Anisotropy of radiation from dense plasma of multiply ionized atoms
It has been study the formation of anisotropic extreme ultraviolet radiation from the plasma of multiply ionized atoms. The mean free path of quantum in dense plasma has been estimated. The critical current for formatting anisotropic radiation in the tin ion plasma has been obtained. The dependences...
Saved in:
| Date: | 2015 |
|---|---|
| Main Authors: | , , , , , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
|
| Series: | Вопросы атомной науки и техники |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/112239 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Anisotropy of radiation from dense plasma of multiply ionized atoms / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Raybchikov, N.N. Vusyk, A.F. Tseluyko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 32-35. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-112239 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1122392025-02-09T15:31:26Z Anisotropy of radiation from dense plasma of multiply ionized atoms Анізотропія випромінювання в щільній плазмі багаторазово іонізованих атомів Анизотропия излучения в плотной плазме многократно ионизированных атомов Hrechko, Ya.O. Azarenkov, N.A. Babenko, Ie.V. Raybchikov, D.L. Vusyk, N.N. Tseluyko, A.F. Нерелятивистская электроника It has been study the formation of anisotropic extreme ultraviolet radiation from the plasma of multiply ionized atoms. The mean free path of quantum in dense plasma has been estimated. The critical current for formatting anisotropic radiation in the tin ion plasma has been obtained. The dependences of the radiation directivity coefficient on the plasma parameters have been derived. Вивчається формування анізотропного випромінювання в діапазоні екстремального вакуумного ультрафіолету з плазми багаторазово іонізованих атомів олова. Наводяться оцінки довжини вільного пробігу кванта в щільній плазмі багатозарядних іонів. Визначено критичний струм формування анізотропного випромінювання в плазмі іонів олова. Отриманo залежності коефіцієнта спрямованості випромінювання від параметрів плазми. Изучается формирование анизотропного излучения в диапазоне экстремального вакуумного ультрафиолета из плазмы многократно ионизированных атомов олова. Приводятся оценки длины свободного пробега кванта в плотной плазме многозарядных ионов. Определен критический ток формирования анизотропного излучения в плазме ионов олова. Получены зависимости коэффициента направленности излучения от параметров плазмы. 2015 Article Anisotropy of radiation from dense plasma of multiply ionized atoms / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Raybchikov, N.N. Vusyk, A.F. Tseluyko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 32-35. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.20.-j, 52.50.Dg https://nasplib.isofts.kiev.ua/handle/123456789/112239 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Нерелятивистская электроника Нерелятивистская электроника |
| spellingShingle |
Нерелятивистская электроника Нерелятивистская электроника Hrechko, Ya.O. Azarenkov, N.A. Babenko, Ie.V. Raybchikov, D.L. Vusyk, N.N. Tseluyko, A.F. Anisotropy of radiation from dense plasma of multiply ionized atoms Вопросы атомной науки и техники |
| description |
It has been study the formation of anisotropic extreme ultraviolet radiation from the plasma of multiply ionized atoms. The mean free path of quantum in dense plasma has been estimated. The critical current for formatting anisotropic radiation in the tin ion plasma has been obtained. The dependences of the radiation directivity coefficient on the plasma parameters have been derived. |
| format |
Article |
| author |
Hrechko, Ya.O. Azarenkov, N.A. Babenko, Ie.V. Raybchikov, D.L. Vusyk, N.N. Tseluyko, A.F. |
| author_facet |
Hrechko, Ya.O. Azarenkov, N.A. Babenko, Ie.V. Raybchikov, D.L. Vusyk, N.N. Tseluyko, A.F. |
| author_sort |
Hrechko, Ya.O. |
| title |
Anisotropy of radiation from dense plasma of multiply ionized atoms |
