Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section
Technique of calculation the pitch-angle, energy and poloidal distributions of the flux of charged fusion products lost to the first wall of axisymmetric tokamak due to first orbit loss mechanism is developed. Analytical model of the magnetic field used in this study takes into account Shafranov shi...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2012 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
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| Цитувати: | Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section / A.O. Moskvitin, V.O. Yavorskij, V.Ya. Goloborod’ko, Yu.K. Moskvitina, O.A. Shyshkin // Вопросы атомной науки и техники. — 2012. — № 6. — С. 28-30. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859864167180140544 |
|---|---|
| author | Moskvitin, A.O. Yavorskij, V.O. Goloborod’ko, V.Ya. Moskvitina, Yu.K. Shyshkin, O.A. |
| author_facet | Moskvitin, A.O. Yavorskij, V.O. Goloborod’ko, V.Ya. Moskvitina, Yu.K. Shyshkin, O.A. |
| citation_txt | Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section / A.O. Moskvitin, V.O. Yavorskij, V.Ya. Goloborod’ko, Yu.K. Moskvitina, O.A. Shyshkin // Вопросы атомной науки и техники. — 2012. — № 6. — С. 28-30. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Technique of calculation the pitch-angle, energy and poloidal distributions of the flux of charged fusion products lost to the first wall of axisymmetric tokamak due to first orbit loss mechanism is developed. Analytical model of the magnetic field used in this study takes into account Shafranov shift, elongation, triangularity and up-down asymmetry. Usage of the drift constant of motion space allows substantial reducing the computational efforts for simulation the lost particles flux at a given point of the first wall.
Разработан метод для расчета распределений по питч-углу, энергии и полоидальному углу потока заряженных продуктов синтеза, теряемых на первой стенке осесимметричного токамака вследствие мгновенных потерь (МП). Используемая в этом исследовании аналитическая модель магнитного поля учитывает шафрановский сдвиг, эллиптичность, треугольность и асимметрию «верх-низ». Использование пространства инвариантов движения дает возможность значительно уменьшить вычислительные усилия при моделировании потока теряемых частиц в заданную точку на первой стенке.
Розроблено метод обчислення розподілів по пітч-куту, енергії та полоїдальному куту потоку заряджених продуктів синтезу, які втрачаються на першій стінці осесиметричного токамака внаслідок миттєвих втрат (МВ). Аналітична модель магнітного поля, яка використовується в цьому дослідженні, враховує шафранівський зсув, еліптичність, трикутність та асиметрію «верх-низ». Використання простору інваріантів руху дає можливість значно зменшити обчислювальні зусилля при моделюванні потоку частинок, що втрачаються, в задану точку на першій стінці.
|
| first_indexed | 2025-12-07T15:47:49Z |
| format | Article |
| fulltext |
28 ISSN 1562-6016. ВАНТ. 2012. №6(82)
ENERGY AND PITCH-ANGLE DISTRIBUTION OF THE PROMPT
LOSSES IN TOKAMAK WITH NON-CIRCULAR CROSS-SECTION
A.O. Moskvitin1, V.O. Yavorskij2,3, V.Ya. Goloborod’ko2,3, Yu.K. Moskvitina1,4, O.A. Shyshkin1
1V.N. Karazin Kharkov National University, Kharkov, Ukraine;
2Institute for Nuclear Research, Ukrainian Academy of Sciences, Kiev, Ukraine;
3Association EURATOM-OEAW, Institute for Theoretical Physics, Innsbruck, Austria;
4National Science Centre “Kharkov Physics and Technology Institute”, Kharkov, Ukraine
E-mail: Anton.Moskvitin@gmail.com
Technique of calculation the pitch-angle, energy and poloidal distributions of the flux of charged fusion products
lost to the first wall of axisymmetric tokamak due to first orbit loss mechanism is developed. Analytical model of
the magnetic field used in this study takes into account Shafranov shift, elongation, triangularity and up-down
asymmetry. Usage of the drift constant of motion space allows substantial reducing the computational efforts for
simulation the lost particles flux at a given point of the first wall.
PACS: 52.55Pi
INTRODUCTION
The first orbit (FO) loss is one of the conventional loss
mechanisms of the charged fusion product (CFP). There
are thorough review on theoretical study [1] and
experimental research activities [2] of this loss mechanism.
