About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes
Parameters of an experimental stellarator reactor operating under conditions of ambipolarity of neoclassical transport fluxes are calculated with the use of a space-time numerical code. Dimensions of the system and the confinement magnetic field are taken the same as in the ITER tokamak reactor. The...
Збережено в:
| Дата: | 2012 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/109085 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes / V.A. Rudakov // Вопросы атомной науки и техники. — 2012. — № 6. — С. 16-18. — Бібліогр.: 5 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-109085 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1090852016-11-21T03:02:08Z About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes Rudakov, V.A. Магнитное удержание Parameters of an experimental stellarator reactor operating under conditions of ambipolarity of neoclassical transport fluxes are calculated with the use of a space-time numerical code. Dimensions of the system and the confinement magnetic field are taken the same as in the ITER tokamak reactor. The paper shows a possibility of engineering development of an experimental stellarator reactor with parameters comparable to these of an experimental tokamak reactor. C использованием пространственно-временного численного кода рассчитаны параметры экспериментального реактора-стелларатора в условиях амбиполярности неоклассических транспортных потоков. Размеры системы и удерживающее магнитное поле приняты такими же, как и в реакторе-токамаке ITER. Показана возможность создания экспериментального реактора-стелларатора с характеристиками, сопоставимыми с характеристиками экспериментального реактора-токамака. З використанням просторово-часового чисельного коду розраховано параметри експериментального реактора-стеларатора в умовах амбіполярності неокласичних транспортних потоків. Розміри системи і утримуюче магнітне поле прийняті такими ж, як і в реакторі-токамаці ITER. Показана можливість створення експериментального реактора-стеларатора з характеристиками, порівнянними з характеристиками експериментального реактора-токамака. 2012 Article About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes / V.A. Rudakov // Вопросы атомной науки и техники. — 2012. — № 6. — С. 16-18. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.55.Hc, 52.55.Rk, 52.55.Dj http://dspace.nbuv.gov.ua/handle/123456789/109085 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. About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes Вопросы атомной науки и техники |
| description |
Parameters of an experimental stellarator reactor operating under conditions of ambipolarity of neoclassical transport fluxes are calculated with the use of a space-time numerical code. Dimensions of the system and the confinement magnetic field are taken the same as in the ITER tokamak reactor. The paper shows a possibility of engineering development of an experimental stellarator reactor with parameters comparable to these of an experimental tokamak reactor. |
| format |
Article |
| author |
Rudakov, V.A. |
| author_facet |
Rudakov, V.A. |
| author_sort |
Rudakov, V.A. |
| title |
About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes |
| title_short |
About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes |
| title_full |
About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes |
| title_fullStr |
About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes |
| title_full_unstemmed |
About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes |
| title_sort |
about physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2012 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/109085 |
| citation_txt |
About physical parameters of experimental reactor- stellarator in the conditions of ambipolarity of neoclassical transport fluxes / V.A. Rudakov // Вопросы атомной науки и техники. — 2012. — № 6. — С. 16-18. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT rudakovva aboutphysicalparametersofexperimentalreactorstellaratorintheconditionsofambipolarityofneoclassicaltransportfluxes |
| first_indexed |
2025-07-07T22:32:58Z |
| last_indexed |
2025-07-07T22:32:58Z |
| _version_ |
1837029213520003072 |
| fulltext |
16 ISSN 1562-6016. ВАНТ. 2012. №6(82)
ABOUT PHYSICAL PARAMETERS OF EXPERIMENTAL
REACTOR- STELLARATOR IN THE CONDITIONS
OF AMBIPOLARITY OF NEOCLASSICAL TRANSPORT FLUXES
V.A. Rudakov
Institute of Plasma Physics NSC “Kharkov Institute of Physics and Technology”,
Kharkov, Ukraine
E-mail: rudakov@kipt.kharkov.ua
Parameters of an experimental stellarator reactor operating under conditions of ambipolarity of neoclassical
transport fluxes are calculated with the use of a space-time numerical code. Dimensions of the system and the
confinement magnetic field are taken the same as in the ITER tokamak reactor. The paper shows a possibility of
engineering development of an experimental stellarator reactor with parameters comparable to these of an
experimental tokamak reactor.
