The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration
Empirical formula of the coefficient decay dependence of strongly coupled plasma from the electron density in the range from 10¹⁷ to 10²² cm⁻³ is given. The dependence of the coefficients of the decay of NP from the temperature in the range from 7×10³ to 45×10³ K and the degree of nonideality of p...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Cite this: | The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration / O.A. Fedorovich, L.M. Voitenko // Вопросы атомной науки и техники. — 2011. — № 1. — С. 122-124. — Бібліогр.: 10 назв. — англ. |
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| author_facet | Fedorovich, O.A. Voitenko, L.M. |
| citation_txt | The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration / O.A. Fedorovich, L.M. Voitenko // Вопросы атомной науки и техники. — 2011. — № 1. — С. 122-124. — Бібліогр.: 10 назв. — англ. |
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| description | Empirical formula of the coefficient decay dependence of strongly coupled plasma from the electron density in the range from 10¹⁷ to 10²² cm⁻³ is given. The dependence of the coefficients of the decay of NP from the temperature in the range from 7×10³ to 45×10³ K and the degree of nonideality of plasma Г in the range from 0.2 to 3 was also experimentally studied.
Наводиться емпірична формула залежності коефіцієнтів розпаду неідеальної плазми (НП) від концентрації електронів в діапазоні від 10¹⁷ до 10²² см⁻³. Досліджено також експериментальні залежності коефіцієнтів розпаду НП від температури у діапазоні (7×10³ )...(45×10³ ) К та ступеню неідеальності плазми Г в діапазоні від 0.2 до 3.
Приводится эмпирическая формула зависимости коэффициентов распада неидеальной плазмы (НП) от концентрации электронов в диапазоне от 10¹⁷ до 10²² см⁻³. Исследованы также экспериментальные зависимости коэффициентов распада НП от температуры в диапазоне (7×10³ )...(45×10³ ) К и степени неидеальности плазмы Г в диапазоне от 0.2 до 3.
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THE EMPIRICAL FORMULA OF DEPENDENCE OF FACTOR
OF DISINTEGRATION OF NONIDEAL PLASMA
FROM ELECTRONS CONCENTRATION
O.A. Fedorovich, L.M. Voitenko
Institute for Nuclear Research NASU, Kiev, Ukraine
E-mail: oafedorovich@kinr.kiev.ua
Empirical formula of the coefficient decay dependence of strongly coupled plasma from the electron density in the
range from 1017 to 1022 cm-3 is given. The dependence of the coefficients of the decay of NP from the temperature in the
range from 7×103 to 45×103 K and the degree of nonideality of plasma Г in the range from 0.2 to 3 was also
experimentally studied.
PACS: 52.80.-s
INTRODUCTION
Recombination processes in a nonideal plasma (NP) is
studied too little. This is due to the complexity of the
theoretical description of processes in nonideal plasmas
[1-3]. Most theoretical models which are valid for an ideal
plasma, in dense (nonideal) plasma does not work. In
describing the dense plasma is also not true
representations of solid state physics. Theory of NP is
developed insufficiently, not only because of the
complexity of calculations of such plasma, but also
because of the lack of reliable experimental data from the
properties of the NP and the relationship of its properties
with the main parameters of the plasma. The experimental
results obtained are also very difficult. Nonideal plasma,
under laboratory conditions, exists a very short time – the
nano- and micro- and milliseconds. No equipment to
measure the basic parameters of the NP for such a short
time. There are no methods for measuring the parameters
of the NP. In the NP can only be measured the time
variation the brightness temperature (Tbr) of the surface
layers of plasma. But with measuring the Tbr at different
wavelengths can be obtained by the difference in the
values of Tbr to 2 times [4]. This may indicate about the
radiation no equilibrium NP. The electron concentration
from the broadening of hydrogen lines Нα (656.3 nm) can
be measured only below to values Ne ≤ 1019 cm-3. This
requires the adjustment of the contour lines Нα [5]. In
dense inhomogeneous plasma there is always the
reabsorption which reduce the intensity contours
reabsorbed lines. Correction of the reabsorbed contour
lines Нα is very time-consuming and uncomfortable
procedure. At higher concentrations (Ne > 4×1019 сm-3)
Нα line (656.3 nm) by the influence of microscopic fields
of the plasma in the spectrum can not be realized [6]. In
recent years, effort have been attempted to determine the
concentration of electrons in the plasma on the effect of
outage of lines under the influence of microscopic fields
of the plasma, the so-called non-realization of the effect
of lines, or on the effect of "gap" in NP [8].This made by
the lines of hydrogen and tungsten. This can be done for
other compositions of plasma where atoms and ions are
sufficiently rich in line emission and absorption spectra.
