Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field
The paper studies integral and one-dimensional distribution of RF electromagnetic field absorption in a helicon plasma with external magnetic field directed at an angle to a plasma plane. A simplified model of a helicon plasma plane layer is used here. Calculation results are used to explain power a...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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| Цитувати: | Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field / O.V. Alexenko, V.I. Miroshnichenko, V.I. Voznyi // Вопросы атомной науки и техники. — 2015. — № 4. — С. 12-17. — Бібліогр.: 15 назв. — англ. |
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irk-123456789-1122422017-01-19T03:02:49Z Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field Alexenko, O.V. Miroshnichenko, V.I. Voznyi, V.I. Нерелятивистская электроника The paper studies integral and one-dimensional distribution of RF electromagnetic field absorption in a helicon plasma with external magnetic field directed at an angle to a plasma plane. A simplified model of a helicon plasma plane layer is used here. Calculation results are used to explain power absorption in a compact helicon ion source with nonuniform external magnetic field. An ion source is a part of a nuclear scanning microprobe (NSMP) injector at the Institute of Applied Physics NAS of Ukraine. Calculations for ion source parameters of the NSMP injector show a resonant behaviour of integral RF power absorption as a function of a magnetic field inclination angle. A model (planar) geometry is verified here for solution of this problem. Досліджуються інтегральний та одномірний розподіли поглинання ВЧ-електромагнітного поля в геліконній плазмі із зовнішнім магнітним полем, яке має напрямок під кутом до поверхні плазми. Використано спрощену модель плоского шару геліконної плазми. Результати розрахунків застосовуються для пояснення поглинання потужності в компактному геліконному джерелі іонів з неоднорідним зовнішнім магнітним полем. Джерело іонів входить до складу інжектора ядерного скануючого мікрозонда (ЯСМЗ) Інституту прикладної фізики НАН України. Розрахунки для параметрів джерела іонів інжектора ЯСМЗ демонструють резонансний характер інтегрального поглинання ВЧ-потужності в залежності від кута нахилу магнітного поля. Виконано перевірку правомірності застосування модельної (плоскої) геометрії для вирішення задачі. Исследуются интегральное и одномерное распределения поглощения ВЧ-электромагнитного поля в геликонной плазме с внешним магнитным полем, которое направлено под углом к поверхности плазмы. Используется упрощенная модель плоского слоя геликонной плазмы. Результаты расчетов применяются для объяснения поглощения мощности в компактном геликонном источнике ионов с неоднородным внешним магнитным полем. Источник ионов входит в состав инжектора ядерного сканирующего микрозонда (ЯСМЗ) Иститута прикладной физики НАН Украины. Расчеты для параметров источника ионов инжектора ЯСМЗ показывают резонансный характер интегрального поглощения ВЧ-мощности в зависимости от угла наклона магнитного поля. Выполнена проверка правомерности применения модельной (плоской) геометрии для решения задачи. 2015 Article Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field / O.V. Alexenko, V.I. Miroshnichenko, V.I. Voznyi // Вопросы атомной науки и техники. — 2015. — № 4. — С. 12-17. — Бібліогр.: 15 назв. — англ. 1562-6016 PACS: 52.50.Dg, 52.50.Qt, 41.47.Ak http://dspace.nbuv.gov.ua/handle/123456789/112242 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Нерелятивистская электроника Нерелятивистская электроника |
| spellingShingle |
Нерелятивистская электроника Нерелятивистская электроника Alexenko, O.V. Miroshnichenko, V.I. Voznyi, V.I. Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field Вопросы атомной науки и техники |
| description |
The paper studies integral and one-dimensional distribution of RF electromagnetic field absorption in a helicon plasma with external magnetic field directed at an angle to a plasma plane. A simplified model of a helicon plasma plane layer is used here. Calculation results are used to explain power absorption in a compact helicon ion source with nonuniform external magnetic field. An ion source is a part of a nuclear scanning microprobe (NSMP) injector at the Institute of Applied Physics NAS of Ukraine. Calculations for ion source parameters of the NSMP injector show a resonant behaviour of integral RF power absorption as a function of a magnetic field inclination angle. A model (planar) geometry is verified here for solution of this problem. |
