Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas
The magnetic field model of the original IFOSIT code was improved by the analytical model of the magnetic field, which takes into account Shafranov shift, elongation, triangularity and up-down asymmetry. The spatial and velocity dependence of the CFP source can be taken into account in the renewed c...
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irk-123456789-1092482016-11-22T03:03:10Z Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas Moskvitin, A.O. Moskvitina, Yu.K. Shyshkin, O.A. Yavorskij, V.O. Schoepf, K. Магнитное удержание The magnetic field model of the original IFOSIT code was improved by the analytical model of the magnetic field, which takes into account Shafranov shift, elongation, triangularity and up-down asymmetry. The spatial and velocity dependence of the CFP source can be taken into account in the renewed code. New options are employed in renewed IFOSIT: calculation of energy and particle fluxes, calculation of the spatial and velocity distributions of lost and confined particles and time evolution of these distributions. Модель магнитного поля в коде IFOSIT была расширена при помощи аналитической модели магнитного поля, которая учитывает шафрановский сдвиг, эллиптичность, треугольность и асимметрию «верх-низ». В обновленном коде теперь учитывается форма профиля источника заряженных продуктов синтеза как в реальном пространстве, так и в пространстве скоростей. В новой версии кода IFOSIT реализованы новые возможности: вычисление потоков энергии и частиц, расчет распределений теряемых и удерживаемых частиц в реальном и скоростном пространствах и эволюция этих распределений. Модель магнітного поля в коді IFOSIT була розширена за допомогою аналітичної моделі магнітного поля, яка враховує шафранівський зсув, еліптичність, трикутність та асиметрію «верх-низ». У оновленому коді тепер враховується форма профілю джерела заряджених продуктів синтезу як в реальному просторі, так і в просторі швидкостей. У новій версії коду IFOSIT реалізовані нові можливості: розрахунок потоків енергії та частинок; розрахунок розподілів у реальному та швидкісному просторах для частинок, які втрачаються, та тих, які утримуються, та еволюція цих розподілів. 2013 2013 Article Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas / A.O. Moskvitin, Yu.K. Moskvitina, O.A. Shyshkin, V.O. Yavorskij, K. Schoepf // Вопросы атомной науки и техники. — 2013. — № 1. — С. 36-38. — Бібліогр.: 16 назв. — англ. 1562-6016 PACS: 52.55Pi http://dspace.nbuv.gov.ua/handle/123456789/109248 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Магнитное удержание Магнитное удержание |
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Магнитное удержание Магнитное удержание Moskvitin, A.O. Moskvitina, Yu.K. Shyshkin, O.A. Yavorskij, V.O. Schoepf, K. Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas Вопросы атомной науки и техники |
| description |
The magnetic field model of the original IFOSIT code was improved by the analytical model of the magnetic field, which takes into account Shafranov shift, elongation, triangularity and up-down asymmetry. The spatial and velocity dependence of the CFP source can be taken into account in the renewed code. New options are employed in renewed IFOSIT: calculation of energy and particle fluxes, calculation of the spatial and velocity distributions of lost and confined particles and time evolution of these distributions. |
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Moskvitin, A.O. Moskvitina, Yu.K. Shyshkin, O.A. Yavorskij, V.O. Schoepf, K. |
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Moskvitin, A.O. Moskvitina, Yu.K. Shyshkin, O.A. Yavorskij, V.O. Schoepf, K. |
| author_sort |
Moskvitin, A.O. |
| title |
Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas |
| title_short |
Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas |
| title_full |
Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas |
| title_fullStr |
Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas |
| title_full_unstemmed |
Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas |
| title_sort |
energy and particle fluxes in presence of rmp in axissymetric 2d tokamak plasmas |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2013 |
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Магнитное удержание |
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http://dspace.nbuv.gov.ua/handle/123456789/109248 |
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Energy and particle fluxes in presence of RMP in axissymetric 2D tokamak plasmas / A.O. Moskvitin, Yu.K. Moskvitina, O.A. Shyshkin, V.O. Yavorskij, K. Schoepf // Вопросы атомной науки и техники. — 2013. — № 1. — С. 36-38. — Бібліогр.: 16 назв. — англ. |
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36 ISSN 1562-6016. ВАНТ. 2013. №1(83)
ENERGY AND PARTICLE FLUXES IN PRESENCE OF RMP
IN AXISSYMETRIC 2D TOKAMAK PLASMAS
A.O. Moskvitin1, Yu.K. Moskvitina2,1, O.A. Shyshkin1, V.O. Yavorskij3,4, K. Schoepf 4
1V.N. Karazin Kharkov National University, Kharkov, Ukraine;
2National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
3Institute for Nuclear Research, Ukrainian Academy of Sciences, Kiev, Ukraine;
4Association EURATOM-OEAW, Institute for Theoretical Physics, Innsbruck, Austria
E-mail: Yu.Moskvitina@gmail.com
The magnetic field model of the original IFOSIT code was improved by the analytical model of the magnetic
field, which takes into account Shafranov shift, elongation, triangularity and up-down asymmetry. The spatial and
velocity dependence of the CFP source can be taken into account in the renewed code. New options are employed in
renewed IFOSIT: calculation of energy and particle fluxes, calculation of the spatial and velocity distributions of
lost and confined particles and time evolution of these distributions.