Analytical approaches for FO flux calculation were derived
in [1, 3]. It should be noted that these models were
provided for poloidal distributions of FO loss of CFPs in
tokamak with circular cross-section. The numerical code
presented in current study in addition to poloidal
distributions allows also examination of pitch-angle and
energy distributions of the FO loss in tokamaks with
elliptic and triangular flux surfaces.
After the first experiments in TFTR [4], it became
obvious that FO losses can be decreased significantly due
to increasing the plasma current above 3MA .
Nevertheless, interest to these losses in this study is caused
by necessity to develop common approach for simulation
of FO loss signal in scintillator probe in order to
distinguish contributions from the studied processes and
from the FO losses. For example, the toroidal field ripple
induced losses were observed in addition to the
conventional FO losses of DD CFPs in JET [5].
Thus, the main aim of this study is to develop the
theoretical approach for simulation spatial and velocity
distributions of FO losses in order to model the
scintillator probe signal of pure FO losses. This
approach should cover variety of existing magnetic
configurations, the magnetic field model should be
flexible for predictive modeling, should maintain test
particle simulations for crosscheck validation. Smooth,
axially symmetric wall is assumed. The finite Larmor
orbit width has been neglected yet, in order to introduce
the main ideas of developed approach. Test particle
simulations were carried out using the same magnetic
configuration in order to provide a cross-check.
1. FLUX CALCULATION MODEL
In current study, magnetic configuration of tokamak
is assumed to be axisymmetric with non-circular flux
surfaces. The analytical model for such configurations is
described in details in [6]. Using this model, it is also
possible to carry out test particle simulations using the
same numerical model of the magnetic configuration
[7]. It is supposed that flux surfaces are determined by
the parametric dependence of the cylindrical coordinates
( ) ( ) ( )0, cosR Rρ χ ρ ρ χ= + Δ + , (1)
( ) ( ) ( ) ( ) ( ), sin 1 cosaxZ Z k
α
ρ χ ρ ρ χ ρ χ= − −Λ⎡ ⎤⎣ ⎦ , (2)
where R and Z represent the spatial variables of the
cylindrical coordinates { }, ,R Zϕ , ρ and χ represent
variables of the new flux-like coordinates { }, ,ρ χ ϕ ,
( )ρΔ , ( )k ρ , ( )ρΛ are flux surface parameters: the
Shafranov’s shift, the elongation parameter and the
triangularity parameter respectively, α is a flux surface
model parameter, 0R is a vacuum vessel major radius,
axZ is a Z coordinate of the magnetic axis. The
coordinate ρ is a flux surface label and its value is
equal to distance between the magnetic axis and the flux
surface in the equatorial midplane, and χ is the analog
of poloidal angle. The angle ϕ is the toroidal angle, and
its value and direction coincide in both coordinate
systems { }, ,R Zϕ and { }, ,ρ χ ϕ .
Commonly total flux of lost particles can be written as
( ),loss fus
LD
R d dΓ = ∫ r v r v , (3)
where ( ),fusR r v source of CFP particles; r , v −
radius vector and velocity vector respectively. The
integration domain “LD” (Loss Domain) is defined by
the full set of particle orbits, which intersects
confinement boundary, e.g. last closed flux surface or
vacuum vessel wall. Here we assume that particle is lost
if its trajectory intersects plasma boundary plaρ = .
Generally, the integration domain is six-
dimensional. However, taking into account axial
symmetry of the problem and using guiding center
approximation, this domain becomes four-dimensional.
Thus, the concrete set of four numbers defines only one
specific orbit. Certainly, it is true if the effect of
Coulomb collisions is neglected.
ISSN 1562-6016. ВАНТ. 2012. №6(82) 29
Diagnostic techniques, such as a scintillator probe or
a Faraday cup, give a tip to choose the set of variables
in the following way { }, , ,a aa Vχ ξ , where , aa χ define
the position of the probe in the { },ρ χ coordinates, and
,a Vξ describe the orbit parameters (pitch V Vξ = and
particle speed V , where V is the parallel particle
velocity). Nevertheless, it is possible to derive the
alternative representation of the lost particle flux in the
terms of the variables { }, , ,a aa Vχ ξ
22 2loss fus a a a
LD
R g J d d V d dVπ ρ χ π ξΓ = ∫ (4)
where g Jacobian of coordinate system { }, ,ρ χ ϕ ,
aJ Jacobian of coordinates transition
( ) ( ), , , , , ,a aV a Vρ χ ξ χ ξ∂ ∂ and it is supposed that
source of CFP particles ( ), ,fus aR Vρ ξ in real space
depends only on flux label ρ and it is axially
symmetric in velocity space regarding to the direction of
magnetic field. First assumption is based on the thesis
that fusR depends only on plasma specie densities and
temperatures, which are commonly supposed to be
constant on the flux surface. The second one is a
consequence of the fast phase mixing due to cyclotron
gyration.