| format |
Article |
| author |
Alexenko, O.V. Miroshnichenko, V.I. Voznyi, V.I. |
| author_facet |
Alexenko, O.V. Miroshnichenko, V.I. Voznyi, V.I. |
| author_sort |
Alexenko, O.V. |
| title |
Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field |
| title_short |
Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field |
| title_full |
Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field |
| title_fullStr |
Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field |
| title_full_unstemmed |
Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field |
| title_sort |
power absorption inside helicon plasma of helium rf ion source in nonaxial magnetic field |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Нерелятивистская электроника |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112242 |
| citation_txt |
Power absorption inside helicon plasma of helium RF ion source in nonaxial magnetic field / O.V. Alexenko, V.I. Miroshnichenko, V.I. Voznyi // Вопросы атомной науки и техники. — 2015. — № 4. — С. 12-17. — Бібліогр.: 15 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT alexenkoov powerabsorptioninsideheliconplasmaofheliumrfionsourceinnonaxialmagneticfield AT miroshnichenkovi powerabsorptioninsideheliconplasmaofheliumrfionsourceinnonaxialmagneticfield AT voznyivi powerabsorptioninsideheliconplasmaofheliumrfionsourceinnonaxialmagneticfield |
| first_indexed |
2025-07-08T03:35:16Z |
| last_indexed |
2025-07-08T03:35:16Z |
| _version_ |
1837048231476854784 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №4(98) 12
NONRELATIVISTIC ELECTRONICS
POWER ABSORPTION INSIDE HELICON PLASMA
OF HELIUM RF ION SOURCE IN NONAXIAL MAGNETIC FIELD
O.V. Alexenko, V.I. Miroshnichenko, V.I. Voznyi
Institute of Applied Physics NAS of Ukraine, Sumy, Ukraine
E-mail: oleg-alexenko@mail.ru
The paper studies integral and one-dimensional distribution of RF electromagnetic field absorption in a helicon
plasma with external magnetic field directed at an angle to a plasma plane. A simplified model of a helicon plasma
plane layer is used here. Calculation results are used to explain power absorption in a compact helicon ion source
with nonuniform external magnetic field. An ion source is a part of a nuclear scanning microprobe (NSMP) injector
at the Institute of Applied Physics NAS of Ukraine. Calculations for ion source parameters of the NSMP injector
show a resonant behaviour of integral RF power absorption as a function of a magnetic field inclination angle.
A model (planar) geometry is verified here for solution of this problem.
PACS: 52.50.Dg, 52.50.Qt, 41.47.Ak
INTRODUCTION
Among various inductively coupled low pressure
sources RF plasma sources are widely used because
they meet economic requirements and have sufficiently
long service life. They can operate in different modes;
RF sources operating in a helicon mode generate plasma
more effectively [1 - 4].
In helicon ion sources, input power may be concen-
trated at a periphery under an antenna, may be uniform-
ly absorbed by volume or be concentrated in a paraxial
region of a discharge chamber. The latter case is more
suitable for the NSMP ion source, since a precision ion
beam is formed out the paraxial plasma region where
the plasma density is supposed to be maximal. Increase
of plasma density in an ion source is important question
as it is one of ways to obtain high brightness ion beams
[5].
In articles [6, 7] power absorption resonances are
shown to be not equivalent as to their power distribution
by volume of the discharge chamber in the case of uni-
form external magnetic field, generator frequencies of
27.12 MHz, definite geometry of the discharge cham-
bers and with neutral gas pressure and electron tempera-
ture considered. Ranges of magnetic field where input
power is paraxially absorbed are also recommended.
Numerical estimates were compared to experimental
data and were found in a good agreement.
In the article [8] increase of plasma was experimen-
tally found for the first time in a helicon source with a
nonuniform magnetic field. Later various hypotheses
were suggested for explanation of the plasma density
increase in a nonuniform magnetic field like reduction
of helicon wave phase velocity, formation of a neutral
gas barrier, reflection of helicons from a surface behind
the antenna [9 - 12].
