Impurity dynamics in tokamak like magnetic configuration with X-point
Expressions for plasma flow velocities are obtained in invariant form in non ideal MHD approach. Simulation of
 plasma flow trajectories in tokamak like magnetic configuration with X-point is carried out. The method of plasma
 flow regulating in the vicinity of separatrix by varying...
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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: | Impurity dynamics in tokamak like magnetic configuration with X-point / A.O. Moskvitin, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 4. — С. 89-94. — Бібліогр.: 10 назв. — англ. |
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| author | Moskvitin, A.O. Shishkin, A.A. |
| author_facet | Moskvitin, A.O. Shishkin, A.A. |
| citation_txt | Impurity dynamics in tokamak like magnetic configuration with X-point / A.O. Moskvitin, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 4. — С. 89-94. — Бібліогр.: 10 назв. — англ. |
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| description | Expressions for plasma flow velocities are obtained in invariant form in non ideal MHD approach. Simulation of
plasma flow trajectories in tokamak like magnetic configuration with X-point is carried out. The method of plasma
flow regulating in the vicinity of separatrix by varying divertor coil current is proposed. To sustain MHD simulation
the impurity ion Newton-Lorentz simulations near X-point are carried out.
Отримано вирази для швидкостей потоків плазми в інваріантній формі у наближені неідеальної МГД.
Проведено моделювання траєкторій потоків плазми в магнітній конфігурації типу токамак з Х-точкою.
Запропоновано метод регулювання потоку плазми на диверторні пластини шляхом змінювання струму в
диверторних провідниках. Для підтвердження МГД-моделювання було проведено Ньютон-Лоренц-
моделювання иона домішки поблизу Х-точки.
Получены выражения для скоростей потоков плазмы в инвариантной форме в приближении неидеальной
МГД. Проведено моделирование траекторий потоков плазмы в магнитной конфигурации типа токамак с Х-
точкой. Предложен метод регулирования потока плазмы на диверторные пластины путем изменения тока в
диверторных проводниках. Для подтверждения МГД-моделирования было проведено Ньютон-Лоренц-моде-
лирование примесного иона вблизи Х-точки.
|
| first_indexed | 2025-12-07T18:54:42Z |
| format | Article |
| fulltext |
IMPURITY DYNAMICS IN TOKAMAK LIKE MAGNETIC CONFIGURA-
TION WITH X-POINT
A.O. Moskvitin1, A.A. Shishkin2,1
1Department of Physics and Technology,
Kharkiv “V.N.Karazin” National University, Kharkiv, Ukraine;
2National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: Anton.Moskvitin@gmail.com
Expressions for plasma flow velocities are obtained in invariant form in non ideal MHD approach. Simulation of
plasma flow trajectories in tokamak like magnetic configuration with X-point is carried out. The method of plasma
flow regulating in the vicinity of separatrix by varying divertor coil current is proposed. To sustain MHD simulation
the impurity ion Newton-Lorentz simulations near X-point are carried out.
PACS: 52.55.Fa
1. MOTIVATION OF STUDY
A lot of experimental investigations on tokamaks are
devoted to decreasing heat load on plasma faced compo-
nents of the divertor and controlling impurity transport
at plasma edge. The interest to this problem is caused by
attempts to model fusion reactor scenarios on nowadays
fusion devices. Method of X-point position sweeping is
considered in framework of these studies.
In this paper a simple analytical model is proposed
for analyzing the efficiency of the controlling the impu-
rity ions with the divertor configuration. This approach
is based on non ideal MHD consideration supplemented
by single particle gyro-orbits simulation. The effect of
vertical sweeping of the magnetic rib is considered for
cylindrical geometry. The simplicity of magnetic con-
figuration is provided by authors’ wish to select the ef-
fect of X-point on plasma transport at the edge.
The simplest configuration (Fig. 1) is described in
the Section 2. MHD fluxes are investigated in the Sec-
tion 3. The dynamics of the impurity ions are considered
in the Section 4. The principal conclusions are summa-
rized in the Section 5.
2. MAGNETIC CONFIGURATION
WITH X-POINT
Uniform magnetic field 0B is parallel to z-axis and
is maintained externally. Rotational transform of mag-
netic lines is created due to plasma current.
