The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge
For 0-dimensional the task of a hydrogen plasma formation at initial stage of a charge is considered. For these conditions the dynamics of atomic and molecular ions density and energy balance in a hydrogen plasma are considered. У 0-вимірному наближенні розглянуто задачу створення водневої плазми на...
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| Zitieren: | The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge / V.B. Yuferov, E.I. Skibenko, V.I. Tkachov, V.V. Katrechko, A.S. Svichkar // Problems of atomic science and technology. — 2019. — № 4. — С. 105-109. — Бібліогр.: 21 назв. — англ. |
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Yuferov, V.B. Skibenko, E.I. Tkachov, V.I. Katrechko, V.V. Svichkar, A.S. 2023-12-03T14:48:09Z 2023-12-03T14:48:09Z 2019 The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge / V.B. Yuferov, E.I. Skibenko, V.I. Tkachov, V.V. Katrechko, A.S. Svichkar // Problems of atomic science and technology. — 2019. — № 4. — С. 105-109. — Бібліогр.: 21 назв. — англ. 1562-6016 PACS: 52.50.Qt, 52.55.Hc https://nasplib.isofts.kiev.ua/handle/123456789/195185 For 0-dimensional the task of a hydrogen plasma formation at initial stage of a charge is considered. For these conditions the dynamics of atomic and molecular ions density and energy balance in a hydrogen plasma are considered. У 0-вимірному наближенні розглянуто задачу створення водневої плазми на початковій стадії розряду. Для цих умов розглянуто динаміку щільності атомарних і молекулярних іонів водню та енергетику процесу. В 0-мерном приближении рассмотрена задача создания водородной плазмы на начальной стадии разряда. Для этих условий рассматриваются динамика плотности атомарных и молекулярных ионов водорода и энергетика процесса. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Gas and plasma-beam discharges and their applications The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge Атомарно-молекулярні процеси у водневій плазмі на початковій стадії розряду Атомарно-молекулярные процессы в водородной плазме на начальной стадии разряда Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge |
| spellingShingle |
The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge Yuferov, V.B. Skibenko, E.I. Tkachov, V.I. Katrechko, V.V. Svichkar, A.S. Gas and plasma-beam discharges and their applications |
| title_short |
The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge |
| title_full |
The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge |
| title_fullStr |
The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge |
| title_full_unstemmed |
The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge |
| title_sort |
atomic-molecular processes in a hydrogen plasma at initial stage of a discharge |
| author |
Yuferov, V.B. Skibenko, E.I. Tkachov, V.I. Katrechko, V.V. Svichkar, A.S. |
| author_facet |
Yuferov, V.B. Skibenko, E.I. Tkachov, V.I. Katrechko, V.V. Svichkar, A.S. |
| topic |
Gas and plasma-beam discharges and their applications |
| topic_facet |
Gas and plasma-beam discharges and their applications |
| publishDate |
2019 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Атомарно-молекулярні процеси у водневій плазмі на початковій стадії розряду Атомарно-молекулярные процессы в водородной плазме на начальной стадии разряда |
| description |
For 0-dimensional the task of a hydrogen plasma formation at initial stage of a charge is considered. For these conditions the dynamics of atomic and molecular ions density and energy balance in a hydrogen plasma are considered.
У 0-вимірному наближенні розглянуто задачу створення водневої плазми на початковій стадії розряду. Для цих умов розглянуто динаміку щільності атомарних і молекулярних іонів водню та енергетику процесу.