PACS: 52.55.Hc, 52.55.Rk, 52.55.Dj
INTRODUCTION
Successful results of investigations at tokamaks
were used as a base for development of an experimental
ITER tokamak reactor [1]. The ITER project
implementation will allow one to carry out
investigations on the plasma with characteristics
corresponding to a full-scale fusion reactor and to solve
engineering problems concerned with construction and
exploitation of many systems providing the reactor
operation.
Similarly, investigations at the experimental
stellarator rector will be a necessary stage of works
aimed to solving the problems of controlled
thermonuclear fusion with the use of such a system.
Despite attractive features which allow steady-state
operation of a stellarator, investigations with such traps
are limited because of the high plasma losses predicted
by the neoclassical theory.
Investigations with the purpose of stellarator
optimization have demonstrated that it is possible to
reduce the neoclassical losses by decreasing the helical
magnetic field ripple hε [2]. Solutions of the system of
equations determining the plasma loss-energy balance
under ambipolarity conditions have shown that the
plasma confinement can be much improved under
conditions of fuel injection into the plasma center [3].
The present paper considers the process of starting
and sustaining of the steady-state fusion burn in the
experimental stellarator-reactor having plasma
parameters and magnetic characteristics corresponding
to the design objectives of the ITER reactor.
SYSTEM OF EQUATIONS
A system of equations which is a combination of the
heat conduction equations for electrons and ions and the
diffusion equations has been solved. The system
describes the time-space plasma behavior in the 1D
space case under the assumption of the minor plasma
radius averaged over magnetic surface.
Ecbeieh
2
e
e
4
QQQQQE
σvNK
r
rr
1
t
T
N
2
3
α
f +−−−++
∂
∂
−=
∂
∂
Π , (1)
Eiheii
i QQQr
rr
1
t
T
N
2
3
−++
∂
∂
−=
∂
∂
Π , (2)
δSrS
rr
1
t
N
+
∂
∂
−=
∂
∂
j . (3)
Here Πi, Πe, Si and Se are the heat fluxes and fluxes
of ion and electron particles corresponding to the
electron transfer mode 1/ν and to the square root of ion
collision frequency [4], Eα − α − particle energy;
eiQ − collision heat exchange; bQ − bremsstrahlung;
cQ − cyclotron radiation; jhQ − external source heating.
Here and below the index j marks a particle type. The
content of deuterium and tritium in the reactor plasma
was taken equal. The coefficient fK =0.95 determines
the α− particle energy part transferred to electrons. It
has been supposed that the most part of cyclotron
radiation is absorbed in the plasma and the power loss is
only 5 %.
In calculations it has been assumed that the specific
heating power is proportional to the plasma density. The
ambipolar electric field influence on the plasma particle
energy was taken into account by QE =-Sj·Er. The term
with a source δS in the right side of equation (3)
provide the plasma density maintenance at a level close
to the constant one.
To the system of equations (1)-(3) added were
boundary and initial conditions in which the spatial
derivatives of density, temperature and potential are
equal to zero in the plasma center, and the values of
these parameters at the boundary are equal to the low
constant values. The electric field was determined from
the equation of balance between ion and electric fluxes
at every step of numerical code spatial grid. In all cases
the solution was corresponding to the left (ion) root
giving the negative values of Er.
CALCULATION RESULTS
In the paper, similarly to the case of ITER reactor,
the tore radius R=6.2 m, minor radius a-2 m,
confinement field B0=5.3 Т.
Plasma losses substantially depend on the
quantity hε , the value of which at the plasma boundary
is taken equal to 0.06, as in [3], that approximately
corresponds to its value in the LHD facility where the
ISSN 1562-6016. ВАНТ. 2012. №6(82) 17
magnetic configuration center position is located at the
radius R=3.53 m [2].
The injection of fuel pellets has been simulated by
the expression )x/(1nδn Δ−= p , which determines their
throwing into the plasma center from the half-width
evaporation region Δ . The expenditure of energy for
injected particle heating is taken into account.
Fig. 1 shows the reactor fusion power behavior
during the plasma heating with 40 MW power. In this
case the energy input to plasma ions and electrons was
20 MW. The fusion power reached approximately
600 MW with heating power conservation. If the
heating power decreases to 10 MW, then the steady-
state burn is set with a fusion power of about 440 MW.
