Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field
The mechanism of controlled resonant particle transport in the closed magnetic traps is studied. The resonance condition of the particle-magnetic field interaction is presented. The dependence of the resonance radial position on the particle kinetic energy and parameter value is demonstrated. The co...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
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| Цитувати: | Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field / Yu.K. Moskvitina, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 6. — С. 19-21. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859632947240370176 |
|---|---|
| author | Moskvitina, Yu.K. Shishkin, A.A. |
| author_facet | Moskvitina, Yu.K. Shishkin, A.A. |
| citation_txt | Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field / Yu.K. Moskvitina, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 6. — С. 19-21. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The mechanism of controlled resonant particle transport in the closed magnetic traps is studied. The resonance condition of the particle-magnetic field interaction is presented. The dependence of the resonance radial position on the particle kinetic energy and parameter value is demonstrated. The cold α-particle motion in close vicinity to the resonance position is analyzed with the use of numerical integration of the guiding center equations under Coulomb scattering.
Вивчено механізм керованого переносу резонансних заряджених частинок в замкнутих магнітних пастках. Представлено резонансну умову в разі взаємодії частинка-магнітне поле. Досліджено залежність радіального положення резонансу від кінетичної енергії та значення параметра частинки. Проаналізовано рух α-частинки поблизу резонансу шляхом чисельного інтегрування рівнянь ведучого центру за наявності кулонівського розсіювання.
Изучен механизм управляемого переноса резонансных заряженных частиц в замкнутых магнитных ловушках. Представлено резонансное условие в случае взаимодействия частица-магнитное поле. Исследована зависимость радиального положения резонанса от кинетической энергии и значения параметра частицы. Проанализировано движение α-частицы вблизи резонанса путём численного интегрирования уравнений движения ведущего центра при наличии кулоновского рассеяния.
|
| first_indexed | 2025-12-07T13:12:41Z |
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| fulltext |
EFFECT OF THE RESONANCE PHENOMENA ON HIGH ENERGETIC
PARTICLE LOSSES IN CLOSED MAGNETIC TRAP
WITH THE ROTATIONAL TRANSFORM OF THE MAGNETIC FIELD
Yu.K. Moskvitina1, A.A. Shishkin 1, 2
1V.N. Karazin Kharkov National University, Kharkov, Ukraine,
E-mail:Yu.Moskvitina@gmail.com
2 National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The mechanism of controlled resonant particle transport in the closed magnetic traps is studied. The resonance con-
dition of the particle-magnetic field interaction is presented. The dependence of the resonance radial position on the par-
ticle kinetic energy W and parameter value VV|| is demonstrated. The cold α-particle motion in close vicinity to the
resonance position is analyzed with the use of numerical integration of the guiding center equations under Coulomb
scattering.
PACS: 52.55.Pi, 52.65.Cc, 52.55.Dy, 52.35.Mw, 52.20.Hv
1. INTRODUCTION AND MOTIVATION
An essential problem of the nuclear fusion in closed
magnetic traps is fusion product particle confinement. On
the one hand, huge (~1 MeV) birth energy of these ions
should be transferred to background plasma to maintain
ignition. Under maintaining ignition it is meant the heat-
ing of new portions of fuel. On the other hand, cooled
(~10 keV) ions should be removed for maintaining energy
balance through decreasing radiation losses.
From the first DT experiments on JET and TFTR it
became obvious that large MHD activity causes a fast ion
loss fraction up to ≈ 50%, which would be intolerably
large for a reactor [1, 2]. As it was shown analytically in
works [3-8] resonant interaction between a spectrum of
Alfven waves and α-particles can take place, leading to
significant anomalous transport of the particles. Much at-
tention is devoted to dynamics of shear Alfven waves col-
lectively excited by energetic particles (see, e.g., [9]).
The resonant interaction is also very important for he-
lical systems, because spectrum of these phenomena is
wider due to helical symmetry. The experimental study of
this problem is carried out on LHD [10-11], analytical ap-
proach is realized in Refs [3, 5].
