Pulse generator with intermediate inductive storage

Pulse generator with intermediate inductive storage as a lightning simulator B. M. Kovalchuk, A. V. Kharlov, A. A. Zherlytsyn, E. V. Kumpyak, and N. V. Tsoy Citation: Review of Scientific Instruments 87, 063505 (2016); doi: 10.1063/1.4954504 View online: http://dx.doi.org/10.1063/1.4954504 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/87/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Note: Compact, reusable inductive-storage-cum-opening-switch based 1.5 GW single-shot pulsed power generator Rev. Sci. Instrum. 85, 036101 (2014); 10.1063/1.4867079 A 70 kV solid-state high voltage pulse generator based on saturable pulse transformer Rev. Sci. Instrum. 85, 024708 (2014); 10.1063/1.4864194 A compact bipolar pulse-forming network-Marx generator based on pulse transformers Rev. Sci. Instrum. 84, 114705 (2013); 10.1063/1.4828793 Optimal design of semiconductor opening switches for use in the inductive stage of high power pulse generators J. Appl. Phys. 95, 5828 (2004); 10.1063/1.1707207 All-solid-state triggerless repetitive pulsed power generator utilizing a semiconductor opening switch Rev. Sci. Instrum. 72, 4464 (2001); 10.1063/1.1416115

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REVIEW OF SCIENTIFIC INSTRUMENTS 87, 063505 (2016)

Pulse generator with intermediate inductive storage as a lightning simulator B. M. Kovalchuk,1 A. V. Kharlov,1,a) A. A. Zherlytsyn,1,2 E. V. Kumpyak,1 and N. V. Tsoy1 1 2

Institute of High Current Electronics 2/3 Academichesky Ave., 634055 Tomsk, Russia National Research Tomsk Polytechnic University, 30 Lenin Ave., Tomsk 634050, Russia

(Received 26 April 2016; accepted 10 June 2016; published online 27 June 2016) Compact transportable generators are required for simulating a lightning current pulse for electrical apparatus testing. A bi-exponential current pulse has to be formed by such a generator (with a current rise time of about two orders of magnitude faster than the damping time). The objective of this study was to develop and investigate a compact pulse generator with intermediate inductive storage and a fuse opening switch as a simulator of lightning discharge. A Marx generator (six stages) with a capacitance of 1 µF and an output voltage of 240 kV was employed as primary storage. In each of the stages, two IK–50/3 (50 kV, 3 µF) capacitors are connected in parallel. The generator inductance is 2 µH. A test bed for the investigations was assembled with this generator. The generator operates without SF6 and without oil in atmospheric air, which is very important in practice. Straight copper wires with adjustable lengths and diameters were used for the electro-explosive opening switch. Tests were made with active-inductive loads (up to 0.1 Ω and up to 6.3 µH). The current rise time is lower than 1200 ns, and the damping time can be varied from 35 to 125 µs, following the definition of standard lightning current pulse in the IEC standard. Moreover, 1D MHD calculations of the fuse explosion were carried out self-consistently with the electric circuit equations, in order to calculate more accurately the load pulse parameters. The calculations agree fairly well with the tests. On the basis of the obtained results, the design of a transportable generator was developed for a lightning simulator with current of 50 kA and a pulse shape corresponding to the IEEE standard. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4954504]

I. INTRODUCTION

Lightning and lightning protection issues have been under investigation for a very long time. The history of these investigations can be found in Ref. 1. Both direct lightning action and the impact of generated electromagnetic pulses cause serious problems for buildings, aircraft, and all sorts of electrical equipment.2 4-1995—IEEE Standard Techniques3 for HighVoltage (HV) Testing establishes standard methods to measure high-voltage and basic testing techniques, so far as they are generally applicable, to all types of apparatus for alternating voltages, direct voltages, lightning impulse voltages, switching impulse voltages, and impulse currents. It implements also new procedures to improve accuracy, provide greater flexibility, and address practical problems associated with highvoltage measurements. Review4 summarizes major publications and advances on lightning and lightning protection. The review is organized into the following five sections: lightning discharge-observations, lightning discharge modeling, lightning occurrence characteristics/lightning locating systems, lightning electromagnetic pulse and lightning-induced effects, and protection against lightning-induced effects. The very complex nature of lightning and lightning-induced effects stipulates very limited possibilities for numerical simulation. It was shown in Ref. 5 that the electric and magnetic fields’ waveforms can be expressed only very approximately by the channel-base current waveform with difference factors at a)[email protected]

