Multiple-switch pulsed power generation based on a transmission line transformer

Citation for published version (APA): Liu, Z. (2008). Multiple-switch pulsed power generation based on a transmission line transformer. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR632557

DOI: 10.6100/IR632557

Document status and date: Published: 01/01/2008

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Multiple-switch pulsed power generation based on a transmission line transformer

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op dinsdag 22 januari 2008 om 16.00 uur

door

Zhen Liu

geboren te Xiang Cheng, China

Dit proefschrift is goedgekeurd door de promotoren:

prof.dr.ir. J.H. Blom en prof.dr. M.J. van der Wiel

Copromotor: dr.ing. A.J.M. Pemen

This work is carried out with the financial support from the Dutch IOP-EMVT program (Innovatiegerichte Onderzoeksprogramma’s – Electromagnetische Vermogens Techniek).

CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

Liu, Zhen

Multiple-switch pulsed power generation based on a transmission line transformer / by Zhen Liu. – Eindhoven : Technische Universiteit Eindhoven, 2008. Proefschrift. – ISBN 978-90-386-1764-0 NUR 959

Trefw.: hoogspanningstechniek / hoogspanningspulsen / elektrische doorslag / transformatorschakelingen / transmissielijnen. Subject headings: high-voltage techniques / pulsed power supplies / spark gaps / pulse transformers / transmission lines.

…To my parents and my wife

i Table of Contents

Summary...... iii Chapter 1 Introduction...... 1 1.1 Background ...... 1 1.2 State-of-the-art of pulsed power...... 2 1.2.1 Switching devices...... 3 1.2.2 Traditional multiple-switch pulsed power circuit...... 5 1.3 Objective of this dissertation...... 8 References...... 9 Chapter 2 Transmission line transformer based multiple-switch technology ...... 15 2.1 Principle of the multiple-switch technology ...... 16 2.2 Experimental studies ...... 20 2.2.1 Characteristics of the synchronization and the output...... 21 2.2.2 Other observations...... 24 2.3 Variations for square pulse generation...... 30 2.4 Summary...... 32 References...... 32 Chapter 3 Multiple-switch Blumlein generator...... 35 3.1 Introduction...... 36 3.2 Single-switch (traditional) Blumlein generator...... 36 3.3 Novel multiple-switch Blumlein generator ...... 37 3.4 Experimental studies ...... 45 3.4.1 Experiments on a resistive load...... 45 3.4.2 Experiments on a bipolar corona reactor...... 48 3.5 Summary...... 52 References...... 52 Chapter 4 Four-switch pilot setup ...... 53 4.1 Introduction...... 54 4.2 The four-switch pilot setup ...... 54 4.3 Experiments with resistive loads...... 56 4.3.1 Four independent loads ...... 56 4.3.2 Parallel output configuration...... 57 4.3.3 Series output configuration ...... 59 4.3.4 Analysis...... 60 4.4 Demonstration of the pilot setup on a corona-in-water reactor ...... 63 4.4.1 Discharging in deionized water...... 64 4.4.2 Discharging in tap water ...... 66 4.4.3 The dye degradation...... 68 4.5 Conclusions...... 69 References...... 69 Chapter 5 Ten-switch prototype system...... 71 5.1 Overview of the system...... 72 5.2 Resonant charging system...... 74 5.3 Transformer...... 75 5.3.1 Introduction...... 75 5.3.2 Effects of the coupling coefficient k ...... 76 5.3.3 Design and construction...... 78

ii Table of Contents

5.3.4 Testing of the transformer ...... 82 5.4 Ten-switch system...... 86 5.4.1 Charging inductors ...... 86 5.4.2 Spark gap switches...... 86 5.4.3 The TLT ...... 87 5.4.4 Integration of components into one compact unit ...... 92 5.4.5 The load...... 92 5.5 Characteristics of the system...... 94 5.5.1 Repetitive operation by the LCR...... 94 5.5.2 Output characteristics...... 97 5.5.3 The energy conversion efficiency ...... 102 5.6 Summary...... 104 References...... 105 Chapter 6 Exploration of using semiconductor switches and other … ...... 107 6.1 Synchronization of multiple semiconductor switches...... 108 6.1.1 Thyristors ...... 108 6.1.2 MOSFET/IGBT...... 113 6.2 Other multiple-switch circuit topologies...... 114 6.2.1 Inductive adder...... 114 6.2.2 Magnetically coupled multiple-switch circuits ...... 116 References...... 120 Chapter 7 Conclusions...... 121 7.1 Conclusions...... 121 7.1.1 TLT based multiple-switch circuit technology...... 121 7.1.2 Multiple-switch Blumlein generator...... 123 7.1.3 Repetitive resonant charging system...... 123 7.2 Outlook ...... 123 References...... 124 Appendix A. Coupled resonant circuit...... 127 A.I Complete energy transfer...... 128 A.II Effect of the coupling coefficient k on the first peak value of V H ...... 131 A.III Efficient resonant charging ...... 133 Appendix B. Repetitive resonant charging ...... 135 Appendix C. Calibration of current probe ...... 137 Appendix D. Schematic diagram of high-pressure spark gap switches...... 141 Acknowledgements...... 143 Curriculum Vitae ...... 145

Summary

Repetitive pulsed power techniques have enormous potential for a wide range of applications, such as gas and water processing and sterilization, intense short-wavelength UV sources, high-power acoustics and nanoparticle processing. The main difficulty for industrial applications of pulsed power technologies arises from simultaneous requirements on power rating, energy conversion efficiency, lifetime and cost. Significant improvements are especially possible in the field of repetitive ultra-short high-voltage and large-current spark gap switches.

This dissertation investigates a novel multiple-switch pulsed power technology. The basic idea is that the heavy switching duty is shared by multiple switches. The multiple switches are interconnected via a transmission line transformer (TLT), in such a way that all switches can be synchronized automatically and no special external synchronization trigger circuit is required. In comparison with a single-switch circuit, the switching duty or switching current for each switch is reduced by a factor n (where n is the number of switches). As a result, the switch lifetime can be expected to improve significantly. It can produce either exponential or square pulses, with various voltage and current gains and with a high degree of freedom in choosing output impedances. The proposed multiple- switch topology can also be applied in a Blumlein configuration.

To gain insight into the principle and characteristics of this technology, an equivalent circuit model was developed and an experimental setup with two spark gap switches and a two-stage TLT was constructed. It was found that the closing of the first switch will overcharge the other switch, which subsequently forces it to close. During this process, the discharging of capacitors is prevented due to the high secondary mode impedance of the TLT. When the closing process is finished and all switches are closed, the energy storage capacitors discharge simultaneously into the load(s) via the TLT. Now the TLT behaves as a current balance transformer and the switching currents are determined by the characteristic impedance of the TLT. In terms of the currents, the equivalent circuit has good agreement with the experimental results. An interesting feature of this topology is that the risetime of the output pulse can be determined by the switch that closes lastly. This was verified by combining a fast multiple-gap switch with a conventionally triggered spark gap switch; the output current risetime was improved by almost a factor of 2 (from 21 ns to 11 ns).

As for the Blumlein configuration, an equivalent model was also proposed. The model was verified by experiments on a two-switch Blumlein generator with a resistive load and a more complex load (i.e. a plasma reactor). It was observed that the synchronization process of the multiple switches is similar to that of the multiple-switch TLT circuit and is independent of the type of load. After all the switches have closed, the charged lines at the

switch side are shorted, and then the pulse is generated in the same way as for a traditional (single-switch) Blumlein generator. Moreover, the experimental results fit the model.

For the generation of large pulsed power (500 MW-1 GW) with a short pulse (~50 ns) using this technology, the input impedance of the TLT must be low. There are two approaches to realize low input impedance, namely (i) using a TLT with multiple coaxial cables per stage and a few switches, and (ii) using a TLT with one single coaxial cable per stage. Both of them are investigated. A pilot setup with four spark gap switches and a four-stage TLT (four parallel coaxial cables per stage) was developed to study the first approach. It was evaluated with different output configurations (with independent loads, a parallel output configuration or a series output configuration). The application of this setup to generate a pulsed corona discharge in water was demonstrated. It was observed that the multiple switches can be synchronized for each of the output configurations. However, the peak output power is significantly limited by the low damping coefficient ξ of the input loop of the TLT. To generate large pulsed power effectively, the damping coefficient must be improved significantly.

A ten-switch prototype system was developed according to the second approach. Compared to the four-switch pilot setup, several improvements were made: (i) the setup was much more compact to minimize stray inductance, (ii) one coaxial cable per stage was used instead of four parallel cables, and (iii) the number of switches was increased to ten. With these improvements, a high damping coefficient ξ of the input loop of the TLT and a low input impedance of the TLT were obtained. As expected, efficient large pulsed power generation with a fast rise-time and a short pulse was realized on the ten-switch prototype system. Ten switches can be synchronized to within about 10ns. The system produces a pulse with a rise-time of about 10 ns and a width of about 55 ns. And it has good reproducibility. An output power of more than 800 MW was obtained. The energy conversion efficiency varies between 93% and 98%.

In addition, to charge the prototype system, a high-ratio pulse transformer with a magnetic core was developed. An equivalent circuit model was proposed to evaluate the swing of the flux density in the core. It was observed that the minimal required volume of magnetic material to keep the core unsaturated depends on the coupling coefficient. The transformer was developed on the basis of this observation. The core is made from 68 glued ferrite blocks. There are 17 air gaps along the flux path due to the inevitable joints between the ferrite blocks, and the total gap distance is about 0.67 mm. The primary and secondary windings are 16 turns and 1280 turns respectively, and the ratio actually obtained is about 1:75.4. A coupling coefficient of 99.6% was obtained. Experimental results are in good agreement with the model, and the glued ferrite core works well. Using this transformer, the high-voltage capacitors can be charged to more than 70 kV from a capacitor with an initial charging voltage of about 965 V. With 26.9 J energy transfer, the increased flux density inside the core was about 0.23 T, which is below the usable flux density swing (0.35 T-0.5 T). The energy transfer efficiency from the primary to the secondary was around 92%.

Finally, the use of semiconductor switches in the multiple-switch circuits was explored. The application of thyristors has been successfully verified on a small-scale testing setup. A circuit topology for using MOSFET/IGBT was proposed. Also other multiple-switch circuit topologies (i.e. multiple-switch inductive adder and magnetic-coupled multiple- switch technique) are discussed as well.

Chapter 1 Introduction

1.1 Background

Pulsed power is a technology that accumulates energy over a relatively long period and releases it into a load within a short time interval, thus generating high instantaneous power. It was first developed during the Second World War for use in radar. From that time on, the defense-related applications were one of the key driving forces behind pulsed power technology [Lev(1992)], primarily in connection with nuclear weapons simulation, applications of high-power microwave sources, high-power laser sources, electromagnetic guns, etc. The pulsed power systems for these applications are typically large machines and are operated in a single-shot mode or at a low repetition rate. The performance of the pulsed power system is the most important issue, while the cost and lifetime are of secondary concern [Kri( 1993 )].

Over the last two decades, more and more non-military applications of pulsed power technology have been studied. More than one hundred possible applications can now be listed [Lev( 1992 ), Kri( 1993 ), and Yan( 2001 )]. In particular, repetitive pulsed power techniques have enormous potential in areas such as gas and water processing [Vel( 2000 )], sterilization [Kim( 2004 )], intense short-wavelength UV sources [Kie( 2006 )], high-power acoustics [Hee( 2004 )], nanoparticle processing [Ost( 2005 )], surface treatment, etc. However, the repetitive pulsed power supply is still a barrier for large-scale industrial applications. The technical difficulty arises from simultaneous requirements on power rating, energy conversion efficiency, lifetime, and cost [Hee( 2004 )] . The investigations in this work will contribute to realize a breakthrough in large pulsed power generation for industrial applications.

In more specific terms, the typical ranges of parameters involved in pulsed power technology are summarized in Table 1.1 [Pai( 1995)]. It is clear that the encountered properties have an enormous span, ranging for example from megawatt peak powers to terawatt levels. Generally, the very high peak power levels are obtained for longer pulse durations and at single shot or very low repetition rates. This can be seen in Figure 1.1, where the solid line represents peak power levels versus pulse duration for state-of-the-art pulsed power systems (situation around 2000). For pulses in the nanosecond range, typical peak powers are much lower – far below 100 MW.

2 Chapter1

Table 1.1 Ranges of parameters involved in pulsed power technology

This nanosecond range is the regime where we want to focus our research. In summary, our targets are: much higher peak power at much shorter pulse durations and at much higher repetition rates, as compared to current capabilities. To be more specific, our challenge is to reach about 1 GW of peak power within a pulse width of less than 100 ns and at a repetition rate of >100 pps. The typical ranges focused on in our research are also shown in Table 1.1. Figure 1.1 presents our achievement in relation to our previous milestones (1994, 2001) [Yan( 2001 )].

Fig. 1.1 Visualization of the achievement as described in this thesis (TU/e 2007) as compared to previous milestones obtained at TU/e and the state-of-the-art pulsed power technology (as of 2000)

1.2 State-of-the-art of pulsed power

Capacitive (energy stored in a capacitor) and inductive (energy stored in an inductor) systems are often used for the repetitive pulsed power systems with medium energy per pulse. Though the energy density of an inductive system can be 25 times higher compared

Introduction 3 with a capacitive system, capacitive systems are more frequently adopted since they are much easier to realize and require simpler closing switches instead of highly complex opening switches [Pem( 2003 )]. The pulsed power systems discussed in this thesis utilize capacitive energy storage.

1.2.1 Switching devices

The most critical component in repetitive pulsed power systems is the switch. It plays an important role in the performance of a system, affecting factors such as rise-time, efficiency, repetition rate, lifetime, etc. Systems with capacitive energy storage require closing switches such as: (i) magnetic switches, (ii) semiconductor switches, (iii) spark gap switches.

(1) Magnetic switches are saturable inductors that utilize the nonlinear magnetization of magnetic material, especially the saturation. When the magnetic material used in the switch is unsaturated, the magnetic switch has a high impedance which represents the “off state.” When the core becomes saturated, it has a much lower (typically a factor µr lower) impedance which is the “on state.” Magnetic switches are robust and can be used for high repetition rates (several kHz) [Jia( 2002a )]. A long lifetime can also be realized (>10 10 shots) [Har( 1990 )]. They are usually used in combination with slower semiconductor switches [Ber( 1992 ), Oh( 2002 ), Jia( 2002a ), Rim( 2005 )] or thyratrons [Oh( 1997 )], where the magnetic switch is used to compress the pulse to much shorter pulse widths. Typically, the energy conversion efficiency of magnetic switches is low (i.e. around 60-80%).

(2) Semiconductor switches used in pulsed power systems include thyristors, MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistor), and IGBTs (Insulated Gate Bipolar Transistor). Thyristors can hold a high voltage in excess of several kV and carry a large current (kA). However, the switching time is slow (on the order of µs), and thyristors are often used for microsecond pulse generation [Ren( 1997 ), Yan( 2004 ), Gli( 2004 )]. Compared with thyristors, MOSFETs and IGBTs are much faster devices, and their switching times are typically about 20 ns and 200 ns [Hic( 2001 )] respectively. Generally IGBTs are more efficient and have a larger power capacity (up to multiple kV and kA) [And( 2006 )]. Many pulsed power circuits based on IGBTs are available [Gau( 1998 ), Gau( 2001 ), Cas( 2002 ), Bae( 2005 )]. MOSFETs are limited to around 1 kV and 100 A [And( 2006 )]. So, MOSFETS are generally only used when high switching speed (~10ns) or high repetition rate (hundreds of kHz or even MHz) [Wat( 2001 ), Jia( 2002b ), Kot( 2004 )] is needed. The main advantages of semiconductor switches are their long lifetime and high repetition rate. However, the main problems are: (i) their limited power capacity and (ii) the high cost of devices for large-scale industrial applications.

