Physical mechanisms of negative corona current pulse with secondary oscillation
The detailed modelling of the negative corona current pulses including the secondary oscillation (SCO) has been realized, using the continuity differential equations for the fluxes of positive and negative ions and electrons, supplemented by the Poisson’s equation for an electrical field in a qua...
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| Цитувати: | Physical mechanisms of negative corona current pulse with secondary oscillation / V.I. Chyhin // Condensed Matter Physics. — 2002. — Т. 5, № 3(31). — С. 429-448. — Бібліогр.: 52 назв. — англ. |
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Chyhin, V.I. 2017-06-12T16:16:50Z 2017-06-12T16:16:50Z 2002 Physical mechanisms of negative corona current pulse with secondary oscillation / V.I. Chyhin // Condensed Matter Physics. — 2002. — Т. 5, № 3(31). — С. 429-448. — Бібліогр.: 52 назв. — англ. 1607-324X PACS: 52.80.Hc, 52.35.-g, 52.65.-y, 51.50.+v DOI:10.5488/CMP.5.3.429 https://nasplib.isofts.kiev.ua/handle/123456789/120665 The detailed modelling of the negative corona current pulses including the secondary oscillation (SCO) has been realized, using the continuity differential equations for the fluxes of positive and negative ions and electrons, supplemented by the Poisson’s equation for an electrical field in a quasione-dimensional space, as the basis for the numerical computation. The analysis of the basic plasma functions behaviour applicable to the pulsing corona in Ar+O₂ and N₂+O₂ mixtures in the concentration region of O₂ from 2 · 10−3% to 0.04% has been carried out and the physical mechanisms of the secondary current oscillation have been grounded for the first time. Moreover, an effect of the photoprocesses on the parameters of the strikingly different pulses in Ar+O₂ and N₂+O₂ mixtures is estimated for the first time. It has been determined that the SCO is caused by the field intensity oscillation in the antiphase in the surface region and in the end of the sheath. The SCO pulse can transfer into the full modes of the Trichel’s pulse. Characteristics of the “precursor” and the “step” in the leading pulse front are determined by the dynamics of the volumetric charges in the sheath, whereas the SCO shape is determined by the variable flow of the positive ions to the cathode. In N₂+O₂ the ionization of O₂ molecules by the N₂∗emitted photons leads to the adequate current rise. Pulse trailing part duration and current value are operated by the O₂− ions collisions with the N₂∗ metastables. Such processes are slowed in Ar+O₂. Проведено детальне моделювання нерівноважних процесів у від’ємному коронному розряді, зокрема, імпульсів струму із вторинними осциляціями (ВОС) на основі числового розв’язання рівнянь неперервності для позитивних і негативних іонів та електронів, разом із рівнянням Пуассона для електричного поля в квазі-одномірному просторі. Проаналізовано поведінку основних функцій плазми пульсуючої корони у сумішах аргону з киснем та азоту з киснем в області концентрацій 2 * 10-3%-0.04%, що дало змогу вперше обгрунтувати фізичні механізми зародження і розвитку ВОС. Виявлено, що три типи ВОС можуть існувати у різних часових інтервалах імпульсу. Встановлено, що вони є результатом коливання в антифазі напруженості поля в приповерхневій області та в кінці прикатодної оболонки. Характеристики “прекусора” і “сходинки” на провідному фронті імпульсу визначаються динамікою об’ємних зарядів в оболонці, тоді як форма ВОС задається змінним потоком позитивних іонів на катод. Додатково, вперше оцінено впливи фотопроцесів на параметри різко відмінних імпульсів у досліджених сумішах газів. В N₂+0₂ іонізація молекул 0₂ фотонами, емітованими збудженими молекулами N₂ приводить до адекватного росту пікового струму. Тривалість і значення струму у хвостовій частині імпульсу задається зіткненнями іонів О₂- із метастабілями N₂. У суміші Аг+0₂ такі процеси є слабими. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Physical mechanisms of negative corona current pulse with secondary oscillation Фізичні механізми формування імпульсів струму від’ємної корони із вторинною структурою Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Physical mechanisms of negative corona current pulse with secondary oscillation |
| spellingShingle |
Physical mechanisms of negative corona current pulse with secondary oscillation Chyhin, V.I. |
| title_short |
Physical mechanisms of negative corona current pulse with secondary oscillation |
| title_full |
Physical mechanisms of negative corona current pulse with secondary oscillation |
| title_fullStr |
Physical mechanisms of negative corona current pulse with secondary oscillation |
| title_full_unstemmed |
Physical mechanisms of negative corona current pulse with secondary oscillation |
| title_sort |
physical mechanisms of negative corona current pulse with secondary oscillation |
| author |
Chyhin, V.I. |
| author_facet |
Chyhin, V.I. |
| publishDate |
2002 |
| language |
English |
| container_title |
Condensed Matter Physics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| format |
Article |
| title_alt |
Фізичні механізми формування імпульсів струму від’ємної корони із вторинною структурою |
| description |
The detailed modelling of the negative corona current pulses including the
secondary oscillation (SCO) has been realized, using the continuity differential
equations for the fluxes of positive and negative ions and electrons,
supplemented by the Poisson’s equation for an electrical field in a quasione-dimensional
space, as the basis for the numerical computation. The
analysis of the basic plasma functions behaviour applicable to the pulsing
corona in Ar+O₂ and N₂+O₂ mixtures in the concentration region of
O₂ from 2 · 10−3% to 0.04% has been carried out and the physical mechanisms
of the secondary current oscillation have been grounded for the
first time. Moreover, an effect of the photoprocesses on the parameters of
the strikingly different pulses in Ar+O₂ and N₂+O₂ mixtures is estimated
for the first time. It has been determined that the SCO is caused by the
field intensity oscillation in the antiphase in the surface region and in the
end of the sheath. The SCO pulse can transfer into the full modes of the
Trichel’s pulse. Characteristics of the “precursor” and the “step” in the leading
pulse front are determined by the dynamics of the volumetric charges
in the sheath, whereas the SCO shape is determined by the variable flow
of the positive ions to the cathode. In N₂+O₂ the ionization of O₂ molecules
by the N₂∗emitted photons leads to the adequate current rise. Pulse trailing
part duration and current value are operated by the O₂−
ions collisions with
the N₂∗ metastables. Such processes are slowed in Ar+O₂.
