On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³
The paper presents the results of comparison between the experimental decay coefficients of the dense plasma produced by pulsed discharges in water with theoretical coefficients calculated using all the known formulas for the three-particle recombination with the plasma ionization taken into account...
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| Cite this: | On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ / О.А. Fedorovich, L.M. Voitenko // Вопросы атомной науки и техники. — 2013. — № 4. — С. 217-222. — Бібліогр.: 24 назв. — англ. |
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| author | Fedorovich, О.А. Voitenko, L.M. |
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| citation_txt | On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ / О.А. Fedorovich, L.M. Voitenko // Вопросы атомной науки и техники. — 2013. — № 4. — С. 217-222. — Бібліогр.: 24 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The paper presents the results of comparison between the experimental decay coefficients of the dense plasma produced by pulsed discharges in water with theoretical coefficients calculated using all the known formulas for the three-particle recombination with the plasma ionization taken into account. The best agreement was obtained in the calculations of the ternary recombination with taking into account only the levels realized in the dense plasma and with taking into account the ionization using the experimental decay coefficients of the dense plasma.
Наведено результати порівняння експериментальних коефіцієнтів розпаду густої плазми імпульсних розрядів у воді з теоретичними коефіцієнтами, розрахованими за всіма відомими формулами для тричасткової рекомбінації з урахуванням іонізації плазми. Найкращу згоду з експериментальними коефіцієнтами розпаду густої плазми отримано при розрахунку коефіцієнтів потрійної рекомбінації з урахуванням тільки тих рівнів, які реалізувалися в щільній плазмі із урахуванням іонізації.
Приведены результаты сравнения экспериментальных коэффициентов распада плотной плазмы импульсных разрядов в воде с теоретическими, рассчитанными по всем известным формулам коэффициентами для трехчастичной рекомбинации с учетом ионизации плазмы. Наилучшее согласие получено при расчете коэффициентов тройной рекомбинации с учетом только реализовавшихся в плотной плазме уровней и учетом ионизации с экспериментальными коэффициентами распада плотной плазмы.
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| first_indexed | 2025-12-01T11:03:50Z |
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ISSN 1562-6016. ВАНТ. 2013. №4(86) 217
ON THE DENSE PLASMA DECAY WITHIN THE ELECTRON
CONCENTRATION RANGE OF 1017 cm-3≤Ne≤1022 cm-3
О.А. Fedorovich, L.M. Voitenko
Institute for Nuclear Research of National Academy of Sciences of Ukraine, Kiev, Ukraine
E-mail: oafedorovich@kinr.kiev.ua
The paper presents the results of comparison between the experimental decay coefficients of the dense plasma
produced by pulsed discharges in water with theoretical coefficients calculated using all the known formulas for the
three-particle recombination with the plasma ionization taken into account. The best agreement was obtained in the
calculations of the ternary recombination with taking into account only the levels realized in the dense plasma and
with taking into account the ionization using the experimental decay coefficients of the dense plasma.
PACS: 52.80.-s. 52.20.Dq
INTRODUCTION
Processes of the dense plasma decay are studied not
satisfactory. In recent years a series of theoretical works
were published presenting the results of numerical
simulation on recombination processes in the dense
plasma [1 - 4]. There the corrections were introduced
into the classical Gurevich-Pitaevsky formula for calcula-
tion of a three-particle recombination in the rarefied
plasma [5, 6]. The corrections leaded to the slight de-
crease in the values of dense plasma recombination coef-
ficients. But the calculated corrections enclose different
models of the electron-ion interaction. The authors of [1 -
3] have made an assumption that there are existing cou-
pled states of atoms; an energy region adjacent to the
ionization limit where pairing states, practically, are ab-
sent (a ”gap” between the pairing coupled and free elec-
tron states); free electron states. In [1 - 3] the effect of
atomic level unrealization in the high electric microfields
was taken into account. In [4] the corrections to the
Gurevich-Pitaevsky formula for the ultracold nonideal
plasma were calculated. Here it has been supposed the
following: “The previously existing viewpoint, asserting
that in the course of the degree of nonideality increasing
in the distribution function a gap arises because of the
pairing state absence, is not quite right” (gap absence).
The authors of [7, 8] proposed a model for the bi-
nary recombination in the dense plasma and derived a
corresponding formula for the strongly nonideal plasma
recombination coefficient. An interaction between the
electron and the nearest ion in the nonideal plasma was
described in the nearest neighbor approximation and by
the cellular model.
