NUMERICAL SIMULATION OF HIGH-CURRENT DISCHARGES IN PULSED PLASMA GENERATORS WITH ENERGY STORAGE INDUCTORS

K.V. Dubovenko institute of Pulse Research and Engineering

43A Zhovtnevy prospekt, Mykoiayiv 32701 8, Ukraine

Abstract

In this paper, results of numerical simulation of high-current discharges in pulsed plasma generators with inductive energy storage are presented. In one case, the circuits with capacitor banks, storage inductors and aluminum fuses for switching (1 00-300) kA currents into plasma loads have been considered. In the other case, discharges in facilities containing compact homopolar generators, energy storage inductors in conjunction with two- stage (mechanical and explosive) opening switches to generate output pulses in plasma channels with (10-20) ps risetime and currents of (200-300) kA are analyzed. An approach to numerical simulation is described. The results obtained allow to agree the parameters of the pulsed generators with plasma load characteristics and evaluate the pulsed plasma generators operating efficiency.

Introduction

The design and construction of high density low temperature plasma generators for efficient transformation of primarily stored energy into energy of shock waves and heat flows is still a complicated problem'. This work deals with numerical simulation of high-current discharges in pulsed plasma generators with inductive energy storage.

The main goal of the work is to develop a model which would be sufficiently general for incorporating electrodynamic, hydrodynamic, thermodynamic interacting discharge phenomena and study their characteristics in a wide range of pulsed plasma generator parameters. The advantage of the approach consists in simultaneous consideration of nonlinear processes in open switches and plasma channels, skin effect and heat energy losses in plasma, description of the media in which discharges take place.

Statement ob the Problem and Its Formulation

The work has been carried out in two steps. At the first step discharge phenomena in circuits with capacitor banks (30 pF, 50 kV; 15.3 pF, 80 kV), storage inductors (0.05 - 0.55 pH) and aluminum fuses for switching currents (400-300 kA) into plasma loads have been considered (Fig.la). At the second step electrical discharges in generators with high level of stored energy have been studied (Fig.? b). In this case each plasma generator circuit contains a compact homopolar generator, energy storage inductor in conjunction with a two-stage

Plasma channel c

Fig.1. Schemes of the plasma generator circuits.

Reverse bar

0-78034214-31971510.00 Q 1997 IEEE 1434

( mechanical and explosive) opening switch to generate output pulses in plasma loads with (10-20) ps riselime and (200-300) kA currents. The circuits’ parameters and characteristics of the mechanical and explosive circuit breakers are chosen corresponding to those of the real facilities2-“ and are shown in Table 1 I Cylindrical pPasma channels are supposed to be initiated between electrodes of plasma load gaps by thin wires. In accordance with the disicharge phenomena the general set of the partial differential equations consists of eRectro- hydro- and thermodynamics equations describing the processes in plasma loads, supplemented with equations of media state, electrical anld heat The heat radiation from the plasma channel is taken into account.

where j is the current density in the plasma load; E,H are the electric rand magnetic field strength respectiveiy; Q is the specific conductivity; f,q are the density of the electromagnetic force and the specific power; p is the pressure; p is the medium density; v is the velocity of the medium in the gap; E

is the internas energy; q~ is the volume heat losses; W is the heat flux; X,XR are the electronic and radiative medium heat conductivity; OB is Stefan-Boltzmann constant; IR is Rosseland radiative range ; T is %he temperature; t is the time; r is the space coordinate; s is the mass Lagrangian coordinate (ds=prdr)

considered as those in gaps of plasma generators.

areT3

The most widely used media in pulsed research

In the case of the gap filled with air the equations of

P = P (PJ), &=E (PI VI 0- =0 (PI v,

and engineering are air and water.

media state, electrical and heat

x = x (PJ T)I IR =lR (PI T )

So they are

conductivity

(6)

In the case of underwater discharge the equation of media state was usedi4 supplemented with the entropy law and known dependencies of electrical and heat conductivity upon pressure and %em perat u re.

E(V,S) = e(V) + exp[ WT(lnV,S)]l p = - ( d ~ / d V ) ~ , T =: (dddS)”# (7)

where V is the specific volume; S is the entropy; ET is the function of cold compression; and WT is the heat function.

