Application of magnetic diagnostics to determine basic energy characteristics of plasma
Method of determination of plasma parameters and magnetic configuration of toroidal magnetic traps according to measurement results of magnetic fields of plasma currents out of volume of plasma confinement is implied now by magnetic diagnostics [1-3]. Rokosovskiy coil, diamagnetic loop and saddle co...
Збережено в:
| Дата: | 2008 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/111025 |
| 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: | Application of magnetic diagnostics to determine basic energy characteristics of plasma / V.K. Pashnev // Вопросы атомной науки и техники. — 2008. — № 6. — С. 225-226. — Бібліогр.: 5 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-111025 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1110252025-02-09T14:51:44Z Application of magnetic diagnostics to determine basic energy characteristics of plasma Застосування магнітної діагностики для визначання основних енергетичних характеристик плазми Применение магнитной диагностики для определения основных энергетических характеристик плазмы Pashnev, V.K. Plasma diagnostics Method of determination of plasma parameters and magnetic configuration of toroidal magnetic traps according to measurement results of magnetic fields of plasma currents out of volume of plasma confinement is implied now by magnetic diagnostics [1-3]. Rokosovskiy coil, diamagnetic loop and saddle coil are now used most often to determine macroscopic plasma parameters; they allow to determine longitudinal current magnitude and energy content of plasma in the confinement volume. The most important characteristics of plasma are energy confinement time of plasma tE and power W injected into plasma. Possibility to determine tE, W and Z (average charge value) values using sensors of magnetic diagnostics in stellarators is discussed. Показано, що при стрибкоподібній зміні потужності нагріву плазми за допомогою датчиків магнітною діагностики може бути визначена величина енергетичного часу життя плазми, потужність, що вводиться в плазму, средний заряд плазми, а також з'являється можливість з'ясування механізмів збудження струму в плазмі. Показано, что при скачкообразном изменении мощности нагрева плазмы с помощью датчиков магнитной диагностики может быть определена величина энергетического времени жизни плазмы tE, вводимая в плазму мощность W, средний заряд плазмы Z, а также появляется возможность выяснения механизмов возбуждения тока в плазме. 2008 Article Application of magnetic diagnostics to determine basic energy characteristics of plasma / V.K. Pashnev // Вопросы атомной науки и техники. — 2008. — № 6. — С. 225-226. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.55.Dy, 52.55.Hc, 52.70.Ds https://nasplib.isofts.kiev.ua/handle/123456789/111025 en Вопросы атомной науки и техники application/pdf 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 |
Plasma diagnostics Plasma diagnostics |
| spellingShingle |
Plasma diagnostics Plasma diagnostics Pashnev, V.K. Application of magnetic diagnostics to determine basic energy characteristics of plasma Вопросы атомной науки и техники |
| description |
Method of determination of plasma parameters and magnetic configuration of toroidal magnetic traps according to measurement results of magnetic fields of plasma currents out of volume of plasma confinement is implied now by magnetic diagnostics [1-3]. Rokosovskiy coil, diamagnetic loop and saddle coil are now used most often to determine macroscopic plasma parameters; they allow to determine longitudinal current magnitude and energy content of plasma in the confinement volume. The most important characteristics of plasma are energy confinement time of plasma tE and power W injected into plasma. Possibility to determine tE, W and Z (average charge value) values using sensors of magnetic diagnostics in stellarators is discussed. |
| format |
Article |
| author |
Pashnev, V.K. |
| author_facet |
Pashnev, V.K. |
| author_sort |
Pashnev, V.K. |
| title |
Application of magnetic diagnostics to determine basic energy characteristics of plasma |
| title_short |
Application of magnetic diagnostics to determine basic energy characteristics of plasma |
| title_full |
Application of magnetic diagnostics to determine basic energy characteristics of plasma |
| title_fullStr |
Application of magnetic diagnostics to determine basic energy characteristics of plasma |
| title_full_unstemmed |
Application of magnetic diagnostics to determine basic energy characteristics of plasma |
| title_sort |
application of magnetic diagnostics to determine basic energy characteristics of plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2008 |
| topic_facet |
Plasma diagnostics |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111025 |
| citation_txt |
Application of magnetic diagnostics to determine basic energy characteristics of plasma / V.K. Pashnev // Вопросы атомной науки и техники. — 2008. — № 6. — С. 225-226. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT pashnevvk applicationofmagneticdiagnosticstodeterminebasicenergycharacteristicsofplasma AT pashnevvk zastosuvannâmagnítnoídíagnostikidlâviznačannâosnovnihenergetičnihharakteristikplazmi AT pashnevvk primeneniemagnitnojdiagnostikidlâopredeleniâosnovnyhénergetičeskihharakteristikplazmy |
| first_indexed |
2025-11-27T00:34:03Z |
| last_indexed |
2025-11-27T00:34:03Z |
| _version_ |
1849901603330457600 |
| fulltext |
APPLICATION OF MAGNETIC DIAGNOSTICS TO DETERMINE BASIC
ENERGY CHARACTERISTICS OF PLASMA
V.K. Pashnev
Institute of Plasma Physics, National Science Center
“Kharkov Institute of Physics and Technology”, 61108 Kharkov, Ukraine
Method of determination of plasma parameters and magnetic configuration of toroidal magnetic traps according to
measurement results of magnetic fields of plasma currents out of volume of plasma confinement is implied now by
magnetic diagnostics [1-3]. Rokosovskiy coil, diamagnetic loop and saddle coil are now used most often to determine
macroscopic plasma parameters; they allow to determine longitudinal current magnitude and energy content of plasma
in the confinement volume. The most important characteristics of plasma are energy confinement time of plasma τE and
power W injected into plasma. Possibility to determine τE, W and Z (average charge value) values using sensors of
magnetic diagnostics in stellarators is discussed.
