moskvitin, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 6. — С. 16-18. — Бібліогр.: 6 назв. — англ. |
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| author | Moskvitin, A.O. Shishkin, A.A. |
| author_facet | Moskvitin, A.O. Shishkin, A.A. |
| citation_txt | Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping / A.O. Moskvitin, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 6. — С. 16-18. — Бібліогр.: 6 назв. — англ. |
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| description | The removal efficiency of the divertor X-point sweeping regimes is considered on the base of the numerical simulation of the tungsten ion motion in the gyroorbit approximation. The dependence of the loss particle fraction from the kinetic energy and initial position is studied. The results of the analysis show that the appropriate choice of the modulation law of the divertor current gives an opportunity to decrease heat load of the plasma facing components.
Ефективність різних режимів розгойдування Х-точки розглянуто на основі результатів моделювання руху іону вольфраму при врахуванні кінцевої величини радіуса Ларморівської орбіти. Вивчено залежність долі втрачених частинок від кінетичної енергії та початкового положення. Результати аналізу вказують на те, що при належному виборі закону модуляції струму в диверторних провідниках можливо зменшити теплове навантаження на матеріальну частину дивертора.
Эффективность различных режимов раскачивания Х-точки рассмотрена на основании результатов моделирования движения иона вольфрама при учёте конечного радиуса Ларморовcкой орбиты. Изучена зависимость доли потерянных частиц от кинетической энергии и начального положения. Результаты анализа показывают, что при правильном выборе закона модуляции тока в диверторных проводниках возможно уменьшить тепловую нагрузку на материальную часть дивертора.
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| first_indexed | 2025-11-29T11:55:19Z |
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SINGLE PARTICLE SIMULATION IN THE VICINITY OF SEPARATRIX
UNDER TOKAMAK X-POINT SWEEPING
A.O. Moskvitin1, A.A. Shishkin1,2
1 V.N. Karazin Kharkov National University, Svobody sq. 4, 61077, Kharkov, Ukraine,
E-mail: Anton.Moskvitin@gmail.com;
2National Science Center “Kharkov Institute of Physics and Technology”,
61108 Kharkov, Ukraine,
The removal efficiency of the divertor X-point sweeping regimes is considered on the base of the numerical
simulation of the tungsten ion motion in the gyroorbit approximation. The dependence of the loss particle fraction from
the kinetic energy and initial position is studied. The results of the analysis show that the appropriate choice of the
modulation law of the divertor current gives an opportunity to decrease heat load of the plasma facing components.
PACS: 52.25.Vy, 52.65.Cc, 52.55.Rk, 52.55.Dy
1. INTRODUCTION AND MOTIVATION
A lot of experimental investigations on tokamaks are
devoted to decreasing of the heat load on plasma facing
components in the divertor region and impurity transport
control at the plasma edge. The interest to this problem is
caused by attempts to model fusion reactor scenarios on
nowadays fusion devices [1,2].
It was shown on tokamak DIII-D that it is possible to
lower peak heat flux on the divertor plates by a factor 3
[3] using X-point sweeping. Besides that this technique is
intensively used at torsatrons for sweeping not only
X-points but the magnetic axis too [4,5].
The MHD consideration [6] of same method gives an
opportunity to analyze particle and energy flows in
plasma volume except the close vicinity of the separatrix
because in mentioned region the effects of finite Larmor
radius become considerable.
In this paper a simple analytical model is proposed for
analyzing the efficiency of the controlling the impurity
ions with the divertor configuration under X-point
sweeping. This approach is based on the single particle
gyro-orbits simulation. The effect of vertical sweeping of
the magnetic rib is considered for toroidal geometry. The
simplicity of magnetic configuration is provided by
authors’ wish to select the effect of X-point on plasma
transport at the edge.
The simplest toroidal configuration with rotational
transform and X-point sweeping is described in the
Section 2. Results of the numerical simulation of the
tungsten ion motion are presented in the Section 3. The
principal conclusions are summarized in the Section 4.
2. MODEL OF THE MAGNETIC FIELD
The following analytic expressions are used for
modeling the tokamak like magnetic configuration with
X-point:
- main confinement field
−
= 1),(,0
cos 00
00)0( r
R
r
rR
RB ι
ϑ
B ; (1)
- additional magnetic field which leads to X-point
formation
{ }0,)cos(),sin()()(
ccc
XX rrb ϑϑϑϑ −−−−=B , (2)
where
( )
( ) ( ))cos(2cos
cos)(2
22
0
0)(
ccc
cccX
rrrrrR
rrR
c
tIb
ϑϑϑ
ϑ
−−+−
−= ,
},,{ ϕϑr are the quasitoroidal coordinates, B0 is the
magnetic field value on the circular axis of the torus, )(rι
is the rotational transform angle, 0R is the major radius of
the torus, },{ ccr ϑ are the coordinates of the divertor coil,
c is the light velocity in vacuum, I(t) is the value of the
divertor coil current, t is time. For further simulations we
will use three modulations of this current:
- “unmodulated”
0)( ItI = , (3a)
- “positive” modulation
))/int()/(()( 0 TtTtIIItI −⋅∆+∆−= , (3b)
- “negative” modulation
))/int()/(()( 0 TtTtIItI −⋅∆−= , (3c)
where I0 is the constant, ΔI is the amplitude of
modulation, T is the period of modulation, int(x) is the
function which gives the integer part of x. These
modulations are presented in Fig.1.