(3) Spark gap switches are widely used in pulsed power systems. In comparison with other switches, the main advantages of spark gap switches are a high hold-off voltage, large conducting current, high energy efficiency, low cost, as shown in Table 1.2.

4 Chapter1

Table 1.2 Comparison of different switches

The switching speed and the spark resistance of spark gap switches depend on many factors such as voltage, current, gap distance, gas species, pressure, etc. [Kus( 1985 ), Sor( 1977 ), Car( 1979 ), Ist( 2005 ), Vla( 1972 )]. When they are used in air, a typical risetime of 20-30 ns can be realized [Liu( 2005 ), Liu( 2006a )]. Very fast switching, with switching times on the order of several ns or less than 1 ns, can be obtained when pressured gas [Bow( 1994 ), Bro( 1994 ), Byk( 2005 )], water [Xia( 2002 )], or a gas with a light molecular weight (e.g. H 2) [Kus( 1985 )] is used as switching medium or when multiple gaps are adopted [Mes( 2005 ), Liu( 2006b )]. When spark gap switches are used in a photoconductive mode, where the gap is fully ionized by a high-power femtosecond laser instantaneously [Hen( 2006 ), Kei( 1996 ), Dav( 2000 )], an extremely fast speed (on the order of ps) and very low jitter (<20 ps) can be obtained. When spark gap switches become fully conductive, their spark resistance is very low (on the order of 0.1-0.2 Ohm [Kus( 1985 ), Hus( 1998)] ). With fast switching and a low spark resistance, the spark gap switch can have a very high energy efficiency (>95%).

The repetition rate of spark gap switches depends on the recovery time of the switching medium. For unblown spark gap switches, the repetition rate is typically less than 100 pps (pulses per second) for most gases such as air, nitrogen, argon, oxygen, and SF 6 [Mor( 1991 )]. When the spark gaps are flushed with a forced gas flow [Fal( 1979 ), Yan (2003 ), Win( 2005 )], or a water flow [Xia( 2003 ), Xia( 2004 )], or are filled with pressurized hydrogen [Mor( 1991 ), Gro( 1992 )], much higher repetition rates (1-3 kHz) can be obtained. By using pressured hydrogen (70 bar) and triggering the spark gap switch below its self- breakdown voltage (50%), 100 µs recovery time (corresponding to 10 kHz) was demonstrated on a two-pulse system [Mor( 1991 )].

As shown in Table 1.2, the main drawback of spark gap switches is their short lifetime. This is affected by several factors such as the material of the electrodes, shape of the electrodes, voltage and current level and duration, electrode erosion. However, the main

Introduction 5 factor for the limited lifetime is the erosion of electrodes. After a number of shots, the erosion will reach a level at which the spark gap becomes unstable and difficult to trigger. Solutions to increase the lifetime of a spark gap switch are to maximize the allowable erosion volume of electrode material or to minimize the erosion rate. The first can be realized by using electrodes with a large volume, success with which is described in [Win( 2005 )]. The latter can be realized by choosing a good electrode material or by reducing the switching duty. However, the effect of the electrode material is not so significant that major improvements can be expected. Based on the following literature [Dic( 1993 ), Don( 1989 ), Leh( 1989 )], the erosion rate was observed to be a nonlinear function of the transferred charge per shot (i.e. switching current). When the transferred charge per shot is reduced by a factor n, the erosion rate can be reduced by a factor in excess of n 2. Thus, sharing the heavy switching duty by multiple switches is an effective way to significantly increase the lifetime of spark gap switches.

From the above discussions, one can see that the spark gap switch is superior to other switches for efficient large pulsed power generation with a short pulse width and a fast speed.

1.2.2 Traditional multiple-switch pulsed power circuit

For the generation of very high pulsed power ratings, multiple-switch based circuit topologies are normally used to produce high-voltage or large-current pulse and/or their combination. When multiple switches are used in series, large pulsed-power generation is realized by producing a higher voltage pulse. On the other hand, when the multiple switches are used in parallel, large pulsed power generation is realized by producing a large current pulse. Typical conventional multiple-switch circuit topologies are listed below.

(1) Hard stack Load Load

Fig. 1.2 Hard stack of multiple switches

A simple way to utilize multiple switches is to directly stack them in series or in parallel, as shown in Figure 1.2. Within this dissertation, we call these configurations a “hard stack.” Obviously, critical issues in a hard stack configuration are how to synchronize the individual devices within a short time interval and how to get the voltage

6 Chapter1 or current balance among individual devices. Failure of the switches can be easily caused by an overvoltage or overcurrent in individual devices due to poor switch timing, especially when semiconductor switches are used. Normally, careful selection of switching devices with similar specifications is required. Also, the use of highly- simultaneous, sufficient drive signals or timing-adjustable trigger signals is required.

(2) Marx generator

Fig. 1.3 Schematic diagram of a Marx generator with three switches

A widely used multiple-switch topology is the Marx generator (Figure 1.3), as proposed by Marx in 1924, for high-voltage pulse generation [Mar( 1952 )]. Capacitors are initially charged in parallel and are then discharged in series via multiple spark gap switches, thus achieving voltage multiplication. The main advantage of this generator is that the multiple spark gap switches will be synchronized automatically. The closing of the first switch leads to an overvoltage across the other switches that are not yet closed. Subsequently, this overvoltage forces them to close. During the closing process of the spark gap switches, the discharging of capacitors is prevented by the large impedance of the charging resistors. The Marx generator is used extensively in pulsed power applications, and many different Marx based systems have been developed, such as large X-ray machines (e.g. the PBFA-Z at Sandia National Labs [Spi(1997 )] and the MAGPIE at Imperial College, London [Mit( 1998 )]), PFN (pulse-forming network) generators [Wan( 1999 ), Tur( 1998 ), Mac( 1996 )] , high repetition rate solid-state setups [Red( 2005 )].

(3) LC generator

Another multiple-switch topology is the classical LC generator (Figure 1.4 (a)), as proposed by Fitch and Howell in 1964 [Fit( 1964 )]. Initially, the capacitors are charged to a voltage V0, where the various capacitors have different polarities as shown in Fig. 1.4. After charging, the switches are closed simultaneously, and after half an LC oscillation cycle, the voltages on the capacitors with even numbers are fully reversed. The voltage on an open output will now be NV 0, where N is the number of capacitors. The advantage of the LC generator over the Marx generator is that the number of switches is reduced by a factor of 2 [Har( 1975 ), Mes( 2005 )]. However, compared with the Marx generator, it is difficult to synchronize all switches within a short time interval because the closing of

Introduction 7 switches does not lead to an overvoltage across the switches that are not yet closed. In addition, oscillations take place in the various LC loops. Adding additional diodes and a main switch S into the circuit, as shown in Fig. 1.4 (b), can reduce the oscillations and improve the problematic synchronization of multiple switches, since the main switch S will only be closed until the voltages on all capacitors with even numbers have been fully reversed.

Fig. 1.4 (a) Classical LC generator, (b) diode and main switch used to prevent oscillations

(4) Inductive adder

As a fourth example of a commonly used multiple-switch topology, we discuss the inductive adder configuration. In a classical inductive adder configuration, as shown in Figure 1.5 (a), the secondary windings of the pulse transformers (1:1) are all connected in series and the capacitors are discharged simultaneously into the primary sides of the pulse transformers [Coo( 2002 ), Coo( 2005 )]. The total output voltage on the secondary windings is the sum of all the voltages on the primary windings. Using transformers with single- turn primary and secondary windings, Coo( 2005 ) successfully developed solid-state modulators with a fast rise-time (10 ns) and high repetition rate (on the order of MHz). In addition, by putting diodes in parallel with the primary windings of the transformers, as shown in Fig. 1.5 (b), this technology can be used to develop voltage-adjustable pulsers by turning on different numbers of switches.

8 Chapter1

Fig. 1.5 (a) Classical inductive adder, (b) voltage-adjustable topology

1.3 Objective of this dissertation

In 2001, Yan proposed a novel multiple-switch pulsed power topology [Yan( 2001 )], which was first verified on a small-scale model with three spark gap switches [Yan( 2003 )]. The proposed topology is different from the multiple-switch circuit topologies described above. The multiple switches are interconnected via a transmission line transformer (TLT) in such a way that all spark gap switches close almost simultaneously. No special synchronization trigger circuit is required. At the output side of the TLT, various connections in series and/or in parallel can be used; it can even synchronize multiple independent loads. It can produce either exponential or square wave pulses, with various voltage and current gains and with a high degree of freedom in choosing output impedances. The proposed multiple-switch topology can also be applied in a Blumlein configuration. In comparison to a single-switch circuit, the switching duty or switching current for each switch is reduced by a factor n (where n is the number of switches). As a result, the switch lifetime can be expected to improve by a factor in excess of n 2.

The proposed topologies are very promising for the development of high pulsed power systems for large-scale industrial applications. For this reason, we began investigating this technology systematically. The main objectives of this dissertation are to get a better understanding of this technology and to realize efficient large pulsed power generation through use of this technology. The main work will be presented in the following chapters.

In Chapter 2, a novel transmission line based multiple-switch technology is described. To gain insight into the mechanism and the characteristics of this technology, an equivalent circuit was introduced and experimental studies were carried out on a two- switch experimental setup with a resistive load.

Introduction 9

In Chapter 3, another novel pulsed power circuit, namely a multiple-switch Blumlein generator, is presented. As in chapter 2, in this chapter an equivalent circuit model was introduced, and an experimental setup was developed and tested to gain a deep understanding of the circuit’s mechanism and characteristics.

There are two possible approaches to generating large pulsed power levels with a short pulse width by means of the presented multiple switch technology. These are investigated in Chapter 4 and Chapter 5 respectively.

In Chapter 4, a four-switch pilot setup was developed for investigation of the first approach, and was evaluated under different output configurations. The factors affecting the output power are systematically analyzed. In addition, the application of this technology to generate a pulsed corona discharge in water is demonstrated.

Chapter 5 describes the development of a ten-switch prototype system for investigation of the second approach. Efficient high pulsed power generation was achieved. In addition, to charge this system, a 50 kW high-voltage pulse transformer was developed using a ferrite core made from many small ferrite blocks.

Chapter 6 explores the use of semiconductor switches for the proposed multiple- switch circuits. Other multiple-switch circuit topologies, such as a multiple-switch inductive adder and magnetic-coupled multiple-switch technique, are discussed as well.

Finally, Chapter 7 contains the conclusions of the research and the outlook for the multiple-switch technology investigated within this dissertation.

This dissertation also contains four appendices. Appendix A presents a detailed analysis of coupled resonant circuits; in particular, the role of the coupling coefficient k of a transformer in a resonant circuit is discussed. Appendix B presents the analysis of a repetitive resonant charging circuit for the case in which the low-voltage capacitor is larger than the matching value. Appendix C describes the calibration of a single-turn Rogowski coil, which was used in Chapter 5 of this thesis for the measurement of very large, fast currents. Appendix D presents the mechanical sketch of the construction of high-pressure spark gap switches used in the ten-switch system.

References

[And( 2006 )] D. E. Anderson. Recent developments in pulsed high-power systems. Proc. of LINAC 2006, pp. 541-545. [Bae( 2005 )] J. W. Baek, D. W. Yoo, G. H. Rim, and J. S. Lai. Solid state Marx generator using series-connected IGBTs. IEEE Trans. on Plasma Science , Vol. 33, No. 4, August 2005, pp. 1198-1204.

10 Chapter1

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Introduction 11

[Gau( 1998 )] M. P. J. Gaudreau, J. Casey, T. Hawkey, J. M. Mulvaney, and M. A. Kempkes. Solid-state pulsed power systems. 23 rd IEEE International Power Modulator Symposium , June 1998, pp. 60-163. [Gli( 2004 )] S. C. Glidden, and H. D. Sanders. Solid state spark gap replacement switches. 27 th International Power Modulator Symposium , May 2006, pp. 244-247. [Gro( 1992 )] M. G. Grothaus, S. L. Moran, and L. W. Hardesty. High-repetition-rate hydrogen Marx generator. 20 th Power Modulator Symposium , 1992, pp. 119-122. [Har( 1975 )] N. W. Harris, and H. I. Milde. 15-kJ LC generator: low inductance device for a 100-GW pulsed electron accelerator. J. Vac. Sci. Technol. , Vol. 2, No. 6, Nov./Dec. 1975, pp. 1188-1190. [Har( 1990 )] H. C. Harjes, K. W. Reed, M. T. Buttram, B. N. Turman, E. L. Neau, et al. The repetitive high energy pulsed power module. 19 th IEEE Power Modulator Symposium , June 1990, pp. 168-173. [Hee( 2004 )] E. J. M. van Heesch, K. Yan, A. J. M. Pemen, S. A. Nair, G. J. J. Winands, and I. de Jong. Matching repetitive pulsed power to industrial processes. IEEJ Trans. FM , Vol. 124, No. 7, 2004, pp. 607-612. [Hen(2006 )] J. Hendriks, and G. J. H. Brussaard. Photoconductive switching of an air- filled high-voltage spark gap: Pushing the limits of spark gap switching, Proceedings of 27 th International Power Modulator Symposium , May 2006, pp. 431-434. [Hic( 2001 )] B. Hickman, and E. Cook. Evaluation of MOSFETs and IGBTs for pulsed power application. Proceedings of 2001 Pulsed Power Plasma Science Conference , June 2001, pp.1047-1050. [Ist( 2005 )] M. Istenic, I. R. Smith, and B. M. Novac. The resistance of nanosecond spark gaps. Proceedings of IEEE Pulsed Power Symposium , 2005, pp. 15/1-15/5. [Jia( 2002a )] W. Jiang, T. Matsuda, and K. Yatsui. High repetition-rate, low jitter pulsed power generator for excimer laser applications. 25 th Power Modulator Symposium , June-July 2002, pp. 605-607. [Jia( 2002b )] W. Jiang, T. Matsuda, and K. Yatsui. MHz pulsed power generator using MOS-FET. 25 th International Power Modulator Symposium , 2002, pp. 599-601. [Kei( 1996 )] U. D. Keil, and D. R. Dykaar. Ultrafast pulse generation in photoconductive switches. IEEE Journal of Quantum Electronics , Vol. 32, No. 9, Sep. 1996, pp. 1664-1671. [Kie(2 006 )] E. R. Kieft. Transient behavior of EUV emitting discharge plasmas a study by optical methods. PhD diss., Eindhoven University of Technology (available at http://alexandria.tue.nl/extra2/200512577.pdf). [Kim( 2004 )] H. H. Kim. Nonthermal plasma processing for air-pollution control: A historical review, current issues and future prospects. Plasma Process. Polym ,. Vol. 1, No. 2, pp. 91-110. [Kot( 2004 )] Y. Kotlyar, W. Eng, C. Pai, J. Sandberg, J. Tuozzolo, and W. Zhang. Principle design of 300 kHz MECO RF kicker bipolar solid state modulator. 26 th International Power Modulator Symposium , pp. 250-253. [Kri( 1993 )] M. Kristiansen. Pulsed power applications. 9 th IEEE International Pulsed Power Conference , June 1993, pp. 6-10.

