Total current oscillations in Trichel pulse
The numerical simulations of negative corona at constant voltage in air are made. Two peaks of total current in Trichel pulse in absence of photoemission appear for very small values of ion-electron emission coefficient. In presence of photoemission the total current oscillations connected with the...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1121342017-01-18T03:02:12Z Total current oscillations in Trichel pulse Bolotov, O. Golota, V. Kadolin, B. Mankovskyi, S. Markov, P. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. Плазменно-пучковый разряд, газовый разряд и плазмохимия The numerical simulations of negative corona at constant voltage in air are made. Two peaks of total current in Trichel pulse in absence of photoemission appear for very small values of ion-electron emission coefficient. In presence of photoemission the total current oscillations connected with the instability based on photon radiation, photo-emission, and avalanche multiplication take place. Виконанo числове моделювання негативної корони при постійній докладеній напрузі в повітрі. Два піки повного струму в імпульсі Тричела за відсутності фотоемісії з’являються при дуже малих значеннях коефіцієнта іонно-електронної емісії. За наявності фотоемісії мають місце коливання повного струму, що пов’язані з нестійкістю, яка ґрунтується на випромінюванні фотонів, фотоемісії та лавинному розмноженні. Выполнено численное моделирование отрицательной короны при постоянном приложенном напряжении в воздухе. Два пика полного тока в импульсе Тричела при отсутствии фотоэмиссии появляются при очень малых значениях коэффициента ионно-электронной эмиссии. При наличии фотоэмиссии имеют место колебания полного тока, связанные с неустойчивостью, основанной на излучении фотонов, фотоэмиссии и лавинном размножении. 2015 Article Total current oscillations in Trichel pulse / O. Bolotov, V. Golota, B. Kadolin, S. Mankovskyi, P. Markov, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada // Вопросы атомной науки и техники. — 2015. — № 4. — С. 181-184. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 52.80.Hc http://dspace.nbuv.gov.ua/handle/123456789/112134 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия Bolotov, O. Golota, V. Kadolin, B. Mankovskyi, S. Markov, P. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. Total current oscillations in Trichel pulse Вопросы атомной науки и техники |
| description |
The numerical simulations of negative corona at constant voltage in air are made. Two peaks of total current in Trichel pulse in absence of photoemission appear for very small values of ion-electron emission coefficient. In presence of photoemission the total current oscillations connected with the instability based on photon radiation, photo-emission, and avalanche multiplication take place. |
| format |
Article |
| author |
Bolotov, O. Golota, V. Kadolin, B. Mankovskyi, S. Markov, P. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. |
| author_facet |
Bolotov, O. Golota, V. Kadolin, B. Mankovskyi, S. Markov, P. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. |
| author_sort |
Bolotov, O. |
| title |
Total current oscillations in Trichel pulse |
| title_short |
Total current oscillations in Trichel pulse |
| title_full |
Total current oscillations in Trichel pulse |
| title_fullStr |
Total current oscillations in Trichel pulse |
| title_full_unstemmed |
Total current oscillations in Trichel pulse |
| title_sort |
total current oscillations in trichel pulse |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2015 |
| topic_facet |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112134 |
| citation_txt |
Total current oscillations in Trichel pulse / O. Bolotov, V. Golota, B. Kadolin, S. Mankovskyi, P. Markov, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada // Вопросы атомной науки и техники. — 2015. — № 4. — С. 181-184. — Бібліогр.: 4 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-08T03:26:40Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №4(98) 181
TOTAL CURRENT OSCILLATIONS IN TRICHEL PULSE
O. Bolotov, V. Golota, B. Kadolin, S. Mankovskyi, P. Markov, V. Ostroushko, I. Pashchenko,
G. Taran, L. Zavada
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: ostroushko-v@kipt.kharkov.ua
The numerical simulations of negative corona at constant voltage in air are made. Two peaks of total current in
Trichel pulse in absence of photoemission appear for very small values of ion-electron emission coefficient. In pres-
ence of photoemission the total current oscillations connected with the instability based on photon radiation, photo-
emission, and avalanche multiplication take place.