В 0-мерном приближении рассмотрена задача создания водородной плазмы на начальной стадии разряда. Для этих условий рассматриваются динамика плотности атомарных и молекулярных ионов водорода и энергетика процесса.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195185 |
| citation_txt |
The atomic-molecular processes in a hydrogen plasma at initial stage of a discharge / V.B. Yuferov, E.I. Skibenko, V.I. Tkachov, V.V. Katrechko, A.S. Svichkar // Problems of atomic science and technology. — 2019. — № 4. — С. 105-109. — Бібліогр.: 21 назв. — англ. |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2019. №4(122) 105
GAS AND PLASMA-BEAM DISCHARGES
AND THEIR APPLICATIONS
THE ATOMIC-MOLECULAR PROCESSES IN A HYDROGEN PLASMA
AT INITIAL STAGE OF A DISCHARGE
V.B. Yuferov, E.I. Skibenko, V.I. Tkachov, V.V. Katrechko, A.S. Svichkar
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: v.yuferov@kipt.kharkov.ua
For 0-dimensional the task of a hydrogen plasma formation at initial stage of a charge is considered. For these
conditions the dynamics of atomic and molecular ions density and energy balance in a hydrogen plasma are consi-
dered.
PACS: 52.50.Qt, 52.55.Hc
INTRODUCTION
In recent times, significant progress has been made
in obtaining pure plasma in thermonuclear installations,
and if a few years ago the concentration of impurities in
the plasma reached 5...10% and effective plasma charge
Zeff was at the level 3...8, now the concentration of im-
purities is reduced to ~ 0.1...1% and Zeff to 1...1.5; at the
same the plasma temperature also increased [1, 2]. This
progress is associated with identifying the main sources
of pollution, and the use of measures to reduce the flow
of impurities. It has been shown in experiments that
even in a well-cleaned system, impurities enter the
plasma already at the first stage of the discharge, when
breakdown occurs and the plasma touches the walls. In
this case, impurities enter the plasma due to several
mechanisms, the main ones are unipolar arcs and ion-
stimulated desorption. The specific impurity yield in
both processes is very high and these mechanisms can
create a significant initial impurity concentration. For
example, according to [3] Zeff is 3 and 7, respectively in
modes with and without divertor, through 0.1...0.15 s
after the start of the discharge, there are both light and
heavy impurities. The further course of the impurity
concentration determines by the processes of their
transport in the plasma and the boundary. At the time of
~0.5 s after the start of the discharge, the plasma is
purified from impurities up to Zeff ~ 1 when the divertor
is working, and ~1.3...1.5 in the divertorless case. A
similar course was observed in other installations, with
sources of impurities in the stationary phase being de-
sorption (light impurities) and spraying or self-spraying
(heavy) stimulated by fast ions and neutrals. In the theo-
retical consideration of the impurities entering the plas-
ma, usually, the stimulated desorption and spraying are
taken into account [4, 5].
It should be noted two areas of work. The first is to
determine the flow of impurities to the plasma boundary
with its subsequent averaging over the entire volume,
which gives an average concentration of impurities in
the plasma. Such calculations are carried out in a 0-
dimensional approximation in order to study and com-
pare the characteristics of various wall materials and the
specific contribution of various erosion mechanisms.
Secondly, for a given impurity flux onto the plasma
boundary, the concentration distribution or charge com-
position of the impurity in a plasma of a given density
and temperature is determined (one or two-dimensional
approximation is used to study plasma confinement and
energy balance). Both approaches have a fairly good
quantitative agreement with the experiment in the sta-
tionary phase of the discharge, but do not explain the
burst of light impurities at the initial stage of the dis-
charge. The exclusion of the initial stage of discharge
from consideration does not allow a complete analysis,
although at this time there are no flows of highly ener-
getic charge-exchange atoms that have a high erosion
coefficient Ki in both light and heavy impurities. At the
same time, at the initial stage, there are large flows of
atomic hydrogen Fh and ultraviolet radiation with sig-
nificant erosion ability with respect to light impurities,
which is especially important for systems with insuffi-
ciently good cleaning of surfaces and for attached vo-
lumes, from which contamination of the initially
cleaned surface through the gas phase can occur. Light
impurities that fall into the discharge at the initial stage
are almost completely captured by the plasma and
heated together with the main component. However,
they can become the main cause of the appearance of
heavy impurities. This situation may be relevant for
stellarator type systems in which magnetic diaphragm
isolates the place of formation of the plasma filament
away from the walls, and in the presence of the divertor
[6, 7], when the angles separatrix not rely on the materi-
al wall and formation unipolar arcs at these locations is
difficult or impossible.