The boundary conditions on the plasma channel axis ( ~ 0 ) and on another boundary which is far off the media disturbances (r = rb 1 are the following

where I is the plasma channel current, To is the initial value of the medium temperature.

with the codes developed and verified with high-current electrical discharge experimental data in 1i,i2.

In every case the model equations are solved by a digital iteration metho~d’~ on a space-time grid

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Plasma Generators’ Parameters

Parameter

Energy Storage Capacitor Bank Total Capacitance Rated Voltage Homopolar Generator Resistance Inductance Armature Radius Magnetic Induction Rotational Velocity Stored Energy Energy Storage inductor (without cooling’) Resistance Inductance Opening Switch Stage 1 TY Pe Initial Resistance Inductance Material Length Width Thickness Stage 2

Initial Resistance Inductance Load Gap Spacing Medium Reverse Bar Radius Storage lnductor Feeding Contour Total resistance of bars Rei and closing switch RSI after breakdown Total lnductance of Bars LB1 and Closing Switch Lsl Load Feeding Contour Total Resistance of Bass RB2 and Closing Switch RS2 after Breakdown Total Inductance of Bars hB2 and Closing Switch Ls2 Closing Switch Breakdown Voltage

TY Pe

RT1, mOhm

30 50

1 0.25

fuse 15 0.1 8 Aluminum 0.55 0.12 1.51 0-5

0.2 air 0.13

1

0.05

1

0.09 75

15,3 80

0.5-1.5 0.05-0.55

fuse 10-40 0.13-0.45 Aluminum 0.55-1.1 0.12 1.51 0-5

0.2 air 0.13

1

0.05

0.7

0.09-0.75 120

12 30 0.29 1.75 580 5

0.03 3

mechan 2 0.05

explos. 20 40

0.4 air 01 3

0.01 8

0.05

1

0.1 20

Table1

30 50 0.35 1.6 300 1

0.03 3

mechan 5 0.008

explos. 20 100

0.1 water 0.2

0.01

0.05

1

0.13 25

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Discharge processes in the circuits with plasma Iloads, energy storage iriductors and aluminum fuses

To carry out modeling of the discharge processes in air the plasma load equations (1 - 10) are suppsemented with the circuit equations based on KirchhofPs laws, and ,the dependencies modeling the resistance of the electrically exploded conductors2 (aluminum foils) R,, during the period of explosion time as fundioris of energy dissipated QP1 and current density amplitude j,:

b$pf = ~ p l ~ f m , Q p i ) , Qpf = / 1 i 2 R p l df . (1 1) * The discharge processes are considered for the circuits #I ,2 with parameters shown in the Tablel. In this case tRe temporal current characteristics of the circuit performance are presented in Fig.2(a). Space-time distributions of the current density and plasma

0 5 10 15

T(l0'lK)

2.5

1.2!5

0 0.5 4.0 1.5 2.0 0 i .o 2.0 3.0

TlPAE (PI SPACE COORDINATE (io-2 m> SPACE COORDINATE (1 o - ~ m)

Fag.2. Plasma generator (circuit #1) performance (a) and space-time plasma channel current density (b) and temperature (c) distributions

temperature in the plasma channel are depicted in Fig.2(b,c). The results show that skin effect in the plasma channel is observed from the very beginning of the energy delivering to the plasma load. But to the end of the second microsecond of the discharge processes in plasma #channel the heat flux En the region of maximum energy dissipation is smoothing out the profile of the spacie temperature distribution.

The influence ~d the circuit #2 parameters on the discharge characteristics were studied. Calculated dependencies of pressure pm and velocity of the shock wave propagation vm amplitudes, discharge efficiency q (q is the ratio 0% %he energy delivered to plasma load to the energy stored) as functions of the storage inductor inductance e,,, switch inductance L,, and the aluminum foil length d are shown in F i g 3

These results of numerical simulation allow to agree the parameters of pulsed plasma generators with the shapes and amplitudes of the pressure, temperature, current pulses and expedient values of the discharge efficiency corresponding to a technological process under design.

