Features of active power definition in high-current pulsed discharge
The calculation method of active power dynamics in high-current plasma diode has been presented in this paper. The main features that should be considered in the calculations have been identified. It is shown that it is possible to obtain the high power levels (over 100 MW) at a slight stored ener...
Збережено в:
| Дата: | 2016 |
|---|---|
| Автори: | , , , , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2016
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/115288 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Features of active power definition in high-current pulsed discharge / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Ryabchikov, I.N. Sereda, M.A. Shovkun, A.F. Tseluyko // Вопросы атомной науки и техники. — 2016. — № 6. — С. 48-51. — Бібліогр.: 2 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-115288 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1152882017-04-06T16:39:01Z Features of active power definition in high-current pulsed discharge Hrechko, Ya.O Azarenkov, N.A. Babenko, Ie.V. Ryabchikov, D.L. Sereda, I.N. Shovkun, M.A. Tseluyko, A.F. Plasma heating and current drive The calculation method of active power dynamics in high-current plasma diode has been presented in this paper. The main features that should be considered in the calculations have been identified. It is shown that it is possible to obtain the high power levels (over 100 MW) at a slight stored energy of capacitor bank (up to 200 J) under the conditions of the space charge double layer formation in the plasma. Представлена методика расчёта динамики активной мощности в сильноточном импульсном плазменном диоде. Выделены основные особенности, которые необходимо учитывать при проведении расчётов. Показано, что в условиях образования в плазме двойного электрического слоя объёмного заряда возможно получение высоких уровней мощности (свыше 100 МВт) при незначительном (до 200 Дж) энергозапасе конденсаторной батареи. Представлена методика розрахунку динаміки активної потужності у сильнострумовому імпульсному плазмовому діоді. Виділені основні особливості, які необхідно враховувати при проведенні розрахунків. Показано, що в умовах утворення в плазмі подвійного електричного шару об’ємного заряду можливо отримувати високі рівні потужності (більше 100 МВт) при незначному (до 200 Дж) энергозапасі конденсаторної батареї. 2016 Article Features of active power definition in high-current pulsed discharge / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Ryabchikov, I.N. Sereda, M.A. Shovkun, A.F. Tseluyko // Вопросы атомной науки и техники. — 2016. — № 6. — С. 48-51. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 52.58.Lq, 52.59.Mv http://dspace.nbuv.gov.ua/handle/123456789/115288 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Plasma heating and current drive Plasma heating and current drive |
| spellingShingle |
Plasma heating and current drive Plasma heating and current drive Hrechko, Ya.O Azarenkov, N.A. Babenko, Ie.V. Ryabchikov, D.L. Sereda, I.N. Shovkun, M.A. Tseluyko, A.F. Features of active power definition in high-current pulsed discharge Вопросы атомной науки и техники |
| description |
The calculation method of active power dynamics in high-current plasma diode has been presented in this paper.
The main features that should be considered in the calculations have been identified. It is shown that it is possible to
obtain the high power levels (over 100 MW) at a slight stored energy of capacitor bank (up to 200 J) under the
conditions of the space charge double layer formation in the plasma. |
| format |
Article |
| author |
Hrechko, Ya.O Azarenkov, N.A. Babenko, Ie.V. Ryabchikov, D.L. Sereda, I.N. Shovkun, M.A. Tseluyko, A.F. |
| author_facet |
Hrechko, Ya.O Azarenkov, N.A. Babenko, Ie.V. Ryabchikov, D.L. Sereda, I.N. Shovkun, M.A. Tseluyko, A.F. |
| author_sort |
Hrechko, Ya.O |
| title |
Features of active power definition in high-current pulsed discharge |
| title_short |
Features of active power definition in high-current pulsed discharge |
| title_full |
Features of active power definition in high-current pulsed discharge |
| title_fullStr |
Features of active power definition in high-current pulsed discharge |
| title_full_unstemmed |
Features of active power definition in high-current pulsed discharge |
| title_sort |
features of active power definition in high-current pulsed discharge |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2016 |
| topic_facet |
Plasma heating and current drive |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/115288 |
| citation_txt |
Features of active power definition in high-current pulsed discharge / Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Ryabchikov, I.N. Sereda, M.A. Shovkun,
A.F. Tseluyko // Вопросы атомной науки и техники. — 2016. — № 6. — С. 48-51. — Бібліогр.: 2 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT hrechkoyao featuresofactivepowerdefinitioninhighcurrentpulseddischarge AT azarenkovna featuresofactivepowerdefinitioninhighcurrentpulseddischarge AT babenkoiev featuresofactivepowerdefinitioninhighcurrentpulseddischarge AT ryabchikovdl featuresofactivepowerdefinitioninhighcurrentpulseddischarge AT seredain featuresofactivepowerdefinitioninhighcurrentpulseddischarge AT shovkunma featuresofactivepowerdefinitioninhighcurrentpulseddischarge AT tseluykoaf featuresofactivepowerdefinitioninhighcurrentpulseddischarge |
| first_indexed |
2025-07-08T08:32:22Z |
| last_indexed |
2025-07-08T08:32:22Z |
| _version_ |
1837066925655457792 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2016. №6(106)
48 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2016, № 6. Series: Plasma Physics (22), p. 48-51.
