Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling
The spatial distributions of plasma parameters in the stellarators LHD and U-2M, operating under recycling conditions with the assumption of neoclassical transport realization, are calculated using the one-dimensional space-time numerical code. The stable solutions of the system of equations for the...
Gespeichert in:
| Datum: | 2015 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
|
| Schriftenreihe: | Вопросы атомной науки и техники |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/82104 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling / V.A. Rudakov // Вопросы атомной науки и техники. — 2015. — № 1. — С. 41-44. — Бібліогр.: 9 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-82104 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-821042015-05-26T03:02:18Z Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling Rudakov, V.A. Магнитное удержание The spatial distributions of plasma parameters in the stellarators LHD and U-2M, operating under recycling conditions with the assumption of neoclassical transport realization, are calculated using the one-dimensional space-time numerical code. The stable solutions of the system of equations for the spatial distributions of ion and electron temperatures, plasma and neutral neutron density and ambipolar electric field are obtained. The flat spots formation in the radial profiles of plasma parameters near the plasma boundary is shown. PACS: 52.55.HC, 52.25.Fi, 52.25.Ya C использованием одномерного пространственно-временного численного кода рассчитаны пространственные распределения параметров плазмы в стеллараторах LHD и У-2М, работающих в условиях рециклинга в предположении реализации неоклассического переноса. Получены устойчивые решения системы уравнений для пространственных распределений температур ионов и электронов, плотности плазмы и нейтральных атомов, амбиполярного электрического поля. Показано образование плоских участков в радиальных профилях параметров плазмы вблизи границы плазмы. З використанням одновимірного просторово-часового числового коду розраховано просторові розподіли параметрів плазми в стелараторах LHD і У-2М, працюючих в умовах рециклінгу в припущенні реалізації неокласичного перенесення. Отримані стійкі рішення системи рівнянь для просторових розподілів температур іонів і електронів, щільності плазми та нейтральних атомів, амбіполярного електричного поля. Показано утворення плоских ділянок у радіальних профілях параметрів плазми поблизу межі плазми. 2015 Article Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling / V.A. Rudakov // Вопросы атомной науки и техники. — 2015. — № 1. — С. 41-44. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.55.HC, 52.25.Fi, 52.25.Ya http://dspace.nbuv.gov.ua/handle/123456789/82104 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Магнитное удержание Магнитное удержание |
| spellingShingle |
Магнитное удержание Магнитное удержание Rudakov, V.A. Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling Вопросы атомной науки и техники |
| description |
The spatial distributions of plasma parameters in the stellarators LHD and U-2M, operating under recycling conditions with the assumption of neoclassical transport realization, are calculated using the one-dimensional space-time numerical code. The stable solutions of the system of equations for the spatial distributions of ion and electron temperatures, plasma and neutral neutron density and ambipolar electric field are obtained. The flat spots formation in the radial profiles of plasma parameters near the plasma boundary is shown.
PACS: 52.55.HC, 52.25.Fi, 52.25.Ya |
| format |
Article |
| author |
Rudakov, V.A. |
| author_facet |
Rudakov, V.A. |
| author_sort |
Rudakov, V.A. |
| title |
Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling |
| title_short |
Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling |
| title_full |
Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling |
| title_fullStr |
Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling |
| title_full_unstemmed |
Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling |
| title_sort |
distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/82104 |
| citation_txt |
Distribution of plasma parameters in the stellarator at neoclassical transport under conditions of recycling / V.A. Rudakov // Вопросы атомной науки и техники. — 2015. — № 1. — С. 41-44. — Бібліогр.: 9 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT rudakovva distributionofplasmaparametersinthestellaratoratneoclassicaltransportunderconditionsofrecycling |
| first_indexed |
2025-07-06T08:14:36Z |
| last_indexed |
2025-07-06T08:14:36Z |
| _version_ |
1836884616513847296 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №1(95)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2015, № 1. Series: Plasma Physics (21), p. 41-44. 41
DISTRIBUTION OF PLASMA PARAMETERS IN THE STELLARATOR
AT NEOCLASSICAL TRANSPORT UNDER CONDITIONS OF
RECYCLING
V.A. Rudakov
Institute of Plasma Physics of the NSC KIPT, Kharkov, Ukraine
E-mail: rudakov@kipt.kharkov.ua
The spatial distributions of plasma parameters in the stellarators LHD and U-2M, operating under recycling
conditions with the assumption of neoclassical transport realization, are calculated using the one-dimensional space-
time numerical code. The stable solutions of the system of equations for the spatial distributions of ion and electron
temperatures, plasma and neutral neutron density and ambipolar electric field are obtained. The flat spots formation
in the radial profiles of plasma parameters near the plasma boundary is shown.