| title_short |
Anisotropy of radiation from dense plasma of multiply ionized atoms |
| title_full |
Anisotropy of radiation from dense plasma of multiply ionized atoms |
| title_fullStr |
Anisotropy of radiation from dense plasma of multiply ionized atoms |
| title_full_unstemmed |
Anisotropy of radiation from dense plasma of multiply ionized atoms |
| title_sort |
anisotropy of radiation from dense plasma of multiply ionized atoms |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Нерелятивистская электроника |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112239 |
| citation_txt |
Anisotropy of radiation from dense plasma of multiply ionized atoms / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Raybchikov, N.N. Vusyk, A.F. Tseluyko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 32-35. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT hrechkoyao anisotropyofradiationfromdenseplasmaofmultiplyionizedatoms AT azarenkovna anisotropyofradiationfromdenseplasmaofmultiplyionizedatoms AT babenkoiev anisotropyofradiationfromdenseplasmaofmultiplyionizedatoms AT raybchikovdl anisotropyofradiationfromdenseplasmaofmultiplyionizedatoms AT vusyknn anisotropyofradiationfromdenseplasmaofmultiplyionizedatoms AT tseluykoaf anisotropyofradiationfromdenseplasmaofmultiplyionizedatoms AT hrechkoyao anízotropíâvipromínûvannâvŝílʹníjplazmíbagatorazovoíonízovanihatomív AT azarenkovna anízotropíâvipromínûvannâvŝílʹníjplazmíbagatorazovoíonízovanihatomív AT babenkoiev anízotropíâvipromínûvannâvŝílʹníjplazmíbagatorazovoíonízovanihatomív AT raybchikovdl anízotropíâvipromínûvannâvŝílʹníjplazmíbagatorazovoíonízovanihatomív AT vusyknn anízotropíâvipromínûvannâvŝílʹníjplazmíbagatorazovoíonízovanihatomív AT tseluykoaf anízotropíâvipromínûvannâvŝílʹníjplazmíbagatorazovoíonízovanihatomív AT hrechkoyao anizotropiâizlučeniâvplotnojplazmemnogokratnoionizirovannyhatomov AT azarenkovna anizotropiâizlučeniâvplotnojplazmemnogokratnoionizirovannyhatomov AT babenkoiev anizotropiâizlučeniâvplotnojplazmemnogokratnoionizirovannyhatomov AT raybchikovdl anizotropiâizlučeniâvplotnojplazmemnogokratnoionizirovannyhatomov AT vusyknn anizotropiâizlučeniâvplotnojplazmemnogokratnoionizirovannyhatomov AT tseluykoaf anizotropiâizlučeniâvplotnojplazmemnogokratnoionizirovannyhatomov |
| first_indexed |
2025-11-27T10:21:55Z |
| last_indexed |
2025-11-27T10:21:55Z |
| _version_ |
1849938591776505856 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №4(98) 32
ANISOTROPY OF RADIATION FROM DENSE PLASMA
OF MULTIPLY IONIZED ATOMS
Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Raybchikov,
N.N. Vusyk, A.F. Tseluyko
V.N. Karazin Kharkiv National University, Kharkov, Ukraine
E-mail: ievgeniia.borgun@mail.ru
It has been study the formation of anisotropic extreme ultraviolet radiation from the plasma of multiply ionized
atoms. The mean free path of quantum in dense plasma has been estimated. The critical current for formatting aniso-
tropic radiation in the tin ion plasma has been obtained. The dependences of the radiation directivity coefficient on
the plasma parameters have been derived.
PACS: 52.20.-j, 52.50.Dg
The work associated with the development of plas-
ma sources of extreme ultraviolet radiation on the basis
of high-current discharges. The main challenges to the
creation of the plasma source are a low conversion rate
of external electrical energy into radiation energy and a
strong destruction of the radiation focus system by the
discharge products. In [1] it was shown that one of the
possible solutions of these problems is the use of direc-
tional radiation generated in a pulsed high-current diode
with a limited surface of the potential electrode. As
shown in [2], for the efficient collection of radiation it is
necessary to select the optimum location and configura-
tion of the collecting mirror, taking into account the
radiation direction. This work is devoted to the defini-
tion of functional dependencies of the radiation from the
plasma parameters.