PACS: 52.55.Dy, 52.55.Hc, 52.70.Ds
THE OBTAINED RESULTS
Longitudinal unidirectional plasma current
∫=
a
rdrjI
0
02π (1)
is measured by Rogovski coil. Here, α – average small
radius of plasma column, j0 – density of longitudinal
current and r – current radius. Longitudinal current is
usually generated by ohmic discharge or is a consequence
of “neoclassical effects” (bootstrap-current) [4].
Longitudinal current can also be a result of heating
process (drag current) at heating using neutral injection,
RF or HF waves.
Diamagnetic flow ΔΦ is bounded in magnetic traps
with plasma parameters and magnetic configuration with
the following ratio [5]
∆Φ = drdxxr
r
j
cRBc
Idr
B
a a
st
a
∫ ∫∫
∂
∂++
0 0
2
0
2
0 0
2
2
0
2 44Pr8 ιπππ
. (2)
Here, B0 – magnetic field value on the axis of facility,
P – gas-kinetic plasma pressure and ιst – angle of
rotational transformation generated by stellarator field.
As it is clear from the expression (2), diamagnetic
flow consists of two terms that are general for tokamaks
and stellarators (the first and the second component) and
stellarator additive. This additive can turn out rather
essential in a number of cases.
Magnetic field flow generated by Pfirsch-Schlüter
currents
j = ϑ
ι
cos'2
0B
cP− (3)
is measured by saddle coil and is described by the
expression [5]
dr
b
rj
R
rj
R
N
B
cP
c
b
R
cR
I
s
a
st
2
2
0
00
0
'1'22
18ln
∫
+∆+
∆+
−
−=Λ Ψ
ι
ι
π
, (4)
where ι = ιc + ιst – is a total angle of rotational
transformation, ιc – current angle of rotational
transformation, ϑ - poloidal angle, S – area of saddle
coil, b – radius where the coil is located, Δ – drift of
magnetic surfaces, N – number of stellarator field periods
and ()’ – dash means radius derivative.
As it is seen from expressions (1), (2) and (4), using
magnetic sensors one can determine value of plasma
energy content Г, knowing basic characteristics of
magnetic system and plasma current
PRa222π=Γ , ∫=
a
dr
a
P
0
2 Pr2
. (5)
Plasma energy balance is described by the known
expression
W
t E
=Γ+Γ
∂
∂
τ2
3
2
3
, (6)
In statical situation, as it is known, expression (6) is
simplified to the following form:
E
W
τ
Γ=
2
3
. (7)
Study of transient process while measuring power
injected into plasma is of a certain interest. If the
discharge process passes a step-like increase of power on
a value of WW < <δ for the time Et τ< < , then,
according to the expression (6), temporal modification of
energy-content of plasma can be described in the
following way:
)1()( /
0
Etet τδδ −−Γ=Γ . (8)
Here, 0Γδ - value on which energy content increases
for the time Et τ> > . From the expression (8) it is clear,
that at a step-like increase of power the energy-content of
plasma will change with typical time Et τ≅ . Value of
energy life time can be determined by the expression
0
0
→
Γ
∂
∂
Γ
=
t
E
t
δ
τ
. (9)
At emergency shut-down of power for the time
Et τ< < changes of energy-content of plasma are
determined according to (6) by the following expression:
Ete τδδ /
0
−Γ=Γ . (10)
i.e. after shut-down of heating source the energy-content
of plasma decreases exponentially with typical time
Et τ≅ . Energy time Eτ According to (10) is determined
by the expression:
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6. 225
Series: Plasma Physics (14), p. 225-226.