PACS: 52.80.Hc
INTRODUCTION
The negative corona discharge in air usually oper-
ates in Trichel pulse mode. In some experimental condi-
tions, a total current time dependence of one Trichel
pulse has several maximums [1]. Before, the numerical
simulations were carried out for one-dimensional parti-
cle distribution with the electric field corresponding to
disks [2, 3], and for three-dimensional axially symmet-
ric model [4]. In [3] and [4] only ion-electron emission
was taken into account for the electron flow from cath-
ode, while in [2] the photoemission also was taken into
consideration. Two peaks were obtained in [2] and [3].
In [2], the first peak was accompanied with the intensive
photoemission, and the second one appeared with ion
going out of discharge gap. The authors [3] connected
the second peak with a maximum of the conduction
current at the cathode, whereas the first peak is connect-
ed with a maximum of displacement current caused by
the ionization wave in discharge gap. The total current
time dependence in [4] has only one maximum, alt-
hough the propagation of the ionization wave towards
the cathode tip was observed.
The explanation proposed in [1] and grounded on
the decisive role of ionization wave, does not indicate
clearly the causes of total current decrease between its
maximums. The results of numerical simulations sug-
gest two possible causes of this decrease. One of then is
connected with a fast decay of the ionization wave with
subsequent a slow rising of the ion current on the cath-
ode or with field enhancement and ionization rate in-
crease near the transverse ends of plasma region in con-
sequence of transverse expansion of the ionization
wave. Another possible cause of appearance the peaks is
connected with the instability of the process based on
radiation of photons, photoemission, and impact ioniza-
tion.
For more detailed study of the factors, which deter-
mine the characteristics of Trichel pulses, the different
dependences of the ion drift velocity on the field
strength and the different values of the ion-electron
emission coefficient were used. In the known papers, a
constant value for the ion mobility is often used, or it is
assumed that ion mobility increases with the field
strength increase. Emission properties of cathode
strongly depend on the chemical composition of the
cathode surface during discharge, and they may be con-
siderably different for the different experimental condi-
tions.
1. IONIZATION WAVE
AND POSITIVE ION FLOW
In the simulations carried out without taking into ac-
count a photoemission, the pulses with two peaks of the
total current, and, also, the pulses with the step before
the main peak were obtained, for the different depend-
ences of the ion mobility on the field strength. Namely,
the mobility decrease with the strength increase leads to
two peaks, while the mobility increase leads to the step.
The current increase before the first peak or before the
step is connected with the development of ionization
wave. The second peak and the single peak (in particu-
lar, the peak after the step) are connected with intensive
going out of ions to cathode.
The ionization wave developed near cathode is
somewhat similar to the cathode directed streamer, but
neighborhood of needle cathode leads to some differ-
ences of this wave from the cathode directed streamer,
developing in the mid-space far from the needle. The
great field strength near the top of the mid-space
streamer is caused by the great charge of the top, and
farther from the top the strength is less. Like the mid-
space streamer, the near-cathode ionization wave is ac-
companied with the formation of plasma region and
with increase of the field strength near some part of the
plasma region up to the values characteristic for stream-
er. But the field strength increases in the whole space
between the plasma region and cathode, and the strength
is greater in the part of space nearer to cathode. After
formation, the plasma region expands to cathode, the
distance between it and cathode decreases, and approx-
imately the same voltage drop between the plasma re-
gion and cathode becomes correspondent to the de-
creased distance. As a result, in the space between the
plasma region and cathode the field strength and ioniza-
tion coefficient increase, and to do the same number of
ionization acts an electron needs the shorter drift path.
The finish of such drift with ionizations corresponds to
the entering of the electron into the end of plasma re-
gion nearer to cathode with the plasma region forming
in this place. In the stronger field such drift is ended at
the nearer distance from the cathode. After the strength
increase up to the values, at which the dependence of
the ionization coefficient on the strength is slight, the
development of the described ionization wave is consid-
erably slowing down, and the displacement current con-
siderably decreases, leading to some decrease of the
total current.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 182
The near-cathode ionization wave has some com-
mon features with the plane wave. But as cathode is a
needle, the field near it is not uniform in the transverse
direction, too. So, in the neighboring areas over the
cathode surface, the ionization wave develops with the
different rates. The development is faster in the stronger
field near the needle tip, and it is slower in the weaker
field farther in the direction transverse to the field
strength. As a whole, the process has the form of the
transverse ionization wave expansion after the consider-
able slowing down of its expansion along the field
strength. In [4] such expansion was named ‘spreading’.