certain distances. Direct experiments are required for electrical apparatus testing, and compact transportable generators are required for those tests. Several approaches can be pointed out in the design of lightning simulators. One type was developed in the Russian Federal Nuclear Center—VNIIEF. Those simulators are based on a cascade of magnetic cumulative generators MCG-80 and MCG-160 with energy capacity of several MJ and current pulses with an amplitude of 30–50 kA (i.e., average statistical lightning) for a rise time of several 10s µs and pulse duration at halfheight of 80–250 µs.6,7 Obvious disadvantages of such an approach are the very complex installation, low efficiency, and too long a rise time of the current. A second approach is a conventional gigantic MV-scale Marx generator design, as adopted in many high-voltage pulsed power systems.8 Here, the disadvantages are the tremendous cost and again very complicated design, because it usually consists of a large number of capacitors of low capacitances in series to build up bank voltage to MV or higher, yet reducing its erected capacitance, thus requiring several parallel banks of series capacitors to render the sufficient desired system capacitance. Inductive energy storage, in combination with an opening switch, offers several attractive features for pulsed power applications when compared to the aforementioned Marx techno1ogy. The advantages are compactness and the low cost of the primary energy store.9,10 The objective of this study was to develop and investigate a compact pulse generator with intermediate inductive storage and a fuse opening switch as a simulator of lightning discharge. The ultimate intended

0034-6748/2016/87(6)/063505/8/$30.00 87, 063505-1 Published by AIP Publishing. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 84.237.1.92 On: Tue, 28 Jun 2016 02:08:30

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parameters of the generator are current of 50 kA with the rising time of 1.2 µs, and time of current fall to the half-amplitude value during 35 µ , 70 µ, or 125 µs on an active-inductive load (0.1 Ω and 6.3 µH). To prove the developed regimes and simulation techniques for the generator parameters, a test bed was assembled and control tests were carried out. The obtained results were used to develop a project of the generator with a current of 50 kA.

II. DESCRIPTION OF TEST BED A. Structure and operation principles

A block-diagram of the test bed is presented in Fig. 1. The Marx generator is charged by a positive polarity voltage from power supply 1. The generator is triggered by the pulse from the triggering generator 2 supplying voltage through the capacitors C7, C8 to the electrodes of the spark gap switches S1 and S2 of the first and second stages. With operation of Marx generator, energy is pumped into the storage L 2 through the electrically explosive fuse opening switch F. At the fuse opening, the energy stored in L 2 is switched into the circuit branch L load, Rload, and Radd through the spark gap switch S7. The load current is derived from the known resistance Radd and voltage measured on Radd. The Marx current is measured by a current transformer T. Fig. 2 shows a picture of the test bed.

B. Main elements of the test bed 1. Marx generator

The generator consists of six stages. In each of the stages, two IK–50/3 (50 kV, 3 µF) capacitors are connected in parallel. The charging resistors R1–R12 (34 Ω each) are wound by nichrome wire on the fiberglass tubes. The generator operates at the charging voltage of 20–40 kV. The generator is mounted on the acryl sheet on three insulators (polyethylene tubes). The return current conductor is made of a zinc-galvanized steel sheet (width 625 mm and thickness 1 mm). The overall dimensions of the generator are (2.5 × 1.4 × 1) m3. The output erected capacitance is 1 µF, the output voltage is 240 kV, and inductance of the Marx discharge circuit is about 2 µH.

FIG. 2. Top (a) and side view (b) of the test bed: 1–6—Marx generator stages; 7—body of the fuse; 8—load inductor; 9—load spark gap; and 10—intermediate storage inductor.