FEATURES OF ACTIVE POWER DEFINITION IN HIGH-CURRENT
PULSED DISCHARGE
Ya.O. Hrechko, N.A. Azarenkov, Ie.V. Babenko, D.L. Ryabchikov, I.N. Sereda, M.A. Shovkun,
A.F. Tseluyko
V.N. Karazin Kharkiv National University, Kharkov, Ukraine
E-mail: yarikgrechko18@gmail.com
The calculation method of active power dynamics in high-current plasma diode has been presented in this paper.
The main features that should be considered in the calculations have been identified. It is shown that it is possible to
obtain the high power levels (over 100 MW) at a slight stored energy of capacitor bank (up to 200 J) under the
conditions of the space charge double layer formation in the plasma.
PACS: 52.58.Lq, 52.59.Mv
INTRODUCTION
High-current pulsed discharges are widely used in
various fields of science and technology. This is directly
connected with a relatively simple obtaining method of
the pulse power 10
6
…10
12
W. Thus, the relevant issue is
the correct calculation of the active power dynamics
released in the discharge. Using high-speed digital
oscilloscope allows carrying out such work with high
efficiency and degree of precision. However in this case
it is required a specific accuracy since neglect, although
small, but important components, leads to fundamental
errors, such as “negative energy in the spark
discharges”.
The method of power calculation in the microsecond
range discharges when the discharge current is
measured by the integrating current transformer is given
in this paper. Accents on the fundamental points that
should be considered in these measurements were made.
As an example, the calculation method of the active
power dynamics in a plasma diode with a limited
working surface of high-voltage electrode has been
given.
1. PHYSICAL MODEL
Calculation of the active power dynamics released in
the discharge is based on the discharge circuit equation
of the high-current pulsed discharge:
0
0
1
.
t
d
c
d c
d i t L tdi t
V i d L
C dt dt
R t i t R i t
(1)
An equivalent electrical scheme of this circuit is shown
in Fig. 1.
Fig. 1. The equivalent scheme of the discharge circuit
The capacitor bank С0 is charged to a voltage V0.
After the closure of switch Sw (breakdown of discharge
gap) the capacitor bank is discharged via inductance of
the supply circuit Lc, inductance of the discharge gap Ld,
active resistance of supply circuit Rc and active
resistance of the discharge gap Rd. In this case the
inductance of discharge gap and its active resistance
changed during the discharge: Ld = Ld(t) и Rd = Rd(t).
The dynamics of active power released in the
discharge tRtitP dd 2 according to equation (1)
is given by expression (2):
2
0
0 0
2 2
1
2
.
t
c d
d
d
c
L L t di t
P t i t V i d
C dt
dL t
i t i t R
dt
(2)
Pd(t) includes the ohmic and beam heating of the
plasma. To obtain high values of power it is necessary
to reduce the discharge gap inductance and to create
conditions for the space charge double layer formation
in the current-carrying plasma. This electric double
layer of space charge is responsible for the powerful
electron beam generation [1]. To provide the formation
conditions of the double layer the working surface of
the high-voltage electrode specifically has been limited
in this work.
The following calculation of the active power
dynamics released in the discharge was carried out on
the basis of the discharge current waveform from the
digital oscilloscope Tektronix TDS 2014. In addition,
the parameters of the discharge supply circuit, the
measurement circuit of the current sensor and the model
of the discharge gap inductance changes have been used
in the calculation. The capacity of the capacitor bank
was С0 = 1.94 μF and the charging voltage
V0 = 4…14 kV.