MATERIAL IS LOCATED AS FOLLOWS
An analysis of the experimental data, obtained earli-
er by the authors, can explain the mechanism of intense
directional radiation peaks using the following phenom-
enological physical model. The model assumes that at
any point of the radiating volume is generated by the
primary photon, which is distributed in a random direc-
tion. On a mean free path λ in the interaction with the
ion capture an electron the primary radiation photon
induces secondary photon in the same direction (radia-
tion-induced effect). Second quantum together with the
primary again induces at the length of λ new photons in
the same direction. Avalanche increased flow comes to
the boundary of the radiating volume.
To simplify the calculations it was used a simple
model of a homogeneous radiating volume in the form
of a cylinder of length L and diameter D. Schematic
representation of the physical model of the radiating
volume is shown in Fig. 1.
One of the main elements in a phenomenological
model of the formation of directional stimulated emis-
sion is the mean free path λ of the quantum in plasma.
To assess its value, it can be used the approach pro-
posed in [3]. In this paper is given an expression for the
quantum mean free path in the dense plasma of multiply
ionized atoms. The calculations have been performed
for the case when the dense plasma forms a plasma
pinch with a radius determined from the condition of
equality the surface radiation losses and plasma ohmic
heating
Fig. 1. Schematic representation
of the phenomenological physical model.
Ls and Ds – the length and diameter of a homogeneous
radiating volume; Nsl, Nsr и Nsf – the number
of partitions, respectively, the length,
radius and azimuth angle into elementary cells
( ) ( )eqJeq rQrQ =3 . (1)
Equating the loss of the line emission of plasma col-
umn lineQ to Joule heating JQ the authors have ob-
tained the critical current for heavy ion plasma
Jline QQ =
3 4
214 , kÀe ef
cr
n
T Z
I
Z
= ⋅ . (2)
It is shown that at the electron temperature Те the
average energy of photons leaving the plasma is about
( )1...2 .eE Tν ≅ ⋅ (3)
An approximate expression for the mean free path of
the quantum in plasma has been obtained
3 3
13 13 10 , cmef e
e n
Z T
n Zνλ ≅ ⋅ . (4)
At the Fig. 2 it have been shown the results of calcu-
lation of the dependence of the reduced mean free path
of quantum λν⋅10–16ne of the electron temperature Te for
different effective charges of ions Zef.
Taking into account the criterion of the Bennett
equilibrium (balance between a radial plasma pressure
and the pressure of the magnetic field of the current) the
mean free path can be rewritten as
2 3 5
3
27,5 10 , сm,pc ef e
B
n
d Z T
ZIνλ
−≅ ⋅ ⋅ (5)
Ls
∅
D
s
Nsl Nsf
N
sr
hν
ISSN 1562-6016. ВАНТ. 2015. №4(98) 33
where it is considered that iefe nZn = , and at
efefef ZZZ ≈+>> 1,1 .
0 10 20 30 40 50
1E-3
0.01
0.1
1
10
1211
5
4
10
98
6 7
λ ν
1
0-1
6 n e
, с
m
-2
Te, eV
Zef=2
3
Fig. 2. Dependence of the reduced mean free path of
quantum in a dense plasma λν⋅10–16ne of the electron
temperature Te for different effective charges of ions Zef
Using cylindrical rod electrode with diameter da
with isolated lateral surface (so that the current flows
only through the end of the electrode) the expression for
the mean free path of quantum can be written, express-
ing ne through the discharge current I.