In the theoretical work [9] the corrections to the
Gurevich-Pitaevsky formula [5, 6] were derived too.
The corrections to the coefficient of the three-particle
recombination depending on the temperature (T) and
electron concentration (Ne) were calculated. Independ-
ently on the charged particle concentration in the
plasma, there obtained were three variants of corrections
to the formula showing the recombination coefficient
decreasing versus Ne. According to [9] the three-particle
electron recombination rate decreases by a factor of ė
(2.718) occurs, when Г ee≥ 0.55 (Гee is the degree of
plasma nonideality). This is the condition for almost full
closing of the three-particle electron recombination
channel (by Pitaevsky) [9]. It should be also noted, that
the magnetic field influence on the dense (nonideal)
plasma recombination rate is insignificant [9].
In [10] the decrease of the nonideal plasma recom-
bination coefficient as a result of upper level unrealiza-
tion in the high microfields was estimated. There it has
been assumed that the levels, onto which the recombina-
tion can occur, are not broadened.
Before, the decay and recombination coefficients
were determined experimentally for the electron con-
centrations to Ne ≤ 2⋅1017 сm-3 at 64⋅103 K [11]. Dis-
crepancies between the predicted and experimental val-
ues were insignificant. However, a slight decrease of
experimental values in comparison with theoretical cal-
culations by the formula for three-particle recombina-
tion has been already observed [5, 6]. The subsequent
investigations on the hydrogen-oxygen plasma produced
the high-voltage pulse discharges in water [12 - 16]
have revealed a significant disagreement between ex-
perimental and theoretical results at high values of Ne.
For the electron concentration Ne ≤ 2⋅1017 сm-3 the ex-
perimental values of the decay coefficient are practi-
cally coinciding with the theory, as in [11]. For higher
Ne the values of the decay coefficient obtained experi-
mentally were lower than the calculated values by 6
orders of magnitude and more. And the difference was
increasing with electron concentration increasing, the
calculations being carried out with the use of the three-
particle recombination model. The purpose of the pre-
sent work is to compare the experimental results with
calculation results obtained by different theoretical
models and to determine dependences of the decay coef-
ficient on plasma temperature, electron concentration,
degree of plasma nonideality within the ranges of elec-
tron concentration of 1017 сm-3 ≤ Ne ≤ 1022 сm-3 and
temperature of 5⋅103 К ≤ Т ≤ 5⋅104 К.
EXPERIMENTAL RESULTS
AND DISCUSSION
Experimental investigations of dense plasma decay
coefficients at electron concentrations of
1017сm-3 ≤ Ne ≤ 1022 сm-3 were carried out under condi-
tions of relaxation of the plasma produced by pulsed
discharges in water. To obtain a good reproducibility
and high electron densities, the discharges in water were
initiated by the thin exploding wires. The diameter of
tungsten conductors initiating discharges was varying
from 20 to 500 μm. The storage battery capacity
С = 14.6 μF, discharge circuit inductance was 0.43 μH.
The discharge period under short-circuit conditions was
15.5 μs. The initial voltage on the battery was varying
ISSN 1562-6016. ВАНТ. 2013. №4(86) 218
from 3 to 37 kV, and the maximum accumulated energy
did not exceed 10 kJ. The discharge gap length was
changing from 10 to 100 mm. The discharges in water
were initiated by conductors of iron, molybdenum, cop-
per, brass, constantan, carbon, nickel and other materi-
als. The most interesting were discharges initiated by
the tungsten conductor. A peculiarity of such discharges
consisted in that the tungsten conductors might be
heated before the metal vapor breakdown to the tem-
perature of 13⋅103 К [17] at tungsten melting tempera-
ture of 3689 K and boiling temperature of 5930 K. The
metal heating to such high temperatures permits to ob-
tain, rather easily, free electrons in vapors and to gener-
ate discharges without a current pause with a very high
degree of ionization and concentrations to the densities
electrons of 1022 сm-3. Besides, the first ionization po-
tential W is 8 eV, the second is 14 eV and the third is
24 eV [18]. For hydrogen the ionization potential
Eи = 13.6 eV; for oxygen the first potential is 13.6 eV
and the second is 35.1 eV. Also, for the water molecule
dissociation it is necessary to use 9.5 eV. Therefore,
when the discharge occurs in the tungsten vapors, the
second tungsten ion ionization is possible and the
plasma with a high temperature and electron concentra-
tion can be obtained. If for the discharge initiation in
water the conductors of other metals are used it is im-
possible to obtain the plasma with such a high concen-
tration. When the discharge initiation in water is per-
formed with the conductors of carbon, constantan,
nickel, these materials are heated up to moderate tem-
peratures. Therefore, the vapor breakdowns are delayed
for long times and, consequently, the low values of the
plasma channel temperature and comparatively low
electron concentrations are observed. In addition, for
investigations of decay coefficients the discharges cho-
sen have contributed a maximum energy into the chan-
nel in the first half-period, practically, without energy
supplements into the plasma in the second and subse-
quent half-periods [13, 14]. Thus, it was possible to ob-
tain minimum errors when determining the decay coef-
ficients. The most interesting were discharges with a
discharge gap length of 100 mm initiated by tungsten
exploding conductors with wire diameter of 20 μm,
voltage U0 =30 kV, as well as, a tungsten exploding
wire of 320 μm in diameter, conductor length of 40 mm
and voltage of 20 kV.