Discovery of the super density core in plasmas on the
LHD has stimulated study of a fusion helical reactor with
a high density and relatively low temperature plasma [12-
14], from the one hand, and, from the other hand, of dif-
ferent methods of α-particle confinement control in heli-
cal devices. One group of these methods is based on pro-
duction of drift resonances by the resonant magnetic per-
turbation of certain mode [15-19].
Here the effect of Coulomb scattering on cold α-parti-
cles drift resonances is studied.
The paper is organized as follows. The model of the
magnetic field and electrical field models are presented in
Section 2.1. The resonance condition for system particle-
magnetic field is analyzed numerically in Section 2.2. The
cold α-particles motion in close vicinity to the resonance
position is analyzed with the use of numerical integration
of the guiding centre equations in Section 3. Principal
conclusions are drawn in Section 4.
2. RESONANCE CONDITION IN TOROIDAL
CONFIGURATION WITH THE ROTATIONAL
TRANSFORM
2.1. MAGNETIC AND ELECTRICAL FIELD
MODELS
The coordinates used in the present calculation are the
quasi-toroidal coordinates ( )ϕϑ ,,r . The main magnetic
field is introduced in the following form
( ){ }1,,0 2
000 rRrRRB ι=B , (1)
where ι is the rotational transform, ϑcos0 rRR += .
The magnetic field perturbations in general case could
be written as
( )0,cos,sin
1
,
00 ΘΘ
=
−m
nm a
rb
R
RBδB , (2)
where ϕϑ nm −=Θ , nmb , is the perturbation field am-
plitude, m and n are the poloidal and toroidal numbers of
the perturbation field, respectively.
The following expression for the electric potential is
used
( )( ) EErΕΕ
2110
αα−Φ=Φ . (3)
Electric field was defined as EΦ− ∇=E . Such profile pa-
rameter values for further simulations are used
2and8,10 210 ==−=Φ EEE kV αα .
2.2. RESONANCE CONDITION
To analyze the dependence of the resonance radial po-
sition from the particle kinetic energy W and parameter
value VV|| we use the resonance condition 0=∆ which
was obtained in [19] for chosen models of magnetic and
electrical field. The analytical expression for ∆ has the
form
−
−
−×
×
−
−−
−
−=∆
υ
υ
ι
υ
υ
υ
υι
υ
υ
υ
υ
ω
DE
DE
c
R
m
nr
R
m
nr
M
W
Ma
mWm
0
||
0
||
2
2
2
2
2
1
12
2
)1(
||
,(4)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6. 19
Series: Plasma Physics (14), p. 19-21.
where ||,,, υυMW are kinetic energy, particle mass, parti-
cle velocity and longitudinal component of velocity, re-
spectively. 0BcErDE =υ is the electric drift velocity and
)(MceBZc =ω is the cyclotron frequency.
The resonance condition takes place at two values of
the radial positions (there exist two roots) under the per-
turbations with “wave” numbers 1,3 == nm .
The analysis of the resonance condition is presented
on the Fig.1 and Fig.2.
Fig.1. Resonance radial position versus ion energy
One can see from the Fig.2 and Fig.3 that the radial
position of the resonances
- weakly depends on the particle energy in the range
MeVWkeV 150 ≤≤ ;
- weakly depends on the parameters VV|| for the values
about unity, but for values about zero the situation is op-
posite, in particular, for negative values resonance shifts
to the plasma core.
Fig.2. Resonance radial position versus parameter value
VV||
It should be noted that during its motion α-particle
collides with background plasma particles, hence its pa-
rameter VV|| decreases. This could effect on particle
drift resonance: the particle could turn out in resonance
with magnetic field perturbation, and escape from reso-
nance. The effect of Coulomb Scattering will be shown in
the next section.
3. Α-PARTICLE DRIFT RESONANCES
In the previous work [19] it was shown that if the res-
onance conditions take place at the plasma periphery, then
the removal of the cold α-particles is noticeable. It should
be noted that the characteristic time of the studied pro-
cesses is of the order 1−10 milliseconds and Coulomb
scattering should be taken into account.