2. DRIFT ORBIT TOPOLOGY ANALYSIS
Taking into account the invariance of the magnetic
moment and the toroidal angular momentum, the
guiding center motion equations take the form
( ) ( ) ( )2 21 , 1 a aR Rξ ρ χ ξ− = − , (5)
( ) ( ), a a aC R C Rρ ξ ρ χ ξΨ + = Ψ + , (6)
where ( ),a aR R a χ= , ( )a aΨ = Ψ and C mV e= .
These equations implicitly define particle trajectory
( ), aρ χ c and pitch-angle variation along orbit
( ), aξ χ c , where { }, ,a a a Vχ ξ=c . Nevertheless, not
only χ can be chosen as the independent parameter, it
is also possible to consider ρ or ξ as independent
variable.
In order to exclude the dependence on χ the
equations (5) and (6) can be rewritten as
( ) ( ), 2aR B D Cξ ξρ = +c , (7)
( ) ( ) 2B D Aξ ξ ξξ ρ = − , (8)
where ( ) ( ) a aA a C Rξ ρ ξ= Ψ −Ψ − , ( )21 a aB R Cξ ξ= −
and 2 24D B Aξ ξ ξ= + , these designations are made for
convenience reasons.
Under given orbit parameters { }, , ,a aa Vχ ξ , it is
possible to reconstruct the guiding center trajectory for
particle with speed V , which passes through point
{ }, aa χ with pitch aξ . For this purpose, one can change
ρ continuously and evaluate R from Eq. (7). Then
using R and ρ it is possible to derive χ
( ) ( ){ }0arccos R Rχ ρ ρ ρ= − − Δ⎡ ⎤⎣ ⎦ . (9)
Finally, using Eq. (2) coordinate Z can be obtained.
Taking into account up-down symmetry of magnetic
configuration, and supposing that point { }, aa χ is the
final point of trajectory, independent parameter ρ
should be changed only in segment [ ]min , aρ , where
minρ is value of variable ρ at the point of intersection
of trajectory with equatorial midplane.
To find minρ one can derive the equation
( ) ( ) ( )2 2 2
min min min min min, , 0C R A B CRξ ξρ χ ρ ρ χ− + = ,(10)
where min 0χ = for intersection point at the ‘low field
side’ and minχ π= for the ‘high field side’. Analysis of
the drift orbit topology in a axisymmetric magnetic
configuration is presented in [8, 9].
According to the provided drift orbit analysis it is
now possible to localize roots of the Eq. (10) and to
finish the definition of ‘Loss domain’ in { }, , ,a aa Vχ ξ .
Thus the expression (4) for the loss particle flux can be
written as
min
1
2
0 1
2 2 2
a
loss a a fus ad dV V d d R g J
π
π ρ
π χ π ξ ρ
∞
− −
Γ = ∫ ∫ ∫ ∫ ,(11)
where g can be derived using [6], and aJ can be
derived using expressions (7) and (8).
RESULTS AND CONCLUSIONS
Commonly, the scintillator probe is placed at the
fixed point. This gives an opportunity to consider only
flux at the given location { }, aa χ . Next point is that this
probe data contains information about separate flux
tubes with the given pitch and particle speed { },a Vξ ,
i.e. the signal from the certain channel of probe is in fact
proportional only to value of the integral over ρ in (11)
. Thus for further study we will consider only
monoenergetic flux ( ), , ,a aI a Vχ ξ of the lost particles at
point { }, aa χ with pitch and velocity { },a Vξ
( )
min
, ,
a
fus a aI d R V g J
ρ
ρ ρ ξ= ∫ . (12)
The expression for metric coefficient aJ can be used
2
2 2
sin 1 1
sin 1 1 4 /
a a
a
a
a
J
G
χ ξ
ρ χ ξ
+
=
− +
, (13)
where /G B Aξ ξ= . It is supposed integration along
orbit in Eq.(12). Thus, the variable χ in Eq. (13) can be
derived using Eq. (9).