The results of theoretical work on recombination [1-3] –
are contradictory. Experimental verification is required
for theoretical work on recombination that has appeared
in recent years. This paper studies the influence of various
plasma parameters on the rate of decay of coupled plasma
and obtaining an empirical formula for the dependence of
the decay rate of NP on the electron density.
RESULTS AND DISCUSSION
In recent years have appeared several experimental
studies on the decay of NP [7-9]. They presented the
results of dependences of the decay of the NP from time.
It is of interest to determine the dependences index of the
decay from various parameters of the NP: temperature,
electron density, the degree of nonideality of plasma
pressure, the concentration of atoms in the NP, etc. In
most theoretical work with the estimation of
recombination coefficients use two basic parameters -
electron density and temperature of the plasma [1, 2]. In
[3] gives such a dependence from the nonideality
parameter of plasma Г. Г (Ratio of potential to kinetic
energy of the plasma) is written as
1/3 2(4 / 3) ( / )eГ N e kπ T= ⋅ ⋅ ,
where Т – plasma temperature, Ne – electron density, k –
Boltzmann constant, e - electron charge.
In [10, 7] have mentioned that direct measuring the
recombination coefficient of the plasma is very difficult
because in addition to the recombination processes are
processes thermal ionization. Experimentally, we can
determine only the coefficient of plasma decay.
It can be seen in Fig. 1 that there is no unique
dependence of the decay coefficients of the hydrogen-
oxygen plasma from the temperature in the range
(20…50)×10 K. When the temperature of the plasma in
the channel is reduced from 20
3
×10 to 83 ×10 K, the decay 3
coefficient increases from 3×10 to 10 cm /s.-16 -12 3 At the
same chart for comparison is adduced the results taken
from [10]. The decay coefficients value is given for the
temperature 50×103 K, when the electron density is
2×1017 cm-3, requisite value the decay coefficients is
10-12 cm3/s. The decay coefficients value at the same
temperature is received approximately 10-15 cm3/s at
concentrations of electrons 5×1019…1021 cm-3 by authors
of this paper. The horizontal shape of the curve of the
decay coefficient from temperature can apparently be
explained by high values of ionization at high
temperatures. Therefore, most likely, the temperature is
122 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2011. № 1.
Series: Plasma Physics (17), p. 122-124.
mailto:oafedorovich@kinr.kiev.ua
not the most important parameter is the NP of which
depend on the coefficients of decomposition. The
dependence of the recombination coefficient from
temperature in all theories of theoretical studies is the
same, proportional to ~ T-9/2. Experimentally, the strong
dependence of the decay from temperature in the NP is
not observed.
Fig.1. Dependence of the decay rate of strongly coupled
plasma on the temperature
Fig. 2 shows the results of determining the
coefficients of plasma decay in depending on the
concentration of electrons. Chart based on a double
logarithmic scale.
Fig. 2. Dependence of the decay rate of strongly coupled
plasma on the concentration
It is seen that with decreasing concentration of electrons
in the NP from 7×1021 to 2×1017 cm-3 the decay
coefficient increases almost linearly from a value of
3×10-18 to 1×10-12 cm3/s.
The plasma temperature was equal to (8…11)×103 К at an
electron density Ne = 7×1021…1020 cm for tungsten
plasma and decreased from
-3
50×103 to 7×103 К at
concentrations of Ne = 5×1020…1017 cm for the
hydrogen-oxygen plasma.
-3
Considering that the almost linear dependence of the
decay coefficient from the electron density in the NP
experimentally was obtained, an empirical formula for
this dependence was picked up and has the form:
68 1,2 8 54,9 10 ( ) 4,9 10eK N −−= ⋅ = ⋅
where 2
)(
e
e
N
dt
dN
K = сm-3 decay rate of NP, Ne (сm-3)
– electron concentration in the NP. This formula describes the
experimentally obtained dependence of the decay coefficient
of NP from the electron density in the range of 1017 сm-3 ≤ Ne
≤ 1022 cm-3. Temperature range (7…50)×103 К.
Data were obtained for the hydrogen-oxygen plasma
in the range of electron densities 1017…1021 сm-3 for
tungsten in the range of 1020…1022 cm-3.