The experimental plasma decay coefficient is deter-
mined from the relation
2
e
e
r Nt
N
K
⋅Δ
Δ
= , where eNΔ is
the electron concentration decrease for the time interval
tΔ , and eN − the electron concentration. The theoreti-
cal calculation of the decay coefficient is determined
from the principle of detailed balancing
i
e
a
2
e
e Nb
N
N
Ndt
dN
⋅α−=
⋅
, where aN is the atomic concen-
tration in plasma, b − the ionization coefficient, iN⋅α −
the recombination coefficient. In this case the decay
coefficient is determined with taking into account the
plasma ionization that can be rather high at a tempera-
ture of (7…45)⋅103 К. Just such temperatures are ob-
served in the case of pulsed discharges in water.
As is shown in [15, 16] the unambiguous depend-
ence of the decay coefficient on the plasma temperature
is not observed. This contradicts to the classical formula
for three-particle plasma recombination by the electron-
electron-ion collision model. The temperature depend-
ence in this model is very strong ~Т-9/2 [5, 6]. When the
temperature changes from 7000 to 64000 K the experi-
mental value of K at equal values of concentration Ne
has practically the same value [15, 16]. According to [5,
6] the recombination coefficient should be different by a
factor of ~ 2.1⋅104 (twenty one thousands times).
Comparison of experimental results on K with val-
ues calculated by the recombination model [7, 8] shows
a satisfactory coincidence only at the electron concen-
tration Ne < 1019 сm-3 [16].
Fig. 1 presents the decay coefficient values Kr versus
time determined experimentally in comparison with
theoretical values calculated by the classical formula for
the three particle recombination. Here also given are the
calculated values of b
N
N
e
a ⋅ , being less by an order of
magnitude and more than the recombination coefficient.
Therefore, in such a discharge regime practically there
is no ionization influence on the calculation results and
the decay coefficient coincides with the recombination
coefficient (an overestimation error < 10 %). The ap-
proach of results goes with concentration decreasing
and sequential appearance of Нα (656.3 nm), Нβ
(486.1 nm) andНγ (434.06 nm) lines in the radiation.
Then the plasma in the continuous spectrum becomes
transparent.
Fig. 1. The dependence on time the decay coefficient
Comparison of experimental values Кр with these
calculated by the Gurevich-Pitaevsky formula [5, 6],
calculations by Johnson and Hinnov [20], as well as,
Lankin-Norman [1 - 3] is given in Fig. 2. In [20] the
hydrogen plasma opacity in the Layman series radiation
lines and the ionization was taken into account. Thus the
approach of experimental and experimental results was
slightly improved (Fig. 2). The calculation results by the
formulas of [1 - 3] practically coincide with the calcula-
tion results for the nonideal plasma formulas at electron
concentrations Ne less than 1019 сm-3 or Гее ≤ 0.6…7, as
it follows from the formulas given in the present paper.
But they are significantly higher than the experimental
values of Kr. According to [19] the decay coefficient Kr
can be determined by the time dependence of the ratio
between the maximum electron concentration max
eN and
the current concentration Ne.
ISSN 1562-6016. ВАНТ. 2013. №4(86) 219
Fig. 2. The dependence on time the decay coefficient
Fig. 3 presents the ratio e
max
e NN as a function of
time. One can see that to 70 µs the curve slope was neg-
ligibly small. Beginning from 70 µs the curve depend-
ence increases and after 80 µs it increases once again.
