Penetration of electrostatic field through Faraday shield of ICRH strap antenna
The penetration of electrostatic field outside the shield at the part the antenna faced to plasma is studied in the framework of two-dimensional numerical model. It is shown that single-layer Faraday shield does not have satisfactory shielding properties. The shielding can be improved sufficiently u...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2005 |
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| Формат: | Стаття |
| Мова: | Англійська |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Penetration of electrostatic field through Faraday shield of ICRH strap antenna / V.E. Moiseenko // Вопросы атомной науки и техники. — 2005. — № 2. — С. 35-37. — Бібліогр.: 2 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859481141391654912 |
|---|---|
| author | Moiseenko, V.E. |
| author_facet | Moiseenko, V.E. |
| citation_txt | Penetration of electrostatic field through Faraday shield of ICRH strap antenna / V.E. Moiseenko // Вопросы атомной науки и техники. — 2005. — № 2. — С. 35-37. — Бібліогр.: 2 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The penetration of electrostatic field outside the shield at the part the antenna faced to plasma is studied in the framework of two-dimensional numerical model. It is shown that single-layer Faraday shield does not have satisfactory shielding properties. The shielding can be improved sufficiently using overlaying two-layer shield.
У рамках двовимірної числової моделі вивчено проникнення електростатичних полів крізь екран на його частині, що звернена до плазми. Показано, що одношаровий Фарадеївський екран не забезпечує екранування на прийнятному рівні. З використанням двошарового екрану екранування може бути суттєво поліпшене.
В рамках двумерной численной модели изучено проникновение электростатических полей сквозь экран на его участке, обращенном к плазме. Показано, что однослойный Фарадеевский экран не обеспечивает экранирование на приемлемом уровне. С использованием двухслойного экрана экранирование может быть существенно улучшено.
|
| first_indexed | 2025-11-24T14:16:14Z |
| format | Article |
| fulltext |
PENETRATION OF ELECTROSTATIC FIELD THROUGH FARADAY
SHIELD OF ICRH STRAP ANTENNA
V.E. Moiseenko
Institute of Plasma Physics, NSC KIPT, Kharkov, Ukraine
The penetration of electrostatic field outside the shield at the part the antenna faced to plasma is studied in the
framework of two-dimensional numerical model. It is shown that single-layer Faraday shield does not have satisfactory
shielding properties. The shielding can be improved sufficiently using overlaying two-layer shield.
PACS: 52.50.Qt
INTRODUCTION
To protect antenna from the direct contact to plasma
and to prevent penetration of the electrostatic field
induced by antenna, the Faraday shield is used. Ideally, it
should be made from anisotropic substance with high
conductivity in one direction and low conductivity in
others. Since such substance does not exist the shield is
normally made from discrete metallic elements. For the
reason of discreteness of the shield, a portion of
electrostatic field can penetrate outside the volume
surrounded by it. Outside the antenna box, both parallel
and perpendicular to the steady magnetic field
components of the electrostatic field cause strong
oscillatory motion of ions and electrons of scrape-off-
layer low-density plasma that normally exists in the shield
vicinity. If the energy of oscillatory motion of ions
exceeds the energy threshold of sputtering the sputtered
material of the shield goes into the plasma increasing the
concentration of impurities.
Another unfavorable effect that is caused by the
penetration of electrostatic field through Faraday shield is
the excitation of waves in plasma by the electrostatic
mechanism [1]. Both slow and fast wave could be excited
with it. While fast wave excitation does not cause
problems, the slow wave excitation is adverse [2].
The electrostatic field penetrates through the shield at
all its surface. The part of the shield faced to plasma is of
primary interest.
DESCRIPTION OF MODEL
We consider the Faraday shield consisting of similar
bended strap elements placed periodically at the same
distance each from other (see Fig.1). We assume that the
period of the shield is much smaller than the wavelength
and than the every size of antenna. The first assumption
allows us to introduce the electric potential ϕ and use
the Laplas equation to describe electric field in small-
scale area near the shield. The second assumption makes
it possible to ignore the dependence of potential from z -
coordinate. Because of the periodicity of the shield in y
direction one could expect that the dependence of the
potential along this coordinate is also periodical with
slowly varying amplitude. In our consideration the last
variation is neglected because it is of the same order as
the already neglected variation of the potential in z -
coordinate. Thus, the problem could be considered at a
single period of the shield accounting periodic boundary
conditions in y direction. At the period, there is a
reflection symmetry. For this reason the domain for
Laplas equation in y direction is chosen as a half of
period.
s t r a p
i n n e r s h i e l d
e l e m e n t
o u t e r s h i e l d
e l e m e n t
D
z
y
x
Fig.1. A fragment of strap antenna covered by two-layer
Faraday shield
To operate with dimensionless quantities and variables
we scale the coordinates by the shield half-period
x=2x /D , y=2y/D and the potential by the
potential at the strap surface ϕ=ϕ /ϕ s . The Laplas
equation reads:
∇2 ϕ=0 . (1)
The boundary conditions are the following. The
condition ϕ∣x=0=1 determines the potential at the
strap. The condition
∂ ϕ
∂ x
∣x=∞=0 nullifies the electric
field at the infinity. Owing to the reflection symmetry and
periodicity, the boundary conditions for potential in y
direction become Neumann’s ones:
∂ ϕ
∂ y
∣y=0=0 and
∂ ϕ
∂ y
∣y=1=0 . There is also the internal boundary
conditions ϕ∣x=δ i , y∈ 0,d i
=0 and
ϕ∣x=δe , y∈1 −d e ,1 =0 nullifying the potential at the
shield elements. Here δ is the normalized distance
between antenna strap and shield element in x direction;
d is the normalized half-width of the shield element;
indices i and e denote inner and outer shield elements.