2. Inductors L2 and Lload

The inductors are wound on a fiberglass tube (diameter 100 mm and length 800 mm) by a copper wire with cross section of 24 mm2. A tube of diameter 100 mm with the wire is inserted into a fiberglass tube (external diameter of 130 mm). The space between the tubes is filled with epoxy compound. The inductor L 2 consists of 32 turns (L 2 = 16 µH, R = 7 mΩ). The inductor L load is wound by 20 turns (L load = 6.3 µH, Rload = 4.5 mΩ). Such a design has been implemented recently in our work11 and tested at magnetic field up to 12 T. Numerical simulation of magnetic fields and mechanical stresses has been also performed in Ref. 11. Here magnetic fields would be 2.8 T and 1.7 T in the inductors L 2 and L load, respectively, at maximum current of 50 kA. Mechanical stresses in copper and fiberglass here are well below elastic limits.

FIG. 1. Test bed schematic: 1—power supply; 2—triggering generator; R 1–R 12—charging resistors, F—fuse; L 2—inductive storage; L load—load inductance; R load—load resistance; R add—additional resistance; S1–S6—Marx generator spark gap switches; S7—load spark gap switch; and T —current transformer. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 84.237.1.92 On: Tue, 28 Jun

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fuse wires is placed into the tube through the open upper end. The high-voltage output of the Marx generator is also connected to the fuse here. 5. Current measurements

Current measurement in the discharge circuit of the Marx generator is made by a Pearson current monitor (model 1423: sensitivity 0.001 V/A +1%/−0%, maximum peak current 500 kA, droop rate 0.7% ms−1, useable rise time 0.3 µs, current time product 75 A × s). The transformer is installed into the circuit of the return current conductor from the low-voltage side of the Marx. The load current is derived from the voltage signal from the additional resistor Radd. In this voltage signal, there is a spike in the front pulse caused by the inductive component provided by the self-inductance of the resistor. If we use this signal to determine the current, then the spike appears at the current front. The end of this spike and transition to the exponential decay allow us to measure the current rise time. 6. Load spark gap switch FIG. 3. One nichrome resistor (a) and the 20 resistors block (b).

3. Additional resistor Radd

An additional resistor Radd is assembled as stacks of the resistors (Fig. 3) connected in parallel. The resistors are made from nichrome wire (diameter of 1 mm), wound on a vinyl tube. The nichrome wire is wound in two layers connected in parallel. To decrease the inductance, the direction of winding of the layers is opposite. The resistance and inductance of one resistor are 2 Ω and ∼0.5 µH, respectively. Three variants of resistor blocks were used in the experiments: a block consisting of 20 resistors (Radd = 0.098 Ω ); a block consisting of 14 resistors (Radd = 0.151 Ω); and a block consisting of seven resistors (Radd = 0.28 Ω). An additional resistor Radd is connected in series with a load inductor L load on the low-voltage side. The voltage signal from the additional resistor Radd is transmitted by two cables. The input of the first cable is connected to the potential side of the load resistor. The input of the second cable is connected to the grounded output of the resistor. The braids of both cables are connected at the input with a very low inductance conductor. Signals are transmitted by both cables to the active voltage dividers. The resistances of the dividers are equal to the wave impedance of the transmitting cables. At analysis, the divider signals are subtracted from each other, thus compensating for the contribution of the inductive voltage drop in the return conductor into the recorded load voltage.

A load spark gap switch is a gap between the two ball electrodes (diameter of 125 mm: Fig. 2 position 9). With the charging voltage of the Marx generator equal to 40 kV, the gap between the electrodes is equal to 100 mm. The air pressure in the switch is atmospheric. The breakdown voltage for the gap of 100 mm is 198 kV.