The charges value of ions and temperature were not
considered. The experimental data of the decay
coefficients was obtained of the three modes of
discharges. In plasma tungsten is possible second
ionization, but it was not considered in the empirical
formula.
Some variation in the coefficients of the decay in the
concentration range of electrons 5·1019…1021 cm-3 can be
attributed to a significant ionization of neutral atoms at
high temperature hydrogen-oxygen plasma
(Т ≈ (40…50)×103 К).
A comparison of experimental results with theoretical
calculations of [1-3] is given.
At comparing the experimental values of the decay
coefficients with theoretical work [1] in which is
supposed to triple-recombination mechanism (electron -
electron - ion), a big difference at high concentrations of
electrons were received
With decreasing the concentration of electrons occurs
convergence of experimental and theoretical results.
In a theoretical paper [2] predicted a reduction in the
decay coefficients with increasing electron concentration.
Qualitatively this is consistent with experimental results.
But it is assumed binary recombination (electron-ion), but
not triple.
In [3] shows the dependence of the recombination
coefficient (decay) in depending on the degree of the
plasma nonideality Г. According to this work should
exhibit a maximum in the ratio of recombination
Г ≈ 0,6…1,2.
Fig. 3. Dependence of the decay rate of strongly coupled
plasma on degree of nonideality
eN ,
Fig. 3 shows the experimental results of the
dependences of the decay coefficient in depending on the
degree of the plasma nonideality Г. The experimental
values of the decay coefficients from the degree of plasma
123
124
nonideality have really a small peak in the region Г =
0,4…2. The region with the degree of nonideality Г =
0,6…1,5 yet we have not been investigated. From this
dependence follows that nature of the decay process
change at Г ≈ 0,3. Perhaps, the binary recombination at
large Ne with a decrease in Ne (Ne ≤ 5×1018 сm-3) is
transformed into a triple.
CONCLUSIONS
Almost linear relationship (on a double logarithmic
scale) the plasma decay coefficient from the electron
density for the NP was discovered. An empirical formula
for this dependence was obtained. A small maximum the
decay coefficients for the degree of nonideality of plasma
Г ~ 0,6…1,5 experimentally observed that agrees
qualitatively with the results of [3].
REFERENCES
1. L.M. Biberman, V.S. Vorob'ev, I.T. Yakubov //
Kinetics of Nonequilibrium Low Temperature Plasmas.
Moscow: “Atomizdat”, 1982.
2. L.M. Biberman, V.S. Vorob'ev, I.T. Yakubov. The
effect of nonideality on the coefficient of recombination
of a dense plasma // Proceedings of the Russian
Academy of Sciences. 1987, v. 296, N 33, p. 576-578.
3. A. Lankin, G. Norman. Density and nonideality effects
in plasmas // Contribution to Plasma Physics. 2009,
v. 49, N 10, p. 723-731.
4. L.L. Pasechnik, P.D. Starchyk, O.A. Fedorovich.
Investigation of the continuous radiation of a pulsed
discharge in water in the range of 400-700 nm //
Abstracts of the VI All-Union Conference on Low
Temperature Plasma Physics. Leningrad, 1983, v. 1,
p. 501-503.
5. O.A. Fedorovich. Methods of restoration contours
reabsorbed emission lines in high-pressure plasma //
Proceedings of the XII International Scientific School
"Physics of pulsed discharge in Condensed Matter".
Nikolaev, 2005, p. 26-28; 2007, p. 118-119.
6. O.A. Fedorovich. The empirical formula for the depen-
dence of the "optical gap" in the nonideal plasma for the
electron density in the range 1017 cm-3 ≤ Ne≤ 1022 cm-3 //
Proceedings of the XI International Scientific School
"Physics of pulsed discharge in Condensed Matter".
Nikolaev, 2003, p. 11-13.
7. O.A. Fedorovich, L.M. Voitenko. Experimental Re-
searches of the Decay Coefficient of Nonideal Plasma
Produced at Pulsed Discharges in Water // Ukrainian
Journal of Physics. 2008, v. 53, N 5, p. 450-457.
8. O.A. Fedorovich, L.M. Voitenko. About factors disin-
tegration of nonideal plasma of pulse discharges in water
at electrons concentration 2·1020 ≥ Ne ≥ 2·1017 cm-3 //
Problems of Atomic Science and Technology. Series
“Plasma Electronics and New Methods of Acceleration”.
2008, N4, p. 288-293.