12 Chapter1

[Kus( 1985 )] M. Mazzola, W. Kimura, and S. Byron. Arc resistance of laser triggered spark gaps. J. Appl. Phys. , Vol. 58, No. 5, Sept. 1985, pp. 1744-1751. [Leh( 1989 )]F. M. Lehr, and M. Kristiansen. Electrode erosion from high current moving arcs. IEEE Transactions on Plasma Science , Vol. 17, No. 5, October 1989. [Lev( 1992 )] S. Levy, M. Nikolich, I. Alexeff, M. T. Buttram, and W. J. Sarieant. Commercial applications for modulators and pulse power technology. 20 th Power Modulator Symposium , June 1992, pp. 8-14. [Liu( 2005 )] Z. Liu, K. Yan, A. J. M. Pemen, G. J. J. Winands, and E. J. M. Van Heesch. Synchronization of multiple spark-gap switches by a transmission line transformer. Review of Scientific Instruments , 76, 113507 (2005). [Liu( 2006a )] Z. Liu, K. Yan, G. J. J. Winands, E. J. M. Van Heesch, and A. J. M. Pemen. Novel multiple-switch Blumlein generator. Review of Scientific Instruments , 77, 033502 (2006). [Liu( 2006b )] Z. Liu, K. Yan, G. J. J. Winands, A. J. M. Pemen, E. J. M. Van Heesch,, and D. B. Pawelek. Multiple-gap spark gap switch. Review of Scientific Instruments , 77, 0735501 (2006). [Mac( 1996 )] S. J. MacGregor, S. M. Turnbull, F. A. Tuema, and J. Harrower, The performance of a simple PFN Marx generator. 22 nd International Power Modulator Symposium , Jun 1996, pp. 194-197. [Mar( 1952 )] E. Marx. Hochspannungs-Praktikum . Berlin: Springer. [Mey( 2005 )] G. A. Mesyats. Pulsed Power , New York: Kluwer Academic. [Mit( 1998 )] I. H. Mitchell, R. Aliaga-Rosssel, S. Lebedev, et al. Mega-amp wire array experiments on the Magpie generator. IEEE Pulsed Power Symposium , April 1998. [Mor( 1991 )] S. L. Moran, and L. W. Hardesty. High-repetition-rate hydrogen spark gap. IEEE Transactions on Electronic Devices , Vol. 38, No. 4, April 1991, pp. 726-730. [Oh( 1997 )] J. S. Oh, M. H. Cho, I. S. Ko, W. Namkung, and G. H. Jang. Operational characteristics of 30-kW average MPC modulator for plasma De-NOx/De-SOx system. 11 th IEEE Pulsed Power Conference , June-July 1997, pp. 1091-1096. [Oh( 2002 )] J. S. Oh, S. D. Jang, Y. G. Son, M. H. Cho, W. Namkung, and D. J. Koh. Average 120-kW MPC modulator for plasma de-NOx/de-SOx system. 25 th Power Modulator Symposium , June-July 2002, pp. 583-586. [Ost( 2005 )] K. Ostrikov. Reactive plasmas as a versatile nanofabrication tool. Reviews of Modern Physics , Vol. 77, April 2005 pp. 489-511. [Pai(1995)] S. T. Pai, and Q. Zhang. Introduction to high-power pulse technology . Singapore: World Scientific Publishing Company. [Pem( 2003 )]A. J. M. Pemen, I. V. Grekhov, E. J. M. Van Heesch, K. Yan, and S. A. Nair. Pulsed corona generation using a diode-based pulsed power generator. Review of Scientific Instruments , Vol. 74, No. 10, Oct. 2003, pp. 4361-4365. [Red( 2005 )] L. M. Redondo, J. F. Silva, P. Tavares, and E. Margato. All silicon Marx- bank topology for high-voltage, high-frequency rectangular pulses. 36 th IEEE Power Electronics Specialists Conference , pp. 1170-1174. [Ren( 1997 )] G. Renz, F. Holzschuh, and E. Zeyfang. PFNs switched with stacked SCRs at 20kV, 500J, and 100 Hz rep-rate. 11 th IEEE Pulsed Power Conference , pp. 390- 395.

Introduction 13

[Rim( 2005 )] G. H. Rim, B. D. Min, E. Pavlov, and J. H. Kim. Repetitive nanosecond all- solid-state pulse generator using magnetic switch and SOS diodes. 2005 IEEE Pulsed Power Conference , pp. 1069-1072. [Sch( 2004 )] E. Schamiloglu, R. J. Baker, M. Gundersen, and A. A. Neuber. Scanning the technology. Modern pulsed power: Charlie Martin and beyond. Proceedings of the IEEE , Vol. 92, No. 7, July 2004. [Sor( 1977 )] T. P. Sorensen, and V. M. Ristic. Rise time and time-dependent spark-gap resistance in nitrogen and helium. J. Appl. Phys. , 48(1), 1977, pp. 114-117. [Spi( 997 )] R. B. Spielmana, W. A. Stygar, et al. Pulsed power performance of PBFA Z. 11 th IEEE International Pulsed Power Conference , 1997. [Tur( 1998 )] S. M. Turnbull, and S. J. MacGregor, The development of a PFN Marx generator. IEEE Pulsed Power Symposium , April 1998. [Vel( 2000 )] E. M. van Veldhuizen. Electrical discharges for environmental purposes: Fundamentals and applications , New York: Nova Science Publishers. [Vla( 1972 )] A. E. Vlastos. The resistance of sparks. J. Appl. Phys. , 43(4), April 1972, pp. 1987-1989. [Wan( 1999 )] X. Wang, Z. Zhang, C. Luo, and M. Han. A compact repetitive Marx generator. 12th IEEE International Pulsed Power Conference , 1999, pp. 815-817. [Wat( 2001 )] J. A. Watson, E. G. Cook, Y. J. Chen, R. M. Anaya, B. S. Lee, et al. A solid- state modulator for high speed kickers. Proceedings of 2001 International Particle Accelerator Conference , 2001, pp. 3738-3740. [Win( 2005 )] G. J. J. Winands, Z. Liu, A. J. M. Pemen, E. J. M. van Heesch, and K. Yan. Long lifetime triggered spark-gap switch for repetitive pulsed power applications. Review of Scientific Instruments , 76(8), 2005. [Xia( 2002 )] S. Xiao, S. Katsuki, J. Kolb, S. Kono, M. Moselhy, and K. H. Schoenbach. Recovery of water switches. Proceedings of 21st International Power Modulator Symposium and High-Voltage Workshop , July 2007, pp. 471-474. [Xia( 2004 )] S. Xiao, J. Kolb, C. Bickes, Y. Minimitani, M. Laroussi, R. P. Joshi, and K. H. Schoenbach. Recovery of high power water switches. 26 th Power Modulator Symposium and High-Voltage Workshop , 2004, pp. 129-132. [Xia( 2003 )] S. Xiao, J. Kolb, S. Kono, S. Katsuki, R. P. Joshi, M. Larousi, and K. H. Schoenbach. High power, high recovery rate water switch. 14 th IEEE International Pulsed Power Conference , June 2003, pp. 649-652. [Yan( 2001 )] K. Yan. Corona plasma generation. PhD diss., Eindhoven University of Technology (available at http://alexandria.tue.nl/extra2/200142096.pdf). [Yan( 2003 )] K. Yan, E. J. M. van Heesch, S. A. Nair, and A. J. M. Pemen. A triggered spark-gap switch for high-repetition-rate high-voltage pulse generation. Journal of Electrostatics 57 (2003), pp. 29-33. [Yan(2004 )] K. Yan, G. J. J. Winands, S. A. Nair, E. J. M. van Heesch, A. J. M. Pemen, and I. de Jong. Evaluation of pulsed power sources for plasma generation. J. Adv. Oxid. Technol , Vol. 7, No. 2, pp. 116-122.

Chapter 2 Transmission line transformer based multiple-switch technology ###

This chapter discusses a novel multiple-switch technology. It is based on the TLT (Transmission Line Transformer) and multiple switches. As a result of the interconnection between the switches and the TLT, multiple switches can be synchronized. Through this technology, not only the high-voltage pulse but also the large-current pulse can be generated. To understand the fundamental mechanism of the multiple-switch synchronization, an equivalent circuit was introduced. The experimental studies were then carried out to gain insight into the characteristics of this technology. It was found that the multiple switches can be closed within a short time interval (nanoseconds) and during this closing process the energy storage capacitors cannot discharge. When the closing process is finished and all switches are closed, the energy storage capacitors discharge simultaneously into the load(s) via the TLT. The TLT behaves as a current balance transformer, and the switching currents are determined by the characteristic impedance of the TLT. In terms of the currents, the equivalent circuit has good agreement with the experimental results. An interesting feature of this topology is that the risetime of the current into the load(s) is determined by the last switch that closes.

# Parts of this chapter have been published previously: Z. Liu, K. Yan, A. J. M. Pemen, G. J. J. Winands, and E. J. M. Van Heesch. 2005. Synchronization of multiple spark-gap switches by a transmission line transformer. Review of Scientific Instruments , Vol. 76, Issue 11. Z. Liu, K. Yan, G. J. J. Winands, A. J. M. Pemen, E. J. M. Van Heesch, and D. B. Pawelek. 2006. Multiple-gap spark-gap. Review of Scientific Instruments , Vol. 77, Issue 07.

16 Chapter 2

2.1 Principle of the multiple-switch technology

The Transmission Line Transformer (TLT) based multiple-switch pulsed power technology was proposed in 2001 [Yan( 2001 )]. By interconnecting multiple switches via a TLT, multiple switches can be synchronized and no external synchronization trigger circuit is needed. This topology was first verified on a small-scale model with three spark- gap switches [Yan( 2003 )].

Stage1 - +

C1 S1 Magneticcores Stage2 - +

C2 S2 TLT (a)withaseriesoutputconnection

Stage1 - +

C1 S1 Magnetic Stage2 - +

C2 S2 TLT (b)withaparalleloutputconnection

Stage1 - +

C1 S1 Magneticcores Stage2 - +

C2 S2 TLT (c)withindependentloads Fig. 2.1 The schematic diagrams of three circuit topologies with two switches and a two- stage TLT

Figure 2.1 presents the schematic diagrams of three circuit topologies with two spark- gap switches S 1 and S 2 and a two-stage TLT. Magnetic cores are placed around the transmission lines to increase the secondary mode impedance Z s, which is defined as the wave impedance between two adjacent stages of the TLT seen from the input side. At the

Transmission line transformer based multiple-switch technology 17

input side of the TLT, two identical capacitors C 1 and C 2 are interconnected to the TLT via two switches, and they are charged in parallel up to V 0. At the output side, the TLT can be put in series for high-voltage generation, as shown in Figure 2.1 (a), or in parallel to produce a large current pulse, as shown in Figure 2.1 (b), or can be used to drive independent loads, as shown in Figure 2.1 (c).

If we assume that the TLT is ideally matched at the output side and the transit time for a pulse propagating along the outsides of the TLT is much longer than the time interval for the synchronization of the multiple switches, an equivalent circuit for the input side of the TLT can be derived as shown in Figure 2.2. Here each transmission line is represented by its characteristic impedance Z 0. Following the connections in Figure 2.2, it can be seen that both stages (i.e. C 1-S1-Z0 and C 2-S2-Z0) are connected in series. The secondary mode impedance is represented by Z s.

Fig. 2.2 The equivalent circuit at the input side of the TLT (I1 and I 2 are the switching currents in S 1 and S 2 respectively)

Because the impedance Z s is designed to be much larger than the characteristic impedance Z 0 of the TLT, a voltage V 12 is generated over the impedance Z s whenever one switch (e.g. S 1) is closed and the other one is still open. Now capacitor C 1 or C 2 will discharge very slowly due to the large Z s, and thus energy transfer to the loads is blocked. The maximum value of V12 is equal to [Z s/ (Z 0+Z s)] ×V 0 = V 12 ≈ V0, where V 0 is the charging voltage on the capacitors. Moreover, because the stray capacitance of the spark gap switch S1 or S 2 is much smaller than the capacitances of C 1 or C 2, the voltage across the unclosed switch can rise from V 0 up to V 0+V 12 ≈ 2V 0. This generated overvoltage will cause the second switch to close.

When all the switches are closed, one can derive the following equations from the equivalent circuit shown in Figure 2.2: t  1 I (t)⋅(Z + Z ) − I (t)⋅ Z =V − I (τ )dτ 1 0 s 2 s 0 ∫ 1  C0 0 (2.1)  t  1 I 2 (t)⋅(Z0 + Z s ) − I1 (t)⋅ Z s =V0 − I 2 (τ )dτ C ∫  0 0

18 Chapter 2

In above equations, I 1(t) and I 2(t) are the currents flowing in switches S 1 and S 2 respectively, and C 0 is the value of capacitors C 1 and C 2 (C 1 and C 2 are identical). Solving these two equations, one can obtain the following expressions for I 1(t) and I 2(t):

V0 −t I1 (t) = I2 (t) = ⋅ exp( ) (2.2) Z0 Z0 ⋅C0

It can be seen that after both switches are closed, the switching currents I 1(t) and I 2(t) are identical and determined by the characteristic impedance Z 0 of the TLT. And the voltage V12 across Z s will drop to zero. Now all stages of the TLT are used in parallel equivalently. After a short time delay (transit time of the TLT) after all the switches have been closed, an exponential pulse will be generated over the loads at the output side. For all the circuits in Figure 2.1, the input impedance Z in of the TLT is the same (i.e. Z 0/2). The pulse duration and the peak output power are also the same; the pulse duration is determined by the constant Z 0C0, and the peak output power is determined by charging voltage V0 and 2 input impedance Z in and equals V 0 /Z in . However, the output voltage and current are different for the different output configurations. For the series output configuration in Figure 2.1 (a), the peak output voltages and currents are 2V 0 and V0/Z 0 respectively. For the parallel output configuration in Figure 2.1 (b), the peak output voltages and currents are V 0 and 2V0/Z 0 respectively. As for the configuration in Figure 2.1 (c), the peak output voltages and currents on each load are V 0 and V0/Z 0 respectively.

It is noted that for a practical circuit, although the described equivalent circuit cannot be used to accurately derive the switching behaviors due to the limited secondary mode impedance Zs and the finite length of the TLT, the model presents the basic principle of the technology. No general model has been available for all kinds of situations (longer pulses, or with mismatching loads) until now. The present model is valid for nanosecond pulse generation, assuming the TLT is matched. For long pulse ( µs-range) generation, the transmission line acts as coupled inductors, and details for this situation are presented in Section 6.1.1.

In principle, the circuit topologies described above can be extended for any number of switches. As an example, Figure 2.3 shows the schematic diagrams of three-switch circuit topologies. At the input side, three identical capacitors are interconnected to the TLT via three switches. And at the output side, the transmission lines can be put in series, in parallel or connected to independent loads. These three circuits, similar to the circuits in Figure 2.1, generate the same output power but at different output voltages and currents. Yan( 2002 ) presented a comprehensive discussion of the different output configurations when the number of switches is scaled up to 50.