The above is confirmed by many experiments. But
we are interested in the situation that was not practically
provided by the latter due to the lack of data on complex
polyatomic molecules present in spent nuclear fuel
SNF and, accordingly, a multicomponent oxide plasma
in which chemical reactions can take place. That is,
hydrogen plasma with impurities is a kind of simulation
environment, allowing you to look at the spent nuclear
fuel plasma from the view of atomic-molecular
processes in SNF plasma formed mainly from actinide
oxides supplemented with a mixture of oxides of lan-
thanides, zirconium, molybdenum, etc. [8].
INITIAL STAGE OF DISCHARGE
The initial stage of plasma formation in the closed
magnetic traps viewed in several studies [9 - 11], for
simplicity only hydrogen atoms. In [9], a one-
dimensional model of gas breakdown in a tokamak was
considered, leading to reasonable estimates of the ioni-
mailto:v.yuferov@kipt.kharkov.ua
ISSN 1562-6016. ВАНТ. 2019. №4(122) 106
zation time and its dependence on the basic parameters
of the plasma. The existence of a critical electric field
has been established, above which there is observed a
skinning of the discharge current, below it is a quasi-
uniform current distribution. The dependences of the
electron temperature Te on the gas ionization time are
given, from which it follows that in a certain region of
the discharge time from 5·10
-5
s to 0.5·10
-3
s (plasma
density from 10
-2
ne to 0.8 ne) the temperature can re-
main constant, for example, about 5 eV. In [10, 11], in
the 0-dimensional approximation (homogeneous distri-
bution of current and plasma density), a scenario of
operation of tokamak-type facilities was considered. It
is shown that under different scenarios both during
current breakdown (ohmic heating) and at RF or micro-
wave initial discharges the electron temperature can
remain for a long time 10...50 ms as the plasma density
increases to 5·10
13
cm
-3
at the level of 2...15 eV. How-
ever, the simplification in these calculations, associated
with a hypothetical situation, when ionizing atomic
hydrogen filling the discharge chamber without interact-
ing with the walls occurs, does not allow us to consider
the problem associated with the appearance of light
impurities at the initial stage of discharge, and correctly
estimate the power losses that are needed to create a
plasma. In contrast to our predecessors, we were inter-
ested in the amount of light impurity streams associated
with the flows of photons and hydrogen atoms Fph and
Fh and entering the plasma boundary, the average densi-
ty of impurities that could be reached by the time of the
heating stage, as well as the role of vacuum conditions.
In contrast to our predecessors, we were interested in
the magnitudes of streams of light impurities associated
with the flows of photons and hydrogen atoms and en-
tering the plasma boundary, the average density of im-
purities that could be reached by the time of the heating
stage, and the role of vacuum conditions. The main
conditions for solving the problem were:
- multicomponent composition protons, molecules,
molecular ions;
- at the initial stage there is no ion heating,
Ti Te<10…15 eV;
- the constancy of the electron temperature at the io-
nization stage.
This simplified the task, although a programmed
case is possible with the dependence of temperature on
time correlated with the input of power into the dis-
charge, the maximum plasma density ne=2·10
13
cm
-3
according to [12]. When the condition of constant num-
ber of particles in the system initial density of molecular
hydrogen n2=1·10
13
cm
-3
. In experimental systems it is
achieved after a large number of pulses, when the hy-
drogen recycling rate at the wall is close to 1, or by
introducing an additional gas flow which compensates
losses in the walls.
To determine the role of chemical and photodesorp-
tion in the process of impurities in the plasma boundary
is sufficient 0-dimensional approximation. This is ex-
plained by the fact that the flow of impurities from the
wall, determined by the fluxes of photons and hydrogen
atoms, practically does not depend on the place of their
appearence, since the photons are not absorbed by the
plasma, and the path length of the hydrogen atom before
ionization, even at maximum density, is much larger
than the system dimensions. In addition, the characteris-
tic times for the growth of the plasma density, or growth
times for the average density of impurities more than an
order of the value greater than time of hydrogen atoms
flow in the system.