The above mentioned hypotheses were refuted by
the experiments described in works [13, 14]. Hot elec-
trons layer was experimentally found. The electron layer
expands into plasma along magnetic field lines. The
experiments have shown the absence of standing elec-
tromagnetic modes in plasma. A small scale wave struc-
ture was identified inside the hot electrons layer. To
explain the experiments with the cylinder discharge
chambers over 7 cm in radius, and over 20 cm in length,
a theoretical model was used: semi-infinite plasma in
plain geometry in a uniform magnetic field directed at
the θ angle. Input power of some kW into plasma is
meant here. For numerical evaluations to be verified,
penetration of 80% power flux into plasma was suggest-
ed to be defined with a model of semi-infinite plasma. If
the penetration was less than a plasma radius, the nu-
merical evaluations were considered proper.
1. PHYSICAL MODEL
A problem of power absorbed in the cylinder dis-
charge chamber with external nonuniform magnetic
field from an assembly of annular permanent magnets is
a very complicated since it requires satisfaction with
boundary conditions at the edges of the discharge
chamber for the electromagnetic field components in
plasma. If unbounded in z-direction plasma cylinder in
nonaxial magnetic field as a physical model is consid-
ered, that analytical solutions for electromagnetic field
components inside plasma can not be obtained.
This article the following model is considered: a
plasma layer is restricted along a vertical x-axis and
unbounded along the y and z axes. Uniform magnetic
flux density B0 is directed at an angle θ to the plasma
plane (Fig. 1). This model was chosen to be used for
consideration absorption of electromagnetic waves in
compact helicon ion sources (length of a discharge
chamber is up to 12 cm, radius is up to 2 cm) with non-
uniform distribution of external magnetic field from the
annular permanent magnets assemblies (Fig. 2).
Fig. 1. Plasma layer in nonaxial magnetic field
All numerical estimates were taken here for standard
experimental conditions: symmetrical electromagnetic
modes excitation, operating frequency is 27.12 MHz,
electron temperature of 5 eV, ion temperature of 0.1 eV.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 13
Accuracy of the numerical estimates was verified as
in works [13, 14] based on definition of 80% power flux
penetration into plasma.
To excite symmetrical electromagnetic waves in
plasma a system of straight current-carrying conductors
was used as an antenna. Such current system is an ana-
logue of a turns (m=0) antenna in a cylindrical geome-
try. There are three current-carrying conductors on an
upper and bottom layer boundary that corresponds to a
three-turn (m=0) antenna for a cylindrical geometry.
The plane plasma layer is 2Lx=2.6 cm in width along
the x-axis and is unbounded along the y and the z-axis.
It is assumed that a partially ionized electron-ion
plasma with a uniform distribution of electron and ion
density n0e=n0i=n0 have already been created in the
plasma layer. Neutral atoms density of the considered
gas is given by the gas pressure.
We study the case when operating frequency ω
is
higher than lower hybrid frequency ωLH in plasma. Here
plasma ions may be considered immovable.
Fig. 2. Helicon ion source layout
The solution is sought for a set of longitudinal wave
numbers kz=(π/12; π/10; π/7) cm-1 only. This corre-
sponds to longitudinal wave numbers that are excited in
the cylinder discharge chamber of Lz=(12; 10; 7) cm in
length. The solution is sought as traveling waves. For
annular permanent magnets assemblies are very im-
portant to know local power absorption which they cre-
ate. For this reason integral power absorption is calcu-
lated through a part of the layer of l=0.1 cm in width
along the z-axis and sides 2Lx, 2Ly along the x and the y
axes, correspondingly, where Lx=1.3 cm, Ly=Lx. Value
S=2Lx×2Ly is about a cross section of the discharge
chamber of 1.5 cm in radius.
2. DIELECTRIC PERMEABILITY TENSOR,
ANTENNA CURRENT AND BOUNDARY
CONDITIONS
For a nonaxial magnetic field, a tensor of dielectric
permeability of cold magnetoactive plasma has a form
[14]:
( )
′−−′
−
′′+
= ⊥
⊥
θεεθθθε
θεθ
θθεθθεε
ωε
2
00
0
2
0
sinsincos sin
sincos
cos sincossin
||ig
igig
ig
ik , (1)
where θ is a inclination angle of a magnetic field to the
z-axis and ε′0=ε|| -ε⊥.