Проведено детальне моделювання нерівноважних процесів у від’ємному коронному розряді, зокрема, імпульсів струму із вторинними осциляціями (ВОС) на основі числового розв’язання рівнянь неперервності для позитивних і негативних іонів та електронів, разом із рівнянням Пуассона для електричного поля в квазі-одномірному просторі. Проаналізовано поведінку основних функцій плазми пульсуючої корони у сумішах аргону з киснем та азоту з киснем в області концентрацій 2 * 10-3%-0.04%, що дало змогу вперше обгрунтувати фізичні механізми зародження і розвитку ВОС. Виявлено, що три типи ВОС можуть існувати у різних часових інтервалах імпульсу. Встановлено, що вони є результатом коливання в антифазі напруженості поля в приповерхневій області та в кінці прикатодної оболонки. Характеристики “прекусора” і “сходинки” на провідному фронті імпульсу визначаються динамікою об’ємних зарядів в оболонці, тоді як форма ВОС задається змінним потоком позитивних іонів на катод. Додатково, вперше оцінено впливи фотопроцесів на параметри різко відмінних імпульсів у досліджених сумішах газів. В N₂+0₂ іонізація молекул 0₂ фотонами, емітованими збудженими молекулами N₂ приводить до адекватного росту пікового струму. Тривалість і значення струму у хвостовій частині імпульсу задається зіткненнями іонів О₂- із метастабілями N₂. У суміші Аг+0₂ такі процеси є слабими.
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/120665 |
| citation_txt |
Physical mechanisms of negative corona current pulse with secondary oscillation / V.I. Chyhin // Condensed Matter Physics. — 2002. — Т. 5, № 3(31). — С. 429-448. — Бібліогр.: 52 назв. — англ. |
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2025-11-26T21:26:26Z |
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2025-11-26T21:26:26Z |
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| fulltext |
Condensed Matter Physics, 2002, Vol. 5, No. 3(31), pp. 429–448
Physical mechanisms of negative
corona current pulse with secondary
oscillation
V.I.Chyhin
National University “Lvivska Polytechnika”,
12 Bandery Str., 79013 Lviv, Ukraine
Received October 9, 2001, in final form January 21, 2002
The detailed modelling of the negative corona current pulses including the
secondary oscillation (SCO) has been realized, using the continuity differ-
ential equations for the fluxes of positive and negative ions and electrons,
supplemented by the Poisson’s equation for an electrical field in a quasi-
one-dimensional space, as the basis for the numerical computation. The
analysis of the basic plasma functions behaviour applicable to the puls-
ing corona in Ar+O2 and N2+O2 mixtures in the concentration region of
O2 from 2 · 10−3% to 0.04% has been carried out and the physical mech-
anisms of the secondary current oscillation have been grounded for the
first time. Moreover, an effect of the photoprocesses on the parameters of
the strikingly different pulses in Ar+O2 and N2+O2 mixtures is estimated
for the first time. It has been determined that the SCO is caused by the
field intensity oscillation in the antiphase in the surface region and in the
end of the sheath. The SCO pulse can transfer into the full modes of the
Trichel’s pulse. Characteristics of the “precursor” and the “step” in the lead-
ing pulse front are determined by the dynamics of the volumetric charges
in the sheath, whereas the SCO shape is determined by the variable flow
of the positive ions to the cathode. In N2+O2 the ionization of O2 molecules
by the N∗
2
emitted photons leads to the adequate current rise. Pulse trailing
part duration and current value are operated by the O−
2
ions collisions with
the N∗
2
metastables. Such processes are slowed in Ar+O2.
Key words: corona discharge, current pulse, pulse fine structure,
secondary current oscillation, photo-processes, numerical modelling
PACS: 52.80.Hc, 52.35.-g, 52.65.-y, 51.50.+v
1. Introduction
The pulsing negative corona is the low current gas discharge arising between the
point with a negative potential and the plane anode with the applied direct high
voltage. Its pulses (discussed by Trichel for the first time [1]) are characterized by a
c© V.I.Chyhin 429
V.I.Chyhin
relaxing shape, a strong periodicity and a temporal constancy of the parameters [2–
7]. They have a complicated structure [8–13], specifically, a secondary high-frequency
current oscillation (SCO) [3–5,9,14–17]. A detailed knowledge of the nature of the
corona pulsation in the gas mixtures makes it possible to develop gas analyzer sen-
sors [18] and gas separating devices [19]. However, nonequilibrium processes in this
discharge are studied insufficiently. So far, there is not a consensus as to the forma-
tion mechanisms of the pulses, in particular regarding the SCO. The first qualitative
explanation of the corona pulsations was grounded on a screening effect created by
the positive ions in a vicinity of the cathode [1]. In the following publications the
main screening role was referred to the negative ions [7]. The pulsation of the nega-
tive corona in a pure electropositive nitrogen is indicated in the work [20]. However,
the authors have linked their calculation of the corona pulsation in the air only with
“a carrying-out of negative ions from drift region” [21]. Such an approach does not
allow to explain the dependence of the double pulse frequency on the admixture
concentration [2,4,5].
In our opinion, there are two main causes of the insufficient study of the nonequi-
librium processes. The first one is the use of too high concentration of electroneg-
ative gas and the second one is an essential simplification of the modelling. The
experiments connected with the direct study of the gas admixture effect on the
pulse parameters were not carried out. The main focus was on an electronegative
gas [10,11] or a mixture of two gases with a high concentration of the electroneg-
ative gas [12,20]. The latter enhances the screening effect and, consequently, only
some elements of the secondary pulse structure were registered [10–12]. But a more
complicated secondary oscillation has been measured for the first time, when an
extremely low concentration of oxygen in argon and in nitrogen was used [2–5,9].
The numerical model simplifications [21–23] have resulted in the inconsistent in-
terpretation of the initial pulse rise [11,16,17], since the secondary elements were
qualitatively compared with the model results obtained under experimentally irrel-
evant conditions [22,23]. Besides, the corona SCO was not described [21]. Thus the
recently registered secondary oscillations [16,17] are explained phenomenologically
by a “back and forth motion of the electric field” [22,24], a “turbulent beam-plasma
interaction” [6,16], or is referred to the “non-Trichel” one and it is recognized that
its “mechanism . . . has yet to be understood” [17].