III. NUMERICAL SIMULATION OF THE GENERATOR A. Schematics

The electric circuit of the test bed is presented in Fig. 4. The main elements of the scheme are C1, L 1, S1—Marx generator; L 2, R—inductive storage; L f , S f —fuse opening switch; S2—load switch; L load, Rload—load parameters; and Radd—additional resistance in the load circuit. With the closing of the switch S1, the capacitive storage C1 = 1 µF is discharged and pumps the current I0 into the inductive storage L 2. With the electrical explosion of the fuse opening switch S f , its resistance increases sharply, thus providing generation of the high-voltage (HV) pulse. This HV pulse leads to the breakdown of the closing switch S2 and switching of the current to the branch L load, Rload, Radd. The circuit parameters will be calculated at output voltage of the generator of 240 kV for obtaining the required current pulse shape and amplitude. The current amplitude in the load is determined as the ratio of the intermediate storage and load ′ inductances: Iload = I0 · L 2/ (L 2 + L load). B. Estimation of the inductance L2

4. Body for the fuse opening switch

The body is made from a fiberglass tube with internal and external diameters of 115 and 130 mm, respectively, and length of 1500 mm (position 7 in Fig. 2). The necessary number of

At disconnection of the Marx generator circuit from the inductive storage-load contour by the fuse S f , the current decay in the load is determined as ′ Iload(t) = Iload · exp (−t/τ) ,

(1)


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FIG. 4. Electric circuit of the test bed: C 1, L 1, S1—Marx generator elements; L 2, R—inductive storage; L f , S f —fuse opening switch; S2—load switch; L load, R load—load parameters; and R add—additional resistance in the load circuit.

where τ = (L 2 + L load) / (R + Rload + Radd). The minimum inductance L 2, which is able to provide the time of the load current drop to the half-amplitude value of t = 125 µs, can be ′ estimated from Equation (1). At Iload(125 × 10−6)/Iload = 0.5: t/τ ≈ 0.69, τ ≈ 180 µs. At R1 ∼ 0.01 Ω and R2 ∼ 0.01 Ω, the inductance (L 2 + L load) should not be less than 20.5 µH. In the test bed, described above, L 2 + L load = 22.3 µH. The load current amplitude for this value of inductance is equal to 72% of the stored current at the time of closing of the switch S2. C. Calculation of damping time

The load current drops to the half-amplitude value at t 0.5/τ ≈ 0.69 at exponential decay low. The values of t 0.5 and τ were calculated for three values of the additional resistor Radd: 0.28, 0.15, and 0.098 Ω. Results are given in Table I. D. Parameters of the fuse opening switch

To obtain the current I ∼ 50 kA in a load L load ∼ 6 µH at the current rise time ∆t ∼ 10−6 s, the fuse opening switch voltage U ∼ L load ∆tI ∼ 3 × 105 V is required. In air at atmospheric pressure, the operating electric field of the fuse is less than 3 kV/cm. Therefore, the single fuse length l should be greater than 1 m. The fuse inductance can be estimated µ as the inductance of a single wire: L f = 2π0 l · ln 4ld − 1 . For the wire diameter d = 0.1–1 mm and length l = 1 m, the inductance L f = (1.5–2) µH. The  impedance of the Marxinductive storage circuit Z = (L 1 + L 2 + L f )/C1 is about 4.5 Ω, taking into account the fuse inductance. The shortcircuit current of the contour is equal to U0/Z = 53 kA.

TABLE I. Values of t 0.5 and τ at R add = 0.28, 0.15, and 0.098 Ω. R add, Ω 0.28 0.15 0.098

(R add + R + R load), Ω

τ, µs

t 0.5, µs

0.295 0.165 0.113

75.59 135.15 193.34

52.38 93.65 133.98

Operation of fuse opening switches depends on many parameters, namely, wire material,12 wire environment,13 voltage pulse, and so on. Plenty of empirical and MHD models have been developed for electro-explosive fuse opening switches simulation.14–17 The parameters of the electroexplosive fuse opening switch, which are required to extract the energy from the Marx generator into the inductive storage, were estimated using the empirical theory of similarity.16,17 Before explosion, the fuse characteristics depend on two dimensional parameters, l (Ω−1 mm−1), n · d2 · Z C1 · U 2 ε = 2 4 0 (J/(mm4 Ω)), n ·d ·Z λ=