PACS: 52.55.HC, 52.25.Fi, 52.25.Ya
INTRODUCTION
In the most of modern experimental stellarator-type
devices the stationary plasma parameters are maintained
by the return into the plasma of particles releasing from
the confinement volume as a result of diffusion or other
loss mechanisms. This process is named as “recycling”.
A recycling effect on the increased plasma losses was
first observed in the investigations using the stellarator
“C” [1]. A cold gas, penetrating into the plasma,
undergoes the ionization in the plasma column region,
and exerts influence on the formation of the plasma
density and temperature profiles. As a result, their
gradients are increased that leads to the plasma loss
increasing.
The recycling influence on the plasma parameters
was investigated in the LHD stellarator. The
investigation results have shown the formation of flat
spots on the density and temperature profiles near the
plasma boundary [2]. Calculations on the parameters of
a reactor-stellarator, where the plasma density
constancy is maintained due to the fuel pellet injection,
have shown that the injection of fuel into the plasma
periphery region significantly decreases the reactor
power level because of plasma loss increasing [3].
In the present paper the spatial distributions of
plasma parameters in the stellarators LHD and U-2M,
operating under recycling conditions with the
assumption of neoclassical transport realization, are
calculated using the one-dimensional space-time
numerical code. As distinct from [2] here we have used
the numerical solution of the system of transport
equations with taking into account ambipolar plasma
fluxes. By this method, in addition to the plasma density
and temperature distributions, we have obtained the
profiles of the radial electric field, density of neutral
atoms outside the plasma and their distributions in the
plasma column volume.
1. PHYSICAL MODEL AND THE SYSTEM
OF EQUATIONS
In the thermonuclear facility the process of plasma-
neutral interaction can occur by the following reactions:
H2 + e → 2H + e; (1)
H2 + e → H+
+ H + 2e ; (2)
H + H+
→ H+
+ H ; (3)
H + e → H+
+ 2e; (4)
H+
+ 2e → H + e. (5)
Expression (1) refers to the hydrogen molecule
dissociation, (2) represents the dissociation with
simultaneous atomic ionization. The last three
expressions determine the charge exchange of atoms,
atomic ionization and recombination. The rates of
reactions are given in ref. [4]. In the active phase of the
plasma discharge the hydrogen ions, escaping from the
confinement volume, are recombining during interaction
with the vacuum chamber walls and return into the
plasma for the most part in the form of neutral atoms
which are ionized due to the interaction with electrons
according to the expression [4]:
<>i=3.0526∙10
-7
(lnTe –2.9017)Te
-1/2
[сm
3
s
-1
, eV]. (6)
From the point of view of the plasma density
maintaining by recycling, in the present study we
consider this process as a main one. The molecule
ionization with subsequent dissociation and other
processes denoted by expression (3)-(5) are neglected
because their contribution to the density increase is
insignificant.