2. RESULTS AND DISCUSSION
In spite of seeming simplicity, the calculation of the
active power dynamics released in the discharge
contains a number of fundamental points.
The first point deals with the fact that the waveforms
V0
C0 Rc
Lc
Rd(t)
Ld(t) R0
discharge
plasma
i(t)
Sw
ISSN 1562-6016. ВАНТ. 2016. №6(106) 49
of digital oscilloscopes always have a certain level of
noise. (The numeralization principle, assuming the
appearance of steps on the signal, immediately imposes
a certain level of noise.) When taking the derivative of
the current signal by numerical methods even micro
noise enough to obtain in equation (2) the noise
derivative but not the derivative of the discharge
current. This value may be ten times greater than the
desired value. Therefore it is very important to choose
an approximation method of the current signal for
cleaning it from unnecessary noise.
It should be noted that the approximation by the
generally accepted method Savitsky-Golay is not always
possible to obtain the necessary results. Sometimes
more acceptable is the multiple (100 times or more)
sequential signal cleaning by sliding window method
using a simple averaging over several points. Here it is
necessary to select the optimal number of averaging
points. A large number of points, although improves the
signal cleaning, but can lead to the signal “fine
structure” loss, which, as a rule, is responsible for input
of high active power into the discharge.
The multiple cleaning by three points with different
weight coefficients shows the acceptable results:
11* 25.05.025.0 kkkk iiii , (3)
where ik* – the new value of the current signal k
th
point;
ik-1, ik, ik+1 – the previous cycle values of the
corresponding points.
Since the obtained data from a digital oscilloscope
look like a spreadsheet, using an appropriate software, it
is possible easily organize the multiple sequential signal
smoothing and thereby completely automate the
process. While processing a large number of signals it is
enough to insert a new waveform into the existing form.
The following feature related to the fact that any
current sensor always distorts the real signal, and it is
necessary to restore the experimentally obtained
dependence of the discharge current.
In this work the current was measured using the
integrating current transformer, the equivalent circuit of
which is shown in Fig. 2.
There are two main factors that distort the shape of
the current for integrating current transformer:
the active resistance consisting of the coil wire
resistance Rw and the measurement resistance R;
the parasitic capacity Сp including the capacity of
the sensor itself, the capacity of the transmission cable
and the input capacity of the oscilloscope.
Fig. 2. The equivalent scheme of the integrating current
transformer: i1(t) – the measured and i2(t) – the
inducible currents; VR(t) – the observed signal; Rw – the
coil wire and R – the measuring resistance; L – the coil
inductance; Cp – the parasitic capacity
The main applicability condition of the integrating
current transformer – multiple excess of the inductive
coil resistance over the total active circuit resistance:
RRL w . (4)
The additional condition – multiple excess of the
capacity resistance of the measuring path parasitic
capacity Ср over the measuring resistance R:
R
Cp
1
. (5)
The last condition limits the maximum value of the
measuring resistance that does not allow raising the
signal level above the certain. In our case, the value of
the measuring resistance was R = 1Ω.
Based on the equations system describing the
currents flowing in the scheme (Fig. 2.) it is possible to
obtain the relationship of the discharge current i(t) and
the observed signal VR(t):
00
1
1
,
w
R
t
R R w
R
t
R RC
i t V t
L
dV t dV t R R
RC V d
dt dt L
(6)
where – the current transformer sensitivity.
The correctness of the current restoration can be
confirmed with the graph of the capacitor bank
discharge UC(t), which should be like the damped
cosine oscillations:
t
C di
C
VtU
00
0
1
. (7)
Fig. 3 shows the waveform of the discharge current
(a) at the charging voltage V0 = 12 kV and the dynamics
of the capacitor bank discharge (b). The index 1
corresponds to the observed discharge current and index
2 corresponds to the restored discharge current. It is
seen that a slight difference between the observed and
the restored current form eventually leads to significant
errors. In case of the restored current signal (curve 2)
takes place a physically plausible dynamics of the
capacitor bank discharge in the damped cosine
oscillations form, while for unrestored (observed)
current (curve 1) there is an abrupt up withdrawal.