Fig.1. Magnetic field model
Assuming plasma current density j in following form
zej
Ψ
Ψ−=
j
b
j
α
10 , (1)
where 0j − plasma current density at magnetic axis, jα
- current density profile parameter, Ψ − magnetic sur-
face function, edgeplasmab Ψ=Ψ , one can obtain com-
ponents of magnetic field from following equation
jB
c
π4rot = , (2)
and then Ψ using
( ) 0=Ψ∇B . (3)
From the very beginning it is assumed that current is
distributed uniformly zej 0
)0( j= . Thus we obtain
= 1,,0 )0(
0
)0( ι
a
rBB , (4)
2
0
)0(
=Ψ
a
rb , (5)
where 00 2 caBIb plΣ= and constb −= 0
)0(ι rotational
transform angle, plIΣ − net current, a − cylindrical ves-
sel radius.
At next step of approximation it is assumed that
plasma current density is distributed as in Eq. (1) with
circular magnetic surfaces )0(Ψ . Thus it is yield
= 1,,0 )1(
0
)1( ι
a
rBB , (6)
( )
+
−+
=Ψ
1
111
22
0
)1(
jj
jar
a
rb
αα
α
, (7)
where ( ) ( )[ ]jarbb j
ααι 2
00
)1( 1 −+= .
For the next step approximation )1(Ψ can be substituted
into Eq. (1) and then expressions for )2(B and )2(Ψ can
be obtained from Eqs. (2,3). We restrict ourselves to
first approximation because obtained expressions give
us satisfied description for magnetic field, in particular,
parabolic profile for safety factor (rotational transform
angle).
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2008. № 4.
Серия: Плазменная электроника и новые методы ускорения (6), с.89-94.
X
Y
Z
I
X
X-point
Separatrix
89
The linear current XI is included to take into con-
sideration the effect of divertor coils on magnetic con-
figuration (see Fig.1). Components of magnetic field
produced by this current are given by following expres-
sion
( ){ }
( ) ( ) )sin(21
0,)sin(,)cos(
2
0)(
ϑ
ϑϑ
arar
arbB XX
++
+−=B . (8)
Then substituting )()1( XBBB += in Eq. (3) and in-
tegrating it we obtain Ψ as )()1( XΨ+Ψ=Ψ , where
( ) ( )( ))sin(21ln
2
1 2)( ϑararbX
X ++=Ψ ,
02 caBIb XX = . (9)
It is convenient to normalize )1(Ψ in following way
),(),(
),(),(),(
OOXX
OO
N rr
rrr
ϑϑ
ϑϑϑ
Ψ−Ψ
Ψ−Ψ=Ψ , (10)
where OOr ϑ, and XXr ϑ, are coordinates of O-point
(magnetic axis) and X-point (magnetic separatrix rib)
respectively. It should be noted that after such proce-
dure NΨ takes value ‘0’ on magnetic axis and ‘1’ on
magnetic separatrix.
Radial profiles of ),( Xz rj ϑ and ),( XN r ϑΨ are pre-
sented on Fig.2.
Fig.2. Radial profiles of ),( Xz rj ϑ and ),( XN r ϑΨ
For simulations following values for magnetic con-
figuration parameters are used:
TB 4,30 = ; MAI pl 2=Σ ; 5,0=jα ; MAI X 2,0= .
3. PLASMA MHD-FLOWS
DISSIPATIVE MODEL
MHD approach is often used for treating impurity
transport at the plasma edge.
3.1. TRANSPORT EQUATIONS
01 =+×++∇− aa
aa
aaa c
nenep FBuE , (11)
0
2
5
2 =+×+∇− a
a
aaa
aa pc
neTn FBq
, (12)
with friction forces 1aF and 2aF taken in following
form [3-4]
∑ +=
b b
bab
b
ab
a p
ll quF 12111 5
2
, (13)
∑ +=
b b
bab
b
ab
a p
ll quF 22212 5
2
, (14)
where a and b denote species of plasma component, ap
, an and aT are the pressure, density and temperature of
the plasma component a, ae is the charge of the single
plasma component a ion, au and aq are particles and
heat flows velocity of plasma component a, E and B
are the electric and magnetic fields, ab
ikl are the trans-
port coefficients.
The transport coefficients ab
ikl can be calculated with
the use of technique proposed [1], and further developed
in Refs [2-5].