Moreover, the equivalent circuit in Figure 2.2 can easily be extended for any n-stage TLT. As an example, Figure 2.4 gives the equivalent circuit at the input side of the three- switch TLT topologies as in Figure 2.3. Zs1 , Z s2 and Z s3 are the impedances between stages 1 and 3, stages 1 and 2, and stages 2 and 3 respectively. Similar to two-switch circuits, one can analyze the three-switch circuit and derive the same results after all the switches are closed, namely:

Transmission line transformer based multiple-switch technology 19

V0 − t I1 (t) = I2 (t) = I3 (t) = ⋅ exp( ) (2.3) Z0 Z0 ⋅ C0

Fig. 2.3 Circuit topologies with three switches and a three-stage TLT

20 Chapter 2

Fig. 2.4 Equivalent circuit for the input side of the three-switch circuit topologies in Figure 2.3

However, according to the equivalent circuit in Figure 2.4, when increasing the number of the switches, the overvoltage to close the switches that are not yet closed after the closing of the first switch becomes less. For instance, if Z s2 =Z s3 in Figure 2.4, then after the switch S 1 is closed, the maximum overvoltage added to switches S 2 and S 3 is about 0.5V 0, which is a factor of 2 lower as compared with that in the two-switch circuits. This may cause the closing of the second switch to fail when a large number of switches are used. To synchronize all the switches properly, special designs may be needed to ensure the closing of the second switch shortly after the closing of the first switch. Detailed discussions of this issue will be presented in Section 5.4.3.

2.2 Experimental studies

The experimental setup, shown in Figure 2.5, was used to study the mechanism of the multiple-switch technology and its characteristics. It consists of three air-core inductors (L1, L 2, L 3), two high-voltage capacitors (CH1 and C H2), two spark gap switches (S1 and S2), a two-stage TLT and a resistive load. The three inductors are used to charge the capacitors, and they behave as a high blocking impedance during the closing process of the switches. As for the two switches, S 1 is a triggered spark gap switch and S 2 is a self– breakdown spark gap switch; the distance of their main gaps is about 12 mm. After the high-voltage capacitors are charged, switch S 1 is triggered and closes first. Now an overvoltage will be generated over switch S 2, which forces it to close almost instantaneously. The TLT is made from 1.5 meters of coaxial cable (RG217) and the distance between the outer conductors of the two cables is about 10 cm. The transmission lines are connected in parallel to a 25 resistive load. Magnetic cores are placed around the cables to increase the impedance Z s. The length covered by the magnetic cores on each

Transmission line transformer based multiple-switch technology 21

cable is 1 m. The value of Z s is estimated to be about 3 k, and the two-way transit time between the outsides of the TLT is estimated to be more than 60 ns. The detailed discussion on the effect of the magnetic material is presented in Chapter 5. The two- switch experimental setup was able to run reliably in air up to 50 pps (pulses per second).

Fig. 2.5 Schematic diagram of the experimental setup

2.2.1 Characteristics of the synchronization and the output

Fig. 2.6 Typical waveforms of the voltages on the positive ends of the high-voltage capacitors C H1 and C H2 , where C H1 =C H2 =1.3 nF

22 Chapter 2

Figure 2.6 presents the typical waveforms of the voltage on the positive ends of capacitors C H1 and C H2 . They clearly show the voltage transient before, during and after the synchronization of switches S 1 and S 2. Initially, the high-voltage capacitors C H1 and CH2 were charged to a voltage of 28 kV. Spark gap S 1 was triggered first. As predicted by the model shown in Figure 2.2, the voltage on the positive end of C H2 starts to increase after the closing of the first switch S 1. And its value was 51.5 kV when the switch S 2 broke down 31 ns after the first switch S 1 closed. This value is equal to 92% of the maximum theoretical value of 56 kV as predicted by the model in Figure 2.2. This difference is simply caused by the fact that the switch S 2 already broke down before the voltage could reach the theoretical value.

Fig. 2.7 Typical waveforms of the switching currents in the switches S 1 and S 2, respectively, when C H1 =C H2 =1.3 nF and the switching voltage was 28 kV

Figure 2.7 shows the typical waveforms of the currents flowing in switches S 1 and S 2 respectively. Here the switching voltage, namely the voltage on the high-voltage capacitors when switch S 1 closed, was 28 kV. From Figure 2.7, one can clearly see that the two switches work in two distinctive phases. After switch S 1 was triggered first, at about -38.8 ns, the first phase starts. Then switch S2 closes about 30 ns after the closing of the first switch. In the first phase, a small prepulse exists in the switching current through S1 due to the introduction of the charging inductors and the finite value of the secondary mode impedance Z s of the TLT. When all the switches are closed, the first phase ends. Then the second phase starts, in which the TLT behaves as a current balance transformer, and the switching currents are determined by the characteristic impedance of the TLT. Now the capacitors will be discharged rapidly and simultaneously into the load via the

Transmission line transformer based multiple-switch technology 23

TLT. The peak values of the currents in S 1 and S 2 are 343 A and 329 A respectively, which are less than the theoretical value of 560 A given by equation (2.1). This is the result of the stray inductance of the connections between components and the energy losses (e.g. spark gap switches and the TLT). The effect of the stray inductance will be presented in Section 4.3.4.

Within the present experimental setup, Z 0 and C 0 are 50 and 1.3 nF respectively, thus the time constant Z0C0 is 65ns. For an exponential pulse as described by equation (2.1), the theoretical decay time (90-10%) is equal to 2.2Z 0C0, namely 143 ns. In fact, the decay time of the measured current shown in Figure 2.7 is 141 ns, which is very close to the theoretical value given by equation (2.1). Thus, from this point of view, one can conclude that the experimental result is in good agreement with the model.

From the above experimental results, one can see that though the proposed model cannot be used to derive the exact behaviors of the presented circuit, it clearly presents the mechanism of synchronization of multiple switches. Furthermore, from Figures 2.6 and 2.7, it can be concluded that even though the two spark-gap switches close within a relatively long period (~30 ns), the capacitors, however, can only be discharged rapidly and simultaneously after all the switches have been closed. It is this property that makes the circuit unique in comparison with conventional multiple-switch pulsed power circuits.

Fig. 2.8 Typical output voltage and current when the TLT was connected in parallel to a resistive load and C H1 =C H2 =1.3 nF

24 Chapter 2

Figure 2.8 shows the typical output voltage and current waveforms when the setup was operated with a charging voltage of 28.3 kV at a repetition rate of 50 pps in air. The peak values of output voltage and current are 19 kV and 698 A, respectively. The risetime of output voltage and current are 22 ns and 25 ns respectively. From the plots shown in Figure 2.8, one can see that there are also small prepulses in the rising parts of both the output voltage and the output current due to the closing process of the switches. Similar to the case of the switching current, the small pulse in Figure 2.8 can be used as an indicator to estimate the time interval for the closing process.

2.2.2 Other observations

(a) Factor affecting the prepulse

To evaluate the factors affecting the small prepulse in the rising part of the pulses, the two-stage TLT was replaced with 50 resistors, as shown in Figure 2.9. The other components, such as the inductors, the switches and the high-voltage capacitors, were kept the same as in the setup in Figure 2.5. Thus during the synchronization process, the influence of the secondary mode impedance of the TLT is eliminated and only the charging inductor is involved. In this situation, the only possible path for the current to flow is as indicated by the dashed line in Figure 2.9. Figure 2.10 plots the typical switching currents in switches S 1 and S 2 respectively when the two-stage TLT was replaced by resistors. It can be seen that the small prepulse still exists. Therefore, it can be concluded that the charging inductors can strongly contribute to the small pre-pulse.

Fig. 2.9 Two-switch experimental setup when the TLT is replaced by two 50 resistors. C1=C 2=1.3 nF (the dotted line shows the path for the pre-pulse current)

Transmission line transformer based multiple-switch technology 25

Fig. 2.10 Typical switching currents when the two-stage TLT is replaced by two 50 resistors

(b) Effect of the charging voltage on the switching process

From the experiments on the TLT, it was observed that the time interval for the closing of the switches and the overvoltage on the second switch varied with the charging voltage. When the charging voltage V0 is lower (e.g. 23 kV) it takes longer (e.g. 60 ns) to close the two switches in sequence, and the voltage seen by the second switch is nearly twice the charging voltage. While when the charging voltage is higher, the time interval for the closing of the switches is less (e.g. 10 ns and even 0), and the overvoltage seen by the second switch is much less since it already closed before the overvoltage reaches its peak value. Figure 2.11 gives the typical voltages on the positive ends of the capacitors and the switching currents when the charging voltage was about 40 kV. From Figure 2.11, it can be seen that both switches close almost simultaneously and both the overvoltage and the small pre-pulse in the switching current have disappeared, compared to Figures 2.7 and 2.10. When the small pre-pulse disappears in the switching current, the pre-pulse is no longer present in the output current into the load, in comparison with Figure 2.8. The switching currents and the output current are nearly identical, as shown in Figure 2.12.

26 Chapter 2 ] A [ t n e r r u C Voltage[kV]

Fig. 2.11 Typical voltages on C H1 + and C H2 + and currents in both switches (CH1 + and CH2 + refer to the positive ends of capacitors C H1 and C H2 )

Inputcurrent[A] Outputcurrent[A]

Fig. 2.12 Typical switching currents and output current when no small pre-pulse occurs

Transmission line transformer based multiple-switch technology 27

(c) Sensitivity to capacitance values

In order to study the circuit’s sensitivity to the value of the main components, Figure 2.13 plots the typical switching currents when C H1 =2.6 nF and C H2 =1.3 nF. As observed with two identical capacitors, there is no problem at all concerning their synchronization. But when both the capacitors do not have the same value, an oscillation at the end of the pulse can be observed due to mismatched capacitors. Also the currents in the two switches become unbalanced. For efficient pulsed power generation, the capacitors need to be as close to identical as possible. Also, each stage of the TLT needs to be identical, including the number of cables per stage and the length of the cables.

Fig. 2.13 Typical switching current waveforms when C H1 =2.6 nF and C H2 =1.3 nF

(d) Dominance of the last-closed switch

As discussed in Section 2.2.1, the switches typically close in sequence within a short time interval. During this closing process, the channel of the switch S 1 (closed first) is heated continuously by the flowing current and hence further ionized. Therefore, the channel of S 1 will become fully conductive and have a very low resistance before the last switch closes. Thus, performance of switch S 2 (closed last), such as the collapse rate of the channel resistance, can strongly affect the performance of the multiple-switch circuit (e.g. the output rise-time).

28 Chapter 2

To verify the above hypothesis, an experiment was conducted in which two different spark gap switches were used for S 2: a single-gap spark gap switch and a multiple-gap spark gap switch, as shown in Figure 2.14.

Fig. 2.14 Experimental setup in which two different switches were used for S2: a single- gap switch and a six-gap switch

Some advantages of the multiple-gap switch over the single-gap switch are [Den( 1989 ), Kov( 1997 ), Mes( 2005 )]: (i) substantial current cannot flow through the switch until the last gap has closed, (ii) before the last gap closes, the gaps closed first will become fully ionized so the last gap mainly determines its switching speed, and (iii) because the last gap is significantly overvolted, it closes very rapidly. Figure 2.15 shows an example of the dependence of the pulse rise-time on the number of gaps. This data was obtained at a switching voltage of about 44 kV [Liu( 2006 )]. One can see that when the gap number was increased from 2 to 6, the rise-time was improved from 13.5 ns to 6 ns.

Within the experimental setup in Figure 2.14, the single-gap spark gap switch has a gap distance of 12.5 mm; the multiple-gap switch is a 6-gap spark gap switch and each gap distance was 1.5 mm. The value of each high-voltage capacitor is 1 nF. At the output side, the TLT was connected in parallel to a 24.4 resistive load. In both cases, switch S 1 was triggered at 32.8 kV. Figure 2.16 shows the typical output currents for both cases. When the single-gap switch was used as S 2, the peak current and the current rise-time were 870 A and 21 ns, respectively. However, when the much faster 6-gap switch was used for S2, the peak current and current rise-time were 993 A and 11 ns respectively, which confirmed that the switch closed last can significantly affect the performance of the multiple-switch circuit.

Transmission line transformer based multiple-switch technology 29

Fig. 2.15 The dependence of the rise-time on the number of gaps

Outputcurrent[A]

Fig. 2.16 Typical output currents when two different switches were used for S2

30 Chapter 2

2.3 Variations for square pulse generation

Load Load 2 Load 1 Load

Fig. 2.17 Two-switch circuit topologies for square pulse generation using PFLs

All the previously described circuit topologies are used to produce exponential pulses. In principle, square pulses can be generated by replacing the capacitors with PFLs (Pulse Forming Line). Figure 2.17 shows the schematic diagrams of two-switch circuit topologies for square pulse generation. At the left side of the TLT, two identical PFLs (PFL 1-2) are interconnected to the TLT via two switches S 1-S2. Magnetic material is put around both the PFLs and the TLT to increase the secondary mode impedance Z s. At the output side, similar to the circuits in Figures 2.1 and 2.3, the TLT can be connected in series or parallel, or to independent loads. Similarly, the multiple switches will be synchronized automatically by interconnecting the PFLs to the TLT via the multiple switches. Suppose that the PFLs have an electrical length of τ, and are charged in parallel to an initial voltage V0. Under ideal conditions, for instance when the TLT is perfectly matched and after all the switches are closed, a square pulse with a width of 2 τ will be generated over the load. The switching current of each individual switch is equal to

Transmission line transformer based multiple-switch technology 31

V0/2Z 0. For the series output configuration in Figure 2.17 (a), the output voltage and current are V 0 and V 0/2Z 0 respectively. For the parallel output configuration in Figure 2.3 (b), the output voltage and current are V 0/2 and V 0/Z 0 respectively. As for the configuration in Figure 2.3 (c), the output voltage and current on each load are V 0/2 and V0/2Z 0 respectively. The output power is, of course, the same for each configuration.

Short pulses (nanoseconds) can be easily generated when using coaxial cables as PFLs. While, for long pulse (microseconds) generation, a PFN (Pulse Forming Network) consisting of lumped capacitors and inductors can be used. Figure 2.18 shows the schematic diagrams of two-switch circuit topologies when the PFL is replaced by a PFN. Assume that each PFN consists of m stages and the values of the capacitors and the inductors are C and L/2 respectively; then the characteristic impedance of the PFN is (L/C) 1/2 and the electrical length is m(LC) 1/2 . For the ideal situation in which both the TLT and the PFN are matched, a pulse with a width of 2m(LC) 1/2 will be produced on the load after all the switches have been closed. The pulse width can be adjusted by changing the number of stages.

Load Load Load 1 Load 2

Fig. 2.18 Schematic diagram of PFN based square pulse generator with two switches

32 Chapter 2

2.4 Summary

The TLT based multiple-switch pulsed power technology was discussed. By interconnecting the energy storage components (capacitors or PFLs) to the TLT via multiple switches, the multiple switches can be synchronized automatically and no external synchronization trigger circuit is needed. This technology can be used to generate either a high-voltage pulse or a large-current pulse or even to drive independent loads simultaneously. Moreover, both exponential pulses and square pulses can be generated.

An equivalent circuit model was developed to understand the mechanism of this technology. An experimental setup with two spark gap switches and a two-stage TLT was constructed to gain insight into the characteristics of this multiple-switch circuit. It was found that the closing of the first switch leads to an overvoltage over the switches that are still open, causing them to be closed in sequence within a short time interval (nanoseconds). During this closing process the energy storage capacitors cannot discharge. When the closing process is finished and all switches are closed, the energy storage capacitors discharge simultaneously in parallel into the load(s) via the TLT. The TLT behaves as a current balance transformer, and the switching currents are determined by the characteristic impedance of the TLT. In terms of the currents, the equivalent circuit shows good agreement with the experimental results. To obtain efficient pulsed power generation, identical components (capacitors and each stage of the TLT) are necessary. An interesting feature of this topology is that the switch closed last can significantly affect the output performance. This was verified by combining a fast multiple-gap switch with a conventionally triggered spark gap switch. The output current risetime was improved by a factor of almost 2 (from 21 ns to 11 ns).