The equation (1) with the above mentioned boundary
conditions is solved numerically using finite difference
method. The boundary condition at x=∞ is substituted
by the same condition at finite value of x : x= x inf .
Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 35-37 35
This value is chosen large enough in order not to
influence on the solution.
s t r a p
x
y
1
x i n f δ i δ e
d e
1 - d i
0
o u t e r s h i e l d
e l e m e n t
i n n e r s h i e l d
e l e m e n t
l 1
l 1 l 2
l 2
Fig.2. The domain of boundary problem for Laplas
equation
Besides the calculation of potential, two average
values of electric field strength
E i= 1
li
∫
l i
Ex
2E y
2 dl are calculated. The first
contour l 1 along which the averaging is performed (see
Fig.2) represents the nearest to the front of the shield
plane from the outer side. The second contour l2 is the
projection of the outer surface of the shield to the plane
x , y .
CALCULATION RESULTS
First the single-layer shield is analyzed. The contours
of the distribution of the potential in the case d e=0 .8
and δ e=1 are shown in Fig.3.
0.20 0.40 0.60 0.80 1.00 1.20 1.40
x
0.20
0.40
0.60
0.80
y
Fig.3. Contours of the distribution of potential in
the case d e=0 .8 and δ e=1 . Shield
element is shown by bold line.
One can see there that the electric field penetrates outside
the shield through the slots between the shield elements.
The dependences of average electric field strength E1
on the width of the shield element d e and on the
distance between the strap and the shield element δ e are
displayed in Figs. 4 and 5. The dependences are apparent:
the electric field strength outside the shield decreases with
decrease of the shield transparency T=1 −d e and
with increase of the distance δ e between shield and
strap. However, even for low shield transparency, it is
order of the electric field strength inside the shield.
0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0
0 . 0 0
0 . 2 0
0 . 4 0
0 . 6 0
0 . 8 0
1 . 0 0
ed
1E
Fig.4. Dependence of average electric field strength E1
from the width of the shield element d e
0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0
0 . 0 0
0 . 4 0
0 . 8 0
1 . 2 0
1 . 6 0
2 . 0 0
1E
eδ
Fig.5. Dependence of average electric field strength E1
from the distance δ e between shield element and strap
For double-layer shield the transparency
T=1 −d e−d i could both positive and negative. The
second case relates to the situation when the inner and
outer shields overlay. The distribution of potential in the
second case is shown in Fig.6.
0.20 0.40 0.60 0.80 1.00 1.20 1.40
x
0.20
0.40
0.60
0.80
y
Fig.6. Contours of the distribution of potential in the case
d e=0 . 6 , d i=0 . 5 , δ e=1 and δ i=0 . 75
In this case the penetration of the potential outside the
shield is less than in the case of single-layer shield.
The dependences of electric field strengths E1 and
E2 on the width d e of outer shield element are
36
displayed in Fig.7. Since the contour l 2 is closer to the
shield than the contour l 1 the strength E2 is always
stronger than E1 .
0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0
0 . 0 0
0 . 2 0
0 . 4 0
0 . 6 0
0 . 8 0
ed
E
1E
2E
Fig.7. Dependences of average electric field strengths
from the width of the outer shield element d e the case
d i=0 . 5 , δ e=1 and δ i=0 . 75
Both strengths decrease with d e . For E2 , the
decrement becomes stronger near the point where the
shield transparency T changes sign.
SUMMARY AND DISCUSSIONS
The calculations of the distribution of electrostatic
fields in the vicinity of Faraday shield show that the field
penetrates outside the shield both in the case of single-
layer and double-layer shields. The fields outside the
shield rapidly decrease with the distance from the shield
with characteristic space scale order of the shield period
D . In this respect the shield with smaller period is
preferable because the volume occupied by the
electrostatic field is smaller. Moreover, the Fourier
spectrum of the electrostatic field strength in y direction
starts from the minimum value k y min=2π /D that
increases with decrease of shield period. For fine shield
the cut-off zone for slow wave is wider and the excitation
of this wave is less effective.
For the single-layer shield, the electric field strength at
the outer surface of the shield is order of that one between
the shield and the strap. It decreases with decrease of the
shield transparency and with increase of the distance
between the shield and antenna strap. However, even for
shields with low transparency its value remains
unacceptably high. If plasma ions are present in the
vicinity of the shield, their energy of motion in the
electrostatic field could exceed the threshold of
sputtering.