The effect of collisions in plasma is expressed in the
guiding center equations through the following term [20]
( ) ( ) ( )vbn
MM
MMZL
v
Z
dt
d
cg
*
1
*
* *
*2*
..3
24 Φ+−= ∑Vp π ,(5)
where ( ) ( ) Φ ′−Φ=Φ xxvb*
1 , and ( )xΦ is the error
function; *** 2TMb = ; L is Coulomb logarithm;
MZ , are particle charge and mass, nT , are background
plasma temperature and density, respectively; superscript
* designates variables which relate to background plasma.
For simulation of the α-particle motion following ini-
tial parameter values were chosen keVW 100= ,
9.0|| =VV , r0 =109 cm; θ0=0, φ0=0 and 50% mixture
DT plasma parameters: 313* 10 −≈ cmn , keVT 20* = .
Parameters of magnetic configuration were chosen
similar to those which are used in JET: 4
0 2 10B G= Ч ,
cma 120= , cmR 2960 = , 2)/(75.01 ar⋅−=ι , bmn=30 G.
a b
Fig.3. The drift islands with the drift transform
3/1* =ι in the vertical cross-sections of the torus w/o
collisions (a); and under Coulomb scattering (b)
Under the same initial conditions α-particle deviates
from the initial surface due to Coulomb scattering on the
contrary to the case without collisions (Fig.3).
Fig.4. Radial position of the α-particles with the initial
energy =W 100 keV versus time w/o collisions (a); and
under Coulomb scattering (b)
As it can be seen from Fig.4(a) the radial coordinate of
the α-particle is oscillating near drift resonance position
during 50 msec. We mean that the equation 0=∆ is satis-
fied. But we see from Fig.4(b) that in the presence of the
collisions the same particle during the period till
t=15 msec is in the resonance interaction with the perturb-
20
ing field, and then leaves the resonance and deviates to
the larger distances from the initial surface.
Summarizing, the conclusion is done that the Coulomb
scattering could lead to both formation and destruction of
the drift islands.
4. SUMMARY AND DISCUSSIONS
The interaction of α-particle with magnetic perturba-
tion of small amplitude leads to resonant structures for-
mation (drift islands).
The resonance condition analysis shows that radial po-
sition of the drift resonance is sensitive to the particle ki-
netic energy in the range 10-100 keV. For small negative
value of the ratio VV|| , the resonance occurs near plasma
core.
The particle collisions could lead to both formation
and destruction of the drift resonance. Besides that reso-
nant interaction with magnetic field perturbation together
with Coulomb scattering increase transport of energetic
particles at the plasma edge.
These mechanisms in couple can be used for the re-
moval controlling of cold the α-particles outward trans-
port from the confinement volume.
ACKNOWLEDGEMENTS
Authors thank Prof. Igor Girka for continuously atten-
tion to their work, support and useful suggestions and
Dr. Oleg Shyshkin for fruitful discussions and invaluable
advices.
The research is supported by Science and Technology
Center in Ukraine, Project # 3685.
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Article received 22.09.08
ВЛИЯНИЕ РЕЗОНАНСНЫХ ЯВЛЕНИЙ НА ПОТЕРИ ВЫСОКОЭНЕРГЕТИЧНЫХ ЧАСТИЦ
В ЗАМКНУТОЙ МАГНИТНОЙ ЛОВУШКЕ С ВРАЩАТЕЛЬНЫМ ПРЕОБРАЗОВАНИЕМ
МАГНИТНОГО ПОЛЯ
Ю.К. Москвитина, А.А. Шишкин
Изучен механизм управляемого переноса резонансных заряженных частиц в замкнутых магнитных ловуш-
ках. Представлено резонансное условие в случае взаимодействия частица-магнитное поле. Исследована зависи-
мость радиального положения резонанса от кинетической энергии W и значения параметра VV|| частицы.
Проанализировано движение α-частицы вблизи резонанса путём численного интегрирования уравнений движе-
ния ведущего центра при наличии кулоновского рассеяния.