For solution of this problem, electromagnetic fields
in plasma and vacuum are found as traveling waves:
( )
( )
( ) ( ) ( ) exp ,
( ) ( ) ( ) exp .
x x y y z z z
x x y y z z z
E e E x e E x e E x i k z t
H e H x e H x e H x i k z t
ω
ω
= + + −
= + + −
.(2)
Current density of the antenna is as follows:
( )[ ]tzkixjej zyya ω−= )exp(
. (3)
Amplitude of the antenna current density is:
( ) ( ) ( )azay xxLIxj −⋅= δ/ , (4)
where Ia is amplitude of current equal to 2 A that is
typical for experimental conditions; xa is a coordinate
position of a current − carrying conductor along the x-
axis, it is assumed as Lx.
Components of dielectric permeability tensor (1) are
in form [3]. Since a condition ω > ωLH is true, then only
electron plasma component in dielectric permeability
tensor is retained. In dielectric permeability tensor com-
ponents ε||, ε⊥, g the items describing Landau damping
of waves are kept. Landau damping is not observed for
considered kz and plasma parameters at f=27.12 MHz
[6, 7], but it is very crucial for f=13.56 MHz [2].
Anti-Hermitian part of dielectric permeability tensor
that defines the electromagnetic waves absorption by an
electron subsystem due to a mechanism of binary colli-
sions is characterized by effective electron collision
frequency with neutral atoms and gas ions formed:
eieneff ννν += . (5)
For helium plasma at electron temperature of 5 eV
and neutral gas pressure of 1 mTorr, νen=2.7 MHz. Cou-
lomb electron-ion collisions were considered with aver-
aging over Maxwellian function of electron velocity
distribution.
Electric and magnetic field strength (2) in plasma
satisfy the Maxwell’s equations with dielectric permea-
bility tensor (1). Substitution (2) to the Maxwell’s equa-
tions gives differential equations system with constant
coefficients for Fourier amplitudes of the field compo-
nents.
( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
1 2 3
4
2 5 6
3 6 7
,
,
,
.
z
y y z
y
z
z
y y z
y
y y z
dE x
iA H x A E x iA E x
dx
dE x
iA H x
dx
dH x
A H x iA E x A E x
dx
dH x
iA H x A E x iA E x
dx
= + −
=
= + −
= − − +
(6)
Explicit analytical form of electromagnetic field
components for equations (6) is cumbersome, expressed
in terms of A1…A7, therefore only A1…A7 gives here:
( ) ,
,
,,
,,,
||||
−−+=
+=
−−==
==
−=
⊥
⊥
εθεε
α
α
ωε
θ
α
θα
ωε
α
θεωεωµ
α
α
α
θ
α
ωµ
2
1
2
3
07
1
3
06
1
22
2
2
0504
1
3
3
1
2
1
2
2
01
sin
sincos
cos
cos1
A
gA
g
k
kAA
kAgkA
k
kA
z
zzz
(7)
where ., θθεαθεεα cos sinsin 03
2
01 ′=′+= ⊥
ISSN 1562-6016. ВАНТ. 2015. №4(98) 14
For areas outside the plasma layer electromagnetic
field components represent as a superposition TE and
TM waves.
Integral absorption of RF power is calculated as:
( ) ( )∫∫∫=
V
abs dVxPxP
2
0ωε
. (8)
The expression under integral (8) defines spatial dis-
tribution of the absorbed RF power. For nonaxial mag-
netic field, taking into account the tensor (1), obtain:
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )(
( ) ( )) ( ) ( )(
( ) ( )) ( ) ( )(
( ) ( ))
2220
0 1
22
|| 0 1
1
1
1 1
1 1
Im Im
2
Im Im Im Re
Im Re Im Im Re
Im Re 2 Re Re
Im Im ,
sin , cos .
x y
z x y
y x y z
z y x z
x z
P x s E x E x
s E x g E x E x
E x E x c g E x E x
E x E x s E x E x
E x E x s c
s c
ωε
ε ε ε
ε ε
θ θ
⊥ ⊥
′= + ⋅ + +
′+ − ⋅ + −
− ⋅ + −
− ⋅ + +
+ ⋅
= =
(9)
Boundary conditions are written for Fourier ampli-
tudes of the field components and for Fourier ampli-
tudes of the antenna current density.
; ;
.
pl vac pl vac
z z y y
pl vac
z z y
E E E E
H H j
= =
− =
.
After determining the unknown constants in a plas-
ma layer and vacuum areas, the expressions for Fouri-
er amplitudes of the electromagnetic field components
in a plasma layer may be obtained.