In the case of overlaying the double-layer shield fully
protects the strap antenna from the fluxes of particles. The
electrostatic field outside this shield is more than order
less strong than the field inside the shield. Thus, the
criterion of non-sputtering could be met. The obvious
disadvantage of the double-layer shield is low
transparency for the electromagnetic field. However, the
last one could be increased keeping the small space
between two layers in the front part of the shield and
enlarging it at the side parts.
ACKNOWLEGEMENT
The author is thankful to Prof. K.N. Stepanov for
stimulating discussions and support and to Dr.
A.I.Lyssoivan for discussion of the calculation results and
of practical aspects of electrostatic shielding.
REFERENCES
1. C. Riccardi, E. Agostini, M. Fontanesi. Measurements
of plasma loading in the presence of electrostatic
waves// Phys. Plasmas, 1995, Vol.2, pp. 3588-3594.
2. V.E. Moiseenko A Fast Wave Antenna for ICRF
Plasma Heating// Transactions of Fusion Technology,
2001, Vol. 39, pp. 65-72.
ПРОНИКНОВЕНИЕ ЭЛЕКТРОСТАТИЧЕСКИХ ПОЛЕЙ СКВОЗЬ ФАРАДЕЕВСКИЙ ЭКРАН
ПОЛУВИТКОВОЙ ВЧ АНТЕННЫ
В.Е.Моисеенко
В рамках двумерной численной модели изучено проникновение электростатических полей сквозь экран на его
участке, обращенном к плазме. Показано, что однослойный Фарадеевский экран не обеспечивает
экранирование на приемлемом уровне. С использованием двухслойного экрана экранирование может быть
существенно улучшено.
ПРОНИКНЕННЯ ЕЛЕКТРОСТАТИЧНИХ ПОЛІВ КРІЗЬ ФАРАДЕЇВСЬКИЙ ЕКРАН
НАПІВВИТКОВОЇ ВЧ АНТЕНИ
В.Є. Моісеєнко
У рамках двовимірної числової моделі вивчено проникнення електростатичних полів крізь екран на його
частині, що звернена до плазми. Показано, що одношаровий Фарадеївський екран не забезпечує екранування на
прийнятному рівні. З використанням двошарового екрану екранування може бути суттєво поліпшене.
37
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| id | nasplib_isofts_kiev_ua-123456789-79338 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-24T14:16:14Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Moiseenko, V.E. 2015-03-31T13:33:52Z 2015-03-31T13:33:52Z 2005 Penetration of electrostatic field through Faraday shield of ICRH strap antenna / V.E. Moiseenko // Вопросы атомной науки и техники. — 2005. — № 2. — С. 35-37. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 52.50.Qt https://nasplib.isofts.kiev.ua/handle/123456789/79338 The penetration of electrostatic field outside the shield at the part the antenna faced to plasma is studied in the framework of two-dimensional numerical model. It is shown that single-layer Faraday shield does not have satisfactory shielding properties. The shielding can be improved sufficiently using overlaying two-layer shield. У рамках двовимірної числової моделі вивчено проникнення електростатичних полів крізь екран на його частині, що звернена до плазми. Показано, що одношаровий Фарадеївський екран не забезпечує екранування на прийнятному рівні. З використанням двошарового екрану екранування може бути суттєво поліпшене. В рамках двумерной численной модели изучено проникновение электростатических полей сквозь экран на его участке, обращенном к плазме. Показано, что однослойный Фарадеевский экран не обеспечивает экранирование на приемлемом уровне. С использованием двухслойного экрана экранирование может быть существенно улучшено. The author is thankful to Prof. K.N. Stepanov for stimulating discussions and support and to Dr. A.I.Lyssoivan for discussion of the calculation results and of practical aspects of electrostatic shielding. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Penetration of electrostatic field through Faraday shield of ICRH strap antenna Проникнення електростатичних полів крізь фарадеївський екран напіввиткової ВЧ антени Проникновение электростатических полей сквозь фарадеевский экран полувитковой ВЧ антенны Article published earlier |
| spellingShingle | Penetration of electrostatic field through Faraday shield of ICRH strap antenna Moiseenko, V.E. Magnetic confinement |
| title | Penetration of electrostatic field through Faraday shield of ICRH strap antenna |
| title_alt | Проникнення електростатичних полів крізь фарадеївський екран напіввиткової ВЧ антени Проникновение электростатических полей сквозь фарадеевский экран полувитковой ВЧ антенны |
| title_full | Penetration of electrostatic field through Faraday shield of ICRH strap antenna |
| title_fullStr | Penetration of electrostatic field through Faraday shield of ICRH strap antenna |
| title_full_unstemmed | Penetration of electrostatic field through Faraday shield of ICRH strap antenna |
| title_short | Penetration of electrostatic field through Faraday shield of ICRH strap antenna |
| title_sort | penetration of electrostatic field through faraday shield of icrh strap antenna |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79338 |
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