3.2. TRANSPORT COEFFICIENTS
Further we consider a simple case of deuterium plas-
ma containing a single species of impurity ion. For such
case the analysis of the force balance was carried out by
Rutherford [2] for a magnetic field model with circular
magnetic surfaces. We suggest to analyze both force
and thermal conduction equations in a same way be-
cause of theirs similarity. On this stage we don’t assume
any special magnetic field configuration.
For this case according to [3] transport coefficients
could be expressed in such way
111111111 lllll IIIDDIDD ==−=−= , (15a)
221211212 lllll DDDIIDDD ==−=−= , (15b)
322 ll DD = , (15c)
0222221211212 ====== IDDIIIIDIIDI llllll , (15d)
)(*
101 DIDI ZCZll = , (16a)
)(*
202 DIDI ZCZll = , (16b)
)(*
303 DIZCll = , (16c)
⋅⋅==
−
−
sec
cmg1069,2
342
7
0
2
3
2
1
D
DDD
DD
DD
T
MZnnml
τ
, (17)
[ ] ⋅⋅== − sec1022,6
ln24
3
22
4
22
2
3
2
1
2
3
2
1
bab
aa
bab
aa
ab ZZn
TM
een
Tm
λπ
τ (18)
14 310 cma an n −= − normalized density; aT − plasma
temperature taken in keV units; aM − mass number of
species a. Effective charge number DIZ is given by fol-
lowing expression DDIIDI neneZ 22= .
Coefficients )(* xCi are obtained in [2] and can be
obtained in a way which is shown in [3]:
x
xC
+
+=
59,0
31,048,0)(*
1 , (19a)
x
xC
+
+=
59,0
41,03,0)(*
2 , (19b)
x
xxxC
+
⋅+⋅+=
59,0
55,05,013,1)(*
3 . (19c)
90
Index D denotes light ion (e.g. deuterium) and index
I denotes impurity ion. Expressions (15), (16) and (19)
are derived assuming Dm << Im (so called Lorentz colli-
sion model).
3.3. STATIONARY
PLASMA MHD VELOCITIES
To obtain equations describing plasma transport par-
allel to magnetic field lines scalar products of Eqs. (11)
and (12) with B are taken
( )BEDDD
D
D nep
p
qlUl +− ∇=+ II
II
II 21 5
2
, (20a)
( )BEIII
D
D nep
p
qlUl +− ∇=−− II
II
II 21 5
2
, (20b)
DD
D
D Tn
p
qlUl II
II
II ∇−=+
2
5
5
2
32 , (20c)
where subscript ‘II’ denotes components parallel to
magnetic field lines, ID uuU −= − relative velocity.
As it seen left hand parts of Eqs.(20a) and (20b) are
equal up to minus sign that is why to have a solution
right hand parts should satisfy such condition
( ) ( ) 0=+∇−+∇− BEBE IIIDDD nepnep IIII (21)
Integrating these equations taking into account con-
dition (21) it is obtained
( )
( )
∇−
+
∇
−= −
−
DD
II
eff Tnl
fZ
pl
lllU II
II
II 21
31
31
2
2 2
5
1
. (22)
If ( )Ψ= DD pp , ( )Ψ= II pp , ( )Ψ= TT then
0=IIU , or IIII ID uu = . (23)
To obtain equations for describing plasma transport
across to magnetic field lines vector products of
Eqs.(11) and (12) with B are taken. After integration of
obtained equations it is yielded
( )
( )DDeff
DD
D
DD
dED
Tnlpl
p
∇+∇
+∇×+=⊥
212
1
1
ωρ
ωρ
hvu
, (24a)
( ) ( ).11
11
212 DDeff
DDII
I
DDII
dEI
Tnlpl
fZ
p
fZ
∇+∇
−∇×+=⊥
ωρ
ωρ
hvu
(24b)
In expressions (22) and (23) following designations
are done: IIIieff pfZpp ∇−∇=∇ − 1)( , cm
eB
D
D =ω ,
DDD nm=ρ , BEv ×= 2B
c
dE , BBh = .
Yielding Eqs.24 we neglect terms proportional
( )2ab
ikl because of its smallness in comparison to those
taken into account. Such approach let us to analyze
main transport processes in rather simple way. Consid-
erable results were obtained with the use of this tech-
nique in [5-7].
3.4. PLASMA PARAMETERS AND
ELECTRIC FIELD MODEL
First of all it is supposed that common temperature
of deuterium and impurity plasma has been settled.