Physically, this means the charging of the capacitor
bank from some additional source that is contrary to the
law of energy conservation and experimental
observations. This pseudo-charging often interpreted as
“energy pumping from the vacuum in the spark
discharge”.
As a rule, in pulsed discharges is very difficult
initially to determine the inductance and active
resistance of the system. These values are calculated
from the discharge characteristics. Therefore, in the
third step it is very important to choose the adequate
i(t)
i2 i2C
i2R
Rw
R L Cp i2(t) VR(t)
50 ISSN 1562-6016. ВАНТ. 2016. №6(106)
determination methods of these values, and determine
the monitoring methods over the operations correctness.
Fig. 3. The dynamics of the discharge current (a) and
the dynamics of the capacitor bank discharge (b) for the
observed (1) and restored (2) signal
The fourth feature is associated with a changing of
the discharge gap inductance. Since the obtaining of
high discharge current is directly related to decrease the
total inductance of the discharge circuit Lc, the inductive
term i
2
(t)∙Ld(t)/dt in equation (2) associated with a
changing of the discharge gap inductance may have a
significant impact on the obtained results. Therefore,
one should choose the most accurate mathematical
model corresponding to the changing of the discharge
gap inductance Ld(t).
In our case, the total inductance of the discharge
circuit was significantly higher (in 4 times) than the
average inductance of the discharge gap: )(tLL dc .
This allowed us to use a simple model which assumed
that the inductance of the discharge gap synchronously
changes with the value of the discharge current. In this
case the plasma column changes its radius rd(t) from a
maximum to a minimum value in proportion to the
discharge current.
At the coaxial scheme of the discharge cell when the
discharge electrodes are arranged in front of each other
on the axis of the discharge, and the reverse current bus
are on the external cylindrical surface the value of the
discharge gap inductance can be represented as:
)(
ln2)(
tr
r
ltL
d
bc
dd , (8)
where ld – the length of the discharge gap, rbc – the
cylindrical surface radius of the reverse current bus.
The changing of the plasma column radius rd(t) is
proportional to the discharge current and can be
described by the expression:
max1
( )
( ) 1 ,d
d dm
dm
r i t
r t r
r i
(9)
where minmax5.0 ddd rrr – the amplitude
changing of the plasma column radius;
minmax5.0 dddm rrr – the average value of the
plasma column radius; rd max and rd min – maximum and
minimum plasma column radii accordingly (estimated
from the photographic images of the discharge gap in
the visible range); i1 max – the maximum amplitude of
the discharge current in the 1
st
half period.
It is appropriate to note that full scheme of
calculations using proposed method has been
completely automated. The computer realization of the
scheme on the basis of program Microsoft Excel has
been performed. Although this form looks bulky, but it
saves open all steps of the program that is very useful
for tracking the correctness of all procedures
implementation.
In general, this system has the following basic
components:
cleaning of the current signal VR(t) from the noise
using the expression (3);
calculation of the current signal derivative VR(t)/dt for
each cleaning pass with visualization of each tenth
cycle. (This allows to control the efficiency of the signal
cleaning process from the noise);
definition of the average inductance of the discharge
circuit, its active resistance and the current transformer
sensitivity on ratio of signal maximums at half
periods. (The automatic finding of the maximum values
and the corresponding time moments has been applied);
restoring of the current signal by means of the
expression (6), and test check of the capacitor bank
discharge dynamics using expression (7);
calculation of the active power Pd(t) from equation (2)
using the expressions (8) and (9).
During carrying out the calculations it is enough to
enter the initial conditions: the capacity of the capacitor
bank, its charging voltage, the geometric parameters of
the discharge gap, the electrical parameters of the
measurement circuit and download the investigated
waveform. All following calculations performed
automatically.
Fig. 4,a shows the waveform of the discharge
current at the charging voltage V0 = 12 kV. Fig. 4,b
shows the dynamics of total active power P1(t), released
in the whole discharge circuit and active power P2(t),
released on the average active resistance of the
discharge circuit Rc. The difference between P1(t) and
P2(t) is given in the Fig. 4,c and corresponds to the
active power additional inputted into the discharge Pd(t).
It is seen that the level of Pd(t) reaches a value
Pd ~ 100 MW at the stored energy in the capacitor bank
W0 ~ 140 J.