The detailed modelling has allowed us to describe the main characteristics of the
corona pulses with SCO for the first time [2–5,9,14,15]. In our opinion, a parallel
experimental research and modelling of relatively simple systems is more prospective,
particularly, using electropositive gases with different electronegative admixtures
of variable concentration. In this work, the analysis of the basic plasma functions
behaviour applicable to the pulsing negative corona is carried out and the physical
mechanisms of the secondary current oscillation are grounded. Moreover, the effect
of the photoprocesses on the parameters of strikingly different pulses in Ar+O2 and
N2+O2 mixtures in the concentration region from 2 · 10−3% to 0.04% is estimated
for the first time.
430
Negative corona current pulse with secondary oscillation
Figure 1. Corona current pulses oscillograms taken in gas mixture flows of ni-
trogen and oxygen as well as of argon and oxygen. The percentage of the oxygen
is marked by the numbers. The point-plane anode distance is equal to 6 mm
(Ar+O2) and to 12 mm (N2+O2). The applied voltage is equal, accordingly, to
1420 V and to 2460 V. The insertion represents the enlarged graphs top for
N2+O2.
2. Comparative characteristics of the measured pulses in
N2+O2 and Ar+O2 mixtures
The investigations were carried out using the set-up, the scheme of which is
described in detail in the works [2,3]. In figure 1 the typical current oscillograms,
obtained in nitrogen and argon flows with various concentrations of oxygen, are
presented. All the measured dependences I(t) have the shape of the relaxing pulses
with a complicated secondary structure. The sizes and the shapes of the pulses in
N2+O2 and Ar+O2 mixtures differ significantly. In N2+O2 the current increases
sharply to the maximal value and then decreases by 10–50% in the narrow time
interval (of the order of a microsecond), forming a separate peak, after which the
curve falls down more slowly (of the order of dozens of microseconds. In Ar+O2
mixture, the current averaged over the secondary oscillation falls down monotonously
starting from the peak value. The current pulse duration in N2+O2 and Ar+O2
mixtures reduces with an increase of the oxygen concentration. At the same time, in
N2+O2, the maximal current value increases significantly. Simultaneously, in Ar+O2,
the peak height falls weakly. The secondary oscillation in N2+O2 mixture is located
mainly in a peak region, while in Ar+O2 it is located in the “tail” part of the
pulse. The oxygen in both gas mixtures changes the shape and SCO parameters,
specifically, their frequency and damping factor.
3. Modelling the negative pulsing corona
To introduce a kinetic model of the negative corona the following elementary
processes were taken into account: an ionization, an excitation of Ar atoms and N2
431
V.I.Chyhin
molecules by electron collisions, an ionization by photons, an attachment of elec-
trons to O2, their detachment from O−
2 due to the collisions with Ar and N2 in the
ground and in the excited states, a charge drift and a surface photo- and ion-electron
emission. The basis of the numerical computation is the continuity differential equa-
tions for the fluxes of positive and negative ions and electrons, supplemented by the
Poisson’s equation for an electrical field in a quasi-one-dimensional space:
∂ne
∂t
+ div(wene) = αnewe − ηnewe + kdnnn0 + kdmnnnm + Sfi , (1)
∂np
∂t
− div(wpnp) = αnewe + Sfi , (2)
∂nn
∂t
+ div(wnnn) = ηnewe − kdnnn0 − kdmnnnm , (3)
∂nm
∂t
= αmnewe − kdmnmnn − kqnmn0 , (4)
div E = 4πe(np − ne − nn). (5)
Here ne, np, nn – the electron, positive and negative ions density, we, wp, wn – their
drift velocity, respectively, α, η and kd – the ionization, attachment and detachment
coefficients for the main gas molecules of a density n0, Sfi – the charge source due
to photoionization. The boundary conditions for positive and negative ions are self-
evident; their number density is equal to zero at the anode and cathode, respectively.
The boundary condition for electrons at the cathode (x = 0) is formulated in terms
of the secondary ion and photon emission coefficients, γi and γph, accordingly:
je(0, t) = γijp(0, t), (6)
where je = newe and jp = npwp, and
nph
e (0, t) =
1
we(0, t)
·
γph
τ
∫ t
0
exp[−(t − t′)/τ ]
×
∫ d
0
ne(x, t′) |we(x, t′)|α∗(x, t′)Ω(x) exp(−µx) dxdt. (7)
In the equation (7) µ is the coefficient of the photon absorption, τ – the lifetime
of the exited state, α∗ – the excitation coefficient. The quantity Ω(x) is the solid
angle extended at the cathode by the charge at x. For the modelling details see
[2,22,25]. In comparison with the previous model [2,25] the additional equation (4)
is included, describing the dynamics of the nitrogen metastable molecules density
nm. The coefficient αm is their creation rate. The effect of the N∗
2 metastables on the
electron detachment from O−
2 ions is given by kdm, the quenching rate is described
by kq. The current in the external circle is determined using the second Kirchoff’s
law.
Because of very low current density of the negative corona it was assumed (as
in all previous corona modellings [2,4,20–23]), that during the pulsation period the
room gas temperature is kept in all discharge points. Under this condition, the coef-
ficients of kinetic processes including the neutral particles are constant in time, and
432
Negative corona current pulse with secondary oscillation
those related to the ionized particles are dependent only on the local field intensity
[22]. The shape of the current channel was set, picking out two discharge gap re-
gions: the cathode (generating) one as cylindrical and the drift one – as parabolic.
A dependence of the current tube cross section F on the positive ion density np
(F ∼ n
2/3
p ) is suggested [2].
It was assumed, that the basic kinetic gas-discharge processes develop according
to the next following schemes:
• a molecule and atom (M = N2, Ar) ionization by an electron impact
e + M → M+ + 2e; (8)
• an attachment of electron due to a collision of three particles (M is the third
one, N2 or Ar)
e + O2 + M → O−
2 + M; (9)
• an electron detachment from O−
2 ion by a molecule impact (M = N2, Ar)
O−
2 + M → O2 + M + e; (10)
• creating a metastable nitrogen or argon molecule (M∗ = N∗
2, Ar∗)
e + M → M∗ + e; (11)
• quenching a metastable molecule (M∗ = N∗
2, Ar∗)
M∗ + M → 2M; (12)
• an electron detachment from O−
2 ion by a metastable molecule impact (M∗ =
N∗
2, Ar∗)
O−
2 + M∗ → O2 + M + e. (13)
The numerical data for the kinetic coefficients (the main data are entered in table 1)
are determined in the following way.