The written above may be illustrated by the Fig. 1,
where the electron distribution near cathode (hyperbola
in the right bottom corner is the cathode surface) is
shown towards the ends of the longitudinal and trans-
verse ionization wave expansions (separated with
28 ns). In the Fig. 1, the densities are logarithmically
distinguished by the black color density (range at the
top, from white, 109 cm−3 or less, to black, 1015 cm−3 or
greater), in the top right corners the total current time
dependence is shown, and the thick vertical line in it
marks the time instant. The distribution was obtained in
the assumption of ion mobility decrease with field
strength increase.
Fig. 1. Electron density near cathode towards the ends
of the longitudinal and transverse ionization wave
expansions in assumption of ion mobility decrease with
field strength increase
With considerable increase of transverse dimension
of the plasma region without considerable increase of its
longitudinal width, the field strength near the transverse
ends of the plasma region increases (as it takes place
near the needle), and the corresponding increase of ioni-
zation rate may lead to the temporal increase of total
current.
But even if the transverse expansion of the plasma
region does not give considerable field strengthening
near its transverse ends the second peak may arise in
connection with going out of positive ions to cathode.
Development of avalanches, starting by electrons from
cathode forms the ion distribution, in which the density
steeply increases with the distance from cathode. The
going out of such distribution to cathode is accompanied
with the increase of conduction current, which gives the
main contribution to the total current at cathode at this
stage of the pulse development. After the going out of
the main part of the formed positive ions to cathode the
total current decreases.
If the ion mobility in the strong field is sufficiently
large then the considerable increase of the conduction
current at the cathode may take place at the time of the
considerable slowing down of the ionization wave lon-
gitudinal expansion, and instead of minimum between
two peaks of the total current it is formed somewhat
similar to the step before the main peak. Such case is
illustrated in the Fig. 2 by the positive ion distribution at
the beginning of the going out of their main part to
cathode (and the total current step formation). The den-
sity range is the same as one in the Fig. 1, and the lines
in the right corners have the same meaning. The distri-
bution was obtained in the assumption of the ion mobili-
ty increase with the field strength increase.
Fig. 2. Positive ion density at the beginning of going
out of their main part to cathode in assumption of ion
mobility increase with field strength increase
It should be pointed out that the simulations gave
two peaks of the total current for the values of the ion-
electron emission coefficient considerably less than the
usually taken values 10−4…10−3. On the value of the
coefficient, it is dependent how far from cathode the
considerable slowing down of the ionization wave takes
place. For the larger coefficient, it takes place nearer to
cathode, in connection with greater electron flow from
cathode. To come to the cathode from there, the ions
need less time, which may to transform the first peak to
the step or even to make the step before the main peak
practically absent, as it has happened in the simula-
tions [4].
It should be also pointed out that the time interval
between the peaks of total current obtained in the simu-
lations for the considered conditions (atmospheric pres-
sure, needle tip curvature radius 50 µm) is a few tens of
nanoseconds. Such time co-ordinates with one obtained
in the simulations [2], but it is too large, in comparing
with one obtained in the experiment [1].
ISSN 1562-6016. ВАНТ. 2015. №4(98) 183
2. OSCILLATIONS WITH PHOTON
PARTICIPATION
If photoemission is considerable then the process of
the expansion of plasma region to cathode practically
stops when the space with the strong field is decreased
to the dimensions not sufficient for the self-consistent
process development on the base of photon radiation,
photoemission, and impact ionization. But the trans-
verse expansion of the plasma region with the field en-
hancement near its ends may give the total current in-
crease and its second peak forming.
Moreover, even a few maximums of total current
may be formed, in connection with two effects:
(1) enlarging of ionization rate in the part of space and
photon radiation from there when the electric field
strength there increases, (2) increase of the electric field
strength in front of the cloud of electrons, which were
knocked out from cathode by photons and are moving
away from cathode. The decrease of the field strength in
the same part of space after the electron cloud dis-
placement leads to the decrease of the rates of ionization
and photon radiation there.