Then it is assumed that plasma parameters depend on
),( ϑrNΨ in following way
( ) nDnD
NDOD nn 217.01 ααΨ−= , (25a)
( ) TT
NOTT 217.01 ααΨ−= , (25b)
nI
NIXI nn αΨ= , (25c)
where Dn and In are plasma densities of deuterium and
impurity respectively, T is plasma common temperature,
iα − are profile parameters, subscripts ‘O’ and ‘X’ de-
notes plasma parameters values on magnetic axis (O-
point) and magnetic separatrix rib (X-point).
Numerical coefficient 0,7 is inputted in Eqs.(25) to
describe non zero temperature and deuterium density
beyond separatrix. After T , Dn and In are defined
plasma component partial pressures are yielded in natu-
ral way
kTnp DD = , (26a)
kTnp II = . (26b)
Radial profiles of plasma parameters at angle direc-
tion of X-point ( 23πϑ = ) are shown at Fig.3 for fol-
lowing profile parameters
81 =nDα , 12 =nDα , 121 == TT αα , 4=nIα .
These profile parameters are used for further simula-
tions with such values of
14 310 cmDOn −= , 13 310 cmIXn −= and 20OT = keV.
Fig.3. Radial profiles of plasma parameters at angle di-
rection of X-point ( 23πϑ = )
For electric potential following expression is used
( ) EE
NEE
2110
ααΨ−Φ=Φ . (27)
Electric field was defined as EΦ− ∇=E .
For further simulations such parameter values are
used 0 10 kVEΦ = − , 81 =Eα and 12 =Eα .
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2008. № 4.
Серия: Плазменная электроника и новые методы ускорения (6), с.89-94. 91
3.5. FLOW TRAJECTORY
SIMULATION RESULTS
To simulate flow trajectory we use following equa-
tion
0, =× IDd ur . (28)
In this section we try to simulate separatrix position
varying. At Fig.4 flow trajectories of impurity plasma in
deuterium plasma are shown in the vicinity of separatrix
with the same start position in two magnetic configura-
tions with IX = 0,2 MA and IX = 0,22 MA. Due to diver-
tor coil current increasing separatrix is shifted inside. As
it shown at Fig.4 separatrix 1XΨ which corresponds to
IX = 0,2 MA is above start point and separatrix 2XΨ
which corresponds to IX = 0,22 MA is under start point.
This difference in initial conditions leads to increasing
outside separatrix flow. Another aspect is that flow tra-
jectories in both case don’t differ much along separatrix
and only near X-point flows deviates from each other
(Fig.4,b) In first case flow stays in confinement volume
and in second case flow moves out to imaginary diver-
tor plate at position sin( ) 110 cmr ϑ = − under X-point (
sin( ) 108 cmX Xr ϑ = − ).
Fig.4. Flow trajectories of impurity plasma
in deuterium plasma in the vicinity of separatrix
with the same start position in magnetic configurations
with IX = 0,2 MA and IX = 0,22 MA
At Fig.5 poloidal velocity of impurity plasma flow is
presented. As it seen from Fig.5 poloidal velocity has
the smallest value near X-point. On poloidal motion ra-
dial electric field plays the key role [9], [10]. As soon as
electrostatic potential is function of Ψ at X-point Er=0
because 0=∂
Ψ∂
r .
Fig.5. Poloidal flow velocity ϑu of impurity plasma
flow in deuterium plasma in the vicinity of separatrix
in magnetic configuration with IX = 0,22 MA
Fig.6. Flow trajectories of deuterium plasma
in plasma with impurity (W+1) in the vicinity
of separatrix with the same start position in magnetic
configurations with IX = 0,2 MA and IX = 0,22 MA
As it seen from Fig.6 deuterium plasma flow in the
vicinity of separatrix don’t differ from impurity plasma
flow.
The effect of plasma flow escape due to divertor coil
current increasing can be used as method of improving
divertor regime. Application of similar technique on
LHD (Japan) gives considerable results in long pulse
experiments [8]. Efficiency of plasma edge refinement
by X-point sweeping depends on impurity fraction at the
plasma edge and current modulation.
a
b
92
4. SINGLE PARTICLE GYROORBIT MOD-
EL
The MHD results obtained above can be supported
with the single gyro-orbit particle motion simulation.