The ionization processes of an atom and a molecule by an electron impact (8)
in the wide energy region are described sufficiently in the literature [7,26,27,42].
In our computations, the nitrogen molecule ionization coefficients have been taken
from the monograph [7] (table 5.1, Townsend formula 5.25 α/p = A exp(−Bp/E),
and the extrapolation of the experimental graphs figure 5.4–5.6). For a compar-
ison there was also used a universal formula for the velocity constant of various
reactions [26], K = 10−A−B/(E/n) cm3/s. The coefficients of the argon atom ion-
ization have been calculated using the formulas α/p = C exp [−D(p/E)0.5] and
α/p = A1(E/p) exp(−B1p/E) [7]. The last one takes into account the consider-
able inelastic losses of the electron energy, which are connected, first of all, with the
excitation of the low energy levels of the argon atom. The A1 and B1 coefficients
433
V.I.Chyhin
were calculated using a relation between the Townsend ionization coefficient, the
ionization frequency and the ion drift velocity.
To model the process of three-body electron attachment with the oxygen molecule
in the gas mixture of nitrogen-oxygen (9) there were used the coefficients given in [7]:
kaO2
– in the presence of the oxygen molecules only and kaN2
– in nitrogen molecules
presence. The values kaN2
= 0.16 · 10−30 cm6/s and kaO2
= 2.5 · 10−30 cm6/s coincide
with the data in [43]. The attachment velocity dependence in pure O2 and O2–N2
mixtures on the middle electron energy measured in the region of 0.01–1 eV [28], are
in agreement with the data in [7] and [38] within the bounds of the multiplier 2. The
data presented in work [42] are close to them as well. In our opinion, the attachment
coefficient value 2 · 10−33 cm6/s given in [27], is extremely understated. A field
effect on the electron attachment velocity has been simulated using the formula
represented in [22] for pure oxygen. Here the value kaO2
is divided by the function
ka = kaO2
[1 + (E/g/n)1.5]
−1
, where g is the constant for a given gaseous mixture.
An attachment in Ar + O2 mixture has been modelled, making use of the data
[28] and extrapolating the graphs in figure 8.7.5 of a dependence of ka on the middle
electron energy for pure O2, O2 in N2 and O2 in He. These functions come to an
agreement with the separate data [43] for the process O2 + Ar + e = O−
2 + Ar.
In our opinion, comprehension of the electron separation from the negative oxy-
gen ion in N2 +O2 and Ar + O2 mixtures according to the scheme (10) is still weak.
The main problem attached to the study of this process is the effect of the compet-
itive processes forming O−, O−
2 and O−
3 ions. A complete examination of the basic
reactions connected with the oxygen negative ions has been done in the work [44].
As it appeared, in the dissociative attachment process, the atomic ions O− with the
essential kinetic energy are generated. A separation of an electron from ions O− can
take place, since only these ions relax to the steady energy states. During this energy
relaxation, the detachment process competes with the charge exchange forming O−
2
or with the complicated formation of O−
3 at the three bodies collision. That’s why
one has to estimate correctly a contribution into the channels of these negative ions
development.
A velocity of the electron detachment from O−
2 at an impact of the unexcited
nitrogen molecule under the room temperature and with the middle ion energy
value E/n is low: “. . . at kT = 0.026 eV a part of particles with the energy greater
than 1 eV ≈ 40kT , is small . . . ” [7]. At the electric field intensity of the order of
the 104 V/cm under the atmospheric pressure of nitrogen, the detachment velocity
is of an order of 10−13 cm3/s [27]. Evidently, just due to a small effect of this
process at the low ion energy, it was not taken into consideration in most of the
modellings, as the negative corona [8,22,23] and the positive corona [29,45]. However,
taking into account that in the cathode region (the sheath playing a decisive role in
forming the current pulse and its secondary structure [2]) the field intensity amounts
to considerably higher values (in separate discharge stages – of the order of 105–
106 V/cm), in this work, as in [21], this electron detachment type was taken into
account. The authors of [30] have investigated the electron separation from O−
2 at
the collision with N2 under extremely high ion energies (> 20 eV). A problem of our
434
N
egative
corona
currentpulse
w
ith
secondary
oscillation
Table 1. Formulas and coefficient constants of kinetic processes
Coefficient
Process
Symbol,
dimension
Particle Formula
Values of
constants
Energy
range
References
A B E/p
V /(cm · tor)
N2 8.8 275 27–200
Ionization α, cm−1 α/p = A exp(−Bp/E) 12.0 342 200–600 [7]
Ar 0.01 31 5–22
12.0 180 22–600
kaN2
= 0.16 · 10−30
N2 + O2 kaN2
· nN2
· nO2
+ kaO2
· n2
O2
T = 300 K [7]
Attachment ka, cm6/s kaO2
= 2.5 · 10−30
Ar + O2 kaAr · nAr · nO2
+ kaO2
· n2
O2
kaAr = 0.1 · 10−30 T = 300 K [28]
f(E/n), 2 · 10−14 E/n = 100 Td
N2 + O−
2 graphic & tabular data 3.8 · 10−9 E/n = 1000 Td [27,42]
Detachment kd, cm3/s f(E/n), 2.1 · 10−13 E/n = 150 Td
Ar + O−
2 graphic data 1.1 · 10−9 E/n = 3800 Td [31]
Excitation km, cm3/s N2(A
3Σ+
u ) 10−A−B/(E/n) A = 8.4; B = 14
2 < (E/n)·1016
< 30 V · cm2
[26,32]
Quenching kq, cm3/s N2(A
3Σ+
u ) N2(A
3Σ) + N2 → N2 + N2 3.7 · 10−16 [27]
Detachment kdm, cm3/s N∗
2+O−
2 O−
2 + N2(A
3Σ) → O2 + N2 + e 2.1 · 10−9 [32]435
V.I.Chyhin
work is partially identical to that considered in the works [46,47], where the electron
detachment effect on the statistic time delay of the negative corona current pulses
in the air is discussed.
There seem to be no papers discussing the electron detachment in O−
2 + Ar
mixture. The cross sections of such process were measured at the collisions of the
atomic ion O− with Ar, and the ions O− and O−
2 with helium [31]. In this connection,
the electron detachment cross section in O−
2 + Ar mixture was estimated, making
use of the measured sections for O− + Ar and comparing the corresponding sections
for O− and O−
2 in helium [31]. Here, the differences in the detachment threshold
energies and the transformation from laboratory to center-of-mass energies were
taken into account.