The calculation model is based on the system of
equations, given in [5, 6] for description of the space-
time behavior of the plasma in the reactor-stellarator,
which is supplemented by the equation for neutral
atoms. In these equations the terms relating to the
synthesis are omitted and instead of the pellet injection
model we use, as a plasma source, the source taking into
account the charged particle influx due to the neutral
atom ionization. At last, the system of equation takes a
following form
ee ;
3 1
Q
2
e
e ei c Eh b
T
n r Q Q Q Q Q
t r r
(7)
i ;
3 1
Q Q
2
i
i ei Ehi
T
n r Q Q
t r r
(8)
e
1
S ;
n
rS
t r r
(9)
a .a δ
n 1
rS S
t r r
(10)
The first two equations describe temperature behavior
of the electron Eq. (7) and the ion Eq. (8) in the space
and time. The next two are a plasma particle and neutral
diffusion equations. The first terms on the right side of
mailto:rudakov@kipt.kharkov.ua
42 ISSN 1562-6016. ВАНТ. 2015. №1(95)
Equations (7), (8) for the electron and ion heat
conductions determine the temperature variation caused
by the heat flux corresponding to the neoclassical theory
Kovrizhnykh [7]. The rest terms on the right sides of
Eqs. (7), (8) Qhi
and Qhe are, respectively, the heating
of ions and electrons emitted by the external sources;
Qei electron-ion heat exchange as a result of Coulomb
collisions; Qb bremsstrahlung; Qc cyclotron
radiation; QE energy change of particles in the
ambipolar electric field during their radial motion;
eQ and iQ are thermal expenses for heating the ions
and electrons that erased in result of ionization. The
charged particle flow Si and Se also correspond to [7].
The neutral atom flux is Sa= an T0/where T0 is the
their thermal velocity. And the charged particle source
is determined by the expression: δS = an n <>i.
The ambipolar electric field value was calculated
from the flux equality Se= Si at each time-space array
pitch. The system of equations (7)-(10) was
supplemented by the initial and boundary conditions.
The total number of charged and neutral particles in the
plasma and in the chamber volume was maintained to
be constant. In all calculations the neutral atom velocity
is taken corresponds to the temperature of 1 eV.
The different models of plasma heating by the
external sources were used: the electron heating only,
the ion heating only or simultaneous heating of two
components. It has been supposed that the specific
heating power is proportional to the plasma
density: nkQ hh .
2. CALCULATION RESULTS
Calculations were performed by the example of two
devices LHD and U-2M, the parameters of which are
given in papers [8, 9]. For U-2M it has been assumed
that the plasma radius is 17cm, the chamber radius is
34 cm, and in the case of LHD the radii are 60 and
80 cm respectively. The confinement field values are
2.5 T for LHD and 1 T for U-2M.
The dependences of helical field amplitude
modulations εh on the plasma radius, taken for the flux
definition, were characteristic for the devices under
consideration. In particular, a maximum value of εh is
0.6 for LHD and 0.25 for U-2M.
Calculations were carried out assuming different
plasma density values (conventionally with high and
low densities) and different plasma heating values. For
the initial plasma density and temperature distributions
we have used the expression such as N=N0(1-x
j
), where
j is an integral number. Most of calculations have been
performed under the assumptions that the initial
distribution of neutral atom concentration is uniform
throughout the vacuum chamber volume, the “burning”
of which in the plasma occurs during the evolution of
plasma parameters. The value of the neutral density
outside the plasma was defined as a result of the balance
between the opposite streams of plasma and atoms at
the plasma column boundary.
2.1. LHD RESULTS
Fig. 1 shows the time dependences of average
electron and ion temperature values in LHD in the
course of electron heating using the 2 MW source. The
initial values of the plasma density and neutral atom
density were equal to n0=5∙10
19
m
-3
and nh0=5∙10
18
m
-3
respectively. In the process of transition to the
stationary mode the neutral atom combusting up to
8∙10
14
m
-3
in the volume outside the plasma boundary
occur. The average plasma density value is increased to
5.85∙10
19
m
-3
and the constant level is reached during
0.4 s after the process start.
0,0 0,2 0,4 0,6 0,8 1,0
0,00
0,01
0,02
0,03
0,04
0,05
1
0
k
e
V
Time, s
Te
Ti
Fig. 1. LHD, Temperatures time dependences,
Phe =2 MW, <n>=5.85·10
19
m
-3
, na0=8·10
14
m
-3
The next Figs. 2-5 represent the radial profiles of ion
and electron temperatures, plasma densities, ambipolar
electric field and neutral atom density. All the profiles
evidence on the large plasma parameter gradients at the
plasma boundary.
Figs. 6 and 7 show the radial plasma density and
plasma temperature profiles corresponding to the mode
of a relatively low density <n>~3.3∙10
19
m
-3
. In this case
the plasma heating of electron and ions was done in
equal parts Phe=Phi=2 MW.