3. WAVE DISPERSION
Eigenvalues that satisfy the system of equations (6)
are, in fact, transverse wave numbers of electromagnetic
waves excited in a plasma layer.
A problem on eigenvalues gives the equation of the
fourth degree:
4 3 2 0.a b c d eκ κ κ κ+ + + + = . (10)
The coefficients a, b, c, d, e are cumbersome, and
they are not mentioned here.
Fig. 3. Transparency region and dispersive characteris-
tics of waves in a plasma layer at magnetic field inclina-
tion angle θ =1°, n0 = 3·1012 cm-3: kz=π/12 cm-1 (a, b);
kz=π/10 cm-1 (c, d)
Numerical analysis of the equation (10) in a colli-
sionless limit provides the results for electromagnetic
wave dispersion as follows.
Figs. 3, 4 shows two essentially different cases of
electromagnetic wave dispersion. A TG wave
(Figs. 3,b,d) and a helicon wave (area kx>0), and local
oscillations of an electromagnetic field (area kx<0) may
exist in plasma. These oscillations are originated inside
a hot electrons layer and are transferred into depth of
plasma along the field lines [13, 14].
A helicon wave (area kx > 0) may exist in plasma
(Fig. 4,b,d), other three solutions correspond to the
above mentioned oscillations.
Fig. 4. Transparency region and dispersive characteris-
tics of waves in a plasma layer at magnetic field inclina-
tion angle θ =5°, n0=3·1012 cm-3: kz=π/12 cm-1 (a, b);
kz=π/10 cm-1 (c, d)
As kz increases, the oscillations become more small-
scale at the same external magnetic field inclination
angle.
As inclination angle increases, the oscillations be-
come more large-scale at the same kz.
The dispersion curves show that a magnetic flux
density range is related to a specified value of plasma
density, inclination angle of a magnetic field, and kz
value. Tables 1, 2 refer to plasma with density
n0=3·1012 cm-3.
Table 1
Angle, grad Magnet field, G
1 300…823
2 368…823
3 444…823
4 526…823
5 613…823
Table 2
Angle, grad Magnet field, G
1 241…823
2 286…823
3 337…823
4 392…823
5 449…823
Table 1 is related to a case of kz=π/12 cm-1; Table 2
classifies a case of kz=π/10 cm-1. From Figs. 3, 4 it fol-
a b
c d
a b
c d
ISSN 1562-6016. ВАНТ. 2015. №4(98) 15
lows that transparency region narrows as an inclination
angle grows.
4. RESULTS
Numerical results were obtained with Fouri-
er amplitudes of the electromagnetic field components
in a plasma layer and the expression (9). These numeri-
cal estimates are needed for local power absorption
analysis inside a plasma layer as function of a magnetic
field inclination angle, neutral gas pressure, operating
frequency.
For above volume element of the plasma layer
Figs. 5, 6 shows for plasma of density n0 = 3·1012 cm-3,
and kz=π/12 cm-1; π/10 cm-1, correspondingly, an inte-
gral power absorption and absorption distribution in the
x-direction, as function of an angle between the magnet-
ic field and plasma and the magnetic field value. As
pressure grows, maxima of integral power absorption
are seen to be slightly shifted to magnetic field increase.
For pressure р=6 mTorr, maxima of integral power ab-
sorption in Fig. 5,a,c are related to the magnetic flux
density of 626 G, 742 G; for pressure of 10 mTorr they
are related to 628 G, 748 G; for pressure of 15 mTorr
they are related to 632 G, 757 G.
Fig. 6,a,c show that for pressure р=6 mTorr, maxi-
ma of integral power absorption are related to the mag-
netic flux density of 503, 578 G; for pressure of
10 mTorr, they are related to 507, 585 G; for pressure of
15 mTorr, they are related to 512, 590 G.
Graphs of absorption distribution along the x-axis
(Figs. 5,b,d; 6,b,d) are plotted for the above mentioned
values of the magnet field. Here magnetic field is seen
to be 100 G less than that of case where kz = π/12 cm-1.