ВПЛИВ РЕЗОНАНСНИХ ЯВИЩ НА ВТРАТИ ВИСОКОEНЕРГЕТИЧНИХ ЧАСТИНОК В ЗАМКНУТІЙ
МАГНІТНІЙ ПАСТЦІ З ОБЕРТАЛЬНИМ ПЕРЕТВОРЕННЯМ МАГНІТНОГО ПОЛЯ
Ю.К. Москвітіна, О.О. Шишкін
Вивчено механізм керованого переносу резонансних заряджених частинок в замкнутих магнітних пастках.
Представлено резонансну умову в разі взаємодії частинка-магнітне поле. Досліджено залежність радіального
положення резонансу від кінетичної енергії W та значення параметра VV|| частинки. Проаналізовано рух α-
частинки поблизу резонансу шляхом чисельного інтегрування рівнянь ведучого центру за наявності
кулонівського розсіювання.
21
2.1. Magnetic and electrical field models
2.2. resonance condition
4. Summary and discussions
Влияние резонансных явлений на потери высокоэнергетичных частиц в замкнутой магнитной ловушке с вращательным преобразованием магнитного поля
ВПлив резонансних явищ на втрати високоeнергетичних частинок в замкнутій магнітній пастці з обертальним перетворенням магнітного поля
|
| id | nasplib_isofts_kiev_ua-123456789-110808 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:12:41Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Moskvitina, Yu.K. Shishkin, A.A. 2017-01-06T13:31:35Z 2017-01-06T13:31:35Z 2008 Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field / Yu.K. Moskvitina, A.A. Shishkin // Вопросы атомной науки и техники. — 2008. — № 6. — С. 19-21. — Бібліогр.: 20 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/110808 PACS: 52.55.Pi, 52.65.Cc, 52.55.Dy, 52.35.Mw, 52.20.Hv The mechanism of controlled resonant particle transport in the closed magnetic traps is studied. The resonance condition of the particle-magnetic field interaction is presented. The dependence of the resonance radial position on the particle kinetic energy and parameter value is demonstrated. The cold α-particle motion in close vicinity to the resonance position is analyzed with the use of numerical integration of the guiding center equations under Coulomb scattering. Вивчено механізм керованого переносу резонансних заряджених частинок в замкнутих магнітних пастках. Представлено резонансну умову в разі взаємодії частинка-магнітне поле. Досліджено залежність радіального положення резонансу від кінетичної енергії та значення параметра частинки. Проаналізовано рух α-частинки поблизу резонансу шляхом чисельного інтегрування рівнянь ведучого центру за наявності кулонівського розсіювання. Изучен механизм управляемого переноса резонансных заряженных частиц в замкнутых магнитных ловушках. Представлено резонансное условие в случае взаимодействия частица-магнитное поле. Исследована зависимость радиального положения резонанса от кинетической энергии и значения параметра частицы. Проанализировано движение α-частицы вблизи резонанса путём численного интегрирования уравнений движения ведущего центра при наличии кулоновского рассеяния. Authors thank Prof. Igor Girka for continuously attention to their work, support and useful suggestions and Dr. Oleg Shyshkin for fruitful discussions and invaluable advices. The research is supported by Science and Technology Center in Ukraine, Project # 3685. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field Вплив резонансних явищ на втрати високоенергетичних частинок в замкнутій магнітній пастці з обертальним перетворенням магнітного поля Влияние резонансных явлений на потери высокоэнергетичных частиц в замкнутой магнитной ловушке с вращательным преобразованием магнитного поля Article published earlier |
| spellingShingle | Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field Moskvitina, Yu.K. Shishkin, A.A. Magnetic confinement |
| title | Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field |
| title_alt | Вплив резонансних явищ на втрати високоенергетичних частинок в замкнутій магнітній пастці з обертальним перетворенням магнітного поля Влияние резонансных явлений на потери высокоэнергетичных частиц в замкнутой магнитной ловушке с вращательным преобразованием магнитного поля |
| title_full | Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field |
| title_fullStr | Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field |
| title_full_unstemmed | Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field |
| title_short | Effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field |
| title_sort | effect of the resonance phenomena on high energetic particle losses in closed magnetic trap with the rotational transform of the magnetic field |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110808 |
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