References

[Den( 1989 )] G. J. Denison, J. A. Alexander, J. P. Corley, D. L. Johnson, K. C. Hodge, M. M. Manzanares, G. Weber, R. A. Hamil, L. P. Schanwald, and J. J. Ramire. Performance of the Hermes-III Laser-Triggered Gas Switches. Proc. 7 th IEEE Pulsed Power Conference , June 11-14, 1989, pp. 579-582. [Kov( 1997 )] B. M. Kovalchuk. Multiple gap spark switches. Proc. 11 th IEEE Pulsed Power Conference , 1997, pp. 59-67. [Liu( 2006 )] Z. Liu, K. Yan, G. J. J. Winands, A. J. M. Pemen, E. J. M. Van Heesch, and D. B. Pawelek. Mutliple-gap spark gap switch. Review of Scientific Instruments , 77, 073501 (2006). [Mes( 2005 )] G. A. Mesyats. Pulsed Power . New York: Kluwer Academic. [Yan( 2001 )] K. Yan. Corona plasma generation. PhD diss., Eindhoven University of Technology (available at http://alexandria.tue.nl/extra2/200142096.pdf ). [Yan( 2002 )] K. Yan, E. J. M. van Heesch, P. A. A. F. Wouters, A. J. M. Pemen, and S. A. Nair. Transmission line transformers for up to 100 kW pulsed power generation.

Transmission line transformer based multiple-switch technology 33

Proc. 25 th international Power Modulator Symposium and High-Voltage Workshop , 30 June-3 July 2002, pp. 420-423. [Yan( 2003 )] K. Yan, H. W. M. Smulders, P. A. A. F. Wouters, S. Kapora, S. A. Nair, E. J. M. van Heesch, P. C. T. van der Laan, and A. J. M. Pemen. A novel circuit topology for pulsed power generation. Journal of Electrostatics , Volume 58, Issues 3-4, June 2003, pp. 221-228.

Chapter 3 Multiple-switch Blumlein generator ###

The Blumlein generator has been one of the most popular pulsed power circuits. Traditionally, it was commutated by a single switch. One critical issue for such a single-switch based circuit topology is related to the large switching currents. In this chapter, a novel multiple-switch based Blumlein generator will be presented. The Blumlein generator can be commutated by multiple switches and the heavy switching duty can be shared identically by multiple switches. To gain a deep understanding of this technology, an equivalent circuit model was introduced, and an experimental setup was developed. It was observed that the mechanism of the multiple-switch synchronization is similar to that of the TLT based multiple-switch circuit, namely the multiple switches are closed in sequence and after all the switches have closed the charged PFLs discharge simultaneously and identically. The experimental results are in good agreement with the equivalent circuit model. Moreover, the experimental setup was successfully used to generate the bipolar corona plasma.

# Parts of this chapter have been published previously: Z. Liu, K. Yan, G. J. J. Winands, E. J. M. Van Heesch, and A. J. M. Pemen. 2006. Novel multiple-switch Blumlein generator. Review of Scientific Instruments , Vol. 77, Issue 03.

36 Chapter 3

3.1 Introduction

The Blumlein generator [Blu( 1941 ) and Blu(1945 )] is commonly used for generating square pulses. The main advantage is that the output voltage on a matched load is equal to the charging voltage [Sim( 2002) ]. Conventionally, the pulse forming lines are charged in parallel and synchronously commutated by a single switch, such as a spark gap [Ros( 2001 ), Dav( 1991 ), Bor( 1995 ), Ver( 2004 )]. For such a single-switch based generator, the main problem when increasing the power is the large switching current. Multiple switches are preferred in heavy-duty pulsed power systems. The critical issue for multiple switches is how to synchronize them. In this chapter, a novel multiple-switch based Blumlein generator will be presented. The charged pulse-forming lines can be synchronously commutated by multiple switches and no external synchronization trigger circuit is needed.

3.2 Single-switch (traditional) Blumlein generator

Figure 3.1 shows an example of a single-switch based stacked Blumleins. It consists of four identical coaxial cables (Line 1 - Line 4), a spark-gap switch S and a load. Line 1 and Line 2 are used in parallel, which is identical to a single line with a characteristic impedance of 0.5Z 0, where Z 0 is the characteristic impedance of the cables. This is also true for Lines 3 and 4. Initially, the four lines are charged to a voltage of V 0. When switch S is closed, EM waves will be excited inside lines 1 and 2 and the switching current is equal to 2V 0/Z 0. After the transit time τ of lines 1 and 2, the excited EM wave will reach the load. With a matched load (Z 0), a square pulse with a width of 2τ will be generated, and the output voltage and current are V 0 and V 0/Z 0 respectively.

Fig. 3.1 Single-switch based Blumleins stacked in parallel

Multiple-switch Blumlein generator 37

Such an experimental example is given in Figure 3.2. Here the four pulse-forming lines are 4.5-meter-long RG217 (50 ) cables, and the switch is a triggered spark gap. The charging voltage is 27 kV, and the resistive load is 49.8 . One can see that the switching current is twice the output current, as described above. The switching current would increase significantly when using a larger number of stacked Blumleins (i.e. to increase the power) or a low characteristic impedance cable.

Fig. 3.2 Typical voltage and current waveforms for single switch Blumlein

3.3 Novel multiple-switch Blumlein generator

Figure 3.3 gives three examples of two-switch based Blumlein generators with parallel output configurations. The circuit shown in Figure 3.3 (a) consists of four identical coaxial cables (Line 1 - Line 4), two switches S 1 and S 2 and a load. At the left side, Line 1 and Line 2 are interconnected via switches S 1 and S 2. Magnetic cores are placed around Line 1 and Line 2 to increase the secondary mode impedance. At the right side, Line 1 and Line 2, and Line 3 and Line 4 are connected in parallel to a load. Actually, the circuit in Figure 3.3 (a) is a two-stage Blumlein stacked in parallel and is identical to the circuit in Figure 3.3 (b) in which a single line (Line 3) with a characteristic impedance of 0.5Z 0 is used to replace Line 3 and Line 4. In both circuits, the load is connected to the inner conductors of the lines, and thus the output pulse is bipolar, namely the potentials at positions A and B are positive and negative respectively. In contrast, in the circuit shown in Figure 3.3 (c) the load is connected to the outer conductors of the lines; the output is unipolar, and it can be positive (when position A is grounded) or negative (when position B is grounded).

38 Chapter 3

Fig. 3.3 Three two-switch Blumlein circuits with parallel output configurations

Multiple-switch Blumlein generator 39

Fig. 3.4 Equivalent circuit models at the switch side of the circuits as shown in Fig. 3.3 during and after the synchronization

Suppose that all the lines of the circuits in Figure 3.3 are charged to an initial voltage of V 0. When switch S 1 is closed first, charged Line 1 will discharge via the secondary mode impedance Z s, as shown in Figure 3.4 (a). A voltage V Zs will also be generated over Z s. This voltage V Zs is equal to [Z s/(Z 0+Z s)]×V 0. In addition, a voltage pulse with an amplitude of -[Z 0/(Z 0+Z s)]×V 0 will travel towards the load along Line 1. When the Z s is designed to be much larger than the characteristic impedance Z 0 of the lines, the values of VZs and -[Z 0/(Z 0+Z s)]×V 0 will be almost V 0 and 0 respectively, which means that the

40 Chapter 3

discharging of Line 1 can be neglected. Since the voltage on Line 1 almost maintains a constant value of V 0, it can be treated as a DC voltage source with an amplitude of V 0 or as a capacitor with a charging voltage of V 0. Moreover, Line 2 cannot discharge before switch S 2 closes, so it can also be regarded as a DC voltage source. When the transit time τs between the outer conductors of Line 1 and Line 2 is long enough, that is 2 τs is larger than the time interval for the synchronization, a simplified equivalent circuit at the switch side can be derived, as shown in Figure 3.4 (b). It can be seen that the voltage across S 2 can theoretically rise from V 0 up to V 0+V Zs ≈ 2V 0 during the synchronization process. The generated overvoltage will force switch S 2 to close subsequent to the closing of S 1.

After all the switches have been closed, the equivalent circuit shown in Figure 3.4 (b) is no longer valid, since Line 1 and Line 2 start to discharge into each other simultaneously, as shown in Figure 3.4(c). Now a voltage pulse will travel towards the load in both Line 1 and Line 2, which is contributed to by the discharging of both Line 1 and Line 2. Assume that in Line 1 the contributions from the discharging of Line 1 and the discharging of Line 2 are represented by V 11 and V 12 respectively. The expressions of V 11 and V 12 can be written as:

 Z0 V11 = − ⋅V0  Z + Z // Z  0 0 s (3.1) Z // Z V = − 0 s ⋅V  12 0  Z0 + Z0 // Zs

At the switch side, the total voltage over Line 1 now becomes V 0+V 11 +V 12 =0, which implies Line 1 is shorted. The same result is obtained for Line 2. Moreover, the voltage across Z s is equal to V 12 +V 21 =0, which indicates that no energy flows into the Zs. The switching currents I 1 and I 2 through switches S 1 and S 2 are identical and written as:

V11 V12 V0 I1 = I 2 = + = − (3.2) Z0 Z0 Z0

From the discussions above, it can be seen that after all the switches have closed, Line 1 and Line 2 are shorted at the switch side. This is similar to the situation in the traditional Blumlein configuration, and the output pulse will be generated in the same manner as in the single-switch circuit. Namely, after transit time τ, the excited pulse inside Line 1 and Line 2 will reach the load. Ideally (i.e. with matched loads), a square pulse with a width of 2τ is generated for all the circuits in Figure 3.3. For example: the pulse forming process of the circuits shown in Figures 3.3 (a) and (b) is shown in Table 3.1. For all the circuits in Figure 3.3, the output voltage is same, namely V 0. Their polarities, however, are different. The potentials at positions A and B, in the circuits shown in Figures 3.3 (a) and (b), are +V 0/2 and –V0/2 respectively. For the circuit in Figure 3.3 (c), the output voltage can be either V 0 or –V0 when position A or B is grounded, respectively. It is noted that although the above model is not exactly accurate due to the finite secondary mode impedance Z s, it presents the fundamental principle of the synchronization of the multiple-switch Blumlein generator.

Multiple-switch Blumlein generator 41

Table 3.1 Pulse forming process of the circuits in Figures 3.3 (a) and (b) with matched loads

Fig. 3.5 Two-switch Blumlein generators with series output configuration

42 Chapter 3

Besides the parallel output configuration, at the output side the Blumlein can also be connected in series to obtain a high-voltage pulse. Figure 3.5 shows two circuit topologies of two-switch Blumleins stacked in a series configuration, where Line 1 and Line 2 form one Blumlein and Line 3 and Line 4 form the other stage. At the left side, Line 1 and Line 3 are interconnected via the switches S 1 and S 2. And at the output side, the two-stage Blumleins are put in series. The closing process of multiple switches is exactly the same as that of the circuits with a parallel output configuration. If all the lines are charged to V 0 and the Blumleins are ideally matched, then after closing of all the switches, the switching current per switch is V 0/Z 0. And after transient time τ the output pulse with 2 τ duration will be generated over the load. The output voltage and current are 2V 0 and V 0/2Z 0 respectively. However, the polarities of the output pulses generated by the circuits in Figures 3.5 (a) and (b) are different. For the circuit in Figure 3.5 (a), the potentials at positions A and B are +V 0 and –V0 respectively; as for the circuit in Figure 3.5 (b), the polarity of the output pulse can be either positive or negative when position A or B is grounded, respectively.

In principle, the circuit topologies described in Figures 3.3 and 3.5 can be extended for any number of switches. Figures 3.6 and 3.7 show circuit topologies of the three-switch Blumleins stacked in parallel and in series respectively.

In Figure 3.6, at the left side, lines Line 1-Line 3 are interconnected via the switches S 1- S3. At the output side, the lines Line 1-Line 3 are put in parallel. The load is connected to the inner/outer conductors of the lines. Line 4 has a characteristic impedance of Z 0/3. After the closing of all the switches, the output pulse with a duration of 2 τ will be produced on a matched load. The output voltage and current are V 0 and 3V 0/2Z 0. The output polarities of the circuits in Figures 3.6 (a) and (b) are positive and negative respectively. However, the switching current per switch is V 0/Z 0, which is one-third of that of the single-switch circuit.

For the circuits in Figure 3.7, actually they include 3-stage Blumleins, i.e. Line 1 and Line 2, Line 3 and Line 4, and Line 5 and Line 6 form one stage Blumlein, respectively. At the left side, Line 1, Line 3, and Line 5 are interconnected via the switches S 1-S3. And at the output side, the three-stage Blumleins are connected in series. After all the switches are closed, a pulse with a duration of 2 τ will be produced on a matched load. And the output voltage and current are 3V 0 and V 0/2Z 0, respectively. The output polarities of the circuits in Figures 3.7 (a) and (b) are positive and negative, respectively. Same to the circuits in Figure 3.6, the switching current per switch is V 0/Z 0.

Moreover, the equivalent circuit model shown in Figure 3.4 can be extended for any n-switch circuit. As an example, Figure 3.8 shows the equivalent circuit at the switch side of the three-switch Blumlein generators shown in Figures 3.6 and 3.7 during the synchronization process. The DC voltage sources with an amplitude of V 0 represent the charged lines Line 1-Line 3, and Z s1 , Z s2 , and Z s3 represent the secondary mode impedances formed by Line 1 and Line 2, Line 2 and Line 3, and Line 3 and Line 2 respectively.

Multiple-switch Blumlein generator 43

Fig. 3.6 Three-switch Blumlein generators with parallel output configurations

44 Chapter 3

Fig. 3.7 Three-switch Blumlein generators with series output configurations

Multiple-switch Blumlein generator 45

Fig. 3.8 Equivalent circuit at the switch side of the three-switch Blumlein generators shown in Figures 3.6 and 3.7 during the synchronization process

3.4 Experimental studies

To verify the novel multiple-switch Blumlein circuit topology and the proposed model, and to gain a deep understanding of the characteristics of the multiple-switch Blumlein circuit and its characteristics, an experimental setup with two switches was developed. It was then evaluated for both a resistive load and a corona plasma reactor.

3.4.1 Experiments on a resistive load

The schematic diagram of the experimental setup with a resistive load is as shown in Figure 3.3 (a). The four identical lines (Line 1-Line 4) are made from 4.5-meter-long RG217 coaxial cables with a characteristic impedance Z 0=50 . The distance between the outer conductors of Line 1 and Line 2 is about 10 cm. The length of the magnetic cores around Line 1 and Line 2 is about 1 meter. The value of Z s is estimated to be about 3 k, and the two-way transit time between the outsides of Line 1 and Line 2 is estimated to be more than 60 ns. A detailed discussion of the effect of the magnetic material is presented in Chapter 5. Switch S 1 is a triggered spark gap switch, while switch S 2 is a self- breakdown spark gap type. The 49.8 resistive load is made from HVR disc-type resistors.

Figure 3.9 gives typical voltage waveforms of V 1 and V 2, where V 1 and V 2 are the voltages over switches S 1 and S 2 respectively. The four lines are charged to an initial voltage of 26.8 kV. The triggered spark gap S 1 is closed first. As predicted by the model shown in Figure 3.4, the voltage on the second switch S 2 starts to increase after the closing of the first switch S 1. This increment continues until the overvoltage forces switch S 2 to

46 Chapter 3

breakdown 29 ns after switch S 1 has been closed. The obtained voltage of 44.5 kV over S 2 is lower than the maximum theoretical value of 53.6 kV given by the model, since S 2 already broke down before V 2 could reach the maximum value.