9. O.A. Fedorovich, L.M. Voitenko. About factors of
disintegration of nonideal plasma at explosion of tungsten
conductor in water // Problems of Atomic Science and
Technology. 2010, N 4, p. 354-359.
10. O.A. Malkin. Pulsed current and relaxation in the gas.
Moscow: “Atomizdat”, 1974.
Article received 05.10.10
ЭМПИРИЧЕСКАЯ ФОРМУЛА ЗАВИСИМОСТИ КОЭФФИЦИЕНТОВ РАСПАДА
НЕИДЕАЛЬНОЙ ПЛАЗМЫ ОТ КОНЦЕНТРАЦИИ ЭЛЕКТРОНОВ
О.А. Федорович, Л.М. Войтенко
Приводится эмпирическая формула зависимости коэффициентов распада неидеальной плазмы (НП) от
концентрации электронов в диапазоне от 1017 до 1022 см-3. Исследованы также экспериментальные зависимости
коэффициентов распада НП от температуры в диапазоне (7×103)...(45×103) К и степени неидеальности плазмы Г в
диапазоне от 0.2 до 3.
ЕМПІРИЧНА ФОРМУЛА ЗАЛЕЖНОСТІ КОЕФІЦІЄНТІВ РОЗПАДУ
НЕІДЕАЛЬНОЇ ПЛАЗМИ ВІД КОНЦЕНТРАЦІЇ ЕЛЕКТРОНІВ
О.А. Федорович, Л.М. Войтенко
Наводиться емпірична формула залежності коефіцієнтів розпаду неідеальної плазми (НП) від концентрації
електронів в діапазоні від 1017 до 1022 см-3. Досліджено також експериментальні залежності коефіцієнтів розпаду
НП від температури у діапазоні (7×103) ...(45×103) К та ступеню неідеальності плазми Г в діапазоні від 0.2 до 3.
|
| id | nasplib_isofts_kiev_ua-123456789-90896 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:15:06Z |
| publishDate | 2011 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Fedorovich, O.A. Voitenko, L.M. 2016-01-05T18:40:42Z 2016-01-05T18:40:42Z 2011 The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration / O.A. Fedorovich, L.M. Voitenko // Вопросы атомной науки и техники. — 2011. — № 1. — С. 122-124. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 52.80.-s https://nasplib.isofts.kiev.ua/handle/123456789/90896 Empirical formula of the coefficient decay dependence of strongly coupled plasma from the electron density in the range from 10¹⁷ to 10²² cm⁻³ is given. The dependence of the coefficients of the decay of NP from the temperature in the range from 7×10³ to 45×10³ K and the degree of nonideality of plasma Г in the range from 0.2 to 3 was also experimentally studied. Наводиться емпірична формула залежності коефіцієнтів розпаду неідеальної плазми (НП) від концентрації електронів в діапазоні від 10¹⁷ до 10²² см⁻³. Досліджено також експериментальні залежності коефіцієнтів розпаду НП від температури у діапазоні (7×10³ )...(45×10³ ) К та ступеню неідеальності плазми Г в діапазоні від 0.2 до 3. Приводится эмпирическая формула зависимости коэффициентов распада неидеальной плазмы (НП) от концентрации электронов в диапазоне от 10¹⁷ до 10²² см⁻³. Исследованы также экспериментальные зависимости коэффициентов распада НП от температуры в диапазоне (7×10³ )...(45×10³ ) К и степени неидеальности плазмы Г в диапазоне от 0.2 до 3. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Низкотемпературная плазма и плазменные технологии The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration Емпірична формула залежності коефіцієнтів розпаду неідеальної плазми від концентрації електронів Эмпирическая формула зависимости коэффициентов распада неидеальной плазмы от концентрации электронов Article published earlier |
| spellingShingle | The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration Fedorovich, O.A. Voitenko, L.M. Низкотемпературная плазма и плазменные технологии |
| title | The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration |
| title_alt | Емпірична формула залежності коефіцієнтів розпаду неідеальної плазми від концентрації електронів Эмпирическая формула зависимости коэффициентов распада неидеальной плазмы от концентрации электронов |
| title_full | The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration |
| title_fullStr | The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration |
| title_full_unstemmed | The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration |
| title_short | The empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration |
| title_sort | empirical formula of dependence of factor of disintegration of nonideal plasma from electrons concentration |
| topic | Низкотемпературная плазма и плазменные технологии |
| topic_facet | Низкотемпературная плазма и плазменные технологии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/90896 |
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