To provide numerical integration in Eq. (12) it is
used Gauss scheme with 32 points. This scheme doesn’t
require the evaluation of integrand at the integration
domain ends. This feature of the scheme becomes very
useful taking into account singularity of Eq. (13) at
0χ = and χ π= , which takes place for minρ ρ= .
30 ISSN 1562-6016. ВАНТ. 2012. №6(82)
It is obvious that FLR effects play significant role in
the CFP dynamics. However, to simplify the analysis of
FO loss distributions in this paper we neglect the finite
Larmor orbit width. Nevertheless, gyro-orbit simulation
of 400000 test particles was carried out, in order to
provide a cross-check. All parameters of magnetic
configuration were the same as used for Eq. (12).
The results of this calculation are demonstrated in
Figure. It is seen that distributions of both approaches
are in reasonable agreement. For this calculation the
source term was supposed monoenergetic.
Comparison of the pitch angle distribution of the lost
CFP, which are calculated using “full orbit”
and “drift orbit” models
In conclusion, we would like to summarize main
results of the presented study. The earlier developed
approach for poloidal distribution of prompt losses of
CFP is extended to calculate pitch-angle and velocity
distributions of the lost ions. The numerical code for
simulation of the FO losses of CFP is developed for
axisymmetric magnetic configuration of tokamak taking
into account non-circular flux surfaces. Smooth axially
symmetric 2D wall is assumed I this model. Cross-
check of the newly upgraded approach against full orbit
calculations shows good agreement.
The approach used in this paper gives an opportunity
to decrease calculation efforts for simulating the
experimental data from scintillator probe, or other point
probe. Results of the test numerical simulation agree
with earlier conducted calculations [1, 3] and
experimental data [4, 5].
REFERENCES
Ya.I. Kolesnichenko The role of alpha particles in
tokamak reactors // Nuclear Fusion. 1980, v. 20, №6,
p. 727-780.
W.W. Heidbrink, G.J. Sadler. The behaviour of fast
ions in tokamak experiments // Nuclear Fusion. 1994,
v. 34, №4, p. 535-615.
3. L.M. Hively, G.H. Miley. Fusion product
bombardment of a tokamak first wall // Nuclear Fusion.
1977, v. 17, №5, p. 1031-1046.
4. S.J. Zweben, R.L. Boivin, M. Diesso, et al. Loss of
Alpha-Like MeV Fusion Products from TFTR //
Nuclear Fusion. 1990, v. 30, №8, p. 1551-1574.
5. Yu. Baranov, I. Jenkins, et al. Evidence of anomalous
losses of fusion products on JET // 37th EPS Conference
on Plasma Physics, Dublin, Ireland, June 21−25, 2010.
P5.141.
6. V.A. Yavorskij, K. Schoepf, et al. Analytical models
of axisymmetric toroidal magnetic fields with non-
circular flux surfaces // Plasma Physics and Controlled
Fusion. 2001, v. 43, №3, p. 249-269.
7. V. Yavorskij, Yu. Baranov, et al. Modelling of spatial
and velocity distributions of diffusive fast ion loss in
JET // 38th EPS Conf. on Plasma Phys., Strasbourg,
France, June 27–July 1, 2011. P.4.029.
8. J.A. Rome, Y-K.M. Peng. The topology of tokamak
orbits // Nuclear Fusion. 1979, v. 19, №9, p. 1193-1205.
9. A.O. Moskvitin, V.O. Yavorskij, et al. First orbit
losses of charged fusion products in tokamak:
fluxcalculation // Journal of Kharkiv University,
physical series “Nuclei, Particles, Fields”. 2012,
v. 2/54/, №1001, p. 4-14.
Article received 27.09.12
РАСПРЕДЕЛЕНИЯ ПО ЭНЕРГИИ И ПИТЧ-УГЛУ ПРЯМЫХ ДРЕЙФОВЫХ ПОТЕРЬ
В ТОКАМАКЕ С НЕКРУГЛЫМ СЕЧЕНИЕМ
А.А. Москвитин, В.А. Яворский, В.Я. Голобородько, Ю.К. Москвитина, О.А. Шишкин
Разработан метод для расчета распределений по питч-углу, энергии и полоидальному углу потока
заряженных продуктов синтеза, теряемых на первой стенке осесимметричного токамака вследствие
мгновенных потерь (МП). Используемая в этом исследовании аналитическая модель магнитного поля
учитывает шафрановский сдвиг, эллиптичность, треугольность и асимметрию «верх-низ». Использование
пространства инвариантов движения дает возможность значительно уменьшить вычислительные усилия при
моделировании потока теряемых частиц в заданную точку на первой стенке.