We can see how the principle physics deduction based
on MHD approach can be enriched with the single parti-
cle study. The particle trajectory due to drifts in the in-
homogeneous magnetic and electric fields distinguishes
from the magnetic surface. The consequences of this
feature demonstrates itself in the different streamlines of
the MHD flows and particle trajectories near separatrix.
4.1. NEWTON-LORENTZ EQUATION
For simulation ion gyro-orbit we use following
equations
vr =
dt
d
, (29)
×+= BvEv
c
ee
mdt
d 1
, (30)
where r and v are particle radius vector and velocity re-
spectively, e and m are charge and mass of ion under
consideration. Models for electric and magnetic field are
used the same as in MHD approach.
For simulations we use tungsten ion W+16. Tungsten
is the most probable material of divertor face compo-
nents. At the plasma edge charge number can be
changed in wide range due to ionization/recombination
processes.
4.2. SINGLE PARTICLE GYROORBIT SIMULA-
TION RESULTS
On Fig.7 particle trajectory is presented. It is should
be noted that due to drifts particle trajectory deflects
from magnetic field line. As it shown on Fig.7,c mag-
netic field line escapes from confinement volume be-
cause its start position is above separatrix. In spite of
start positions of magnetic field line and particle are the
same (see Fig.7,b) particle stays in confinement volume.
On Fig.7,b some simulation parameters are presented.
0.01startr∆ = + cm means that start position is 0.01 cm
above separatrix. In presented case 5Lstartr ρ=∆
where Lρ is particle Larmor radius.
It should be noted that during motion ion crosses
magnetic separatrix and become inside separatrix
(Fig.7,c). Then it crosses separatrix once more and be-
come outside separatrix. As it seen from Fig.7,b particle
has done two full turns in poloidal direction and each
time returns to its start position outside separatrix. Parti-
cle trajectory differs from magnetic field line due to
drifts in inhomogeneous electric and magnetic fields
We’d like to mention that poloidal velocity of ion at
start position is smaller than near X-point. Due to this
effect near start position gyro-orbit spiral is seen well
and near X-point only solid thick line is seen. As soon
as space scale at Fig.7,b and Fig.7,c is the same it is
possible to see that thickness of this thick line is about
2 Larmor radii. The same behavior of poloidal velocity
is demonstrated above for plasma flow (Fig.5).
CONCLUSIONS.
SIMULATION MODELS COMPARISON
Simple analytical non ideal MHD model is formulat-
ed. This model is applied for description of X-point
sweeping effect on plasma flow near separatrix. It is
demonstrated that it is possible to control plasma flow
towards divertor plates by small variance of divertor
coils (Fig.4).
The efficiency of such control could be investigated
analytically for more complicate configurations with the
help of proposed model.
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2008. № 4.
Серия: Плазменная электроника и новые методы ускорения (6), с.89-94.
a
b
93
Fig.7. Single particle trajectory and magnetic field line
which crosses particle orbit at start position in magnet-
ic configuration with IX = 0,2 MA
a)Full scale trajectory; b) enlarged fragment near start
position; c) enlarged fragment near X-point
The results of single particle gyro-orbit motion sim-
ulation matches in main aspects with MHD-flows tra-
jectories. As it seen from Fig.7 discrepancy is caused by
drifts in the inhomogeneous magnetic and electric
fields. MHD approach should be supplemented with
Newton-Lorentz investigation of impurity ion motion
near separatrix because near X-point even small varia-
tions in initial position and gyro phase defines escaping
or penetration of ion under consideration.
ACKNOWLEDGMENTS
This work is supported by Science and Technology
Center in Ukraine (Project 3685).
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Статья поступила в редакцию 08.05.2008 г.
ДИНАМИКА ПРИМЕСИ В МАГНИТНОЙ КОНФИГУРАЦИИ ТИПА ТОКАМАК С Х-ТОЧКОЙ
А.А. Москвитин, А.А. Шишкин
Получены выражения для скоростей потоков плазмы в инвариантной форме в приближении неидеальной
МГД. Проведено моделирование траекторий потоков плазмы в магнитной конфигурации типа токамак с Х-
точкой. Предложен метод регулирования потока плазмы на диверторные пластины путем изменения тока в
диверторных проводниках. Для подтверждения МГД-моделирования было проведено Ньютон-Лоренц-моде-
лирование примесного иона вблизи Х-точки.