PACS: 52.55Pi
INTRODUCTION AND MOTIVATION
The particle transport and the confinement of fusion
produced α-particles are important issues for a fusion
reactor [1-2]. Resonant magnetic perturbations (RMPs)
have become a powerful tool for modifying the edge
transport properties and for plasma stability control in
present day tokamaks. The application of non-
axisymmetric RMP fields in the plasma edge region is a
promising technique to suppress and mitigate ELMs for
H-mode tokamak plasmas. It is confirmed by experi-
ments on the DIII-D tokamak [3], and later on JET [4]
and TEXTOR [5]. The alteration of transport properties
of charged fusion products (CFP) induced by these per-
turbations can be regarded as the crucial point for ap-
proving the application of RMPs in future tokamak re-
actors [6]. Note that strong effect of RMPs on the con-
finement of NBI ions in ITER have been predicted re-
cently in [7]. Because, a deeper understanding of how
RMP fields modify charged particle dynamics; edge
transport and stability are needed.
In order to understand the CFP losses driven by
RMPs, a specific numerical code IFOSIT (Ion Full Or-
bit Simulation in Torus) has been developed [8]. The
simulation is based on the test-particle approach. To
calculate each particle trajectory the numerical solution
of the full orbit equation is performed by the Runge-
Kutta method. Coulomb collisions in the code are taken
into account by a 3D Monte-Carlo operator employing a
continuous spectrum of random velocity changes [9].
1. MAGNETIC FIELD 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 [10]. It is supposed that flux sur-
faces 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 and ( )ρΛ are flux surface parameters:
the Shafranov’s shift, the elongation parameter and the
triangularity parameter respectively, and α is a flux
surface model parameter, 0R is 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 sys-
tems { }, ,R Zϕ and { }, ,ρ χ ϕ .
Parameters of the magnetic field model
Parameter name, unit Parameter
value
Vacuum vessel major radius, m 0 2.89R =
Magnetic axis Z coordinate, m 0.323axZ =
Flux surface model parameter 0.5α = −
Maximum minor plasma radius
in equatorial plane, m
0.961pla =
Magnetic axis Shafranov shift,
m
0 0.11Δ =
Elongation profile parameters 0 1.36ek = ,
1 0.315ek =
Triangularity profile parameter 0 0.174eΛ =
Total poloidal current parame-
ter, T·m
7.58J = −
Magnetic configuration calculated using parameters
given in Table is in good agreement with typical axi-
symmetric equilibrium magnetic configuration in JET.
This model was used in for calculation first orbit loss
fluxes in tokamaks with non-circular cross-section, and
ISSN 1562-6016. ВАНТ. 2013. №1(83) 37
examples of the flux surfaces, calculated on the basis of
this model, can be found in [11].
2. FIRST ORBIT LOSSES OF α-PARTICLES
During the test runs, the dynamics of D T− first
orbit losses of α − particles was simulated for the cases
without RMPs. We assumed that the background plasma
consists of the 50 % mixture of D- and T-ions. The
number of electrons satisfies the charge neutrality con-
dition e D Tn n n= + . Also, we assumed that the tempera-
ture of ion and electron specie are the same. The radial
profiles of density ( )en and temperature ( )eT of plasma
components were chosen in the form
( ) ( )5
0 1e e Nn r n ρ= − and ( ) ( )2
0 1 NT r T ρ= − , where the
subscript “0” denotes on-axis values. Using these radial
profiles of the densities and temperatures, the CFP
source (reaction rate) profile was calculated (Fig. 1). In
order to simplify calculation of the weights, the para-
bolic fit ( ) ( )521fit NS ρ ρ∝ − was used.