Making use of the results of the investigations [7,26–29,32–39,42,43,45,48,49],
there were analysed such possible photo-processes in the corona discharge, as the
nitrogen molecule and the argon atom excitation, their quenching, the electron de-
tachment from O−
2 ion at the collision with the metastable particles Ar* and N2*, as
well as the ionization by photons emitted spontaneously by the excited molecules.
Despite the fact that the radiation spectrum of the gas-discharge plasma is extremely
wide [34,35,48], almost all experimental and numerical investigations of the nitrogen
and the oxygen excitation processes (11) were associated with the determination of
the corresponding parameters of their basic metastable states [26,32,36,37]. The ki-
netics of the low-energy A3Σ+
u & B3Πg nitrogen metastables has been studied quite in
detail, with a dividing of the separate oscillatory levels, specifically: in the streamer
in the air [48], in N2 : O2 = 4 : 1 [26], and pure nitrogen [35], and gas mixture
with various oxygen concentrations [37] discharges. One can find a large enough
dispersion in the measured values of the quenching of the nitrogen and the argon
metastable levels velocity constants (12) [26,38,49].
The detachment of an electron from O−
2 ion at the collision with the metastable
nitrogen molecule (13), the life time of which is considerable in comparison with
the pulse duration, is some orders stronger than the detachment at the O−
2 impacts
with the unexcited N2 molecules [7,26,27]. It is shown in [26], that while the current
density increases in the N2 : O2 = 4 : 1 discharge, the negative ions concentration
decreases almost twice simultaneously with the proportional increase of the N2 A3Σ+
u
metastable concentration. Under this condition, the O− ions are collapsed more
effectively, specifically due to the growth of two orders of the excited oscillatory
N2 state (v = 6) concentration. A destruction of the negative oxygen ions by the
argon metastable atoms at the thermal energy is a weak process, having the cross
section of the order of 1.6 · 10−16 cm2 [38]. We have not found in the literature the
velocity constant of the oxygen ion decay at its collision with the excited nitrogen
and argon molecules at the energies higher than thermal, although such a process
can be intensive [35].
It is believed that the photo-ionization of the air molecules is the essential process
providing a generation of free electrons in the ionization front and determines the
streamer propagation velocity [29,33,45,50]. However, the coefficients of transitions
in the ultra-violet region, which can play an important role in forming the “fast”
436
Negative corona current pulse with secondary oscillation
plasma kinetics, are almost absent in the literature. The photo-ionization processes
of the air, the nitrogen and the oxygen by the integral radiation (of common photon
energies) of the corona discharge have been experimentally studied in [39]. The em-
piric formula taken for the photoelectrons source (as a direct ionization of the oxygen
molecules by the photons radiated from the nonresonance nitrogen molecules) was
reduced to a more convenient form [33]. It was shown that the ionization of oxygen
molecules is generally possible by photons with the wavelengths λ 6 1025 Å, and in
the nitrogen discharge – in the region of 980 Å 6 λ 6 1025 Å [33].
Making use of the research [29,33] results, the photo-ionization term Sfi (the
velocity of photo-electron formation in the volume unit) for the nitrogen and oxygen
mixture was calculated in the form of:
Sfi(x) = pO2
dx
V (x)
x∫
x0
|neαwe|x′Ψ(x′, x)V (x′)dx′, (14)
where |neαwe|x′ is the amount of ionization cases in the volume unit in the point
x′, V (x) is the volume element in the point x, dx is the thickness of the photon
absorption region, pO2
is the O2 molecule partial pressure. The function Ψ(x′, x)
determination [33] as a probability of the photo-electron appearance in the point
x caused by one ionization act in the point x′, was used in the case of simplified
computations:
Ψ =
ω
α
· ξ · f, (15)
where α is the first Townsend ionization coefficient, ω – a number of the ionizing
photons, which are generated by electrons in the length unit when the quenching
is absent, ξ – an effectiveness of the photo-ionization averaged in the spectrum of
a radiation by the excited nitrogen molecules. The integral coefficient of the photo-
absorption f is as follows
f(x) =
exp(−κmnpO2
· x) − exp(−κmxpO2
· x)
x · ln(κmx/κmn)
, (16)
where κmx = 2, κmn = 3.5 · 10−2 (cm−1 (mm Hg)−1) – the maximum and minimum
cross sections of the absorption by the oxygen molecule of the photons emitted by
the nitrogen molecules in the wavelength region of 980–1025 Å. The parameter ω
α
· ξ
was taken from the work [33], where it is set in the form of the dependence on the
reduced field intensity E/p. In the field value region from 30 to 200 V/(cm · mm
Hg) the parameter ω
α
· ξ changes faintly and non-monotonously within the limits of
0.05–0.12.
Excitation of the high energy argon states in Ar+O2 mixture by the electrons is
an improbable process [7]. Here, the electron energy lowering takes place because of
the essential losses for the low energy states excitation. Furthermore, the resonant
argon base-line lengths 1065.6 and 1048.2 Å at 31S0-3
3P1 and 31S0-3
1P1 transitions
in the low temperature discharge [49] lie beyond the admissible bounds of the oxygen
molecule ionization λ 6 1025 Å [33].
437
V.I.Chyhin
The drift velocity of the electrons, positive nitrogen and argon ions and negative
oxygen ions we, wp, wn, just as in [2] were taken from works [7,28,51].
In our modelling, some processes have been excluded from a consideration. For
instance, the effect of the electron detachment from O−
2 ion by the photon impact
is low [43,52] – at the energy of 1.9–2.7 eV, the O−
2 decay section does not exceed
2 · 10−18 cm2 [52]. Taking into account the low concentrations of both particles (O−
2
and photon) this process was neglected. The velocity of the dissociative electron
attachment in e + O2 → O− + O [27,28,42,43] is known to be sufficiently high.