(2) (3)

where n is the number of parallel wires in the fuse, d (mm), l (mm) are the diameter and length of the wire, respectively, C1, U0 are, respectively, the capacitance and the output voltage of the Marx generator, and Z is the generator impedance. Parameters (2) and (3) determine the normalized value of the current amplitude in the contour, ym = Im

α Z = A · 10−6 · ε · λ 1/3 , U0

(4)

where constants A and α depend on the wire material and have been derived in other experiments. For copper wires, A = 0.78 and α = −0.25. Fig. 5(a) demonstrates the dependence ym (d) for a single wire of the length l = 1 m and 1.5 m; Fig. 5(b) shows the same curves for two wires of the length l = 1 and 1.5 m. It may be seen from these curves that the current amplitude in the contour weakly depends on the fuse length. To obtain the current at the level of 80% of the short-circuit current amplitude U0/Z, it is necessary to use one copper wire of diameter d ≈ 0.5 mm, or two copper wires of the diameter d ≈ 0.35 mm, in the fuse. The time of the current rise to maximum is determined by the dimensional parameters (2) and (3), β  (5) t m = B · 10−6 · ε · λ 1/3 · C(L 1 + L 2 + L f ).


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FIG. 5. Normalized current amplitude in the contour vs. wire diameter at n = 1 (a); the same at n = 2 (b).

From Equation (5), we obtain that for the fuse with n = 1, d = 0.5 mm, l = 1500 mm and n = 2, d = 0.35 mm, l = 1500 mm; the time of the current rise t m is approximately 6 µs.

amplitude on the load increases up to 440 kV, while the time of the current switching into the load decreases to 0.7 µs.

IV. EXPERIMENTAL RESULTS E. Calculation results

1D MHD calculations of the electric explosion for two variants of the fuse (n = 1, d = 0.5 mm, l = 1500 mm) and (n = 2, d = 0.35 mm, l = 1500 mm) were carried out in order to calculate more accurately the circuit current and load pulse parameters for the electric circuit of Fig. 4. The inductance of the fuse is L f = 2.5 µH for a single wire and L f = 1.3 µH for two wires. In these calculations, the load switch, S2 breaks down at a voltage of about 270 kV. Calculations reveal that for the single wire fuse (n = 1, d = 0.5 mm, l = 1500 mm), the current in the inductive storage L 2 increases to 44 kA, which is 85% of the amplitude of the short-circuit current. At the moment of S2 closing, the inductive storage current is 39 kA. A current of 28 kA is switched into the load in 0.9 µs. The load voltage is about 330 kV. Calculation results with the second variant of the fuse (n = 2, d = 0.35 mm, l = 1500 mm) are shown in Fig. 6. In this case, the total cross section of the wires has changed slightly from 0.196 to 0.192 mm2. The current amplitudes are approximately the same (both in the inductive storage and load). For two parallel wires of a smaller diameter, the voltage

A. Radd = 0.098 Ω, Lload = 6.3 µH

1. Experimental conditions: charging voltage of 40 kV, one copper conductor of diameter 0.5 mm and length 1450 mm in the fuse. The block of 20 resistors is connected to the lower end of the load inductor. Voltage at the resistors block (Radd) is acquired. The load current is calculated. Fig. 7 presents the current waveforms in the Marx and calculated current in the load. 2. The experimental conditions are the same as in 1, except that in the fuse, there are two copper conductors of diameter 0.35 mm and length 1450 mm. Experimental results of regimes A.1–A.2 are summarized in Table II. Here, we have the following: I L 2(max) is the maximum current value in L 2; I L 2(t start) is the current value in L 2 at the start of switching; Iload(max) is the load current amplitude; t start is the time of switching start; Iload(max)/I L 2(t start) is the load current vs. the current in L 2 at the moment of switching; t exp(0.5·Iload) is the time of the load current decay to the level

FIG. 6. Calculation results of the electric circuit with two copper wires of diameter 0.35 mm and length 1500 mm in the fuse. (a) Currents in the inductive storage I L2 and load Iload, and short-circuit current I0; (b) voltage on the load switch US2 and load Uload. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 84.237.1.92 On: Tue, 28 Jun

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FIG. 7. Generator and load currents for regime A.1 in the long (a) and short (b) time-base. TABLE II. Experimental results at R add = 0.098 Ω, L load = 6.3 µH.