Processes Sections
0
2
H e
2
2H e
1
0
1 1
2H H e
2
0
1
2 H e 3
2
H e
0
1 1
H H e
4
1
2 2H e
5
0
1
2 H 6
0
1
H e
1
2H e
7
0
2 2
H H
0
3 1
H H
8
3
H e
0
1 1
2 H H e
9
0
1
3 H 10
0
1
H e
1
H e
11
0
2
H e
2
H e
12
1 1
2H H e
13
* Excited atoms and hydrogen molecules
It should be immediately noted that in order to de-
termine the radial distribution of the density of impuri-
ties, at least a one-dimensional approximation is neces-
sary. Moreover, it can be applied only to one equation
that relates the concentration of impurities with their
flow. This is beyond the scope of our tasks. However, it
is clear from simple considerations that, due to the low
speeds of the passage of impurity molecules coming
from the walls at thermal velocity and significant ioni-
zation cross sections of the mean free path of impurity
molecules before ionization at plasma densities above
10
12
cm
-3
become smaller than the system size, i.e. dur-
ing the plasma density increase, impurities begin to be
trapped in an increasingly thin surface layer, reaching
about 1 cm at the end of the ionization stage. And for
the characteristic time tn growth of plasma density,
they do not have time to diffuse into the plasma at a
considerable distance. Even with DZ=4·10
3
сm
2
/s taken
in [11] for hot plasma ∆r=√Dtn=2 сm. However, in the
process of heating, as is well known, impurities are
fairly quickly transported deep into the plasma, so the
operation of averaging impurities over the entire vo-
lume, used in the 0-dimensional approximation, gives
essentially the initial (not zero) impurity concentration
at the beginning of the stationary phase. As mentioned
earlier in [1 - 4], it is from the moment of the end of
heating that the process of accumulation of impurities in
the plasma begins, as a result of other erosion processes.
The main processes occurring in a hydrogen plasma
and determining its charge and component composition
are presented in Table. The initial stage of the dis-
ISSN 1562-6016. ВАНТ. 2019. №4(122) 107
charge, as well as the subsequent stationary phase, can
be described by the following system of differential
equations (1) - (11), which allows determining the time
variation in the discharge chamber of the electron densi-
ty ne, atomic hydrogen ni, hydrogen molecules n2, ions
H1
+
, H2
+
, H3
+
respectively n1
+
, n2
+
, n3
+
, plasma produc-
tion powers Wp ionization of gas Pion, atomic hydrogen
and photon fluxes to the wall Fh and Fph
j
, where j – is
the photon energy; the time variation of the concentra-
tion of light impurities averaged over the entire volume
of n
c
, n
o
– carbon and oxygen.
2 1 2 2 5 6 1 7
1
,
e
e
p
d n
n n n n
d
(1)
1 1 1
2 2 3 2 4 6 3 9 1 0 1 7 2 2 8 1
1 1
2 2 2 3 ,
e m mm
d n n n
n n n n n n n
d
(2)
where m is the number of collisions of a hydrogen
atom with a wall before recombination.
2
1 1 2 3
1 1 3
,
2 2 2
d n d
n n n n
d d
(3)
1 1
2 2 2 4 5 1 3 9
2 ,
e Z
p
d n n
n n n n n
d
(4)
2 2
2 1 2 4 5 6 2 2 8
,
e
p
d n n
n n n n n
d
(5)
3 3
2 2 8 3 9 1 0
,
e
p
d n n
n n n n
d
(6)
,
p p
h io n r ra d
E
d W W
P P P P
d
(7)
3
,
2
p e e i p
W kn T T V (8)
where Ph, Pion, Pr, Prad going to plasma heating, ioniza-
tion, recharging, emission of impurities; Vp – plasma
volume; k - is the Boltzmann constant.
