Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode
Gespeichert in:
| Datum: | 2001 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
|
| Schriftenreihe: | Вопросы атомной науки и техники |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/78406 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode / Yu.E. Kolyada, O.N. Bulanchuk, V.I. Fedun // Вопросы атомной науки и техники. — 2001. — № 5. — С. 27-29. — Бібліогр.: 4 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-78406 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-784062015-03-17T03:02:01Z Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode Kolyada, Yu.E. Bulanchuk, O.N. Fedun, V.I. 2001 Article Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode / Yu.E. Kolyada, O.N. Bulanchuk, V.I. Fedun // Вопросы атомной науки и техники. — 2001. — № 5. — С. 27-29. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS numbers: 29.27.Fh http://dspace.nbuv.gov.ua/handle/123456789/78406 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 |
| format |
Article |
| author |
Kolyada, Yu.E. Bulanchuk, O.N. Fedun, V.I. |
| spellingShingle |
Kolyada, Yu.E. Bulanchuk, O.N. Fedun, V.I. Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode Вопросы атомной науки и техники |
| author_facet |
Kolyada, Yu.E. Bulanchuk, O.N. Fedun, V.I. |
| author_sort |
Kolyada, Yu.E. |
| title |
Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode |
| title_short |
Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode |
| title_full |
Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode |
| title_fullStr |
Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode |
| title_full_unstemmed |
Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode |
| title_sort |
numerical simulation of the marx–generator behavior on nonlinear load-high-current vacuum diode |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2001 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/78406 |
| citation_txt |
Numerical simulation of the Marx–Generator behavior on nonlinear load-high-current vacuum diode / Yu.E. Kolyada, O.N. Bulanchuk, V.I. Fedun // Вопросы атомной науки и техники. — 2001. — № 5. — С. 27-29. — Бібліогр.: 4 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT kolyadayue numericalsimulationofthemarxgeneratorbehavioronnonlinearloadhighcurrentvacuumdiode AT bulanchukon numericalsimulationofthemarxgeneratorbehavioronnonlinearloadhighcurrentvacuumdiode AT fedunvi numericalsimulationofthemarxgeneratorbehavioronnonlinearloadhighcurrentvacuumdiode |
| first_indexed |
2025-07-06T02:30:53Z |
| last_indexed |
2025-07-06T02:30:53Z |
| _version_ |
1836862987389894656 |
| fulltext |
NUMERICAL SIMULATION OF THE MARX–GENERATOR
BEHAVIOR ON NONLINEAR
LOAD - HIGH-CURRENT VACUUM DIODE
Yu.E. Kolyada, O.N. Bulanchuk, V.I. Fedun
Priazovsky State Technical University,
Universitetskaya street, 7, Mariupol, Ukraine
e-mail: KOLYADA@PSTU.EDU
PACS numbers: 29.27.Fh
One of the microsecond high-current beam genera-
tion techniques is the implementation of Marx Genera-
tor (MG) discharge on the cold diode working under ex-
plosive electron emission condition. However at the
pointed above-mentioned condition such a diode is a
strongly nonlinear load (in a sense of voltage-current
characteristic). Therefore there is a problem of the load
matching MG to a high-voltage vacuum diode with the
purpose of the most effective transfer of the energy ac-
cumulated in the MG and getting the greatest possible
voltage amplitude value on the diode (for given MG).
The no less important problem is the shaping diode volt-
age pulse by close to rectangular.