For magnetic field configuration presented with
Eqs.(1) and (2) the magnetic flux function is obtained
from equation ( ) 0=Ψ∇B as the following expression
( ).)cos(2ln))(2(
)(
22
0
ccc rrrrctI
drrrB
ϑϑ
ι
−−++
+=Ψ ∫ (4)
This function Ψ can be normalized
),(),(
),(),(),(
OOXX
OO
N rr
rrr
ϑϑ
ϑϑϑ
Ψ−Ψ
Ψ−Ψ=Ψ , (5)
where },{ OOr ϑ and },{ XXr ϑ are coordinates of the
O-point and X-point, respectively. This normalization
leads to the following: NΨ is equal ‘1’ at the separatrix,
and ‘0’ at the magnetic axis.
3. NUMERICAL SIMULATION
OF THE TUNGSTEN ION MOTION
To analyze the efficiency of the different X-point
sweeping regimes the numerical simulation of the ion
trajectories was carried out. In calculations, 800 test
particles (tungsten ions W+1) were distributed in the
vicinity of the separatrix at 10 flux surfaces in 8 s at each
16 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6.
Series: Plasma Physics (14), p. 16-18.
mailto:Anton.Moskvitin@gmail.com
surface. The value of NΨ for these positions varies in the
range 0,9 − 0,99 with step 0,01. The initial space
distribution of test particles is presented in Fig.2. For each
test particle initial velocities were chosen randomly from
the Maxwellian distribution with the temperature 100 eV.
This temperature is usually considered as the temperature
of the plasma edge. It should be noted that for different
modulations of the divertor current the set of particle
parameters remains invariable.
Fig.1. The divertor current modulation regimes and the
dependence from time of the loss particle fraction
relatively to initial quantity
The numerical calculation shows that 111 particles are
lost during the first 10 ms for any of suggested
modulations. Then during next 2 s particles aren’t lost in
“unmodulated” case and for modulated cases nearly 100
particles are lost in addition to mentioned. This shows
that due to small modulation of divertor current it is
possible to increase the removal of impurity ions from the
plasma edge by a factor 2. The time evolution of these
losses is presented on Fig.1 (n0 is the initial quantity of
test particles). It can be seen that “positive” modulation is
more favorable because under this modulation particle
flow is prolonged in contrary to “negative” modulation
case when flow is presented by rare peaks at the
beginning of each modulation period.
Fig.2. The initial and final spatial distribution of test
particles (W+1) in vertical cross section of the torus
The fraction of lost particle from each chosen flux
surface (Fig.3) and the energy range (Fig.4) are presented
( n0(ΨN) and n0(W) are the initial quantity at given surface
ΨN and the given energy range near W ).
Fig.3. The dependence from magnetic flux label (ΨN) of
the lost particle fraction relatively to initial quantity at
given surface
Fig.4. The lost particle fraction
It can be seen that losses under modulation from
different surfaces (energy intervals) are nearly
proportional to those which take place in “unmodulated”
case.
On Fig.5 the deposition of lost test particles on
imaginary divertor plates (see Fig.2) is presented as
difference between flow under modulation and flow
without modulation. It is seen that modulation leads to
increasing of the particle flow on these plates. Besides
that small redistribution of load occurs on low field side
plate (Fig.5a): at the region from R=303−306 cm flow is
decreased and at the region R=301−303 cm is increased in
comparison with the “unmodulated” case. The same
picture is seen in Fig.5b. However, it should be noted that
in “positive” modulation case the losses are prolonged
and that’s why are less destructive then in “unmodulated”
case and under “negative ” modulation.
17
time, s
Fig.5. The difference between modulated and
unmodulated cases of test particle deposition on the
imaginary divertor plate a) at the low field side and
b) at the high field side
4. CONCLUSIONS
From the carried out analysis it is seen that regime
with “positive” modulation of divertor current has several
advantages:
- increased the impurity ion removal;
- this increased flow is rather moderate and prolonged;
- the region of ion deposition is widen.
The right choice of the modulation law of the divertor
current gives an opportunity to decrease heat load of the
plasma facing components under the increased impurity
removal.
ACKNOWLEDGEMENTS
Authors are thankful Prof. Igor Girka for his constant
support of this work and useful notes and
Dr. Oleg Shihskin for fruitful discussions.
The research is supported by Science and Technology
Center in Ukraine, Project # 3685.
REFERENCES
1. V. Pericoli , E. Joffrin et al.// Proc. of the 30th EPS
Conference on Contr. Fusion and Plasma Phys.,
St.Petersburg, 7-11 July 2003/ ECA, v.27A, P-2.89.
2. X. Litaudon, G. Arnoux, M. Beurskens et al. //
Plasma Physics and Controlled Fusion. 2007, v. 49,
N 12, p. B529-B550.