Figure 3.10 shows the current waveforms of I s1 , I s2 and I out , where I s1 and I s2 are the switching currents through the switches S 1 and S 2, and I out is the output current. As predicted by the model, the two switching current pulses are almost identical and approximately equal to the output current. The switching current is about a factor of two lower compared with that of the single-switch Blumlein circuit shown in Figure 3.1. In addition, the measured values of switching currents are smaller than the theoretical value of 536 A given by (3.2) due to mismatching and energy losses. Figure 3.11 shows the typical waveforms of the output voltage V out and current I out . The rise-time and width are around 20 ns and 50 ns respectively, and the peak output voltage and current are 25.5 kV and 510 A respectively. It can be seen that, although there is some time delay between the closing of both switches S 1 and S 2, their outputs are nearly synchronous and identical in terms of their switching currents. This unique feature is the same as that of the TLT based multiple-switch circuits discussed in Chapter 2. In addition, in contrast to the TLT based multiple-switch circuit shown in Figure 2.5, no charging inductors are required, thus no small pre-pulse (see Figures 2.7 and 2.10) occurred in the rising part of the currents.

Fig. 3.9 Typical voltage waveforms of V 1 and V 2, where V 1 and V 2 are the voltages on the inner conductors of Line 1 and Line 2 at the switch side in Fig. 3.3 (a)

Multiple-switch Blumlein generator 47

Fig. 3.10 Typical switching currents and output current in Fig. 3.3 (a)

Current[A] Voltage[kV]

Fig. 3.11 Typical output voltage and current in Fig. 3.3 (a)

48 Chapter 3

To evaluate the energy conversion efficiency, the output power P out , the output energy

Eout and the energy conversion efficiency ηR are calculated according to the following equations: E = P dt = V I dt (3.3) out ∫ out ∫ out out 2 ηR = Eout Etotal = Eout 5.0 CHV0 (3.4)

In (3.4), E total and CH refer to the energy stored in the four lines and the total capacitance of the four lines (1.8 nF) respectively. The typical output power and energy waveforms are shown in Figure 3.12. The output peak power and energy are 13 MW and 0.568 J, respectively. The calculated energy efficiency ηR is 82%. The energy loss is caused by the spark gaps and the secondary mode impedance, and the loss caused by the secondary mode impedance is negligibly small within the present design.

Fig. 3.12 Output power and energy when the load is resistive in Fig. 3.3 (a)

3.4.2 Experiments on a bipolar corona reactor

To evaluate the multiple-switch Blumlein topology for a more complex load, experiments were done on a bipolar corona reactor [Yan (1990) ]. The schematic diagram of the setup with a corona reactor is shown in Figure 3.13. Compared with the circuit shown in Figure 3.3 (a), the resistive load is replaced by a plasma reactor and an inductor L is added for charging the lines. The inductor L is designed to have a high impedance during the pulse-forming process. The corona plasma reactor consists of two steel “saw blade” arrays. Each array includes nine steel saw blades connected in parallel. The length of each saw blade is 80 cm, and the distance between two arrays is about 8 mm. Details of

Multiple-switch Blumlein generator 49 the reactor are shown in Figures 3.14 (a) and (b). Because the potentials on the two arrays are positive and negative respectively during plasma generation, we call this a bipolar plasma reactor. Figure 3.14 (c) shows a time integrated (0.5 s) photo of the generated corona plasma.

Fig. 3.13 Schematic diagram of the two-switch Blumlein experimental setup with a bipolar corona plasma reactor

Fig. 3.14 Reactor configuration and plasma photo

50 Chapter 3

Fig. 3.15 Typical switching currents in Fig. 3.13

Fig. 3.16 Typical voltage and current on the plasma reactor in Fig 3.13

Multiple-switch Blumlein generator 51

Fig. 3.17 Typical plasma power and energy in Fig. 3.13

Figure 3.15 shows the typical waveforms of the switching currents I s1 and I s2 in switches S 1 and S 2, respectively. As observed with a 49.8 resistive load, the currents are synchronized and identical. Figure 3.16 shows the typical plasma voltage and current waveforms. The peak values of voltage and current are 29 kV and 506 A, respectively. Figure 3.17 shows the typical waveforms of plasma power P plasma and energy E plasma . The peak value of plasma power is 12 MW, and there is nearly no reflection after the first power pulse, which means that most of the electrical energy is transferred to the plasma. The energy conversion efficiency of plasma generation is calculated as: η = E E = P dt 5.0 C V 2 (3.5) plasma plasma total ∫ plasma H 0 where E plasma is the energy absorbed by the corona plasma, as shown in Figure 3.17.

Within the present setup, the energy efficiency η plasma is in the range of 73.2-76.8%, which agrees with previous works [Yan( 2001 )]. For comparison of this efficiency with that for a matched resistive load, we define the relative efficiency as:

ηrelative = η plasma ηR (3.6) The relative efficiency η is in the range of 89.3-93.7%, which indicates that the plasma reactor is well matched and the energy conversion efficiency is in reasonable agreement with that for a matched load.

52 Chapter 3

3.5 Summary

In this chapter, a novel multiple-switch based Blumlein generator was introduced and the circuit topologies with different output configurations were discussed. To gain insight into the mechanism and the characteristics of the multiple-switch Blumlein circuits, an equivalent circuit was introduced and an experimental setup with two spark gap switches was developed.

It was observed that the mechanism of the multiple-switch synchronization is quite similar to that of the TLT based multiple-switch circuit, namely the closing of the first switches will overcharge the switches that are not yet closed. This forces them to close sequentially. During the closing process of the multiple switches, the discharging of the initially charged lines is blocked by the high secondary mode impedance. After all the switches have been closed, the charged lines at the switch side become shorted, at which point the multiple-switch Blumlein behaves similarly to a traditional (single-switch) Blumlein and the output pulse is generated in a similar manner as in the traditional one. The experimental results clearly show that multiple switches can be synchronized for either a resistive load or a plasma reactor. An efficient plasma can be generated by means of this technology, and the switching duty can be reduced by a factor of n (the number of switches).

References

[Blu( 1941 )] A. D. Blumlein. Improvements in or relating to apparatus for generating electrical impulses. UK Patent 589,127, filed Oct. 10, 1941. [Blu( 1945 )] A. D. Blumlein. Apparatus for generating electrical impulses. US Patent 2,496,979, filed Sept. 24, 1945. [Bor( 1995 )] D. L. Borovina, R. K. Krause, F. Davanloo, C. B. Collins, F. J. Agee, and L. E. Kingsley. Pulsed Power Conference. July 3-6, pp. 1394-1399. [Dav( 1991 )] F. Davanloo, R. K. Krause, J. D. Bhawalkar, and C. B. Collins. Pulsed Power Conference. June 16-19, pp. 971-974. [Ros( 2001 )] J. O. Rossi, and M. Ueda. Pulsed Power Plasma Science. Volume 1, June 17-22, pp. 536-539. [Smi( 2002 )] P. W. Smith. Transient electronics: pulsed circuit technology . Chichester: Wiley. [Ver( 2004 )] R. Verma, A. Shyam, S. Chaturvedi, R. Kumar, D. Lathi, et al. Proceedings of the 26 th International Power Modulator Symposium and High-Voltage Workshop . May 23-26, pp. 526-529. [Yan (1990) ] K. Yan, R. Li, M. Cui, L. Zhou, H. Zhao, and H. Zhang. 4th Int. Conf. on Electrostatic Precipitation . Beijing, China, pp. 635-649. [Yan (2001) ] K. Yan. Corona plasma generation. Phd diss., Eindhoven University of Technology (available at http://alexandria.tue.nl/extra2/200142096.pdf ).

Chapter 4 Four-switch pilot setup

There are two possible approaches to generate large pulsed power using the TLT based multiple-switch circuit topology: (i) using a TLT with multiple parallel cables per stage and a few switches, or (ii) using a TLT with a single cable per stage and a large number of switches. In this chapter, a four-switch pilot setup was built for investigation of the first approach. Resistive loads were used to evaluate it and the application of this setup to generate a pulsed corona discharge in water was demonstrated. The synchronization of multiple switches is performed correctly for different output configurations (series/parallel or with independent loads) and different loads. However, the peak output power of the setup was much lower than the expected value. This is mainly caused by the low damping coefficient ξ of the input loop of the TLT. To generate large pulsed power effectively, improvements need to be made to obtain a damping coefficient that is as high as possible as well as a low input impedance of the TLT.

54 Chapter 4

4.1 Introduction

We know from Chapter 2 that after all the switches have been closed, all stages of the TLT are used in parallel equivalently and the output power of the multiple-switch circuit is determined by the switching voltage V s and the input impedance Z in of the TLT and is 2 theoretically equal to V s /Z in . Thus, for generation of a pulse with a large peak power (500 MW-1 GW) and a short width (~50 ns), the input impedance Z in of the TLT must be low. There are two ways to realize a low Z in : (i) using a TLT with multiple parallel cables per stage and a few switches, or (ii) using a TLT with one single cable per stage and a large number of switches. Both approaches have different advantages and disadvantages. For the first approach it is easy to realize the synchronization of a few switches; however, it is complex in mechanical construction. As for the second approach, it is easy for the connection of a TLT with a single cable per stage; however, it becomes critical for the synchronization of a large number of switches. This chapter presents the investigation of the first approach.

4.2 The four-switch pilot setup

To investigate the generation of a large pulsed power using a TLT with multiple parallel cables and a few switches, a four-switch experimental setup was developed. This setup was also used to verify the synchronization of multiple switches for different output configurations; (i) with independent loads, (ii) with a parallel output configuration, and (iii) with a series output configuration. Moreover, this technology was demonstrated on a more complex load, namely a corona-in-water reactor.

Fig. 4.1 Schematic diagram of the four-switch pilot setup

Four-switch pilot setup 55

. Fig. 4.2 Two different output configurations

Fig. 4.3 Photos of the four-switch pilot setup

56 Chapter 4

Figure 4.1 shows the schematic diagram of the pilot setup. It includes seven charging inductors L 1-L7, four high-voltage capacitors CH1 -CH4 , four switches S 1-S4, a 4-stage TLT with four parallel cables per stage, and four independent loads. The inductors have a value of 150 µH. The capacitance value of each capacitor is 3.9 nF. All of the four switches are spark gap switches and one of them (S1) is a triggered switch, while the other three are self-breakdown spark gap switches. The TLT is made from a 1.5-meter-long coaxial cable of type RG217; thus each stage has a characteristic impedance Z 0 of 12.5 , and the input impedance Z in of the TLT is 3.125 . Magnetic cores are placed around stages 1, 2, and 4 to increase secondary mode impedances between two adjacent stages of the TLT (for detailed information about the effect of magnetic cores, please see Section 5.4.3). At the output side, as shown in Figure 4.1, the TLT is connected to independent loads Load 1- Load 4. However, experiments were also conducted with parallel and series output configurations, as shown in Figure 4.2. The photo of the pilot setup with independent loads is shown in Figure 4.3.

4.3 Experiments with resistive loads

4.3.1 Four independent loads

To study the synchronization process of the four switches, an experiment was conducted with four independent loads, as shown in Figure 4.1. The value of each resistive load is about 12.9 , while the characteristic impedance Z0 of each stage of the TLT is 12.5 ; thus the output current on each load is approximately equal to that in the corresponding switch. Therefore, the output currents can be used to monitor the switching behaviors of the four switches. Figure 4.4 gives the typical waveforms of output currents I1-I4, where I 1-I4 refer to the currents in loads Load 1-Load 4 respectively. As observed on the two-switch experimental setup described in Section 2.2, the switching process has two distinctive phases. After switch S 1 is first triggered at -57 ns, the first phase starts. During this first phase switches S 2-S4 closed at -32 ns, -15 ns and -4 ns respectively. The time lag between the closing of two switches becomes shorter since more overvoltage occurs on the switches that are not yet closed. The small pre-pulse of switching currents in the first phase is caused by the charging inductors and secondary mode impedance, and almost no energy will be transferred to the load. When all the switches are closed, the first phase ends. Then, the second phase starts, in which the TLT behaves as a current balance transformer and the switching currents are determined by the characteristic impedance of the TLT. Now the capacitors will be discharged rapidly and simultaneously into the load via the TLT. The peak values of currents I 1-I4 are 980 A, 947 A, 939 A and 947 A, respectively.

Four-switch pilot setup 57

Fig. 4.4 Typical output currents through the four independent loads in Fig. 4.1

4.3.2 Parallel output configuration

Outputcurrent[kA]

Fig. 4.5 Typical output current for the parallel output configuration (Fig. 4.2 (a)) at a switching voltage of about 27 kV

58 Chapter 4

Fig. 4.6 The calculated output power and energy for the measured current shown in Figure 4.5

Figure 4.5 gives the typical output current when all the stages of the TLT are connected in parallel to a load, as shown in Figure 4.2 (a). For the parallel configuration, the output impedance of the TLT is very low (i.e. 3.125 ). The value of the load is about 3.25 . In Figure 4.5, the peak value and the rise-time (10-90%) of the output current are 3.72 kA and 37 ns respectively. The peak value of the output current approximately equals that of the sum of the currents I 1-I4 (3.81 kA) shown in Figure 4.4. In addition, the output power P out and the output energy E out were calculated as: 2 Pout = I out RLoad (4.1) E = P dt (4.2) out ∫ out

In the above equations, I out and R Load refer to the output current and the value of the resistive load respectively. Figure 4.6 shows the calculated P out and E out according to the current in Figure 4.5. The peak output power and the output energy were 45.2 MW and 4.15 J respectively.

Four-switch pilot setup 59

4.3.3 Series output configuration

Fig. 4.7 Typical output current waveform for a series output configuration with R Load =49.8 in Fig. 4.2 (b)

Fig. 4.8 The calculated output power and energy for the measurement shown in Figure 4.7

60 Chapter 4

Experiments were also done on a series output configuration, as shown in Figure 4.2 (b). For the series configuration, the output impedance of the TLT is 50 . The resistance value of the load used in this experiment was about 49.8 . Figure 4.7 shows the typical output current at a switching voltage of about 27 kV. The peak value and the rise-time (10-90%) of the output current are 971 A and 30 ns respectively. The output current is roughly equal to the values of the currents shown in Figure 4.4. Based on the measured output current, the output power P out and the output energy E out were calculated using (4.1) and (4.2), and are shown in Figure 4.8. The peak output power and the output energy were 47 MW and 4.19 J respectively.

4.3.4 Analysis

According to the experiments on resistive loads described above, the synchronization of the four switches is performed correctly and is independent of the output configuration. Since the present setup was operated at a switching voltage of 27 kV and has an input 2 impedance Z in of 3.125 , the theoretical peak output power P theoretical given by V s /Z in should be 233 MW. However, the obtained output peak power P out is 45-47 MW, which is much smaller than the theoretical value and is only about 20% of P theoretical .