0,0 0,2 0,4 0,6 0,8 1,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1
0
1
4
c
m
-3
Radius
n(r)
Fig. 2. Radial profile of the plasma density
0,0 0,2 0,4 0,6 0,8 1,0
0,00
0,01
0,02
0,03
0,04
0,05
0,06
1
0
k
e
V
Radius
Te
Ti
Fig. 3. Profiles of the electron and ion temperatures
ISSN 1562-6016. ВАНТ. 2015. №1(95) 43
0,0 0,2 0,4 0,6 0,8 1,0
0,0
2,0x10
-6
4,0x10
-6
6,0x10
-6
8,0x10
-6
Radius
Nh(r)
x1014
cm-3
Fig. 4. Radial profile of the neutral density
0,0 0,2 0,4 0,6 0,8 1,0
-3,0
-2,5
-2,0
-1,5
-1,0
-0,5
0,0
1
0
k
V
/m
Radius
Er
Fig. 5. Radial profile of the ambipolar electric filed
Here the power contribution, counting on a single
charged particle, is larger approximately by a factor of
3.5 compared to the case of <n>~5.85∙10
19
m
-3
. As a
result, higher temperatures were obtained. Moreover, in
the profiles of n(r), Te(r) and Ti(r) different features are
observed. A dip in the density curve with a step near the
plasma edge takes place. In the ion temperature curve a
flat region is formed. The dependence of Er on the
radius, in main, is similar to the case with a high
density, but there is a sharp dip to the negative values
near the jump on the Ti profile. In this case the energy
confinement time is 60 ms.
3. U-2M RESULTES
The stellarator U-2M has significantly less sizes and
a lower magnetic field as compared with LHD. In U-2M
helical magnetic field ripples are much larger.
Moreover, for plasma heating in U-2M one uses lower
0,0 0,2 0,4 0,6 0,8 1,0
0,0
0,1
0,2
0,3
0,4
0,5
1
0
1
4
c
m
-3
Radius
n(r)
Fig. 6. Radial plasma density profile, LHD, case of low
density, <n>=3.3·10
19
m
-3
0,0 0,2 0,4 0,6 0,8 1,0
0,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
1
0
k
e
V
Radius
Te
Ti
Fig. 7. Electron and ion temperature profiles,
<n>=3.3·10
19
m
-3
powers Ph = 200 kW. As a result, the plasma density in
this device does not exceed several units per 10
18
m
-3
.
The mentioned features were taken into consideration
when defining the parameters of calculations.
Figs. 8-10 represents the profiles of temperature,
plasma density and electric field for U-2M with the
initial average plasma density value n=2.5∙10
18
m
-3
and
the neutral density in the chamber nh=5∙10
17
m
-3
. The
plasma heating of electrons and ions was done in equal
parts Phe=Phi=0.1 MW. In that case the average electron
and ion temperature values were set at a level of
Te~400, Ti~170 eV and the neutral atom concentration
outside the plasma was nh0~5∙10
16
m
-3
. Within the
confinement volume the concentration of neutral atoms
quickly decreases with the distance from the plasma
boundary. The profile of plasma density has a maximum
in the vicinity of the boundary of the plasma column.
This feature, apparently, is the result of the presence of
an intense source δS in this area.
The calculations of plasma parameters with the
initial plasma density value n=1∙10
18
m
-3
and density
neutrals in the chamber nh=2∙10
17
m
-3
, for the same
heating variant as in the case with n=2.5∙10
18
m
-3
, shows
that the electric field and temperature distributions are
of a similar form. However, the plasma density profile
has a flat view along the main part of the plasma radius.
There is observed a little decrease of n in the vicinity of
the plasma center (Fig. 11). Note, that in the case of
U-2M the energy confinement time was of 1…1.5 ms.