The full heating stopping leads to the reaction damping.
Fig. 2 and 3 illustrate the spatial distribution of the
plasma density and ambipolar electric field for three
values of half-width ablation region (Δ=0.5; 0.75 and
1). Maximum values of the plasma density and the
deepest field minimum Er are formed at minimal values
of ablation region Δ=0.5. A phenomenon of the deepest
minimum Er has been found in experiments and is
confirmed by calculations for the facility W7-AS [5].
To the small width Δ the peak values of the reactor
heat power are corresponding (Fig. 4). Spatial
distributions of ion and electron temperature are shown
in Fig. 5. Their significant difference in the peripheral
region is because of the ambipolar field influence. As a
result there is a notable discrepancy between the
average values of Te and Ti (Fig. 6). The increase of the
average plasma density value from 7·1019 to 8·1019m-3
leads to the heat power increase almost by a factor of
1.5 (Fig. 7). In this case the steady-state burn mode was
sustained by the additional heating power of 10 MW
shared equally between ions and electrons.
0 2 4 6 8 10 12 14
0
100
200
300
400
500
600
M
W
S
Ph=0
10 MW
40 MW
40 MW
Fig. 1. Reactor heat power in the process of ignition
with a plasma heating power
of 40 MW, N=0.7·1020 m-3, Δ=0.5
Besides the additional heating powers, in the plasma
the α− particle energy is absorbed that makes a one fifth
part of the reactor heat power. And a half power is lost
as a result of bremsstrahlung and cyclotron radiation.
Note, that the bremsstrahlung is calculated under the
assumption that Z = 1 that is possible only in the case of
ideal operation of a divertor.
RESULTS AND DISCUSSION
Some variants of stellarator reactor parameters are
given in the Table in comparison with the ITER reactor
parameters. The investigation results show that the
stellarator reactor may have fusion energy release
modes similar to those which have been planned in the
ITER reactor. An important condition in principle is the
necessary fuel injection directly into the plasma center.
Thus the spatial distributions with sharply peaked
profiles of parameters can be realized. The design
quantity β in the plasma center reaches 25 % that can
make a problem in providing the stability of such
modes. The calculations have shown that a significant
part of the plasma heat energy is taken away with
bremsstrahlung and cyclotron radiation despite the
assumption about the high reflection power of the first
wall and minimum value of the plasma charge Z.
Implementation of the above-mentioned conditions can
be realized with appropriate designs of the first wall and
plasma divertor.
0,0 0,2 0,4 0,6 0,8 1,0
-1
0
1
2
3
4
5
6
7
8
9
N
, 1
020
m
-3
radius
Δ=0.5
0.75
1
Fig. 2. Spatial distributions of the plasma density
for different pellet evaporation widths: Δ=0.5; 0.75; 1.
N=0.7·1020 m-3, Ph=40 MW
0,0 0,2 0,4 0,6 0,8 1,0
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
E
r,
10
k
V
/m
radius
Δ=1
0.75
0.5
Fig. 3. Spatial distributions of Er for different pellet
ablation widths: Δ=0.5; 0.75; 1. N=0.7·1020 m-3, Ph=40 MW
0 2 4 6 8 10 12 14 16 18
0
100
200
300
400
500
600
P t, M
W
S
Δ=0.5
Δ=0.75
Δ=1
Fig. 4. Reactor thermal power in the process of ignition
for different pellet evaporation widths: Δ=0.5; 0.75; 1.
N=0.7·1020 m-3, Ph=40 MW
The investigation results obtained enable to
conclude that an experimental stellarator rector can have
characteristics comparable with these of an
experimental tokamak reactor.