Fig. 4.9 Equivalent circuits for each stage of the setup after all switches are closed

Four-switch pilot setup 61

To gain insight into the reason for the low peak output power of the pilot setup, equivalent circuits shown in Figure 4.9 were used. Figure 4.9 (a) represents one stage of the present setup after the synchronization of all switches, where the resistance of the switch is ignored, and L s and Z Load represent the effective stray inductance per stage and the effective load per stage respectively. Representing each stage of the TLT by its characteristic impedance Z 0 at the input side and by a voltage source of 2V in in series with Z0 at the output side, one may derive the simplified circuit shown in Figure 4.9 (b), where Vin and V out are the voltage input into the transmission line and the output voltage across the load respectively. From the simplified circuit, one can derive (4.3) and (4.4).

4Z0 ⋅ Z Load 2 2 λ p = 2 ⋅ 4G ()()ξ ≤ 4G ξ = λ p (4.3) ZLoad =Z0 ()Z0 + Z Load

 2  1 − ξ    − a tan( )    ξ  ξ ⋅ exp   when 0 < ξ < 1  2   1 − ξ      ξ   G(ξ) =  e−1 when ξ = 1 (4.4)    ξ 2 −1   − a tanh( )    ξ  ξ ⋅ exp   when ξ > 1   ξ 2 −1       ξ 

In the above equations, the coefficient λp=P out /P theoretical and ξ is the damping coefficient of the input loop of the TLT, which is equal to Z0 (2 Ls C0 ). From (4.3), it can be seen that coefficient λp is a function of Z 0, Z Load and the damping coefficient ξ. When the TLT is matched (i.e. Z Load =Z 0), λp is equal to λ p and is only determined by the damping ZLoad =Z0 coefficient ξ.

Figure 4.10 gives the dependence of the λp on the damping coefficient ξ when the TLT is matched. It clearly shows that λp changes nonlinearly as a function of ξ, and the higher the value of ξ, the larger λp becomes. Especially values of ξ from 0 to 4 have a significant influence on the λp. Looking at the current waveforms obtained on the pilot setup, one can see that they are apparently under-damped. And the damping coefficient ξ can be calculated by the following equation;  2   π  ξ = 1 1 + 2  (4.5)  ln (λI )  where λI is the absolute ratio of the first positive peak current value to the first negative peak value. Based on the current waveforms, the damping coefficient ξ of the present setup is approximately 0.55. According (4.3), the value of λp when ξ=0.55 is 33% for a

62 Chapter 4 matching situation. Under the assumption of no energy losses, the peak output power should be 76 MW when ξ=0.55. This is still unacceptably low compared to the theoretical 2 value of 233 MW given by V s /Z in .

1

0.8 Zload=Z0 |

p 0.6

λp=0.33

Theratioλ 0.4

ξ=0.55 0.2

0 0 1 2 3 4 5 6 7 8 9 10 11 12 Thedampingcoefficientξ

Fig. 4.10 Dependence of λp on the damping coefficient ξ when Z Load =Z 0

From the above discussions, one can determine that the peak output power of the present setup is significantly limited by the low damping coefficient ξ, namely due to the stray inductance of the input loop of the TLT. To reduce the stray inductance, the structure must be compact. However, it is difficult to improve the compactness due to mechanical complexity when a TLT with multiple parallel cables per stage is used. To obtain a high damping coefficient, a TLT with a single cable per stage has the following advantages: (i) simpler mechanical construction, (ii) each stage has a larger characteristic impedance Z 0, thus the damping coefficient ξ is higher since ξ = Z0 (2 Ls C0 ), (iii) a low input impedance Z in can also be obtained when a large number of stages are used. The development of a prototype system using a TLT with a single cable per stage will be presented in Chapter 5.

Four-switch pilot setup 63

4.4 Demonstration of the pilot setup on a corona-in-water reactor

To verify the application of the four-switch system on a more complex load, experiments were done on a corona-in-water reactor. Pulsed corona generation in water is an interesting application of this technology. The discharge in water creates chemical species such as OH radicals, ozone and hydrogen peroxide (H 2O2) as well as UV and shock waves [Loc(2006), Sat(1996), Gry(2003), Gry(2001)]. It is effective for the degradation of organic compounds (phenol, organic dye, etc.) and for sterilization [Hay(2001), Gry(1999), Gra(2006)]. Within the present work, a corona-in-water reactor as shown in Figure 4.11, was built and tested. Both anode and cathode are immersed into the liquid. The anode is a 12cm long hollow brass tube with thin pins, so a very strong electrical field can be generated near the tip of the pins. Moreover, small holes with a diameter of 1 mm were drilled along the length of the brass tube. Thus the air can be bubbled into the liquid via the hollow brass tube and the air bubbles are diffused along the brass tube over the entire reactor volume. The cathode is a metal mesh cylinder, and its diameter and length are 9 cm and 20 cm respectively. The vessel was made from Perspex, and it holds 1.4 liters of liquid. The discharge in water was realized using the present pilot setup with a series output configuration. Both deionized water and tap water were tested; moreover, the degradation of dye (Methylene blue) was tested.

Fig. 4.11 Photo of the corona-in-water reactor

64 Chapter 4

4.4.1 Discharging in deionized water

Figure 4.12 shows photos of the discharge in deionized water. Figure 4.12 (a) shows the discharge when no air bubbling was used, while Figure 4.12 (b) shows the discharge when air bubbling was used. When no air was bubbled into the water, multiple strong streamers were generated near the pin tips. When air bubbling was used, the streamers were produced in air bubbles.

Fig. 4.12 Photos of the discharge in deionized water: (a) no air bubbling, (b) with air bubbling

Figures 4.13 and 4.14 show typical waveforms of the reactor voltage and current without and with air bubbling respectively. Some time difference can be observed between the peaks of the current and voltage; obviously the voltage is lagging the current. This is because the reactor behaves like a capacitor before corona inception. The capacitance of the reactor is estimated to be 330 pF. The initial water resistance of the reactor was 6.4 k. From Figure 4.13, one can see that the peak output voltage and current are 100 kV and 882 A, respectively. However, with air bubbling the peak output voltage and current are 89.3 kV and 885 A respectively. Furthermore, the negative peak current was reduced from -540 A to -367 A. The power and energy injected into the reactor are shown in Figure 4.15, where P 1 and E 1 are the output power and energy respectively in the case of no air bubbling; and P 2 and E 2 are the output power and energy respectively in the case of air bubbling. The peak values of P 1 and P 2 are 47 MW and 51 MW, respectively; the energy values E1 and E 2 are 0.77 J and 1.62 J, respectively. One can see that by using the air bubbles much more energy can be injected into the reactor.

Four-switch pilot setup 65

Fig. 4.13 Typical voltage and current when deionized water and no air bubbles were used

Fig. 4.14 Typical voltage and current when deionized water and air bubbles were used

66 Chapter 4

Fig. 4.15 Typical power and energy injected into the reactor filled with deionized water (P1 and E 1 are the power and energy in the case of no air bubbling; P 2 and E 2 are the power and energy in the case of air bubbling)

4.4.2 Discharging in tap water

As was the case with deionized water, tap water was also tested under two conditions (i.e. with and without air bubbling). The initial resistance of the reactor filled with the tap water was 103 . In the case of no air bubbling, only a very few weak streamers occurred near the pin tips; while in the case of the air bubbling, more streamers were generated, which seemed similar with the streamers shown in Figure 4.12 (b). In terms of the electrical characteristics, the discharge in tap water was found to be quite different from that in the deionized water, and the reactor acted more like a resistive load. Figure 4.16 gives the typical voltage and current for the discharge in tap water without air bubbles. The peak output voltage and current were 62.2 kV and 984 A, respectively. In addition, it was observed that the electrical characteristics of discharging in tap water for both cases (i.e. no air bubbling and with air bubbling) were quite similar. The power and energy injected into the reactor are almost the same for both situations, as shown in Figure 4.17. This implies that, for the discharge into a liquid with a high conductivity, air bubbling does not contribute much to the total energy injection.

Four-switch pilot setup 67

Fig. 4.16 Typical voltage and current of the discharging into tap water without air bubbles

Fig. 4.17 Typical power and energy injected into the reactor filled with tap water (P1 and E1 are the power and energy in the case of no air bubbling; P 2 and E 2 are the power and energy in the case of air bubbling)

68 Chapter 4

4.4.3 The dye degradation

A volume of 1.4 liters of dye (Methylene blue) solution at an initial concentration of 10 mg/l was tested with air bubbling at a flow rate of 20 l/min. The pulsed discharge was generated at a repetition rate of 15 pps (pulses per second). The resistance of the reactor and the dye concentration were measured every 30 minutes. Figure 4.18 shows the dependence of the reactor resistance and dye concentration on the treatment time. With increasing treatment time, the resistance of the reactor decreased: it dropped particularly dramatically within the first 30 minutes, from 2.89 k to 458 , and it reached a minimal value of 130 after 150 minutes. This is close to the resistance of the tap water reactor. This indicates that the conductivity of the dye solution increases with treatment time. This is caused by the erosion of the pin electrode and dye decomposition. It was observed that the discharge in the dye solution is initially similar to the discharge in deionized water, while it looked more and more like discharging in tap water with increasing treatment time. From Figure 4.18 one also can see that the dye concentration of the dye solution dropped from 10 mg/l to 6.22 mg/l; this occurred most rapidly during the period from 0 to 30 minutes during which it dropped by 2 mg/l. A detailed chemical analysis during the dye degradation was reported elsewhere [Gra (2006) ].

Fig. 4.18 Dependence of the solution resistance and the dye concentration on treatment time

Four-switch pilot setup 69

4.5 Conclusions

A four-switch pilot setup using a TLT with four parallel cables per stage was developed and tested with different output configurations. Also the application of this setup to generate a pulsed corona discharge in water was demonstrated.

The multiple switches can be synchronized for each of possible output configuration (with independent loads, or the parallel configuration or the series configuration). However, the obtained peak output power was lower than the theoretical value. Analysis shows that the low output power of the pilot setup is mainly caused by the low damping coefficient ξ of the input loop of the TLT, and to generate large pulsed power effectively, the coefficient ξ must be as high as possible. To obtain a high damping coefficient, a TLT with a single cable per stage has the following advantages: (i) simpler mechanical construction; (ii) each stage has a larger characteristic impedance Z 0, thus the damping coefficient ξ is higher since ξ = Z0 (2 Ls C0 ). (iii) a low input impedance Z in can be obtained as well when a large number of stages are used.

Proper operation of the setup was also realized on a more complex load (i.e. a corona- in-water reactor). The experiments showed that the discharge in liquid is sensitive to the conductivity of the liquid. For a liquid with a high conductivity, the reactor behaves as a resistive load and thus more energy can be injected into the reactor; however, the air- bubbling contributes little to the total energy injection.

References

[Hay( 2001 )] D. Hayashi, W. F. L. M. Hoeben, G. Dooms, E. M. van Veldhuizen, W. R. Rutgers, and G. M. W. Kroesen. LIF diagnostic for pulsed-corona-induced degradation of phenol in aqueous solution. J. Phys. D: Appl. Phys . 33, pp. 1484- 1486. [Gra( 2006 )] L. R. Grabowski. Pulsed corona in air for water treatment. PhD diss., Eindhoven University of Technology, ISBN 90-386-2441-7 (http://alexandria.tue.nl/extra2/200610478.pdf). [Gry( 2001 )] D. R. Grymonpre, A. K. Sharma, W. C. Finney, and B. R. Locke. The role of Fenton’s reaction in aqueous phase pulsed streamer corona reactors. Chemical Engineering Journal, 82, pp. 189-207. [Gry( 1999 )] D. R. Grymonpre, W. C. Finney, and B. R. Locke. Aqueous-phase pulsed streamer corona reactor using suspended activated carbon particles for phenol oxidation: Mode-data comparison. Chemical Engineering Science 54, pp. 3095- 3105. [Gry( 2003 )] D. R. Grymonpre, W. C. Finney, R. J. Clark, and B. R. Locke. Suspended activated carbon particles and ozone formation in aqueous-phase pulsed corona discharge reactors. Ind. Eng. Chem. Res. 42, pp. 5117-5134.

70 Chapter 4

[Loc( 2006 )] B. R. Locke, M. Sato, P. Sunka, M. R. Hoffmann, and J. -S. Chang. Electrohydraulic discharge and nonthermal plasma for water treatment. Ind. Eng. Chem. Res. 45, pp. 882-905. [Sat( 1996 )] M. Sato, T. Ohgiyama, and J. S. Clements. Formation of chemical species and their effects on microorganisms using a pulsed high-voltage discharge in water. IEEE Transactions on Industry Applications Vol. 32, No. 1, January/February 1996.

Chapter 5 Ten-switch prototype system

This chapter describes another approach to generate pulsed power by means of the presented multiple-switch technology, namely with a large number of switches and a TLT with one cable per stage. Based on this approach, a prototype system with ten spark gap switches and a ten-stage TLT was developed. It is charged by a resonant charging system.

To charge the system, a high winding ratio (1:80) transformer with a magnetic core has been developed. One critical issue related to the magnetic transformer is the saturation of the core. An equivalent circuit was introduced to analyze the swing of the flux density inside the core. It was found that for a given energy transfer per pulse, the volume of the core must be larger than a critical value, which is dominated by the coupling coefficient. The transformer was designed on the basis of this model. The core was made from 68 ferrite blocks. The experimental results are in good agreement with the values given by the model and the glued ferrite core works well. Using this transformer, the ten-switch system can be charged to more than 70 kV. With 26.9 J of energy conversion transfer per pulse, the energy efficiency of the transformer was around 92%.

Compared with the four-switch setup, this ten-switch prototype consists of ten spark gap switches and a ten-stage TLT with one cable per stage. The ten switches are air pressurized and blown by the forced air flow. They are installed in one single compartment. Consequently, they “see” each other’s UV and other discharge products, which will improve the switching process. Moreover, the high-voltage capacitors, the switches, and the TLT are integrated into one compact structure, which will improve the pulse rise- time. The results show that using the TLT with one cable per stage and a large number of switches is an efficient way to generate large pulsed power. The ten switches can be synchronized within about 10 ns. An output pulse with a rise-time of about 10 ns and a pulse width of about 55 ns has been realized. More than 0.8 GW of output power was obtained. The energy conversion efficiency varies between 93% and 98%.

72 Chapter 5

5.1 Overview of the system

Figure 5.1 shows the schematic diagram of the ten-switch prototype system. It includes a resonant charging system and a ten-switch pulsed power unit.

The resonant charging unit was developed earlier and has been used successfully [Yan( 2001 ), Nai( 2004 ), Win( 2007 )]. It includes a three-phase rectifier, a storage capacitor C0, a low-voltage capacitor C L, a charging inductor L 0 and three thyristors Th 1-Th 3, a transformer TR, a resistor R 1, and diodes D 1 and D 2. It can charge the high-voltage capacitors repetitively (up to 1000 pps). The charging voltage depends on the value of low-voltage capacitor C L and the ratio of the transformer. To charge the high-voltage capacitors to around 70 kV, a high-ratio transformer was developed. An equivalent circuit model was also developed for designing the transformer. Detailed information about the design and the testing results will be presented in Section 5.3.

The ten-switch unit consists of nineteen inductors L 1-19 , ten high-voltage capacitors CH1-H10 , ten switches S 1-10, a ten-stage TLT, and a load. The ten high-voltage capacitors are interconnected in series to the TLT via the ten switches. The ten switches are high- pressure spark gap switches, and the switch S 1 is a triggered switch with an LCR trigger circuit, while the others are self-breakdown switches. The layout of the ten switches was designed to be very compact to minimize stray inductance. The TLT is made from coaxial cable (RG218) and each line is 2 m long. Magnetic cores are placed around the coaxial cables for the purpose of synchronization. The length of each cable that is covered by the magnetic cores is about 1 meter. At the output side of the TLT, the transmission lines are connected in parallel to a 5 resistive load.