This can evidence on the recombination type change
with electron concentration decreasing in the dense
plasma.
Fig. 3. Dependence on time the ratio e
max
e NN
The results on the time dependence of experimental
values of rК and calculated values obtained by different
models for the nonideal plasma are presented in Fig. 4.
Fig. 4. The dependence on time the decay coefficient
The calculation results do not show significant ap-
proach of theoretical and experimental values of rК . If
the ionization is taken into account, the approach of
experimental and theoretical results also is not improved
because the ionization values are < 10% in comparison
with the recombination values, and the calculation re-
sults are practically coinciding. It should be noted that
the used ionization calculation was taken from [20]. But
there one does not take into account the effects of line
level unrealization in the high electrical dense plasma
microfields.
The value of rК is slowly changing with time.
Fig. 5,a presents the results of comparison between the
experimental values of rК and the calculation data with
corrections taking into account the influence of the de-
gree of plasma nonideality on the Gurevich-Pitaevsky
formula.
Fig. 5,a. The dependence of the decay of the degree
of nonideality
Depending on the degree of plasma nonideality in
the case of Гее < 1 the corrections do not lead to the sig-
nificant decrease of calculated values of decay coeffi-
cients in all the three theoretical models [1 - 4, 9]. To
50 µs the value of rК is practically unchangeable. The
electron concentration changing with time in this case
was calculated by the Sakha formula. The total electron
concentration in the plasma was determined from the
pressure. The pressure dependence on time was calcu-
lated by the hydrodynamic characteristics of the plasma
channel. The pressure was calculated by the quasi-
incompressible liquid [21]. The radiance temperature
was taken from the plasma channel radiation measure-
ments by comparison with a standard source EV-45
[22]. In calculations of the partition function only the
levels observed experimentally were taken into account.
The ionization potential decrease was not taken into
account [1 - 3]. The plasma channel has radiated a con-
tinuous spectrum but its radiation strongly differs from
the radiation of an absolutely black body [23]. In the
present case the temperature was measured on the wave-
length of 400 nm. As the plasma is decaying and the
intensity of the continuous spectrum is decreasing, from
this spectrum an emission linear spectrum begins to
appear. At 50 µm a strongly broadened Нα (656.3 nm)
line appears and at 63 µm it is the Нγ (434.06 nm) line.
Therefore, beginning from 65 µm it has been succeeded
to measure the electron concentration change in time by
the Stark broadening of Нα line [24]. With appearance
of Нα, Нβ and Нγ lines the plasma decay rate quickly
increases (see Fig. 2). The value of Кr increases and the
approach between the theoretical calculation results for
the triple recombination and experimental values of Кr
ISSN 1562-6016. ВАНТ. 2013. №4(86) 220
takes place. It is explained by the fact that in the hydro-
gen atom new levels arise onto which the electron re-
combination is observed leading to the Кp increase. Be-
sides, when the electron concentration Ne decreases, the
line broadening and electron orbits in atoms become
more stable that leads to rК increasing. When plotting
rК against the degree of nonideality a peculiarity is ob-
served. As the degree of nonideality decreases from 0.6
(at the plasma decay beginning) to 0.3 then the region of
experimental values of rК arises, where Гее is not
changing and the decay coefficient increases from
10-16 до 10-13 сm3/s. It is due to the appearance of Нα, Нβ
and Нγ line levels and to the beginning of the sharp re-
combination rate increase. The nonideality parameter
Гее includes the temperature-electron concentration rela-
tion. Therefore different values of Ne and T can corre-
spond to the same value of Гее. At the same time in the
calculation curves a kind of a “hysteresis loop” is ob-
served for the dependence of Кr on Гee.
The unambiguous temperature dependence of Кr in
the dense plasma was not revealed. Only the unambigu-
ous dependence on the electron concentration was ob-
served [15]. Evidently, the nonideality parameter is not
a main and unique parameter on which the dense plasma
decay coefficient depends. Indeed, at high degrees of
nonideality there is a correlation between the rК de-
crease and Гее increase (Fig. 5,b).