The start positions of the test particles are uniformly
distributed in the volume of the plasma trap with the
help of the random numbers generator. To each particle
the weight was attributed. This weight is proportional to
the reaction rate in the region, where test particle starts
it motion.
Fig. 1. The reaction rate profiles: calculated and fitted
In velocity space the test-particles were uniformly
distributed on the sphere with radius equal to the birth
velocity of particles.
We calculated the trajectories of 100’000 particles
with next initial parameters: Initial energy (3.5 MeV),
velocity distribution (isotropic), simulated time
(20x10-6 s), Runge-Kutta step (1/200 Tc0 ) and Monte-
Carlo Collisional step (100 Tc0).
To evaluate the net flux of the lost CFP, we assumed
that source is constant in time and used
( )
0
1 t dnt d
t d
τ
τ
Γ = ∫ , which sums the lost rates of fractions
of CFP born at different time. The same procedure can
be done for density evolution. As far as source is sta-
tionary, the net flux reaches the stationary value too. In
contrast to density, which is obviously increasing, be-
cause only certain part of CFP is lost, and others con-
tinue to be confined in trap. The ratio of the lost parti-
cles can be easily estimated as 15 % (Fig. 2).
In conclusion, we would like to present the poloidal
(Fig. 3) and pitch (Fig. 4) distributions of the lost CFP
fluxes. These distributions are in good agreement with
simulation results [11, 12], theoretical predictions for
the first orbit loss mechanism [11, 13, 14] and results of
the experimental study of these losses [15, 16].
Fig. 2. Flux of lost particles
Fig. 3. Poloidal distribution of the flux
Fig. 4. Pitch distribution of the flux
CONCLUSIONS
The magnetic field model of the original IFOSIT
code was improved by the analytical model of the mag-
netic field, which takes into account Shafranov shift,
elongation, triangularity and up-down asymmetry.
38 ISSN 1562-6016. ВАНТ. 2013. №1(83)
The spatial and velocity dependence of the particle
source can be taken into account in the renewed code
now.
Smooth axially symmetric 2D wall is assumed here.
Optimized calculation procedures gives an opportu-
nity to increase number of particles in simulated ensem-
ble and to estimate statistic uncertainties.
New options are employed in the renewed IFOSIT:
• calculation of the energy and particle fluxes;
• calculation of the spatial and velocity distribu-
tions of lost and confined particles;
• the time evolution of the spatial and velocity
distributions.
REFERENCES
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8. Yu.K. Moskvitina, A.O. Moskvitin, et al. The fusion
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Article received 27.09.12
ПОТОКИ ЭНЕРГИИ И ЧАСТИЦ ПРИ НАЛИЧИИ РМВ В ПЛАЗМЕ ОСЕСИММЕТРИЧНОГО
2D-ТОКАМАКА
А.О. Москвитин, Ю.К. Москвитина, О.А. Шишкин, В.А. Яворский, К. Шопф
Модель магнитного поля в коде IFOSIT была расширена при помощи аналитической модели магнитного
поля, которая учитывает шафрановский сдвиг, эллиптичность, треугольность и асимметрию «верх-низ». В
обновленном коде теперь учитывается форма профиля источника заряженных продуктов синтеза как в ре-
альном пространстве, так и в пространстве скоростей. В новой версии кода IFOSIT реализованы новые воз-
можности: вычисление потоков энергии и частиц, расчет распределений теряемых и удерживаемых частиц в
реальном и скоростном пространствах и эволюция этих распределений.
ПОТОКИ ЕНЕРГІЇ ТА ЧАСТИНОК ПРИ НАЯВНОСТІ РМЗ У ПЛАЗМІ ВІСЕСИМЕТРИЧНОГО
2D-ТОКАМАКА
А.О. Москвітін, Ю.К. Москвітіна, О.О. Шишкін, В.О. Яворський, К. Шопф
Модель магнітного поля в коді IFOSIT була розширена за допомогою аналітичної моделі магнітного по-
ля, яка враховує шафранівський зсув, еліптичність, трикутність та асиметрію «верх-низ». У оновленому коді
тепер враховується форма профілю джерела заряджених продуктів синтезу як в реальному просторі, так і в
просторі швидкостей. У новій версії коду IFOSIT реалізовані нові можливості: розрахунок потоків енергії та
частинок; розрахунок розподілів у реальному та швидкісному просторах для частинок, які втрачаються, та
тих, які утримуються, та еволюція цих розподілів.
|