0
0
→∂
Γ∂
Γ
−=
t
E
t
δ
τ
. (11)
It is clear from the given expressions (9) and (11) that
step-like change of power injected into plasma allows to
determine value Eτ . While according to expression (7),
knowing value Eτ allows to determine the power injected
into plasma.
Assuming that longitudinal current in plasma is
generated by “increasing” effect. Then, in case of step-
like increase of heating power the change of current Iδ
will be described by the expression
UIRI
t
L δδδ =+
∂
∂
(12)
Here, Uδ - change of electromotive force related to
the change of heating power value. Solution to this
equation at constU =δ will be
)1( /
0
τδδ teII −−= , (13)
where 0Iδ - increase of current value for the time
R
Lt => > τ . According to the expression (13), value τ
can be determined by the following way
0
0
→∂
∂
=
t
I
t
I
δ
δτ
. (14)
If longitudinal current is determined by neoclassical
effects (bootstrap-current), then, in case of step-like
change of the injected power of the expression (12) it is
changed to the following format
)1( /
0
EteUIRI
t
L τδδδ −−=+
∂
∂
. (15)
Here, 0Uδ - electromotive force change related to
influence of neoclassical effects. As a result of solution of
this equation we will obtain
−
+
−
−= −− ττ
ττ
τ
ττ
τδδ //
0 1 t
E
t
E
E eeII E , (16)
and 0
0
=
∂
∂
→t
I
t
δ . (17)
Then, expression (7) can be rewritten in the format
0
2
2
0
→∂
∂
=
t
E t
I
I
τ
δτ
. (18)
Comparison of expressions (14) and (18) shows that
different mechanisms of current excitation give different
speed of current changes at sharp change of plasma
heating power. By the known value
R
L=τ and the known
profile )(rTe - electron temperature one can determine an
average plasma charge Z. Ties between average plasma
charge and value R
L=τ can be easily obtained from ratio
∫
−=
− a
e rdrT
a
RZ
0
2/3
4
5.18ln10*14.1
τ
. (19)
CONCLUSIONS
Possibilities to use sensors of magnetic diagnostics
(Rogovski coil, diamagnetic loop and saddle coil) to
determine basic energy characteristics of plasma are
discussed in this work.
It is shown that at sharp changes of plasma heating
power Et τ< < , R
L=τ using the enumerated above sensors
of magnetic diagnostics one can determine the following:
Eτ - energy life time of plasma, W is absorbed power
injected into plasma, Z is average charge of plasma and
there is a possibility to find out mechanisms of current
excitation. The most important advantage of the discussed
methodology is absence of necessity to conduct absolute
measurements of plasma parameters to determine Eτ .
REFERENCES
1. V.D. Shafranov. // Plasma Phys. 13, 1971, p. 757.
2. L.E. Zakharov, V.D. Shafranov. // Sov. Journal
theoretical physics, v. 43, 1973, p. 225 (in Russian).
3. V.K. Pasnev. Vozmoznosti magnitnoj diagnostiki v
stelaratorach. Preprint KIPT 91- 35. Moskow, 1991.
4. A.A. Galeev, R.Z. Sagdeev. Voprosy teorii plazmy
(Problems of Plasma Theory) v. 7, (ed. by
Leontovich M.A.), Atomizdat, Moscow, 1973, p.205 (in
Russian).
5. V.K.Pasnev, V.V. Nemov. Use of magnetic diagnostics
in stellarators // Nuclear Fusion, v. 33, N. 3, 1993, p.435.
Article received 15.10.08.
ПРИМЕНЕНИЕ МАГНИТНОЙ ДИАГНОСТИКИ ДЛЯ ОПРЕДЕЛЕНИЯ ОСНОВНЫХ
ЭНЕРГЕТИЧЕСКИХ ХАРАКТЕРИСТИК ПЛАЗМЫ
В.К. Пашнев
Показано, что при скачкообразном изменении мощности нагрева плазмы с помощью датчиков магнитной
диагностики может быть определена величина энергетического времени жизни плазмы τE, вводимая в плазму
мощность W, средний заряд плазмы Z, а также появляется возможность выяснения механизмов возбуждения
тока в плазме.
ЗАСТОСУВАННЯ МАГНІТНОЇ ДІАГНОСТИКИ ДЛЯ ВИЗНАЧЕННЯ ОСНОВНИХ ЕНЕРГЕТИЧНИХ
ХАРАКТЕРИСТИК ПЛАЗМИ
В.К. Пашнєв
Показано, що при стрибкоподібній зміні потужності нагріву плазми за допомогою датчиків магнітною
діагностики може бути визначена величина енергетичного часу життя плазми, потужність, що вводиться в
плазму, средний заряд плазми, а також з'являється можливість з'ясування механізмів збудження струму в
плазмі.
226
|