Fig. 5. Integral power absorption and absorption along
the x-axis for kz = π/12 cm-1: a), b) θ = 3°;
c), d) θ = 3.5°
Numerical estimates show that further increase of kz
would not allow paraxial power absorption for plasma
density n0>3·1012 cm-3. The above mentioned simula-
tion logics considered, for plasma of density
n0=4·1012 cm-3 and kz=π/12 cm-1, kz=π/10 cm-1, the fol-
lowing results were obtained (Fig. 7). Fig. 7,a,c,e show
that for pressure р=6 mTorr maxima of integral absorp-
tion are related to magnetic flux density of 771, 619,
713 G; for pressure of 10 mTorr, they are related to val-
ues of 774, 624, 718 G, and to 780, 632, 728 G for pres-
sure of 15 mTorr.
Graphs of absorption distribution along the x-axis
(Fig. 7,b,d,f) are plotted for the above mentioned values
of magnet field.
Fig. 6. Integral power absorption and absorption along
the x-axis for kz = π/10 cm-1: θ =3.5° (a, b);
θ = 4° (c, d)
Numerical results for penetration of 80% power flux
into plasma are provided. A value ( ) dzHEdQ xx
×=
was preliminary calculated the condition (11) was veri-
fied.
( ) ( )02 ,0 === xQxxQ xx δ . (11)
Fig. 7. Integral power absorption and absorption along
the x-axis for: kz = π/12 cm-1, θ = 3° (a, b);
kz = π/10 cm-1, θ = 3,5° (c, d);
kz = π/10 cm-1, θ = 4° (e, f)
b a
c d
c
a b
d
a b
c d
e f
ISSN 1562-6016. ВАНТ. 2015. №4(98) 16
At Fig. 5,a pressure р=6 mTorr corresponds to
δx=0.95 cm, p=10 mTorr corresponds to δx=0.96 cm,
р=15 mTorr corresponds to δx=1 cm.
At Fig. 6,а pressure р=6 mTorr corresponds to
δx=0.9 cm; р=10 mTorr corresponds to δx=0.91 cm,
р=15 mTorr corresponds to δx=1.05 cm.
At Fig. 7,а pressure р=6 mTorr corresponds to
δx=0.97 cm, р=10 mTorr corresponds to δx=0.99 cm,
р=15 mTorr corresponds to δx=1.03 cm.
At Fig. 7,с pressure р=6 mTorr corresponds to
δx=0,9 cm, р=10 mTorr corresponds to δx=0.91 cm,
р=15 mTorr corresponds to δx=1.07 cm.
All the above mentioned values of δx are less than Lx
thus this simplified physical model may be applied for
numerical estimates of power absorption inside cylinder
discharge chambers compact ion sources.
5. DISCUSSION
Articles [6, 7] show for a uniform magnetic field and
discharge chambers with length Lz=12 cm
(kz=π/12 cm-1) and Lz=7 cm (kz=π/7 cm-1) that power
input into a paraxial region of discharge chamber is pos-
sible at p=6 mTorr up to density n0=1.8·1012 cm-3, at
p=10 mTorr to density n0=1.2·1012 cm-3. Figs. 5-7 for
power distributions over the x-direction show that the
distributions are paraxial even at pressure increase up to
15 mTorr, that is impossible for uniform magnetic field
[6, 7].
Figs. 3, 4 for the transparency regions show that in-
crease of plasma density is accompanied by increase of
magnetic field values for given plasma density. Increase
of a magnetic field value is known to degrade emittance
characteristics of the extracted beam. Increased plasma
density also modifies plasma boundary in an extraction
system and necessitates higher voltage applied onto
plasma electrodes of the extraction system. In these cir-
cumstances possibility of paraxial power absorption is
considered for plasma density n0=3·1012 cm-3;
4·1012 cm-3. Numerical estimates were performed for
kz=π/12; π/10; π/7 cm-1, that allows us to consider the
creation of the same plasma density at various ranges of
the magnetic field values.
For considered kz values, paraxial power absorption
is possible only in a small range of magnetic field incli-
nation angle (up to θ =4°). Other angles provide periph-
eral power absorption.
As integral estimation is done for local power ab-
sorption not every calculation result may be suggested
for a real experiment. In Fig. 5 only mode 5,a may be
recommended, since power of about 10 W would be
absorbed due to binary collisions on a 1 cm interval and
taking into account applied power [15] of about 160 W.