Assuming a uniform current density distribution
over the cross section of the electrode the value I can be
written as
44
1 2
a
ae
dvenI π
⋅= , (6)
where
e
e
a m
Tv
π
8
= – the average arithmetic velocity of
plasma electrons. Then,
212
1
106,18
116
ae
e
e d
I
T
m
e
n ⋅⋅
⋅⋅
⋅⋅= −π
. (7)
The multiplier 1.6⋅10–12 in the denominator of the
radicand emerged from the fact that Те in eV is substi-
tuted in the same way as in (4). Substituting (7) into (4)
we can write
a
A
a
n
ef
e dd
Z
Z
TI ⋅
⋅⋅= −
νλ
3
2310175,4 , (8)
where Zef – an effective ion charge; Zn – the ion atomic
number; I – discharge current (kА); Тe – the plasma
electron temperature (eV); da – an electrode diameter
(cm); λνА – the mean free path of quantum in plasma
(cm) determined throw the electrode diameter
The expression 8 evaluates the minimum current
when the directional radiation peak appearances for the
electrode diameter da. From a physical model of direc-
tional stimulated radiation it can be seen that for format-
ting the significant radiation directivity must be
2ad<νλ . Therefore, as the threshold value it can be
taken 2~νλad .
Further calculation has been performed for tin,
which Zn = 50. The formation of radiation with a wave-
length of 13.5 nm is observed for tin ion with ionization
degree from 6 to 12. Therefore it has been taken the
minimum value of the ionization degree Zef = 6. The
energy of photons with a wavelength of 13.5 nm is
Еν = 92 eV, which corresponds to the value Те = Еν /3, i.e.
Те ≈ 30 eV, which agrees well with the literature [4, 5].
Under these assumptions for the electrode diameter
of 0.5 cm the minimum current value at which there will
be a directional radiation is Imin = 7.8 kА, that is in good
agreement with the experimental data. According to the
expression 8 the mean free path of quantum in plasma
λνА is defined as
n
eefa
A Z
TZ
I
d 432
310175,4 ⋅⋅⋅= −
νλ . (9)
Dependences of the mean free path of a quantum in
plasma on the discharge current I in case the criterion.
Fig. 3. The dependences of the mean free path
of a quantum λν (а) of the discharge current I:
λνВ – under the condition Bennett;
λνА – for a uniform current distribution over
the electrode cross section;
Zn = 50, Zef = 6, Те ≈ 30 eV
Bennett λνВ(I) applied or a uniform current distribu-
tion over the entire electrode cross section λνА(I) are
shown in Fig. 3. The dependences corresponds to the
case where the equilibrium diameter of plasma column
equals to the electrode diameter, Zn = 50; Zef = 6;
Те ≈ 30 eV.
According to Fig. 3, at reducing electrode diameter
da the mean free path of quantum in plasma decreases.
In addition, calculated with the help of expression 5 and
9 the mean free paths of the quantum into plasma for the
same parameters have the different functional depend-
0 10 20 30 40
1E-3
0.01
0.1
1
10
λνA, dа= 0,15 сm
λνA, dа= 0,25 сm
λνA, dа= 0,5 сm
λ ν
, с
m
I, кА
λνB, dpc= 0,5 сm
λνA, dа= 0,5 сm
λνB, dpc= 0,25 сm
λνA, dа= 0,25 сm
λνB, dpc= 0,15 сm
λνA, dа= 0,15 сm
ISSN 1562-6016. ВАНТ. 2015. №4(98) 34
ences of the discharge current I. Under the Bennett cri-
terion − it's inverse square law, and in the case of a uni-
form current distribution over the entire electrode cross
section − an inverse relationship.