Discharges in circuits with storage inductors and two-stage opening switches

Creation of homopolar fenerators (HPG) with high density of stored energy3l4 and systems of multistage current switching' allow to construct compact pulsed plasma generators with high levels of stored energy on the base of inductive storage. So the modeling of the discharge processes in the circuit consisting of the HPG of the disk type4 , storage inductor5 and two-stage opening switch (Fig.1 b) has been carried out. As the first stage of the open switch a current breaker of a mechanical type6 was considered. It commutates current into the second stage under fast divergence of its contacts and increasing resistance of the arc burning between them. As the second stage an explosive current breaker was taken into consideration'. Their parameters are shown in Table 1. Gaps in air and water

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served as plasma generators’ loads. In this case for numerical simulation plasma load equations (1-10) were supplemented with equations of the HPG performance, the circuit equations based on the Kirhhof‘s laws and relations for the circuit breakers’ resistance.

a) b) C)

Fig.3. Influence of the circuit #2 parameters on the plasma generator discharge characteristics

The arc resistance of the circuit breaker in the first stage of the opening switch can be determined from the equation of its volt-ampere characteristic7

~ , , , = ( a * p . l ~ ) / / ~ * ( e * Y / J / ( I ~ ~ ) (1 2) where I, is the arc length of the mechanical circuit breaker, a, 0, 8, y are coefficients. Their values depend on the circuit breaker construction. In this case the values of a=0.28 V, p = 1 .4.103 V/m, 8 = 6.95 A04J, y = 3.9.A08 J/m provided a good approximation for the mechanical switch operation.

The analysis of the explosive circuit breaker operation in the second stage of the opening switch is a separate problem connected with electrical arc extinguishing by the shock wave and the detonation products. But as the detonation products have high electric solidity and in real constructions stand firm the electric field stren th U to q07 V/m , the resistance of the explosive circuit breaker can be approximated with the relation B P

where al, is the coefficient which determines the duration of current switching in the load and depends on the circuit breaker construction. Its value of 2.5.106 s-’ provides really observed in experiments levels of current switching velocity at the circuit breaker operation based on the princi le of conductor (foil) damage by cumulative dielectric jets formed as a result of the explosive detonation .

As shown in Fig.4(a) during the time t=27.4.10” s of the HPG armature braking from 580 rad/s to 570 rad/s the HPG delivers to the circuit energy Q=185 kJ. Almost 75 per cents of this value are stored in the storage inductance . The other part of energy dissipates in the circuit elements: resistance of the HPG armature and brushes, storage inductance, opening switch and bars. At the moment t=20 ms when the contacts of the mechanical circuit breaker start their motion the currents through HPG and storage inductor equal 230 kA. The velocity of the contact divergence is 50 m/s. At this value the time of current commutation from the first stage of the opening switch to the second one is nearly 3.5 10”s (Fig.4b). In this figure temporal dependencies of the first stage circuit breaker resistance R,, and energy dissipation Qp: values are also shown.

Current commutation from the second stage of the opening switch to the plasma load (Fig.5a) begins after the restoration of the high electric solidity of the first stage opening switch arc gap. Here a fast fall of the channel resistance RI, is observed. The temporal dependencies of the opening switch second stage resistance Rp2. voltage Up2, energy dissipation Qp2 are shown in FigS(b). During the second stage of the current commutation the energy delivering to the plasma load is fast. This leads to an abrupt rise of the temperature T and pressure p at the axis of the

plasma channel and to a rapid increasing of the channel radius rk. It is shown in FigS(c), where the moment of the current appearance in the plasma load is taken as initial one.

?

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0 W 20 t(m 20 25 t(ms)

Fig.4. HBG performance at the moments of its armature braking and energy delivering to storage inductor

b)

1 02m)

Fig5 Characteristics of discharge (cir&<##3) iin air at the moments of current switching to plasma load

b) a)

Fig.6. Underwater discharge characteristics (circuit ##4) at the stage of current commutation to plasma load.

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The characteristics of the discharge in water for the plasma generator parameters corresponding to the data in Table 1 are shown in Fig. 6 for the moments of the energy Qkdelivering to the plasma channel . As a result of pulsed processes in high density medium the discharge in water distinguishes by higher vaiues of the pressure and lower values of the plasma radius. For comparison, the curve ps obtained with the use of approach" to the underwater discharge modeling is shown.

Summary

In this work the approach incorporating electrodynamic, hydrodynamic and thermodynamic interacting discharge phenomena in plasma channels of pulsed generators with storage inductors has been developed. The electric energy delivered to the plasma transforms into the energy of media kinetic motion, shock waves and heat radiation during the current switching with high intensity. So the discharge processes in the circuits with plasma loads and storage inductors have to be analyzed with correct consideration of the processes at this stage of discharge.

References

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