3. R.D. Stambaugh and the DIlI-D Team. DIII-D //
Proc. of the 13th on Plasma Physics and Controlled
Nuclear Fusion Research, October 1-6, 1990,
Washington, DC.
4. Y. Nakamura, S. Masuzaki, T. Morisaki et al. //
Nuclear Fusion. 2006, v.46, N7, p. 714-724.
5. A.A. Shishkin, Yu.K. Moskvitina, O. Motojima et al.
// Problems of Atomic Science and Technology.
Series “Plasma Electronics and New Methods of
Acceleration” (6). 2008, N 4, p. 109-114.
6. A.O. Moskvitin, A.A. Shishkin // Problems of
Atomic Science and Technology. Series “Plasma
Electronics and New Methods of Acceleration” (6).
2008, N 4, p. 89-95.
Article received 22.09.08
МОДЕЛИРОВАНИЕ ДВИЖЕНИЯ ЧАСТИЦЫ ВБЛИЗИ СЕПАРАТРИСЫ
ПРИ РАСКАЧИВАНИИ Х-ТОЧКИ ТОКАМАКА
А.А. Москвитин, А.А. Шишкин
Эффективность различных режимов раскачивания Х-точки рассмотрена на основании результатов
моделирования движения иона вольфрама при учёте конечного радиуса Ларморовcкой орбиты. Изучена
зависимость доли потерянных частиц от кинетической энергии и начального положения. Результаты анализа
показывают, что при правильном выборе закона модуляции тока в диверторных проводниках возможно
уменьшить тепловую нагрузку на материальную часть дивертора.
МОДЕЛЮВАННЯ РУХУ ЧАСТИНКИ ПОБЛИЗУ СЕПАРАТРИСИ
ПРИ РОЗГОЙДУВАННІ Х-ТОЧКИ ТОКАМАКА
А.О. Москвітін, О.О. Шишкін
Ефективність різних режимів розгойдування Х-точки розглянуто на основі результатів моделювання руху
іону вольфраму при врахуванні кінцевої величини радіуса Ларморівської орбіти. Вивчено залежність долі
втрачених частинок від кінетичної енергії та початкового положення. Результати аналізу вказують на те, що
при належному виборі закону модуляції струму в диверторних провідниках можливо зменшити теплове
навантаження на матеріальну частину дивертора.
18
b
a
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| id | nasplib_isofts_kiev_ua-123456789-110809 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-29T11:55:19Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Moskvitin, A.O. Shishkin, A.A. 2017-01-06T13:36:50Z 2017-01-06T13:36:50Z 2008 Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping / A.O. Moskvitin, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 6. — С. 16-18. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.25.Vy, 52.65.Cc, 52.55.Rk, 52.55.Dy https://nasplib.isofts.kiev.ua/handle/123456789/110809 The removal efficiency of the divertor X-point sweeping regimes is considered on the base of the numerical simulation of the tungsten ion motion in the gyroorbit approximation. The dependence of the loss particle fraction from the kinetic energy and initial position is studied. The results of the analysis show that the appropriate choice of the modulation law of the divertor current gives an opportunity to decrease heat load of the plasma facing components. Ефективність різних режимів розгойдування Х-точки розглянуто на основі результатів моделювання руху іону вольфраму при врахуванні кінцевої величини радіуса Ларморівської орбіти. Вивчено залежність долі втрачених частинок від кінетичної енергії та початкового положення. Результати аналізу вказують на те, що при належному виборі закону модуляції струму в диверторних провідниках можливо зменшити теплове навантаження на матеріальну частину дивертора. Эффективность различных режимов раскачивания Х-точки рассмотрена на основании результатов моделирования движения иона вольфрама при учёте конечного радиуса Ларморовcкой орбиты. Изучена зависимость доли потерянных частиц от кинетической энергии и начального положения. Результаты анализа показывают, что при правильном выборе закона модуляции тока в диверторных проводниках возможно уменьшить тепловую нагрузку на материальную часть дивертора. Authors are thankful Prof. Igor Girka for his constant support of this work and useful notes and Dr. Oleg Shihskin for fruitful discussions. The research is supported by Science and Technology Center in Ukraine, Project # 3685. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping Моделювання руху частинки поблизу сепаратриси при розгойдуванні Х-точки токамака Моделирование движения частицы вблизи сепаратрисы при раскачивании Х-точки токамака Article published earlier |
| spellingShingle | Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping Moskvitin, A.O. Shishkin, A.A. Magnetic confinement |
| title | Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping |
| title_alt | Моделювання руху частинки поблизу сепаратриси при розгойдуванні Х-точки токамака Моделирование движения частицы вблизи сепаратрисы при раскачивании Х-точки токамака |
| title_full | Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping |
| title_fullStr | Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping |
| title_full_unstemmed | Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping |
| title_short | Single particle simulation in the vicinity of separatrix under tokamak X-point sweeping |
| title_sort | single particle simulation in the vicinity of separatrix under tokamak x-point sweeping |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110809 |
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