In this paper mathematical modeling and numerical
simulation data of processes which take place at MG
discharge on a high-current vacuum diode are submit-
ted. As the base accelerator operating model on the ba-
sis of which the parameters of an equivalent MG circuit
and vacuum diode were determined, the accelerating
complex was served, the construction of which is ex-
plicitly explained in [1, 2]. In the complex located in
open air, the following beam parameters were reached:
energy – 1.2 MeV, current - up to 15 kA, pulse duration
at the pulse base – 10–12 µs. The generator was a multi-
store construction, on each of its eight floors there was a
block of condensers with a capacity of 0.64 µF at volt-
age 125 kV everyone. The grouping of condensers by
their sequential and parallel connection ensures the ca-
pacity 1
0.04C = µF in discharge. The MG limiting volt-
age is 4 MV, the accumulated energy is 320 kJ. The
specific feature of its construction is a height of 12.7 m
and remoteness from the accelerator (20 m), that stipu-
lated its natural inductance 1 101.3L = µH and induc-
tance of the connecting line with the diode 2 52.1L = µ
H. Then the equivalent circuit MG before and after dis-
charge can be presented (Fig. 1).
b)
a)
L1L1
C1 R3
R1 L2
C3 C2
R2
L1
C1 R3
R1 L2
C3 C2
Rn
R2
Fig. 1. An equivalent circuit of the generator before dis-
charge (a) and after discharge (b).
Here in addition to described above, the labels 1R -
active resistance of connecting wires and discharge
gaps, 2R – active resistance of the connecting line with
the diode, 3C – generator parasitic capacity, 2C – diode
and connecting line capacity, 3R – charge-uncharged re-
sistance MG are entered. Calculations, measuring and
the estimates of the indicated magnitudes have given the
following results 2C =300 pF, 3C =330 pF [3]. The re-
sistance 1 2 10R R= = Ohm is artificially introduced
with the goal of discharge current restriction for used
condensers (the admissible discharge current is 50 kA),
3R =7.68 kOhm. The nonlinear load - vacuum diode op-
eration under explosive electron emission condition is
described by a known relation [4]
6 3 / 2 22.33 10 /( )I U S d vt−= ⋅ − (1)
where I – beam current, U – voltage on the diode,
2
4
DS π= – electrodes square, d – distance between
the cathode and anode, t – time, v – dispersion speed
of cathode plasma. The magnitude of v can be accepted
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 27-29.
27
mailto:kolyada@pstu.edu
6 cm1 2 10
sec
÷ ⋅ . The nonlinearity of the diode is specified
by the fact that at the cathode plasma ejection in the an-
ode direction there is a modification of diode resistance.
Actually also there is an anode plasma creation and
movement to the cathode [4]. But in calculations this
circumstance can be eliminated by introduction of a
component to the cathode plasma speed.
The equivalent circuit of a MG discharge circuit
working on the nonlinear element is the fifth order dis-
charge circuit described by the fifth order nonlinear dif-
ferential equations. In a general view these equations
are not analytically resolved, therefore for a tentative es-
timation of discharge circuit parameters we shall take
advantage of some simplifications.
At the beginning let's consider the MG no-load oper-
ation. The equivalent circuit in this case in view of rela-
tions between parameters of a complete equivalent cir-
cuit (Fig. 1a) can be represented in the simplified form
in Fig. 2a, and in the case of the load on the nonlinear
diode in Fig. 2b.
b)
a)
L1+L2 R1+R2
C1 C2
Rn
R3
L1 R1
C1 C3
Fig. 2. MG equivalent circuit: (a) the condition of a no-
load operation; (b) in the mode of operation on the non-
linear diode nR .
In the case а) the second part of the plan the diode
and connecting bus are not plugged in, therefore in the
given figure the left-hand part of the complete circuit is
figured only. In the case b) by virtue of the
3 3 2 nC R C R> > it is possible to eliminate the element
with 3 3C R , therefore the complete circuit will accept the
form shown in this figure. As follows from above rea-
soning the indicated approach has not lead to essential
physical restrictions of real working conditions of the
true circuit. Therefore below represented is the method
and numerical simulation results of MG operation on a
nonlinear load under pointed above assumptions.