Regime A.1 A.2

I L 2(max), kA

I L 2(t start), kA

Iload(max), kA

t start, µs

Iload(max)/ I L 2(t start)

t exp(0.5 · Iload), µs

t calc(0.5 · Iload), µs

tf, µs

39 41

32 33

22 24

6.95 6.95

0.687 0.72

130 125

134 134

0.9 0.85

FIG. 8. Generator and load currents for regime B.1 in the long (a) and short (b) time-base.

of 0.5 of the amplitude; t calc(0.5·Iload) is the time of the load current decay to the level of 0.5 of the amplitude calculated from the values of L 2, L load, Rload; and finally, t f is the rising time of the load current pulse. The appearance of the spike for the rising edge was discussed earlier.

2. The experimental conditions are the same as in regime A.2, except for the load of 0.28 Ω. Fig. 9 presents the current waveforms in the discharge circuit of the generator and calculated current in the load. Experimental results of regimes C.1–C.2 are summarized in Table IV.

B. Radd = 0.15 Ω, Lload = 6.3 µH

1. The experimental conditions are the same as in A.1, except for Radd of 0.15 Ω, consisting of 14 resistors. Fig. 8 presents the current waveforms in the Marx and calculated current in the load. 2. The experimental conditions are the same in A.2 except for Radd of 0.15 Ω. Experimental results of regimes B.1–B.2 are summarized in Table III. C. Radd = 0.28 Ω, Lload = 6.3 µH

1. The experimental conditions are the same as in regime A.1, except for the load of 0.28 Ω.

D. Discussion of experimental results

In the experiments, the current value in L 2 is 39–41 kA. In Part III, this value was estimated as 44 kA. At the moment of the load spark gap switch closing, t = 6.7–6.9 µs (an estimation is 6.5 µs), the current value in L 2 is 31–32 kA (an estimation is 39 kA). The value of the current switched into the load is 22–23 kA at the estimation value of 28 kA. The ratio of the value of the switched current to the current in L 2 at the moment of switching changes in the limits of 0.74–0.67 for the calculated value of 0.72. Any discrepancy in this parameter is likely related to the accuracy of the MHD simulation. The decay time of the load current pulse is in good agreement with the calculated one. Adjusting the duration of the current decay (regimes C and B) down to 35 and 70 µs is


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TABLE III. Experimental results at R add = 0.15 Ω, L load = 6.3 µH. IL2 I L 2 (tstart), Iload (max), t start, Iload t exp (0.5 · Iload), t calc (0.5 · Iload), Regime (max), kA kA kA µs (max)/I L 1(t start) µs µs B.1 B.2

39 41

31 32

23 23.2

6.7 7

0.74 0.72

85 86

94 94

tf, µs 1.07 0.93

FIG. 9. Generator and load currents for regime 3.3.2 in the long (a) and short (b) time-base. TABLE IV. Experimental results at R add of 0.28 Ω, L load = 6.3 µH. IL2 I L 2 (tstart), Iload (max), t start, Iload t exp (0.5 · Iload), t calc (0.5 · Iload), Regime (max), kA kA kA µs (max)/I L 2(t start) µs µs C.1 C.2

39 41

32 32

22 23

6.8 6.9

0.687 0.718

54.3 54.1

52 52

tf, µs 0.87 0.78

possible by increasing the resistance in the load circuit from 0.28 to 0.44 Ω and from 0.15 to 0.22 Ω, respectively. Our results confirm the possibility of obtaining current pulses in the load of 6.3 µH with the rise time of ≤1.2 µs, and the required time of current decay down to the half-amplitude level. The amplitude of the switched current is limited by the test bed parameters.