Fig. 5,b. The dependence of the decay of the degree
of nonideality
Comparison between the experimental results ob-
tained for rК versus Г and the theoretical data shows
that all the calculated values are significantly higher in
the case of Г ≤ 5. The most close values were obtained
in [1 - 3], particularly, if it is assumed that the ion
charge Z = 2. Nevertheless, it is necessary to estimate
additionally the theoretical corrections to the formula
for the three-particle recombination. As is noted in [9] at
high Ne the “three-particle recombination channel is
closed”. In [9] the values of Ne, are lower as compared
to these given in our paper. Also, the results are not im-
proved even if the ionization is taken into account when
the real recombination coefficients are determined. The
ionization coefficient is changing approximately from
10% at Ne concentrations of 1020 сm-3 and T of 45·103 K
to 0.1% at Ne = 1017…1018 сm-3 and Т < 7⋅103 K.
So, at plasma temperatures lower than <20⋅103 К for
the pulsed discharges in water the decay coefficients are
almost coinciding with the recombination coefficients.
And the error does not exceed 10% towards the recom-
bination coefficient overestimation. Taking into account
that none of the corrections to the three-particle recom-
bination formula [1 - 4, 9] leads to a good agreement
with the experimental data on the dense plasma decay
coefficient at the electron concentration Ne > 1019 сm-3, it
is necessary to consider other possible recombination
mechanisms. Besides, it should be kept in mind that the
calculated values are by several orders of magnitude
higher than the experimental values. To be exact, the
triple shock-radiation recombination is by 4-5 orders is
higher than the coefficient corresponding to the electron
capture as a result of triple collisions into the ground
atomic state [19]. The calculation results for the triple
recombination onto the ground hydrogen atomic state
and their comparison with the experimental data are
presented in Fig. 6.
Fig. 6. The dependence on time the decay coefficient
One can see from the figure that the values calcu-
lated by this formula really are less by three orders than
these calculated by the Gurevich-Pitaevsky formula, but
still exceed by several orders the experimental values at
electron densities of > 3·1018 сm-3 and coincides with the
experimental values obtained at Ne = 2·1017 сm-3. If the
ionization coefficient is plotted, it is by an order higher
than the coefficient of recombination onto the ground
state. From the plasma radiation spectra is known that
the second excitation level is not observed (there is no
Нα line in the radiation spectrum) to 50 μs. Therefore
we decided to calculate the recombination coefficient
onto the first level with the excitation energy of
10.2 eV. The results of calculations on the ionization
coefficient and the recombination coefficient practically
are coinciding. The summation of recombination coeffi-
cient values by two levels increases its total value by
10% (see Fig. 6). And the difference between the ioni-
zation values and recombination values is so negligible
that, apparently, in this connection the experimental
values of the decay coefficients are lower by several
orders of magnitude.
For comparison the results of calculations on the
time dependence of photorecombination coefficients for
one of the discharge regime are given in Fig. 7.
ISSN 1562-6016. ВАНТ. 2013. №4(86) 221
Fig. 7. The dependence on time the decay coefficient
They are sufficiently close to the decay coefficient
values at the initial discharge stage. However, the calcu-
lated ionization coefficients are by three-four orders
higher than the photorecombination coefficients and at
Ne = 2·1018 сm-3 they are meeting. But in experiments
the decay coefficient values were higher than the ioniza-
tion coefficient values. Once more contradiction to the
experimental fact takes place. It is shown in [15] that
there is a dependence of rК on the electron concentra-
tion during the decay of the plasma produced by the
pulsed discharge in water. And in the case of the photo-
recombination the recombination coefficient does not
depend on Ne. Consequently, in the dense plasma the
ternary combination occurs, but the recombination coef-
ficients should be calculated only with taking into ac-
count the experimentally observed atomic levels, as well
as, the calculation results for ionization in the dense
plasma.
CONCLUSIONS
The degree of nonideality is not an unambiguous pa-
rameter describing the corrections for recombination
coefficient calculations by the Gurevich-Pitaevsky for-
mula. None of formulas with plasma nonideality correc-
tions to the Gurevich-Pitaevsky formula gives a good
agreement between the calculated values and experi-
mental values of the decay coefficients even if the ioni-
zation is taken into account. The corrections on the elec-
tron density are necessary. The best coincidence with
the experimental values of decay coefficients has been
obtained in the calculations of the coefficients of ternary
electron recombination only onto the experimentally
observed atomic levels and when the ionization was
taken into account.
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Article received 21.05.2013.