РОЗПОДІЛИ ПО ЕНЕРГІЇ ТА ПІТЧ-КУТУ ПРЯМИХ ДРЕЙФОВИХ ВТРАТ
В ТОКАМАЦІ З НЕКРУГЛИМ ПЕРЕРІЗОМ
А.О. Москвітін, В.О. Яворський, В.Я. Голобородько, Ю.К. Москвітіна, О.О. Шишкін
Розроблено метод обчислення розподілів по пітч-куту, енергії та полоїдальному куту потоку заряджених
продуктів синтезу, які втрачаються на першій стінці осесиметричного токамака внаслідок миттєвих втрат
(МВ). Аналітична модель магнітного поля, яка використовується в цьому дослідженні, враховує
шафранівський зсув, еліптичність, трикутність та асиметрію «верх-низ». Використання простору інваріантів
руху дає можливість значно зменшити обчислювальні зусилля при моделюванні потоку частинок, що
втрачаються, в задану точку на першій стінці.
|
| id | nasplib_isofts_kiev_ua-123456789-109093 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:47:49Z |
| publishDate | 2012 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Moskvitin, A.O. Yavorskij, V.O. Goloborod’ko, V.Ya. Moskvitina, Yu.K. Shyshkin, O.A. 2016-11-20T17:16:44Z 2016-11-20T17:16:44Z 2012 Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section / A.O. Moskvitin, V.O. Yavorskij, V.Ya. Goloborod’ko, Yu.K. Moskvitina, O.A. Shyshkin // Вопросы атомной науки и техники. — 2012. — № 6. — С. 28-30. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.55Pi https://nasplib.isofts.kiev.ua/handle/123456789/109093 Technique of calculation the pitch-angle, energy and poloidal distributions of the flux of charged fusion products lost to the first wall of axisymmetric tokamak due to first orbit loss mechanism is developed. Analytical model of the magnetic field used in this study takes into account Shafranov shift, elongation, triangularity and up-down asymmetry. Usage of the drift constant of motion space allows substantial reducing the computational efforts for simulation the lost particles flux at a given point of the first wall. Разработан метод для расчета распределений по питч-углу, энергии и полоидальному углу потока заряженных продуктов синтеза, теряемых на первой стенке осесимметричного токамака вследствие мгновенных потерь (МП). Используемая в этом исследовании аналитическая модель магнитного поля учитывает шафрановский сдвиг, эллиптичность, треугольность и асимметрию «верх-низ». Использование пространства инвариантов движения дает возможность значительно уменьшить вычислительные усилия при моделировании потока теряемых частиц в заданную точку на первой стенке. Розроблено метод обчислення розподілів по пітч-куту, енергії та полоїдальному куту потоку заряджених продуктів синтезу, які втрачаються на першій стінці осесиметричного токамака внаслідок миттєвих втрат (МВ). Аналітична модель магнітного поля, яка використовується в цьому дослідженні, враховує шафранівський зсув, еліптичність, трикутність та асиметрію «верх-низ». Використання простору інваріантів руху дає можливість значно зменшити обчислювальні зусилля при моделюванні потоку частинок, що втрачаються, в задану точку на першій стінці. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Магнитное удержание Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section Распределения по энергии и питч-углу прямых дрейфовых потерь в токамаке с некруглым сечением Розподіли по енергії та пітч-куту прямих дрейфових втрат в токамаці з некруглим перерізом Article published earlier |
| spellingShingle | Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section Moskvitin, A.O. Yavorskij, V.O. Goloborod’ko, V.Ya. Moskvitina, Yu.K. Shyshkin, O.A. Магнитное удержание |
| title | Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section |
| title_alt | Распределения по энергии и питч-углу прямых дрейфовых потерь в токамаке с некруглым сечением Розподіли по енергії та пітч-куту прямих дрейфових втрат в токамаці з некруглим перерізом |
| title_full | Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section |
| title_fullStr | Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section |
| title_full_unstemmed | Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section |
| title_short | Energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section |
| title_sort | energy and pitch-angle distribution of the prompt losses in tokamak with non-circular cross-section |
| topic | Магнитное удержание |
| topic_facet | Магнитное удержание |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/109093 |
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