However, taking into account that the electron detachment from the atomic ion
O− is essentially higher as against the detachment from O−
2 at middle energies (104–
105 eV/cm, typical for the corona cathode region) [28], and that such an attachment
has caused changes of the air corona parameters no more than 5% [21], this process
was eliminated from consideration in our model, where the oxygen content is much
too lower. On the same account, there were not considered the parameters such as the
O2 ionization by electron impact, the direct two-body attachment e+O2 → O−
2 and
the excitation of O2a
1∆g singlet metastables, as it was done in [29,45]. Since positive
and negative ions are almost fully separated in space during the pulsation period
of the negative corona, and since the passing time of electrons through the positive
ions cloud (placed in a very narrow cathode sheath [2]) is short in comparison with
the pulse duration, we have excluded the recombination electron-ion [27] and ion-ion
[22,23] processes from consideration. These processes have been considered in [22,23]
because the region of O+
2 ions existence is greatly expanded in the depressed electric
field of the corona with a large cathode area.
4. Modelling results
4.1. Displacement current effect on the shape of the pulses
Taking into account, that the main current pulse characteristics of the negative
corona are determined by the cathode generating region [2,4,5], there were used the
formulas for the charge flow Ip and the displacement current Idc [25,40], and the
total current at a cathode Ik = Ip + Idc. At the sharp point of the cathode-needle,
the Idc current as the capacitance one, due to the cathode surface field change
dE/dt, is significant in the pulse leading front only, when it approaches a value of
the order of the ion current Ip (figure 2a). After the Idc lowering, the increase of the
total current slows down, forming a weak “step” in the front lines (figure 2a – “St”,
t = 1.91 mcs). At a considerable cathode area (the radius of 0.5 cm, Morrow’s data
[22]), the displacement current at this point significantly exceeds the Ip current,
forming the visible curve inflection – “step” (figure 2b,c, t = 70 ns). The primary
current peak at t < 30 ns (“precursor”) is described almost identically by means
of both Ik and Sato’s current Is [22] including the charges motion in the discharge
volume. As it is seen in figure 2b, both the “precursor” and the “step” origin is due
to Idc displacement current. The total Ik corona current after t = 100 ns displays a
strong secondary oscillation due to a variable p-ions flow to the cathode and namely
438
Negative corona current pulse with secondary oscillation
Figure 2. Calculated temporal corona current dependences at the discharge
parameters: (a) the edge radius r0 = 0.004 cm, the cathode-anode distance
d = 0.6 cm, the applied voltage U = 2300 V, the current tube radius in a
cathode region rg = 0.006 cm, the generation region length x0 = 0.02 cm, the
secondary photon-electron emission is absent; (b,c) data [22]. (a,b) the oxygen
concentration is 5%; (c) the O2 concentration is variable (the percentages are
marked by the numbers).
Ip current results in an increase of the pulse front and the total current oscillation
in the following pulse phases, for instance, the secondary maxima at t = 200 and
380 ns (figure 2b,c). When the secondary photoelectron emission is switched off, the
“precursor” height falls down from 16 to 3 mA. This peak disappears when the edge
radius is sharply decreased: its height falls to parts of mcA (figure 2a). Extending
the modelling [22], the graphs (figure 2c) were obtained. They reflect a gradual
transition from the “simple” Morrow’s pulse at 100% O2 [22] to more complicated
pulses with the “steps” and the secondary oscillations, which are pronounced at
low oxygen concentrations. Evidently, the simulated Morrow’s peak [22] is, in fact,
the Trichel’s pulse “precursor” arising due to the displacement current, caused by
ionization processes in the cathode region and at a strong effect of the secondary
photoelectron emission from the cathode area, taken unrealistically large for the
corona discharge.
4.2. Corona parameters effect on the characteristics of the secondary cur-
rent oscillation
At certain conditions, the current pulses of negative corona include the secondary
current oscillation – a decreasing oscillation or oscillation with the increasing am-
plitude. Conditionally they can be divided into three types – the peak, the tail and
the pre-breakdown ones. The SCO shape strongly depends on the external discharge
resistance R (figure 3 and figure 4). At the high R = 5 · 106 Ohm, this oscillation
adopts the shape of the first damping type, which exists in the short time of the
order of 2 mcs (figure 3a). Its amplitude decreases when the O2 concentration in-
creases and the pulse shape is similar to the measured ones (figure 1a,b). If the R is
439
V.I.Chyhin
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Figure 3. The calculated negative corona pulses with the secondary current os-
cillation of the first and the second types in N2+O2 gas mixture, depending on
the external resistance (a), and on the oxygen concentration (b, c). The common
discharge parameters are the same as in figure 2a. (a) the oxygen concentration
C = 0.4%, the external resistance R, Ohm, is marked by the numbers; (b) the
external resistance R = 5 · 105 Ohm, the oxygen concentration, %, is marked by
the numbers; (c) the external resistance R = 1 · 106 Ohm, the graphs are shifted
along the y-axis.
decreased to 1 · 106 Ohm, the SCO covers the total peak and tail parts of the pulse
(the first and the second types). In the peak part it damps, but at t = 3 mcs its
amplitude increases again. The identical SCO of the second type has been measured
in the work [16]. When the resistance is low (R = 5 · 105 Ohm) and the oxygen
concentration decreases to 0.15% (figure 3b), the oscillation of the second type ap-
pears. At the middle resistance R = 1 · 106 Ohm and at a small enough change
of the O2 concentration from 0.4% to 0.6%, the peak SCO damps fully (figure 3c).
The secondary “after-pulse” current oscillation of the third type can exist as the
damping (figure 4a,b) or with the increasing amplitude (figure 4c), that depends on
the resistance value. At the R smaller than of 5 · 103 Ohm, the corona pulse tran-
sition into the breakdown takes place just after the peak including this type SCO
(figure 4c).
4.3. Clarifying the nature of the corona current secondary oscillation
Studying the effect of corona parameters on the behaviour of the discharge func-
tions, a strong correlation between the corona current and some values in the gener-
ating region (sheath) was discovered. These are the cathode surface field intensity E0
(figure 5a), the surface concentration of the positive ions np0 (figure 5b), the number
of the secondary electrons nie emitted by the cathode under the positive ions impact,
the maximal concentration of the positive ions npmx and electrons nemx, the filling
integral αS1 =
∫ xEmn
0
α dx in the region from 0 to the field minimum co-ordinate
xEmn (figure 5c) and the charges of the positive ions and electrons in the sheath.