The problem of diode voltage and current determina-
tion was solved in two stages. At the first stage the solu-
tion for circuit parameters up to the diode breakdown
moment was found. In this case it was supposed
nR = ∞ (the diode current is equal zero) and equation
for a charge 1rq on the condenser 1C looks like
2 1
1 1 0 1
2
'' 2 ' n
r r r
qq q q
C L
β ω+ + = (2)
where 1 2
2
R R
L
β += ,
2 1 2
0
1 2
C C
C C L
ω += ,
1 1 1 0( 0)r nq t q C U= = = , 0U is the initial voltage on the
condenser 2C . Solution (2) in view of starting condi-
tions for 1 '( 0)rq t = =0 looks like
21
1 0 22
0 2
( ) 1 ( 1)( cos sin )
t
n
r
q eq t C L t t
C L
β
ω ω ω β ω
ωω
−
= + − +
, (3)
where 22 2
0ω ω β= − . At the second stage at reaching
on the condenser 2C the breakdown voltage BU it was
supposed that the diode current flows past under the law
(1). In this case the set of equations describing the pro-
cess of a condenser charge evolution looks like
1 1 1 2
1 2
3/ 26
2
1 2 3/ 2 2
2
1 1'' 2 ' ,
2.33 10' '
( )
q q q q
C L C L
q Sq q
C d vt
β
−
+ + =
⋅+ = −
−
( 4 )
Thus the entry conditions for (4) were determined
from (3) by the determination of an breakdown instant
Bt in view of a charge conservation law
2 1 1 2( ) ( )r B n r B Bq t q q t C U= − = .
Thus
1 1 1 1( 0) ( ), '( 0) '( )r B r Bq t q t q t q t= = = = ,
2 2 2 2( 0) ( ), '( 0) '( )r B r Bq t q t q t q t= = = = .
The set of equations (4) was solved by the numerical
methods. The outcomes of calculations are represented
in Fig. 3.
28
a) b)
Fig. 3. Dependence a) voltage and b) current intensity of the nonlinear diode from time at such parameters:
0.14 ; 0.12 ; 0.1D m m m= , ( 410v = m/s, 6
0 2 10U = ⋅ V, 52 10BU = ⋅ V, 6
1 0.04 10C −= ⋅ F, 12
2 300 10C −= ⋅ F,
6
1 2 150 10L L L −= + = ⋅ H, 1 2 20R R+ = Om, 0.1d = m).
The dependencies obtained are interpreted from gen-
eral reasons of the MG operation and diode behavior de-
scribed by the ‘three second’ law. At the greater cathode
sectional area the greater current flows through the
diode that leads to decrease its resistance and diminu-
tion of a discharge time MG on the load. To voltage
pulse ending practically all the energy stored in the gen-
erator will be released on the load. The diameter diode
increase leads to resistance decrease. Thus to the mo-
ment of the diode voltage pulse ending caused by the
switching of an accelerating gap by plasma, by means of
current feature analyses (the current prolongs to in-
crease) it is possible to conclude, that the further MG
energy liberation will occur in a short circuit mode.
Thus our numerical simulation results allow to receive
beam optimum parameters at fixed parameters of MG
by means of the diode geometrical characteristic varia-
tion.
REFERENCES
1. Yu.E.Kolyada, Yu.V.Tkach et al. Pulsed Voltage
Generator with energy 0.32 MJ and voltage 4 MV //
Pribory i Tekhnika Ehksperimenta. 1986, № 3,
p. 235 (in Russian).
2. Yu.E.Kolyada, Yu.P.Podosinkin et al. High-pulse
accelerator of fresh air making // Pribory i Tekhni-
ka Ehksperimenta. 1988, № 1, p. 226 (in Russian).
3. S.M.Smirnov, P.V.Terent’ev. Pulsed high-voltage
generators. Moscow-Leningrad: Energiya, 1964.
239 p. (in Russian).
4. G.A.Mesyats, D.I.Proskurovskiy. Pulse electrical
vacuum discharge. Novosibirsk: Nauka, Sibirskoye
otdelenie, 1984. 256 p (in Russian).
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 29-29.
29
|