1 2 3
0 ,
e
n n n n
(9)
2 1 1 2 2 3 3 2 4 4 5 5 6 6
1 7 7 3 9 9 1 0 1 0 1 1 2 1 2 2 1 3 1 3
,
io n e
n E E E n E E E
P n
n E n E E n E n E
(10)
,
ra d Z ZZ
P n v E (11)
Ei – the amount of energy loss in this process.
The values of the plasma particle lifetime
τp=10…20 ms, determined through the energy plasma
lifetime τE (τp ≈ 3τE), taken neoclassical [13] with a
magnetic field B = 2 Т, a = 13.5 сm, R=100 сm; t = 0.6 s
[12]. For the real system, we are interested in the time
of the creation of the plasma is not more than 1 ms, so
the members of the energy loss and the plasma particles
during this time is negligible.
The lifetime of hydrogen atoms before going on the
wall τ1= a/1, where 1 – is the average velocity of
hydrogen atoms with allowance for multiple collisions
with the wall before recombination or ionization. The
energy of the hydrogen atoms produced during the dis-
sociation of hydrogen molecules and molecular ions is
in the range of an electron volt to 12 eV with maxima in
the region of 4...6 eV [14 - 16]. There are no exact data
on the values of the reflection coefficients of particles α
and the energy β of the energy range below 10 eV. In
[17, 18], the reflection coefficients were calculated for
an energy E>10 eV, and experimental data are available
only for E>100 eV. Extrapolation of the values of α and
β in the energy range of less than 10 eV gives values of
0.7...0.9. In this case, the average energy of hydrogen
atoms is ≈2 eV. I.e. the correction factor before the
value of the flow of atomic hydrogen onto the wall as a
result of multiple collisions turns out to be 3...3.3. It
should be noted that in all equations, for simplicity, the
quantity σvi replaced by σi.
As initial conditions are taken: n2=1·10
13
cm
-3
,
ne=1·10
11
cm
-3
, n1
+
=5·10
10
cm
-3
, n2
+
=4·10
10
cm
-3
,
n3
+
=1·10
10
cm
-3
, which in real devices are easily achieved
with the help of low-power pre-plasma systems.
Due to the relatively low coefficient of impurity
reuptake by surfaces lying at the level of 0.05...0.3 [19],
low gas-kinetic velocities at the level of 5·10
4
cm/s and
high ionization cross sections, impurities desorbed from
the walls are ionize, dissociate and, thus, are captured
by the plasma with density ne>1·10
12
cm
-3
. For the case
of [12], the mean time of passage of impurities from the
wall to the wall is τ = a/пр≈270 ms and the mean free
path of the impurity before ionization at ne = 1·10
12
cm
-3
and Te = 6 eV, λ = 10 cm.
Analysis of equations (1) - (6) shows that the plasma
electron density increases exponentially with time
ne(t)=ne(0)e
αt
. The exponent α=n2σ1+n2
+
(σ5+σ6)+n1σ7-1/τp
depends on time, decreasing as n2 burns out, n2
+
grows.
However, for a long time, n2 changes little and the density
increases by a factor of e over time t=1/(n2σ1), since n2
+
and n1 are small, i.e. at a given density n2 the plasma
density growth rate ne is determined by the value σ1, the
value of which, for example, for Te, values equal to 3, 4,
6, and 12 eV, is respectively 1·10
-10
; 3.8·10
-10
; 1.5·10
-9
,
and 9·10
-9
cm
-3
·s
-1
. Since the ionization rates for the σ1
and σ7 processes are close in a wide temperature range Te,
the initial speed of creating the plasma using atomic and
molecular components at the same concentrations n1
and n2 are equal, and that allowed the authors of [9 - 11]
to obtain reasonable ionization times.
However, to achieve the same final plasma density,
the concentration must be twice as high as n2, which in
the latter case reduces the plasma formation rate by half.