In Fig. 6 only mode 6a may be recommended, since
power of about 25 W would be absorbed as a result of
binary collisions on a 1 cm interval and taking into ac-
count applied power of about 170 W. In Fig. 7 the
modes 7,a and 7,c may be used.
It is also important that the magnetic field inclina-
tion angles for which volume power distribution was
found be very close to extraction region of charged par-
ticles in an ion source.
A model (planar) geometry is verified here to solve
this problem.
ACKNOWLEDGEMENTS
This work is performed with support of target-
oriented integrated research program of Nuclear Physics
and Power Engineering Department of NAS of Ukraine
“Advanced Research on Plasma Physics, Controlled
Thermonuclear Synthesis and Plasma Technologies”
(State registration № 0114U000895).
We are grateful to Dr of Science Ponomarev Alex-
ander Georgievich for his observations which contribut-
ed to a more complete presentation some important
questions of this article.
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Article received 30.04.2015
ПОГЛОЩЕНИЕ МОЩНОСТИ В ГЕЛИКОННОЙ ПЛАЗМЕ ВЧ-ИСТОЧНИКА ИОНОВ ГЕЛИЯ
В НЕАКСИАЛЬНОМ МАГНИТНОМ ПОЛЕ
О.В. Алексенко, В.И. Мирошниченко, В.И. Возный
Исследуются интегральное и одномерное распределения поглощения ВЧ-электромагнитного поля в ге-
ликонной плазме с внешним магнитным полем, которое направлено под углом к поверхности плазмы. Ис-
пользуется упрощенная модель плоского слоя геликонной плазмы. Результаты расчетов применяются для
объяснения поглощения мощности в компактном геликонном источнике ионов с неоднородным внешним
магнитным полем. Источник ионов входит в состав инжектора ядерного сканирующего микрозонда (ЯСМЗ)
Иститута прикладной физики НАН Украины. Расчеты для параметров источника ионов инжектора ЯСМЗ
показывают резонансный характер интегрального поглощения ВЧ-мощности в зависимости от угла наклона
магнитного поля. Выполнена проверка правомерности применения модельной (плоской) геометрии для ре-
шения задачи.
ПОГЛИНАННЯ ПОТУЖНОСТІ В ГЕЛІКОННІЙ ПЛАЗМІ ВЧ-ДЖЕРЕЛА ІОНІВ ГЕЛІЮ
В НЕАКСІАЛЬНОМУ МАГНІТНОМУ ПОЛІ
О.В. Алексенко, В.І. Мирошніченко, В.І. Возний
Досліджуються інтегральний та одномірний розподіли поглинання ВЧ-електромагнітного поля в гелі-
конній плазмі із зовнішнім магнітним полем, яке має напрямок під кутом до поверхні плазми. Використано
спрощену модель плоского шару геліконної плазми. Результати розрахунків застосовуються для пояснення
поглинання потужності в компактному геліконному джерелі іонів з неоднорідним зовнішнім магнітним по-
лем. Джерело іонів входить до складу інжектора ядерного скануючого мікрозонда (ЯСМЗ) Інституту прик-
ладної фізики НАН України. Розрахунки для параметрів джерела іонів інжектора ЯСМЗ демонструють ре-
зонансний характер інтегрального поглинання ВЧ-потужності в залежності від кута нахилу магнітного поля.
Виконано перевірку правомірності застосування модельної (плоскої) геометрії для вирішення задачі.
INTRODUCTION
1. PHYSICAL MODEL
2. DIELECTRIC PERMEABILITY TENSOR, antenna current and boundary conditions
3. WAVE DISPERSION
4. RESULTS
5. DISCUSSION
ACKNOWLEDGEMENTS
REFERENCES
ПОГЛОЩЕНИЕ МОЩНОСТИ В ГЕЛИКОННОЙ ПЛАЗМЕ ВЧ-ИСТОЧНИКА ИОНОВ ГЕЛИЯ В НЕАКСИАЛЬНОМ МАГНИТНОМ ПОЛЕ
ПОГЛИНАННЯ ПОТУЖНОСТІ В ГЕЛІКОННІЙ ПЛАЗМІ ВЧ-ДЖЕРЕЛА ІОНІВ ГЕЛІЮ В НЕАКСІАЛЬНОМУ МАГНІТНОМУ ПОЛІ
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