In some conditions, perhaps, somewhat artificial, the
oscillations may be found out even in absence of the
impact ionization, only on the base of the processes of
photon radiation from discharge space and photoemis-
sion from cathode. As an example, it may be considered
the model, in which only two spaces in zone of inten-
sive photon radiation are accounted: the space c near
cathode, and the space b somewhat farther from cath-
ode. Negative charge disposed in the space b weakens
the field in the spaces c and b , whereas one disposed
in the space c weakens the field in the space c and
strengthens the field in the space b . It may be so, that at
the field strength values characteristic for the space c ,
the photon generation frequency is great, but its sensi-
tivity to the strength value is comparatively low, where-
as at the strength values characteristic for the space b
the mentioned sensitivity is comparatively high. In the
frames of the considered model, the process develop-
ment may be described with the following equations:
t b c c b bN N Nν ν∂ = − ,
t ( , ) ( , )c c c b c b c b b c cN f N N N f N N N Nν∂ = + − .
Here t∂ is time derivative, the indexes c and b in-
dicate the mentioned spaces, cν and bν are the quanti-
ties reciprocal to the characteristic time of electron re-
moving from the relevant space, cN and bN are elec-
tron densities, cf and bf are photon generation fre-
quencies. The written equations may be considered as
simplification of the equation
t div( )N Nu D N Nf∂ + − ∇ =
,
(where u is drift velocity, D is diffusion coefficient)
for the mentioned spaces after the averaging over them
and the neglecting of electron incoming from the other
spaces. Searching for solution in the linear approxima-
tion, one puts 0 1 exp( )a a aN N N tν= + , where the index
a stands for c or b , the index 0 indicates a stationary
value, and the index 1 indicates a perturbation, which is
assumed to be small. Let us put (0)
0 0( , )a a c bf f N N= and
use the designations (1)
acf and (1)
abf for the values of
( ) ( , )c a c bN f N N∂ ∂ and ( ) ( , )b a c bN f N N∂ ∂ , respec-
tively, at { 0c cN N= , 0b bN N= }. For the stationary
values, one can obtain the equations
(0) (0)
0 0( )c c c b bf N f Nν − = , 0 0c c b bN Nν ν= ,
and the condition (0) (0)
c b b c c bf fν ν ν ν+ = of their nonzero
solution existence. For the perturbations, in the linear
approximation, one gets the equations
(1) (1)
1 1( )c c c b bf N f Nν ν+ − = , 1 1( )b b c cN Nν ν ν+ = ,
where (1) (0) (1) (1)
0 0a a c ca b baf f N f N f= + + . The condition of
their nonzero solution existence may be written in the
form 2(2 )A Bν + = , where (1)
b c cA fν ν= + − ,
(1) 2 (1)( ) 4c c b c bB f fν ν ν= − − + . If the inequality 0A > is
held then an accidental perturbation is dumping. If
0A < then the instability takes place. If 0B > then the
process is monotonous, if 0B < then it is oscillatory. It
is assumed (1) 0cbf < , (1) 0bbf < , (1) 0ccf < , and (1) 0bcf > ,
according to the influence of negative charge disposi-
tion on the field in the corresponding space. For the
instability, it is necessary to hold the inequality
(0) (1) (1)
0 0c b bc b c c ccf N f N fν ν+ > + − .
For the oscillatory process development the ine-
quality
(1) (1) (0)
0 0
(0) (1) (1) 2
0 0
4 ( ) 4
( )
c c cb b bb c b
c b bc b c c cc
N f N f f
f N f N f
ν ν
ν ν
− − > +
+ + + − +
has to be held. In particular, if the value of
(0) (1)
0c b bcf N f+ is sufficiently large then the process is
unstable. And if, in addition, the value of
(1) (1)
0 0c cb b bbN f N f− − is sufficiently large then the instabil-
ity is oscillatory.
Fig. 3. The rates of the field strength change
at the instants with the different rates
of the total current change
In the presence of impact ionization, the instability
based on the photon generation and electron emission
may be considerably enhanced due to electron multipli-
cation. Intervals between maximums correspond to the
time of electron drift from the cathode to the space of
intensive photon radiation near the plasma region. This
time is considerably less than the time of positive ion
drift from plasma region to cathode, and it corresponds
ISSN 1562-6016. ВАНТ. 2015. №4(98) 184
to the time between peaks of total current obtained in
the experiment [1]. In the Fig. 3, the rates of the field
strength change are shown for two instants separated
with 0.5 ns. The total current changes slowly near the
first of them, and increases rapidly near the second. The
color scale range is from −5⋅1013 to +15⋅1013 V/(cm⋅s).