The plasma formation rate will be reduced due to the
second term, since σ6σ5, and the concentration of
growth n1 (third member) at σ1= σ7 compensates for this
decrease. In Fig. 1 shows the dependences ne= f(t) or
four temperatures: 3, 4, 6, and 12 eV. As can be seen
from equations (1) - (6), the density increase n2
+
and n3
+
is limited long before reaching the maximum density ne,
where
2 1
2
4 5 6 2 8
(m ax ) ,
e
e
n n
n
n n
(12)
2 2 8
3
9 1 0
(m ax ) .
e
n n
n
n
(13)
ISSN 1562-6016. ВАНТ. 2019. №4(122) 108
t, s
Fig. 1. The dependence of plasma density on time
for different values of electron temperature:
1 – Te=3; 2 – Te=4; 3 – Te=6; 4 – Te=12 eV
t, s
Fig. 2. The time distribution of the specific energy
consumption for ionization and excitation. (To the right,
the ordinate shows the total energy consumption
for a system similar to [12])
Note that presented in Fig. 2 the energy consumption
for electronic excitation and ionization is less than real,
in which oscillatory processes should be taken into
account, especially strong at temperatures less than
4 eV, and which can be a significant value at Te>4 eV.
Due to the presence of two terms in the denominator
with ne and n2 the maximum for n2
+
is quite wide. The
value of Wp – energy consumption for the creation of a
plasma grows exponentially, like ne. At the same time
Pr and Wp/τE are small, and Prad increases from 0 for n
o
,
n
c
=0 tо 0.08Pion at n
o
+n
c
=0.02ne (see Fig. 2).
t, s
Fig. 3. The time distribution of the electron density
of plasma (1), protons (2) of hydrogen molecules (3),
hydrogen atoms (4) of molecular ions H2
+
(5) and H3
+
(6)
for an electron temperature of 6 eV
With an exponential growth of Wp value Te can re-
main constant, grow or fall, but at Te<10 eV, as can be
seen from σ1, a change in Te by 1...2 eV sharply increas-
es ionization losses, therefore in real systems Te=const
is often observed. In general, as mentioned above, the
course of Wp(Te) is determined by the necessary dis-
charge scenario, as well as by the possibilities of the
energy input (Fig. 3).
CONCLUSIONS
As can be seen, the growth rate of plasma density is
mainly determined by the value of ionization cross sec-
tion. The increase in energy consumption is determined
by ionization losses, since the selected electron tempera-
tures provide low energy costs for vibrational levels. At
the time of 200…400 s, the “burnout” of H2
+
and H3
+
ions begins, respectively.
For a number of molecules of non-electronegative
gases at the electron temperature Te=1…3 eV the main
fraction of the discharge energy input focuses specifi-
cally on the excitation of the vibrational degrees of
freedom of the ground electronic states.
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Article received 25.06.2019
АТОМАРНО-МОЛЕКУЛЯРНЫЕ ПРОЦЕССЫ В ВОДОРОДНОЙ ПЛАЗМЕ
НА НАЧАЛЬНОЙ СТАДИИ РАЗРЯДА
В.Б. Юферов, Е.И. Скибенко, В.И. Ткачев, В.В. Катречко, А.С. Свичкарь
В 0-мерном приближении рассмотрена задача создания водородной плазмы на начальной стадии разряда.
Для этих условий рассматриваются динамика плотности атомарных и молекулярных ионов водорода и энер-
гетика процесса.
АТОМАРНО-МОЛЕКУЛЯРНІ ПРОЦЕСИ У ВОДНЕВІЙ ПЛАЗМІ
НА ПОЧАТКОВІЙ СТАДІЇ РОЗРЯДУ
В.Б. Юферов, Є.І. Скібенко, В.І. Ткачов, В.В. Катречко, О.С. Свічкар
У 0-вимірному наближенні розглянуто задачу створення водневої плазми на початковій стадії розряду.
Для цих умов розглянуто динаміку щільності атомарних і молекулярних іонів водню та енергетику процесу.
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