ДИНАМІКА ДОМІШКИ В МАГНІТНІЙ КОНФІГУРАЦІЇ ТИПУ ТОКАМАК З Х-ТОЧКОЮ
А.О. Москвітін, О.О. Шишкін
Отримано вирази для швидкостей потоків плазми в інваріантній формі у наближені неідеальної МГД.
Проведено моделювання траєкторій потоків плазми в магнітній конфігурації типу токамак з Х-точкою.
Запропоновано метод регулювання потоку плазми на диверторні пластини шляхом змінювання струму в
диверторних провідниках. Для підтвердження МГД-моделювання було проведено Ньютон-Лоренц-
моделювання иона домішки поблизу Х-точки.
c
94
1. Motivation of study
2. Magnetic Configuration
with X-point
3. plasma MHD-flows
dissipative model
3.1. transport equationS
3.2. transport coefficients
3.3. stationarY
plasma MHD velocities
3.4. Plasma parameters and
electric field model
3.5. Flow trajectory
simulation results
4. Single particle gyroorbit model
4.1. Newton-lorentz equation
4.2. single particle gyroorbit simulation results
ConclusionS.
REFERENCES
Динамика примеси в магнитной конфигурации типа токамак с Х-точкой
Динаміка Домішки в магнітній конфігурації типу токамак з Х-точкою
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| id | nasplib_isofts_kiev_ua-123456789-110355 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:54:42Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Moskvitin, A.O. Shishkin, A.A. 2017-01-03T16:52:36Z 2017-01-03T16:52:36Z 2008 Impurity dynamics in tokamak like magnetic configuration with X-point / A.O. Moskvitin, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 4. — С. 89-94. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 52.55.Fa https://nasplib.isofts.kiev.ua/handle/123456789/110355 Expressions for plasma flow velocities are obtained in invariant form in non ideal MHD approach. Simulation of
 plasma flow trajectories in tokamak like magnetic configuration with X-point is carried out. The method of plasma
 flow regulating in the vicinity of separatrix by varying divertor coil current is proposed. To sustain MHD simulation
 the impurity ion Newton-Lorentz simulations near X-point are carried out. Отримано вирази для швидкостей потоків плазми в інваріантній формі у наближені неідеальної МГД.
 Проведено моделювання траєкторій потоків плазми в магнітній конфігурації типу токамак з Х-точкою.
 Запропоновано метод регулювання потоку плазми на диверторні пластини шляхом змінювання струму в
 диверторних провідниках. Для підтвердження МГД-моделювання було проведено Ньютон-Лоренц-
 моделювання иона домішки поблизу Х-точки. Получены выражения для скоростей потоков плазмы в инвариантной форме в приближении неидеальной
 МГД. Проведено моделирование траекторий потоков плазмы в магнитной конфигурации типа токамак с Х-
 точкой. Предложен метод регулирования потока плазмы на диверторные пластины путем изменения тока в
 диверторных проводниках. Для подтверждения МГД-моделирования было проведено Ньютон-Лоренц-моде-
 лирование примесного иона вблизи Х-точки. This work 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 Термоядерный синтез (коллективные процессы) Impurity dynamics in tokamak like magnetic configuration with X-point Динаміка домішки в магнітній конфігурації типу токамак з Х-точкою Динамика примеси в магнитной конфигурации типа токамак с Х-точкой Article published earlier |
| spellingShingle | Impurity dynamics in tokamak like magnetic configuration with X-point Moskvitin, A.O. Shishkin, A.A. Термоядерный синтез (коллективные процессы) |
| title | Impurity dynamics in tokamak like magnetic configuration with X-point |
| title_alt | Динаміка домішки в магнітній конфігурації типу токамак з Х-точкою Динамика примеси в магнитной конфигурации типа токамак с Х-точкой |
| title_full | Impurity dynamics in tokamak like magnetic configuration with X-point |
| title_fullStr | Impurity dynamics in tokamak like magnetic configuration with X-point |
| title_full_unstemmed | Impurity dynamics in tokamak like magnetic configuration with X-point |
| title_short | Impurity dynamics in tokamak like magnetic configuration with X-point |
| title_sort | impurity dynamics in tokamak like magnetic configuration with x-point |
| topic | Термоядерный синтез (коллективные процессы) |
| topic_facet | Термоядерный синтез (коллективные процессы) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110355 |
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