18 ISSN 1562-6016. ВАНТ. 2012. №6(82)
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
10
k
eV
radius
Te
Ti
Fig. 5. Spatial distribution of the
plasma temperature in the steady-
state burn mode: Δ=0.5, N=0.7·1020
m-3, Ph=40 MW
5 10 15 20
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
10
k
eV
S
Te
Ti
Fig. 6. Temperature of ions and
electrons in the process of ignition
and after transition into the steady-
state burn mode: Δ=0.5,
N=0.7·1020 m-3, Ph=20+20 MW
0 5 10 15 20
0
100
200
300
400
500
600
700
800
M
W
S
N=0.8
N=0.75
N=0.7
Fig. 7. Reactor thermal power in the
process of ignition for different
values of the plasma density:
Ph=40 M, Δ=0.5, N=0.7; 0.75;
0.8·1020 m-3
Table of reactor parameters
ERSt-1 ERSt-2 ERSt-
3 ITER
Confinement magnetic
field –B, T 5.3 5.3 5.3 5.3
Major tore
radius – R, m 6.2 6.2 6.2 6.2
Minor radius – a, m 2 2 2 2
Average density – <N>,
1020/m3 0.7 0.7 0.8 0.8…1.0
Electron temperature –
Te, кeV 9.3 9 9 8.9
Ion temperature –
Ti, кeV 6.8 6.7 7 8.1
Helical ripple at the
boundary –εhmax
0.06 0.06 0.06 0
Total heat power – Pt,
MW 540 510 660 500
Load on the first wall –
Qw, МW/m2 0.68 0.64 0.82 0.6
Plasma pressure – <β>, % 1.6 1.55 1.83 2.2
Energy lifetime – τΕ, s 1.1 1.09 1.08 2.1
Particle confinement time
– τn, s 1,8 2.8 2.5 -
Additional heating power,
МW 40 30 40 40
REFERENCES
1. O. Mitarai and K. Muraoka. Ignition analyses with
ITER89P and ITER93HP scaling for burn control and
diagnostics in ITER-ID // Plasma Phys. Control.
Fusion. 1998, v. 40, p. 1349-1372.
2. S. Murakami, A. Wakasa, H. Maaβberg,
C.D. Beidler, H. Yamada, K.Y. Watanabe. LHD
Experimental Group Neoclassical Transport
Optimization of LHD // Nucl. Fusion. 2002, v. 42,
p. L19-L22.
3. V.А. Rudakov On parameters of stellarator reactor
under conditions of ambipolarity of neoclassic transport
fluxes // Visnyk Kharkivs’kogo Natsionalnogo
Universytetu. Seriya fizychna “Yadra, chastynky,
polya”. 2012, N2/54/, p. 15-23 (in Russian),
4. L.M. Kovrizhnykh. The Energy Confinement Time in
Stellarators// Nucl. Fusion. 1984, v. 24, p. 435.
5. Y. Turkin, C.D. Beidler, H. Maaβberg, et al.
Neoclassical transport simulations for stellarators //
Physics of Plasmas. 2011, v. 18, p. 022505.
Article received 10.10.12
О ФИЗИЧЕСКИХ ПАРАМЕТРАХ ЭКСПЕРИМЕНТАЛЬНОГО РЕАКТОРА-СТЕЛЛАРАТОРА
В УСЛОВИЯХ АМБИПОЛЯРНОСТИ НЕОКЛАССИЧЕСКИХ ТРАНСПОРТНЫХ ПОТОКОВ
В.А. Рудаков
C использованием пространственно-временного численного кода рассчитаны параметры
экспериментального реактора-стелларатора в условиях амбиполярности неоклассических транспортных
потоков. Размеры системы и удерживающее магнитное поле приняты такими же, как и в реакторе-токамаке
ITER. Показана возможность создания экспериментального реактора-стелларатора с характеристиками,
сопоставимыми с характеристиками экспериментального реактора-токамака.
ПРО ФІЗИЧНІ ПАРАМЕТРИ ЕКСПЕРИМЕНТАЛЬНОГО РЕАКТОРА-СТЕЛАРАТОРА
В УМОВАХ АМБІПОЛЯРНОСТІ НЕОКЛАСИЧНИХ ТРАНСПОРТНИХ ПОТОКІВ
В.А. Рудаков
З використанням просторово-часового чисельного коду розраховано параметри експериментального
реактора-стеларатора в умовах амбіполярності неокласичних транспортних потоків. Розміри системи і
утримуюче магнітне поле прийняті такими ж, як і в реакторі-токамаці ITER. Показана можливість створення
експериментального реактора-стеларатора з характеристиками, порівнянними з характеристиками
експериментального реактора-токамака.
|