From a phenomenological model of the directional
stimulated radiation, which is based on increased inten-
sity of radiation on the mean free path of quantum into
plasma λν, it has been found that for the directional ra-
diation it is necessary that the size of the emitting area d
is significantly bigger than λν .
d >> λν . (10)
Taking into account the condition 10, for the case of
the directional radiation generation the expressions for
the discharge current for the two cases can be written as
follows:
3 5
2 48.66 10 ef e
B pc
n
Z T
I I d
Z
−>> = ⋅ ⋅ ⋅ , (11)
3 4
34.175 10 ef e
A a
n
Z T
I I d
Z
−>> = ⋅ ⋅ ⋅ . (12)
Fig. 4 shows the dependences of the critical current I
for generating directional radiation in the plasma of
multiply ionized tin atoms on the electron temperature
Те for ionization degrees Zef = 6 и 12 for the rod elec-
trode diameter of 0.15 cm. The dependences ZБ
ef corre-
spond to the critical currents derived from the expres-
sion 11 for the case of equality of the plasma gas-kinetic
pressure and the magnetic field pressure of its own cur-
rent (Bennett criterion). The lines Zef show the depend-
ences of the critical current obtained from the expres-
sion 12, which corresponds to a uniform current distri-
bution over the electrode cross section.
Using estimates of the mean free path for a uniform
current distribution over the electrode cross section,
based on the proposed phenomenological physical mod-
el, the dependences of the radiation directivity coeffi-
cient for 13.5 nm wavelength on the tin plasma parame-
ters have been obtained. Under directivity coefficient α
is supposed the ratio of the longitudinal component of
the radiation intensity the transverse one with respect to
discharge axis, so α = 1 is corresponded to the case of
isotropic radiation registration.
The dependence of the directivity coefficient α on
plasma density for different ratios of plasma pinch
length and its diameter is shown in Fig. 5. According to
Fig. 5 at the plasma density of about 3·1016 сm-3 the
radiation directivity drops sharply to 1. If the plasma
density increases the longitudinal directivity will greatly
amplify. The calculations assumed that the plasma pinch
diameter is determined by the rod electrode diameter
and for this dependence it was 0.25 cm.
Designing the plasma source it is important to know
the effect of electrode diameter on the formation of ani-
sotropic radiation. Therefore at the Fig. 6 it is shown the
dependence of the directivity coefficient α on plasma
density for different electrode diameters. Dependencies
plotted for the case when the plasma pinch length is in
two times more than its diameter Lpl/da = 2.
0 10 20 30 40 50
0
5
10
I,
кА
Te, eV
Zef= 6
ZБ
ef= 6
ZБ
ef= 12
Zef= 12
Fig. 4. The dependence of the critical currents
of the generation of directional radiation I
in the plasma of multiply ionized tin atoms
on the electron temperature Те and the ionization
degrees Zef for rod electrode with diameter of 0.15 cm
1017
1
10
100
dа=0.25 cm
α
npl, сm
-3
Lpl /dа=0.4
Lpl /dа=0.8
Lpl /dа=1.2
Lpl /dа=2
Lpl /dа=3.2
Lpl /dа=4
Lpl /dа=6.4
Lpl /dа=8
Fig. 5. The dependence of the radiation directivity
on plasma density for different ratios of plasma pinch
length and its diameter using electrode with diameter
of 0.25 cm
According to Fig. 6, at the same values of the plas-
ma density, using the electrode of larger diameter it can
greatly amplify the radiation directivity. For example, at
the plasma density of 7·1017 сm-3 if the electrode diame-
ter da is being increased in 10 times, the longitudinal
directivity is amplified in 20 times.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 35
1017
1
10
da =1 cm
da =0.5 cm
da =0.25 cm
da =0.1 cm
α
npl , сm
-3
Lpl /da = 2
Fig. 6. The dependence of the radiation directivity on
plasma density for different electrodes diameters at a
ratio of plasma pinch length to its diameter Lpl/da = 2
CONCLUSIONS
Thus, the estimations of the mean free path of quan-
tum with 13.5 nm wavelength in the dense plasma of
multiply ionized tin atoms have been carried out. The
evaluative formulas of critical discharge current which
corresponds to the case of the directional radiation
forming in plasma diodes with rod electrodes, which
side surface is closed by insulator, and to implementa-
tion of equilibrium condition of plasma pinch have been
given. The dependencies of the radiation directivity on
the plasma density for different ratios of plasma pinch
length to its diameter and the pinch diameter to the
mean free path have been established. It has been shown
that controlling the external discharge parameters such
as the electrodes diameter, the power introduced into the
discharge, the transverse magnetic field value, can be
set the necessary radiation directivity.