О РАСПАДЕ ПЛОТНОЙ ПЛАЗМЫ
В ДИАПАЗОНЕ КОНЦЕНТРАЦИЙ ЭЛЕКТРОНОВ 1017 см-3 ≤ Ne ≤ 1022 см-3
О.А. Федорович, Л.М. Войтенко
Приведены результаты сравнения экспериментальных коэффициентов распада плотной плазмы импульс-
ных разрядов в воде с теоретическими, рассчитанными по всем известным формулам коэффициентами для
трехчастичной рекомбинации с учетом ионизации плазмы. Наилучшее согласие получено при расчете ко-
эффициентов тройной рекомбинации с учетом только реализовавшихся в плотной плазме уровней и учетом
ионизации с экспериментальными коэффициентами распада плотной плазмы.
ПРО РОЗПАД ГУСТОЇ ПЛАЗМИ
В ДІАПАЗОНІ КОНЦЕНТРАЦІЙ ЕЛЕКТРОНІВ 1017 см-3 ≤ Nе ≤ 1022 см-3
О.А. Федорович, Л.М. Войтенко
Наведено результати порівняння експериментальних коефіцієнтів розпаду густої плазми імпульсних роз-
рядів у воді з теоретичними коефіцієнтами, розрахованими за всіма відомими формулами для тричасткової
рекомбінації з урахуванням іонізації плазми. Найкращу згоду з експериментальними коефіцієнтами розпаду
густої плазми отримано при розрахунку коефіцієнтів потрійної рекомбінації з урахуванням тільки тих рів-
нів, які реалізувалися в щільній плазмі із урахуванням іонізації.
|
| id | nasplib_isofts_kiev_ua-123456789-112166 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T11:03:50Z |
| publishDate | 2013 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Fedorovich, О.А. Voitenko, L.M. 2017-01-17T19:52:29Z 2017-01-17T19:52:29Z 2013 On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ / О.А. Fedorovich, L.M. Voitenko // Вопросы атомной науки и техники. — 2013. — № 4. — С. 217-222. — Бібліогр.: 24 назв. — англ. 1562-6016 PACS: 52.80.-s. 52.20.Dq https://nasplib.isofts.kiev.ua/handle/123456789/112166 The paper presents the results of comparison between the experimental decay coefficients of the dense plasma produced by pulsed discharges in water with theoretical coefficients calculated using all the known formulas for the three-particle recombination with the plasma ionization taken into account. The best agreement was obtained in the calculations of the ternary recombination with taking into account only the levels realized in the dense plasma and with taking into account the ionization using the experimental decay coefficients of the dense plasma. Наведено результати порівняння експериментальних коефіцієнтів розпаду густої плазми імпульсних розрядів у воді з теоретичними коефіцієнтами, розрахованими за всіма відомими формулами для тричасткової рекомбінації з урахуванням іонізації плазми. Найкращу згоду з експериментальними коефіцієнтами розпаду густої плазми отримано при розрахунку коефіцієнтів потрійної рекомбінації з урахуванням тільки тих рівнів, які реалізувалися в щільній плазмі із урахуванням іонізації. Приведены результаты сравнения экспериментальных коэффициентов распада плотной плазмы импульсных разрядов в воде с теоретическими, рассчитанными по всем известным формулам коэффициентами для трехчастичной рекомбинации с учетом ионизации плазмы. Наилучшее согласие получено при расчете коэффициентов тройной рекомбинации с учетом только реализовавшихся в плотной плазме уровней и учетом ионизации с экспериментальными коэффициентами распада плотной плазмы. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Плазменно-пучковый разряд, газовый разряд и плазмохимия On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ Про розпад густої плазми в діапазоні концентрацій електронів 10¹⁷ см⁻³ ≤ Nе ≤ 10²² см⁻³ О распаде плотной плазмы в диапазоне концентраций электронов 10¹⁷ см⁻³ ≤ Nе ≤ 10²² см⁻³ Article published earlier |
| spellingShingle | On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ Fedorovich, О.А. Voitenko, L.M. Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| title | On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ |
| title_alt | Про розпад густої плазми в діапазоні концентрацій електронів 10¹⁷ см⁻³ ≤ Nе ≤ 10²² см⁻³ О распаде плотной плазмы в диапазоне концентраций электронов 10¹⁷ см⁻³ ≤ Nе ≤ 10²² см⁻³ |
| title_full | On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ |
| title_fullStr | On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ |
| title_full_unstemmed | On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ |
| title_short | On the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤Ne≤10²² cm⁻³ |
| title_sort | on the dense plasma decay within the electron concentration range of 10¹⁷ cm⁻³≤ne≤10²² cm⁻³ |
| topic | Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| topic_facet | Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112166 |
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