V. DESIGN OF THE GENERATOR ON 50 KA A. Generator design

The Marx generator can be made of HAEFELY capacitors (capacitance 3.9 µF). When two capacitors are connected in parallel in a stage, and five stages are connected in series, the output erected capacitance of the generator equals 1.56 µF. At the charging voltage of the capacitors of 60–65 kV, the output voltage is 300–325 kV and the stored energy is 70–82 kJ. Fig. 10 shows one variant of the generator design. Marx spark-gap switches can be multichannel, multigap, or two-, three-electrodes with adjustable pressure in the switch volume. Charging resistors can be made of nichrome with glass-epoxy insulation; ceramic resistors made by the Company HVR can be used as well. The generator can be mounted on the insulating platform placed on the supporting insulators. The platform can assembled in the truck, providing the possibility of easy transport. During transporting, elements 7–10 are fixed into the car body. The truck body of length 5 m is sufficient to transport the entire installation.

FIG. 10. Location of generator elements: 1—platform of the truck body; 2—Marx generator; 3—insulating platform; 4—supporting insulators; 5—charging device, grounding connection; 6—conductors of fuse; 7—intermediate inductive storage; 8—electrodes of load spark-gap switch; 9—output insulator; and 10—return current conductor.

B. Numerical simulation of operation regimes

The equivalent circuit of the generator is identical to that in Fig. 4. The difference is only in the value of the equivalent capacitance of Marx generator C1 = 1.56 µF (instead of 1 µF) and in the output Marx voltage. When the charging voltage


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of the generator stages is equal to 60 kV, the initial voltage at C1 is 300 kV. When the charging voltage of the generator stages is equal to 65 kV, the initial voltage at C1 is 325 kV. The wave impedance of the Marx discharge circuit will be 3.5 Ω. The amplitude of the short-circuit current is 85–93 kA. The factor of the current switching from the inductive storage into the load remained at the same level of 0.72 at the moment of closing of the switch S2. An estimation of the parameters of the electrically explosive fuse opening switch is made from the condition of providing the circuit current at the level of 80% of the short-circuit current. Using Equation (4), we can see that at the charging voltage of 60 kV, it is necessary to use two copper wires of diameter d ≈ 0.45 mm in the fuse; and at the charging voltage of 65 kV, it is necessary to use two copper wires of diameter d ≈ 0.5 mm. The calculation of the electric circuit of the generator self-consistently with the 1D MHD calculation of the electric explosion of conductors for two variants was carried out: (1) the charging voltage is 60 kV; the fuse parameters are n = 2, d = 0.45 mm, and l = 1500 mm; (2) the charging voltage is 65 kV; the fuse parameters are n = 2, d = 0.5 mm, and l = 1500 mm. At the charging voltage of 60 kV, the current in the inductive storage L 2 is 72 kA, which is 85% of the amplitude of the short-circuit current. The load switch S2 operates at a voltage of about 300 kV. At the moment of the switch S2 closing, the current in the storage is 67 kA. A current of 48 kA is switched into the load over ∼1 µs. The load voltage exceeds 600 kV. An increase of the charging voltage up to 65 kV results in an increase of the current in inductive storage L 2 of up to 82 kA. At the moment of the switch S2 closing, the current in the storage is 74 kA. A current of 54 kA is switched into the load over 1 µs. The voltage amplitude at the load is higher than 600 kV. Figure 11 shows simulated current pulses in the load for three regimes with different velocities of decay using additional resistances Radd = 0.01, 0.11, and 0.33 Ω. It may

FIG. 11. Simulated currents in the inductive storage I L 2 and load Iload at insertion of additional resistances R add = 0.01, 0.11, and 0.33 Ω into the load circuit. Charging voltage is 65 kV.