REFERENCES
1. A.F. Tseluyko, V.T. Lazurik, D.L. Ryabchikov,
Ie. Borgun, I.N. Sereda, D.V. Zinov`ev. Directivity
of superradiation from plasma of high-current pulse
plasma diode // Problems of Atomic Science and
Technology. Series “Plasma Electronics and the
New Methods of Acceleration”. 2010, №4, p. 66-69.
2. Ie.V. Borgun et al. Optimization of the collecting
mirror location in extreme ultraviolet plasma source
// Problems of Atomic Science and Technology. Se-
ries “Plasma Physics” (21). 2015, №1, p. 174-176.
3. E.V. Aglitskiy, А.V. Vihrov, А.V. Gulov, et al.
Spectroscopy of multiple charge ions in hot plasma.
Moscow: “Science”. 1991, 206 p.
4. M. Masnavi, M. Nakajima, E. Hotta, K. Horioka,
G. Niimi, A. Sasaki. Estimation of optimum density
and temperature for maximum efficiency of tin ions
in Z discharge extreme ultraviolet sources // Journal
Of Applied Physics. 2007, Issue 101, p. 033306(9).
5. A. Di Cicco, K. Hatada, E. Giangrisostomi,
R. Gunnella, F. Bencivenga, E. Principi,
C. Masciovecchio, A. Filipponi. Interplay of elec-
tron heating and saturable absorption in ultrafast ex-
treme ultraviolet transmission of condensed matter //
Phys. Rev B. 2014, Issue 90, p. 220303(R).
Article received 29.04.2015
АНИЗОТРОПИЯ ИЗЛУЧЕНИЯ В ПЛОТНОЙ ПЛАЗМЕ МНОГОКРАТНО
ИОНИЗИРОВАННЫХ АТОМОВ
Я.О. Гречко, Н.А. Азаренков, Е.В. Бабенко, Д.Л. Рябчиков, Н.Н. Вусык, A.Ф. Целуйко
Изучается формирование анизотропного излучения в диапазоне экстремального вакуумного ультрафио-
лета из плазмы многократно ионизированных атомов олова. Приводятся оценки длины свободного пробега
кванта в плотной плазме многозарядных ионов. Определен критический ток формирования анизотропного
излучения в плазме ионов олова. Получены зависимости коэффициента направленности излучения от пара-
метров плазмы.
АНІЗОТРОПІЯ ВИПРОМІНЮВАННЯ В ЩІЛЬНІЙ ПЛАЗМІ БАГАТОРАЗОВО ІОНІЗОВАНИХ
АТОМІВ
Я.О. Гречко, М.О. Азарєнков, Є.В. Бабенко, Д.Л. Рябчіков, М.М. Вусик, О.Ф. Целуйко
Вивчається формування анізотропного випромінювання в діапазоні екстремального вакуумного ультра-
фіолету з плазми багаторазово іонізованих атомів олова. Наводяться оцінки довжини вільного пробігу кван-
та в щільній плазмі багатозарядних іонів. Визначено критичний струм формування анізотропного випромі-
нювання в плазмі іонів олова. Отриманo залежності коефіцієнта спрямованості випромінювання від параме-
трів плазми.
Material is located as follows
Conclusions
references
анизотропия излучениЯ в плотной плазме многократно ионизированных атомов
Анізотропія ВИПРОМІНЮВАННЯ В ЩІЛЬНІЙ плазмі БАГАТОРАЗОВО іонізованих АТОМІВ
|