A shift of the current extrema to shorter times takes place due to the displacement
440
Negative corona current pulse with secondary oscillation
Figure 4. The calculated negative corona pulses with the SCO in N2+O2 gas
mixture at the common discharge parameters: the edge radius r0 = 0.004 cm, the
cathode-anode distance d = 0.6 cm, the generation region length x0 = 0.02 cm,
the secondary photon-electron emission is absent: (a) at the external resistance
R = 1 · 106 Ohm, in a dependence on the oxygen concentration, C%, marked
by the numbers, the applied voltage U = 2200 V, the current tube radius in the
cathode region rg = 0.006 cm; (b,c) at the variable current tube radius in the
generation region (rg0 = 0.003− 0.012, rg1 = 0.03 cm), (b) U = 1700 V, C = 5%,
R = 5 · 106 Ohm, c) U = 2400 V, C = 0%, R = 5e3 Ohm.
Figure 5. Calculated temporal dependences of the charge and field functions in
the corona pulse development, which: (a,b,c) are correlated with the secondary
current oscillation (calculated at the data given in figure 3c, 0.6%); (d,e,f) are in
an antiphase with SCO.
441
V.I.Chyhin
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Figure 6. The calculated spatial electron ne, positive np and negative nn ions
concentration distributions, (a,d,e), the field intensity E distribution (b) in the
corona cathode region, which accord with the typical phases of the secondary
current oscillation (c), at the same discharge parameters, as in figure 3c, C =
0.6%.
current Idc. The integral αS1 depending only on the E intensity changes in phase
with the maximal value E0, just like the majority of the mentioned values depend-
ing on this charge reproduction function. Some plasma functions are in a permanent
antiphase with the corona current. These are the field minimum Emn (figure 5d) and
its coordinate xEmn, the second sheath component of the filling integral αS2 (the
range of xEmn . . . xg) (figure 5f).
Taking into account these correlations one can easily explain the nature of sec-
ondary current oscillation. At the moment of the regular current maximum (for
example, at t = 2.4 mcs, figure 5) under a decrease of the field Emn in the region
xEmn . . . xg the number of the created positive ions decreases. In a half-period of
the SCO, these ions will come to the cathode and result in the corresponding cur-
rent lowering – in its next minimum (t = 2.5 mcs). The changes both of the field
in the minimum zone and of the co-ordinate xEmn cause a suitable change of the
potential differences U in this region, in antiphase to SCO oscillation (figure 5e).
At this moment, the total discharge potential fall Ucor practically does not change –
the amplitude of its oscillation does not exceed 1%. Consequently, it is impossible to
discuss the external “trigger” effect on the SCO origin, when in case of the current
increase, the resistance voltage increases and the discharge voltage decreases.
442
Negative corona current pulse with secondary oscillation
The graphs of the calculated spatial distributions, both the electric field E and
the charge concentration n in the sheath in the proper time moments of the SCO
(figure 6c), confirm the correlative character of the main discharge functions. Under
the condition of the after-peak current decrease (time interval 2.05–2.15 mcs), the
ion concentration np decreases in the cathode region (0–0.003 cm) and increases in its
distribution tail (0.003–0.006 cm). At the same time, the electron concentration ne
decreases in the total generation region (0–0.02 cm). During the following current
increase to the next secondary maximum (2.205 mcs), the reverse processes take
place.
4.4. Photoprocesses effect
The increase of the near-cathode field (figure 6b) causes the increase of the N2
high levels excitation and the O2 ionization intensities [33,39] during the growth of
the pulse front in the N2+O2 mixture. This photoionization included in the calcu-
lation in the full corona gap results in the peak current increase of the same order
as the O2 concentration (0.01–0.04%). That accords with the almost constant mea-
sured current in the inflection region of the pulse (0.1–0.2 mcs) at the concentration
of 0.01–0.04%. At the same time, the current increase of the order of 7–10% has
been obtained due to the N2 photoionization in the cathode region (0. . .xEmn). The
dependence of the peak part of the current on the O2 concentration (figure 1) has
been analysed, taking into account the electron detachment from O−
2 ion in the nn
layer (figure 6a). The collision with the excited nitrogen, the accumulation of O2
molecules and their ionization by some channels [7,26,36–38] were included in the
calculation. It appeared that during a few dozens of the pulses, the O2 concentration
increases to the percentage units and, consequently, the ionization coefficient of the
gas mixture increases proportionally [7,37]. The inclusion of the concentration tem-
poral dependence results in the peak current increase of 16.3% and 123.8% at the
initial concentration of 0.01 and 0.04%, accordingly, that is of the order of the exper-
imental values. The effect of the electron detachment due to the O−
2 collision with
the N2(A3Σ
+
u ) metastable [7,27,38] was estimated at the pulse completion stage. The
exclusion of this process from the computation results both in the corona current
decrease by 27% and in the pulse duration decrease by 21% at the 8th microsecond
of the pulse development in N2+O2 mixture with the oxygen concentration of 0.01%.
5. Analysis of the results
The division of the cathode region (generation, sheath) into the zones-layers of
the predominantly one type charge placing (p, n, e) (figure 6) is kept during the full
pulsation period of the negative corona. That forms both the behaviour of the main
plasma functions (figure 5) and the current characteristics in all the pulse stages
(figure 2–4). In the initial phases [22], the avalanche charges (x and p) reproduc-
tion takes place simultaneously with the displacement of the p-density maximum to
the cathode (figure 3b). At this time, both the E-field and the charge reproduction
443
V.I.Chyhin
coefficient α increase sharply in the region immediately close to the surface, and
consequently, the displacement Idc and the conductivity Ip currents increase sharply
(figure 2a). Simultaneously, the field E is essentially reduced behind the layer “p”
and consequently, the intensity of the attachment rate increases (it is inversely pro-
portional to E [22]) and the ion density nn increases (figure 6a). As a result, all the
undercathode functions (E, α, np etc.) and the currents Idc and Ip reach the maximal
values, controlled by the neighbouring negative ions. Accordingly, when the oxygen
concentration in Ar+O2 rises, the peak current Im decreases (figure 1c). Simultane-
ously, the decrease of the integral ∫ α(x)dx to the critical value is accelerated, hence
the pulse duration is shortened (figure 1a,b).