As shown the additional investigations, the active
power is released near the high-voltage electrode
surface in the plasma diode with a limited working
surface of this electrode. Here, due to the double layer
formation, the acceleration of the powerful electron
beam occurs towards the electrode. This electron beam
heats the plasma and evaporates the electrode material
[2]. In this case, the beam power density
reaches ~ 1.5 GW/cm
2
.
4.0µ 6.0µ 8.0µ 10.0µ 12.0µ
-15
0
15
30
1
2
t, s
i(
t)
,
k
A
a
4.0µ 6.0µ 8.0µ 10.0µ 12.0µ
-4
0
4
8
12
1
2
t, s
U
C
(t
),
k
V
b
ISSN 1562-6016. ВАНТ. 2016. №6(106) 51
Fig. 4. Dynamics of the discharge current (a), the total
active power in the circuit (b), the additional active
power released in the discharge (c) and the absorbed
energy (d)
Fig. 4,d shows the dynamics of absorbed capacitor
bank energy. It is seen that the main part of the energy
(~ 80 %) is absorbed in the 1
st
half period of the
discharge current oscillations.
CONCLUSIONS
The method of active power definition which has
been presented in this paper allows determining the
dynamics of active power released in the high-current
pulsed discharge with high degree of precision. The
main features that should be considered in the
calculations have been determined. One of the important
moments is the correct restoring of the discharge current
shape, since any current sensor produces a signal with a
certain degree of precision. It has been noted that this
circumstance leads to significant error. It is shown that
in high current plasma diode with limited working
surface of high voltage electrode the high levels of
power (over 100 MW) are reached at a relatively low
stored energy of capacitor bank (up to 200 J).
REFERENCES
1. C. Charles. A review of recent laboratory double
layer experiments // Plasma Sources Sci. Technol. 16,
2007, p. 1-25.
2. I.V. Borgun et al. Double electric layer influence on
dynamic of EUV radiation from plasma of high-current
pulse diode in tin vapor // Physics Lettres A. 2013,
v. 377, p. 307-309.
Article received 10.10.2016
ОСОБЕННОСТИ ОПРЕДЕЛЕНИЯ АКТИВНОЙ МОЩНОСТИ В СИЛЬНОТОЧНОМ
ИМПУЛЬСНОМ РАЗРЯДЕ
Я.О. Гречко, Н.А. Азаренков, Е.В. Бабенко, Д.Л. Рябчиков, И.Н. Середа, М.А. Шовкун, А.Ф. Целуйко
Представлена методика расчёта динамики активной мощности в сильноточном импульсном плазменном
диоде. Выделены основные особенности, которые необходимо учитывать при проведении расчётов.
Показано, что в условиях образования в плазме двойного электрического слоя объёмного заряда возможно
получение высоких уровней мощности (свыше 100 МВт) при незначительном (до 200 Дж) энергозапасе
конденсаторной батареи.
ОСОБЛИВОСТІ ВИЗНАЧЕННЯ АКТИВНОЇ ПОТУЖНОСТІ В СИЛЬНОСТРУМОВОМУ
ІМПУЛЬСНОМУ РОЗРЯДІ
Я.О. Гречко, М.О. Азарєнков, Є.В. Бабенко, Д.Л. Рябчіков, І.М. Середа, М.О. Шовкун, О.Ф. Целуйко
Представлена методика розрахунку динаміки активної потужності у сильнострумовому імпульсному
плазмовому діоді. Виділені основні особливості, які необхідно враховувати при проведенні розрахунків.
Показано, що в умовах утворення в плазмі подвійного електричного шару об’ємного заряду можливо
отримувати високі рівні потужності (більше 100 МВт) при незначному (до 200 Дж) энергозапасі
конденсаторної батареї.
4.0µ 6.0µ 8.0µ 10.0µ 12.0µ
0
40
80
120
P
1
(t)
P
2
(t)
P
,
M
W
t, s
b
4.0µ 6.0µ 8.0µ 10.0µ 12.0µ
0
20
40
60
80
100
W
d
/
W
0
,
%
t, s
d
4.0µ 6.0µ 8.0µ 10.0µ 12.0µ
-15
0
15
30
t, s
i(
t)
,
k
A a
4.0µ 6.0µ 8.0µ 10.0µ 12.0µ
0
40
80
P
d
,
M
W
t, s
c
|