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be seen from Fig. 11 that it is possible to obtain the current decay time to the half-amplitude values t = 35 µs, 70 µs, and 125 µs. Our results substantiate the choice of the generator parameters for the realization of the load current with an amplitude of 50 kA of the specified current waveform (the rise time is about 1 µs; the decay time to the level of half-amplitude is 35 µ, 70 µ, or 125 µs).

VI. CONCLUSIONS

The possibility to calculate the parameters of the pulses obtained from the generator with intermediate inductive energy storage and electrically explosive fuse opening switch has been demonstrated. The possibility of obtaining current pulses with the required waveform on the active-inductive load has also been shown. An updated design of the generator intended to obtain the load current with an amplitude of 50 kA has been proposed, and different operational regimes were simulated for this generator. ACKNOWLEDGMENTS

We would like to thank ITHPP France for financial support under Contract No. ITHPP/HCEI/15-C04. We also would like to thank Mr. Andrey Chertov for providing us with the 1D MHD simulation code of the wire electric explosion. 1Yu.

P. Raizer, Gas Discharge Physics (Nauka, Moscow, 1992), p. 461. Hasse and J. Wiesinger, Handbuch fur Blitzschutz und Erdung (Pflaum Verlag, Munchen, 1993). 3IEEE Std, 4-1995: IEEE Standard Techniques for High-Voltage Testing (IEEE, 1995), pp. 1–135 E-ISBN: 978-0-7381-0658-8. 4V. A. Rakov and F. Rachidi, IEEE Trans. Electromagn. Compat. 51, 428 (2009). 5Y. Chen, H. Wan, and X. Wang, J. Electrostat. 71, 1020 (2013). 6A. S. Boriskin, N. I. Gusev, V. A. Zolotov, V. I. Zolotovskh, A. S. Kravchenko, and A. S. Yuryzhev, Electr. Technol. 1995(4), 19 (1995). 7V. D. Selemir, A. S. Kravchenko, V. A. Zolotov, Yu.V. Vilkov, A. S. Yurizhev, M. M. Saitkulov, O. M. Tatsenko, A. N. Moiseenko, I. M. Markevtsev, V. F. Bukharov, and S. V. Bulychev, in Proceedings of 13th IEEE Pulsed Power Conference Las Vegas, Nevada, 2001 (IEEE, 2001), p. 928. 8T. Wen, Q. Zhang, L. Zhang, J. Zhao, X. Liu, X. Li, C. Guo, H. You, W. Chen, Y. Yin, and W. Shi, Rev. Sci. Instrum. 87, 035103 (2016). 9K. Senthil, S. Mitra, A. Roy, A. Sharma, and D. P. Chakravarthy, Rev. Sci. Instrum. 83, 054703 (2012). 10B. M. Novac, I. R. Smith, P. Senior, M. Parker, G. Louverdis, L. Pecastaing, A. S. De Ferron, and S. Souakri, IEEE Trans. Plasma Sci. 42, 2919 (2014). 11A. V. Kharlov, B. M. Kovalchuk, E. V. Kumpyak, G. V. Smorudov, and N. V. Tsoy, Laser Part. Beams 32, 471–476 (2014). 12A. W. DeSilva and J. D. Katsouros, Phys. Rev. E 57, 5945 (1998). 13J. Stephens, W. Mischke, and A. Neuber, IEEE Trans. Plasma Sci. 40, 2517 (2012). 14I. R. Lindemuth, J. H. Brownell, A. E. Greene, G. H. Nickel, T. A. Oliphant, and D. L. Weiss, J. Appl. Phys. 57, 4447 (1985). 15J. Stephens and A. Neuber, Phys. Rev. E 86, 066409 (2012). 16A. Yu and A. V. Kotov, “Luchinsky power amplification of a capacitive energy storage by the current opening switch based on the electrically explosive wires,” in Physics and Technology of High-Power Pulsed Systems, edited by E. P. Velikhov (Energoatomizdat, Moscow, 1987), p. 189. 17V. S. Sedoi, G. A. Mesyats, V. I. Oreshkin, V. V. Valevich, and L. I. Chemezova, IEEE Trans. Plasma Sci. 27, 845 (1999). 2P.