The lines in the right corners have the same meaning as
ones in the Fig. 1. The time derivative of the field
strength in the space near the transverse end of the
plasma region is positive, which is partly connected
with the ionization wave expansion in this direction. But
once in a while the rate of the strength change there
increases additionally, due to the next approach of the
increased number of electrons, which were obtained as
consequence of the previous such approach, through the
increase of photon radiation from the space, electron
emission from cathode, and electron multiplication in
avalanches. The field near the plasma region is not so
strong as one near the cathode surface, the photon gen-
eration frequency there is less, but sensitivity of the fre-
quency to the strength value is higher, and the product
of the great (through multiplication) number of elec-
trons and the comparatively small photon generation
frequency gives the photon generation rate, which is
considerable and highly sensitive to the strength value,
so that the comparatively small oscillations of the field
strength near the plasma region leads to the considerable
oscillations of the total current.
CONCLUSIONS
With the aid of the numerical simulations some de-
tails of Trichel pulse development are obtained. During
the transition from the simple avalanche multiplication
to the ionization wave set up, the total current usually
changes monotonously without any temporary decreas-
es. The minimum after the first maximum obtained in
the simulations is connected with considerable slowing
down of longitudinal expansion of ionization wave and
with the following increase of conduction current of
positive ions at cathode. In the case of fast coming of
positive ions to cathode, the step before the main peak
may be formed, without a temporary decrease of the
total current. Several total current maximums with time
intervals of order of nanosecond obtained in experi-
ments, probably, are connected with the instability of
the process based on the photon radiation from the dis-
charge space, photoemission from the cathode, and elec-
tron multiplication through impact ionization. The in-
stability arises due to electric field enhancement in front
of the part of electron flow having enlarged density,
which moves away from cathode to the space of inten-
sive photon generation near the end of plasma region,
and due to the consequent increase of photon generation
rate there, which leads to formation of new enlarging of
the density of the part of electron flow through photoe-
mission.
REFERENCES
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Streamer mechanism for negative corona current
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2. R. Morrow. Theory of stepped pulses in negative
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3. A.P. Napartovich, Yu.S. Akishev, A.A. Deryugin,
I.V. Kochetov, M.V. Pan’kin, N.I. Trushkin. A nu-
merical simulations of Trichel pulse formation in a
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Physics. 1997, v. 30, p. 2726-2736.
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A.P. Napartovich. Numerical simulations of Trichel
pulses in a negative corona in air // Plasma Physics
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Article received 08.05.2015
КОЛЕБАНИЯ ПОЛНОГО ТОКА В ИМПУЛЬСЕ ТРИЧЕЛА
О. Болотов, В. Голота, Б. Кадолин, С. Маньковский, П. Марков, В. Остроушко, И. Пащенко, Г. Таран,
Л. Завада
Выполнено численное моделирование отрицательной короны при постоянном приложенном напряжении
в воздухе. Два пика полного тока в импульсе Тричела при отсутствии фотоэмиссии появляются при очень
малых значениях коэффициента ионно-электронной эмиссии. При наличии фотоэмиссии имеют место коле-
бания полного тока, связанные с неустойчивостью, основанной на излучении фотонов, фотоэмиссии и ла-
винном размножении.
КОЛИВАННЯ ПОВНОГО СТРУМУ В ІМПУЛЬСІ ТРИЧЕЛА
О. Болотов, В. Голота, Б. Кадолін, С. Маньковський, П. Марков, В. Остроушко, І. Пащенко, Г. Таран,
Л. Завада
Виконанo числове моделювання негативної корони при постійній докладеній напрузі в повітрі. Два піки
повного струму в імпульсі Тричела за відсутності фотоемісії з’являються при дуже малих значеннях коефі-
цієнта іонно-електронної емісії. За наявності фотоемісії мають місце коливання повного струму, що
пов’язані з нестійкістю, яка ґрунтується на випромінюванні фотонів, фотоемісії та лавинному розмноженні.
E-mail: ostroushko-v@kipt.kharkov.ua
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