0,0 0,2 0,4 0,6 0,8 1,0
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
1
0
k
e
V
Radius
Te
Ti
Fig. 8. U-2M, Temperature profiles
44 ISSN 1562-6016. ВАНТ. 2015. №1(95)
0,0 0,2 0,4 0,6 0,8 1,0
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
1
0
1
4
c
m
-3
Radius
n(r)
Fig. 9. U-2M, Density profile
0,0 0,2 0,4 0,6 0,8 1,0
-0,40
-0,35
-0,30
-0,25
-0,20
-0,15
-0,10
-0,05
0,00
0,05
1
0
k
V
/m
Radius
Er
Fig. 10. U-2M, Electric field profile
0,0 0,2 0,4 0,6 0,8 1,0
0,000
0,002
0,004
0,006
0,008
0,010
0,012
0,014
0,016
0,018
1
0
1
4
c
m
-3
Radius
n(r)
Fig. 11. U-2M, Density profile, n0=1·10
18
,
Phe=Phi=0.1 MW
CONCLUSIONS
Calculations of spatial plasma parameter
distributions in the stellarators U-2M and LHD,
operating under conditions of recycling and neoclassic
transport realization, show the formation of high
gradients for basic plasma and neutral atom parameters
near the plasma boundary. In some cases the density
profiles are formed with the density decreasing in the
vicinity of the plasma center. There the flat spots
formed before the gradient sharpening near the plasma
boundary are observed.
REFERENCES
1. E. Hinnov, A.S. Bishop, and H. Fallon // Plasma
Physics. 1968, v. 10, № 3, p. 291.
2. G. Kawamura, Y. Tomito, M. Kabayashi, D. Tsaha-
kaya // Proceedings of ITC18. 2008, p. 234-237.
3. V.A. Rudakov // Visnyk Kharkivskogo National’nogo
Universytety. Seriya fizychna “Yadra, chastynky,
polya”. 2012, № 2/54/, p. 15-23 (in Russian).
4. G.G. Lesnyakov // Voprosy Atomnoj Nauki i Techniki.
Seriya “Termoyadernyj sintez”. 1980, № 1, p. 118 (in
Russian).
5. V.A. Rudakov // Journal of Kharkiv National
University. Physical Series: Nuclei, Particles, Fields.
2012, v. 1017 (3/55), p. 66-74.
6. V.A. Rudako // Journal of Kharkiv National
University. Physical Series: Nuclei, Particles, Fields.
2012, v. 1001 (2/54), p. 15-23.
7. L.M. Kovrizhnykh // Nucl. Fusion.1984, v. 24, p. 435.
8. V.E. Bykov, A.V. Georgievskii, V.V. Demchenko, et
al. // Fusion Technology.1990, v. 17, № 1, p. 140-147.
9. A. Iiyoshi, M. Fuiwara, O. Motojima, N. Ohyabu,
K. Yamazaki // Fusion Technology. 1990, v. 17, № 1,
p. 169-187.
Article received 10.12.2014
РАСПРЕДЕЛЕНИЯ ПАРАМЕТРОВ ПЛАЗМЫ В СТЕЛЛАРАТОРЕ В УСЛОВИЯХ
РЕЦИКЛИНГА ПРИ НЕОКЛАССИЧЕСКОМ ПЕРЕНОСЕ
В.А. Рудаков
C использованием одномерного пространственно-временного численного кода рассчитаны
пространственные распределения параметров плазмы в стеллараторах LHD и У-2М, работающих в условиях
рециклинга в предположении реализации неоклассического переноса. Получены устойчивые решения
системы уравнений для пространственных распределений температур ионов и электронов, плотности
плазмы и нейтральных атомов, амбиполярного электрического поля. Показано образование плоских
участков в радиальных профилях параметров плазмы вблизи границы плазмы.
РОЗПОДІЛИ ПАРАМЕТРІВ ПЛАЗМИ В СТЕЛАРАТОРІ В УМОВАХ
РЕЦИКЛІНГУ ПРИ НЕОКЛАСИЧНОМУ ПЕРЕНЕСЕННІ
В.А. Рудаков
З використанням одновимірного просторово-часового числового коду розраховано просторові розподіли
параметрів плазми в стелараторах LHD і У-2М, працюючих в умовах рециклінгу в припущенні реалізації
неокласичного перенесення. Отримані стійкі рішення системи рівнянь для просторових розподілів
температур іонів і електронів, щільності плазми та нейтральних атомів, амбіполярного електричного поля.
Показано утворення плоских ділянок у радіальних профілях параметрів плазми поблизу межі плазми.
http://iopscience.iop.org/0032-1028/
http://iopscience.iop.org/0032-1028/
|