The pulse formation mechanisms in the notions of the Townsend’s discharge with
the decisive role of the secondary photo- and ion-electron emission [22,23] are de-
nied in the papers [11,17,21]. To explain the “step” nature, the comprehension of
the “cathode-directed ionization wave” “like streamer” is brought in [11] and the
photoelectron emission is substituted by the “ionization wave”, as an “alternative
to interpretation” of Morrow [21]. In a number of experimental works [11,16,17]
the attempts to prove the nature of the “step” were made taking into account the
secondary photoelectron emission, and binding the pulse peak with the steamer
nature. The results obtained in this paper show (figure 2c) that such “dualisms”
in the description of these secondary pule elements is connected with an essential
simplifying of the corona geometry by Morrow [22] and with the use of the Sato’s
expression for the current with the undetailed component of the displacement cur-
rent (recently the authors have made appropriate corrections [41]). The cathode was
set artificially like a sphere with the radius of 0.5 cm (too large for the corona), the
emission area of which is greater in dozens of thousands of such ones in the papers
[11,16,17]. As a result, a single pulse was calculated (figure 2c, C is equal to 100%),
mainly for taking into account the essential photoelectron emission. This pulse has
turned out to be a “precursor” (mainly invisible) for the measured pulses in many
of the following papers [11,16,17]. At the essential decrease of the cathode radius
[23], two pulse humps were simulated, and the first one was mistakenly explained by
the same photoelectron emission. Drawing attention to a full disappearance of the
“precursor” at the extremely small cathode radii and making a comparison of the
graph figure 1 [23] with the figure 1 of this work, one can affirm that the first hump
[23] was caused by the displacement current of the “ionization wave”, the photoelec-
trons did not create the current peak owing to a small emission area and fed up the
current with almost constant intensity (see figure 1 [23]). The following maximum
[23] is the ion current (figure 1b,c). Thus, the incorrect identification of the first
hump-“step” results in the above mentioned superfluous denying the photoelectron
effect at a small cathode radius as well as in the incorrect interpretation of the pulse
front secondary structures [11,16,17]. In our case, the pulse “step” was not experi-
mentally registered in N2+O2 (figure 1b) because the total ionization rate remains
extremely high after the arrival of the positive ions to the surface. This accords with
the results of the analysis of the “step” origin in the paper [8]. However, the authors
of the [8] associate a completion moment of the “step” forming with a completion
444
Negative corona current pulse with secondary oscillation
“of a plasma forming”. To our mind, the latter notion is questionable regarding the
expressed separation of the charged layers in the cathode sheath (figure 6).
The three simulated types of the secondary current oscillation (the peak, the
tail and the pre-breakdown ones) have the characteristics similar to those obtained
earlyer experimentally (figure 1), [3,4,11,16,17]. Their predominant position depends
on the discharge geometry [2,21], on the gas type and on the admixture concentra-
tion (figure 1). At a high concentration of electronegative gas, this oscillation can
degenerate (figure 1) [11] and is displayed in the form of the “step” and “hump”,
complicating its interpretation [11,16,17]. The SCO is a cause-consequence series of
the physical processes of various intensity proceeded in the generation region, specif-
ically: the ionization with the “wave displacement” of its centre – the shielding – the
drift – the secondary electron emission etc. The field intensity oscillation in antiphase
in the cathode surface region and in the end of the sheath (figure 5a,d) is the external
“feedback” of this region, that results in a high-frequency current oscillation. In oth-
er words, the SCO is caused by the “negative voltage-current characteristics” of the
generation region (figure 5e). The placement of the negative charge layer adjacent to
the positive ions layer is a precondition for originating the secondary oscillation [2,5].
The excited nitrogen molecules maintain the expanded space between these charged
layers (they play a role of the “protector” of the ionization layer). It is confirmed
by the secondary oscillation absence in the trailing pulse part in N2+O2 (figure 1).
This oscillation can appear in the current peak region, when the detachment process
between the layers just increases. To estimate the duration of this peak part, one
has to consider the excited molecules drift time. Owing to the described mechanisms
it is easy to explain and to simulate, at some conditions, the SCO on a pulse “tail”
[2,16] (figure 4b). This process can transfer into full pulses with the current decreas-
ing to nearly zero values [16], (figure 4c), that is into the Trichel’s pulses since their
nature is similar. At certain conditions, this high frequency oscillation proceeds to
the breakdown (figure 4c).
In the Ar+O2 mixture, the photoprocesses described for the N2+O2 are improb-
able since the intensity of the Ar high levels excitation by electrons of the reduced
average energy has low values [7] and the main resonance short wave-lengths 1065.6
and 1048.2 Å [38] are beyond the accessible region of the O2 ionization ( 6 1025 Å,
[33]). In this gas mixture, the energy losses go mainly for the excitation of the low
energy Ar states [7]. At the stage of the pulse completion in Ar+O2, this causes
a dominance of the attachment process. Consequently, the current pulse decreases
more steeply, and the absolute current value is considerably lower compared with
the ones in N2+O2 mixture (figure 1).
6. Conclusions
1. The shape of the negative corona current pulses with the secondary oscilla-
tion and their characteristics in N2+O2 and Ar+O2 mixtures are distinctly
different.
445
V.I.Chyhin
2. The main processes of changing the charge state and the photoprocesses in
the pulsing corona take place in the cathode region. The decisive process is
the formation of different charged layers, the interaction between them and
the surface that determines a majority of the pulse characteristics.
3. Secondary current oscillation is caused by the periodic “feedback” interac-
tion of different charged layers in the sheath and the emitting surface. The
photoionization and the photodetachment play a significant role. The field
intensity oscillation in antiphase in the surface region and in the end of the
sheath, as well as the “negative voltage-current characteristics” of the sheath
are the causes of the SCO. The pulse secondary oscillation can transfer into the
full mode of the Trichel’s pulse, since it is of the same nature. Such notions as
a “back and forth motion of the electric field” and a “turbulent beam-plasma
interaction” are not adequate to this nature.
4. Characteristics of the “precursor” and the “step” in the leading pulse front are
determined by the dynamics of the volumetric charges in the generation region,
including the secondary emitted electrons. The secondary current oscillation
shape is determined by a variable flow of the positive ions to the cathode
surface. At a small radius of the cathode, the “precursor” height is negligibly
low due to the low photoelectron emission while the “step” duration is very
short due to an extremely high speed of “ionization wave” in the increasing
under-surface electric field.
5. Corona current pulse shape in the nitrogen-oxygen mixture in the peak part is
formed by the ionization of the accumulated oxygen molecules in the cathode
region. In the argon-oxygen mixture such a process is weakened due to the
lowered energy of the electrons.
6. The effect of the electron detachment from O−
2 by the metastables on the
current value and on the pulse duration is distinctly different in the nitrogen
and argon mixtures.
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