Compared with the four-switch pilot setup, several improvements are made: (i) the setup was designed to be very compact to minimize stray inductance, (ii) one cable per stage is used instead of four cables in parallel per stage; (iii) the number of switches is increased to ten; (iv) more efficient (i.e. high-pressure) switches are used (switching voltage can be adjusted by pressure). With these improvements, a high damping coefficient ξ of the input loop of the TLT will be obtained, and the input impedance of the TLT will be low as well. As discussed in Section 4.3.4, a large pulsed power with a faster switching time and a high energy efficiency should be obtained. Efficient large pulsed power can be realized with this approach. The ten switches can be synchronized within about 10 ns. An output pulse with a rise-time of 10 ns and a pulse width of about 55 ns has been realized. More than 800 MW peak output power was obtained. The energy conversion efficiency varies between 93% and 98%. Detailed information about the ten- switch system is presented in Section 5.4.

Ten-switch prototype system 73 Stage9 Stage2 Stage1 TLT Stage10 1 2 9 10 S S S H10 H9 H2 S L C R C C C + + + Tenswitchsystem + H1 3 2 1 16 19 18 17 C L L L L L L L ype 2 1 D 1 D R TR 2 L Th C 0 3 L Th Fig.5.1Schematicdiagramofthetenswitchprotot 1 0 Resonantchargingsystem Th C 1 3 2

74 Chapter 5

5.2 Resonant charging system

The principle of the resonant charging unit was comprehensively discussed previously [Yan( 2001 )]. Initially, the storage capacitor C 0 is charged up to V 0 (~535 V). The system accomplishes one charging cycle via three steps. As an example, Figure 5.2 shows the typical voltages on the low-voltage capacitor C L and the high-voltage capacitor C H during one charging cycle. First, by closing thyristor Th 1, capacitor C L is charged from the storage capacitor C 0 from a voltage ∆VL(i-1) to a voltage V L(i). Secondly, after the charging of C L is finished and thyristor Th 1 is switched off, by closing thyristor Th 2 capacitor C H is charged from 0 to the voltage V H(i) by C L via transformer TR. Then, after the charging of C H is finished and thyristor Th 2 is switched off, CH is discharged via the spark gap switch. Finally, with thyristor Th 3, the polarity of the remaining voltage on C L can be reversed from -∆VL(i) to ∆VL(i). The i is the charging cycle sequence number. Figure 5.2 was obtained with the newly designed transformer within the present charging 2 unit in the case of C L

2 Fig. 5.2 Typical voltages on C L and C H during one charging cycle for the case of C L

Ten-switch prototype system 75

Ideally, namely assuming an ideal transformer and no energy losses in the circuit, one may derive the following expressions of V L(i), ∆VL(i), and V H(i) when the charging system is operated properly. C + n2 C L H ⋅ V when C < n2 C  2 0 L H n CH lim VL (i) =  2 (5.1) i→∞ C + n C  L H ⋅ V when C ≥ n2 C  0 L H  C L  2 n C H − C L 2  2 ⋅V0 when C L < n C H  n C H lim V L(i) =  2 (5.2) i→∞ C − n C  L H ⋅V when C ≥ n 2C  0 L H  C L

 CL 2 2nV 0 ⋅ 2 when CL < n CH lim VH (i) =  n C (5.3) i→∞ H  2 2nV 0 when CL ≥ n CH

From the above equations, it can be seen that the values of V L(i), VL(i), and V H(i) are stabilized when the charging cycle sequence number i approaches infinity. We call this the steady situation. Under the steady situation, the voltage V H on C H is a function of C L for a 2 given value of C H; when C L

5.3 Transformer

5.3.1 Introduction

Transformers are often used in a resonant mode in pulsed power systems to step up the charging voltage. This may be either an air-core transformer or a magnetic-core transformer. For the air-core transformer, there is no saturation problem, and it is light- weight and easy to construct. However, the coupling coefficient k is low (normally k<0.8) [Lee( 2005 ), Zha( 1999 )]. To obtain efficient energy transfer, the air-core transformer is normally used in dual resonant mode (i.e. as a Tesla transformer) [Fin( 1966 )], and at least one primary oscillation cycle is required to accomplish the charging process (when k=0.6) [Den( 2002) ]. Moreover, the charging voltage is bipolar, which makes it difficult to use semiconductor switches (thyristor, IGBT, and MOSFET) or magnetic switches. When a magnetic core is used, a high coupling coefficient (k>0.99) can be obtained [Mas( 1997 ), Win( 2007 )]. By using a magnetic-core transformer, an efficient energy transfer can be realized with only a half of the primary oscillation cycle (i.e. in single resonant mode).

76 Chapter 5

(For more information about the role of the coupling coefficient k in the resonant circuit, please see Appendix A).

One critical issue associated with the magnetic-core transformer is the saturation of the core. Though the coupling coefficient of a magnetic-core transformer is high, it is always less than 1. In a resonant circuit, the unavoidable leakage inductance affects the charging time and thus also affects the flux density in the core. The influence of the coupling coefficient k has never been reported in literature. In this section, an equivalent circuit is developed to evaluate effects of the coupling coefficient k on the core volume and the magnetizing energy. Based on this model, a high-ratio magnetic transformer was developed. Ferrite blocks were adopted to make the core. A total of 68 blocks were used, and they were glued with epoxy resin. Along the magnetic path of the core, there are 17 air gaps due to the inevitable joints between the blocks. The transformer was tested on a resonant charging system. It was found that the glued ferrite core works well and the output capacity of the transformer meets the design requirement. Detailed information about the effect of the coupling coefficient k, the design of the transformer, and the testing results will be presented.

5.3.2 Effects of the coupling coefficient k

Figure 5.3 shows the resonant charging circuit and its equivalent circuits. The resonant circuit, as shown in Figure 5.3 (a), includes a low-voltage capacitor C L, a stray inductor L s induced by connection leads, a transformer TR, a diode D, and a high voltage capacitor CH. When stray capacitance is neglected, the transformer TR can be represented by an ideal transformer in combination with two uncoupled inductors [Tho( 1998 )], as shown in Figure 5.3 (b), where L 1 and L 2 are the primary and secondary inductance of transformer TR respectively. The k is the coupling coefficient of transformer TR and equals M L1L2 (M is the mutual inductance of the transformer) and n is the ratio of the 2 transformer and equal to M/L 1 or k L2 L1 . By transferring the inductance (1-k )L 2 and capacitor C H to the primary side of transformer TR, one can derive the equivalent circuit shown in Figure 5.3 (c). Here the primary inductor L 1 is neglected since its value is much 2 2 larger than L 1(1-k )/k for a magnetic-core transformer.

Suppose that the transformer is operated linearly and under the matching condition (i.e. 2 CL=n CH). Then one may derive the following equations from the model shown in Figure 5.3 (c).

VL (0) L − Ls VPri (t) = (1 + cos ωt) 0 ≤ωt ≤ π (5.4) 2 L + Ls

T = π (L s + L)C (5.5) ∆ T 1 πV )0( CL L 1 B = V (t dt) = L 1 s + ( − )1 (5.6) AN ∫ Pr i 2 N A L k 2 1 0 1 1

Ten-switch prototype system 77

In the above equations, V Pri (t), ∆T, and ∆B are the voltage on the primary, the charging time, and the incremental flux density inside the core respectively. L is the leakage 2 2 inductance and equal to L 1(1-k )/k , and C=C L/2. A and N 1 are the cross-section area of the core and the number of turns of the primary winding respectively. The inductance of the primary winding can be written as: N 2 µA L = 1 (5.7) 1 l In (5.7), µ and l are the permeability of the core and the mean length of the magnetic path respectively. Substituting (5.7) into (5.6), one may derive the relationship between the ∆B and the volume of the core [A ℓ].

Fig. 5.3 (a) the resonant charging circuit, (b) the real transformer is represented by an ideal transformer combined with two uncoupled inductors, (c) the simplified equivalent circuit, where the components at the secondary side are transferred to the primary side

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π E L 1 B = s + ( −1) (5.8) l 2 2 A L1 k 2 where, E is the energy transferred per pulse and equal to CVL (0). From (5.8), it can be seen that ∆B is a function of the energy transferred per pulse E, the volume of the core [A ℓ], the ratio of L s to L 1, and the coupling coefficient k.

For proper operation, ∆B must be less than the allowable swing of the flux density ∆Bm of the applied magnetic material. Therefore the volume of the core must be designed to match the following condition. π2E L 1 π2E 1 l s l [A ] ≥ 2 [ + ( 2 −1)] > 2 ( 2 −1) = [A ]critical (5.9) 4Bm L1 k 4Bm k From the above equation, one can see that the volume of the core must be larger than a critical volume [A ℓ]critical , which is determined by the coupling coefficient k.

In a transformer, energy is needed to support the magnetic flux inside the core during the charging process. This energy is called magnetizing energy E M and can be estimated as: 2 2 π E 1 Ls π E 1 E M = [( 2 −1) + ] > ( 2 −1) (5.10) 8 k L1 8 k

From (5.10) it can be seen that the magnetizing energy E M is a function of the energy per pulse E, the coupling coefficient k and the ratio of L s to L 1. When the stray inductance L s is negligible, the magnetizing energy is mainly determined by the coupling coefficient k. For instance, if k=99.6%, then at least 0.99% of the energy transferred per pulse is used to magnetize the core.

It is noted that the calculated values for T and B on the basis of the model described above are a little larger than the actual values. The higher the coupling coefficient k, the less the difference becomes. Especially when k>99%, the differences for T and B are less than 0.5% and 1.4% respectively.

5.3.3 Design and construction

The transformer is designed for the resonant charging unit to charge the high-voltage capacitor C H (about 10 nF) to a voltage of around 70 kV, where the low-voltage capacitor CL is initially charged to about 1 kV. Thus the voltage transfer ratio of the transfer needs to be at least about 1:70; in practice, the winding ratio was chosen to be 1:80. Ferrite blocks were used to construct the core. With regard to the ferrite material, the relative permeability, the saturation flux density, and the residual flux density are 2400, 0.5 T, and 0.15 T respectively. The dimensions of each ferrite block are 5cm×5cm×10cm. The ferrite blocks are glued together by epoxy resin to obtain the desired core shape and dimensions. The advantage of using discrete ferrite blocks is the flexibility in construction of various kinds of cores (C-type or shell type) with various dimensions.

Ten-switch prototype system 79

(a) Determine the volume of the core

70cm 60cm

Fig. 5.4 The transformer core

To estimate the critical volume of the ferrite core according to (5.9), the following assumptions were made: (i) The stray capacitance of the transformer is assumed to be around 0.5 nF and is added to the high-voltage capacitor C H. So C H becomes 10.5 nF; and 2 thus under the matching condition C L=n CH, the transferred energy per pulse E is about 33 J. (ii) According to the specification of the ferrite material, the allowable swing of the flux density is 0.35 T; in this design, a value of ∆Bm=0.3 T was used. (iii) The coupling coefficient k and the relative permeability r of the core were empirically set to be 0.996 and 1200 respectively. Under these assumptions, from (5.9), the critical volume of the core was estimated to be 11190 cm 3, which means that at least 45 ferrite blocks are needed. Due to the stray inductance, and to ensure the proper operation of the transformer, 68 ferrite blocks were actually used. By gluing these blocks together with epoxy resin, a shell-type core was made, as shown in Figure 5.4. The size of the core is 50cm×10cm×70cm; other dimensions are also shown in Figure 5.4. Except for the two removable blocks on the top, all the blocks are glued together. The mean length of the magnetic path is 1.7 m. Along the magnetic path, there exist 17 air gaps due to the

80 Chapter 5 inevitable joints between the blocks. And the initially estimated length of the 17 gaps is between 0.5 mm and 1 mm.

(b) Select the number of turns of the primary

The number of turns of the primary winding N 1 was chosen according to the specification of the resonant charging unit. To keep the charging unit within safe margins, the maximum primary current must be less than the current rating of thyristor Th 2 in the present resonant unit (2 kA). Based on the model shown in Figure 5.3 (c), with the assumptions of k=0.996 and L s=0 the peak primary current was estimated for different numbers of turns, from 10 to 20. These estimations were made for two different total lengths of air gaps (i.e. 1 mm and 0.5 mm respectively). The primary turn number N 1=16 was chosen, since for this value the primary peak current will stay within safe margins. In addition, other parameters (e.g. the equivalent r, primary inductance L 1) were evaluated when N 1=16, as shown in Table 5.1. One may find the transformer will be operated properly with N 1=16, provided it could be ensured that the total length of air gaps was between 0.5 mm and 1 mm.

Table 5.1 Evaluation of the design when N 1=16

(c) Construction

The 16-turn primary winding was made from copper foil with a thickness of 1 mm and a width of 29 mm. The windings are wound on a square bobbin made from fiberglass. The secondary winding has 1280 turns and is wound on a cone-shaped fiberglass bobbin. It was made from copper wire with a diameter of 0.42 mm. To reduce the winding resistance, two parallel layers were used. They were interconnected at the middle (i.e. the top layer goes to the bottom and the bottom layer goes to the top). Both the primary and the secondary windings are placed around the middle leg of the core. An aluminum cylindrical screen with a 1 cm split was put between primary and the secondary to prevent the capacitive coupling between the primary and the secondary. The secondary winding is equipped with a round ring to control the high electric field. The two outer legs of the core are also provided with field-control aluminum parts. The whole transformer is supported

Ten-switch prototype system 81 by a wooden frame. A photo of the transformer is shown in Figure 5.5. This transformer is immersed into transformer oil. The parameters were measured using an LCR meter and are shown in Table 5.2. According to the primary inductance, the effective µ r and the total length of air gaps are estimated to be 1238 and 0.665 mm respectively; they are within the estimated ranges shown in Table 5.1. A coupling coefficient of 99.62% was obtained, and the actual ratio n is about 1:75.4.

Fig. 5.5 Photo of the transformer

Table 5.2 Parameters of the transformer

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5.3.4 Testing of the transformer

Fig. 5.6 Schematic diagram of the testing setup

The designed transformer (TR) was tested within a setup as shown in Figure 5.6. It consists of a resonant charging unit and a high-voltage pulser. The resonant charging unit is the same as that shown in Figure 5.1. The high-voltage pulser includes a high-voltage capacitor C H, a switch S, an LCR trigger circuit, and a resistive load. The switch S is a multiple-gap spark gap switch [Liu(2006)] consisting of three 9 mm gaps. The LCR trigger circuit consists of an inductor L, a capacitor C and a resistor R [Yan(2003)]. The value of C H is about 10.37 nF, and the load is about 81.5 .

Fig. 5.7 Dependence of the voltage V H on the value of C L when C H=10.37 nF

Ten-switch prototype system 83

Experiments were conducted with values of C L varying from 41.1 µF to 67 µF, while the value of high-voltage capacitor C H was kept the same at 10.37 nF. For these values, the voltage V H on the high-voltage capacitor C H was measured when the test setup was operated in a steady situation. Figure 5.7 shows the dependence of the voltage V H on the value of low-voltage capacitor C L. It can be seen that the voltage on C H increases linearly when increasing the value of low-voltage capacitor C L from 41.1 µF to 57.9 µF. While upon increasing C L from 60.6 µF to 67 µF, voltage V H remains at a constant value of over 2 70 kV, since C L>n CH. We can conclude that the designed transformer meets the voltage requirement. From Figure 5.7, we also can find that the relationship between voltage V H and the value of C L is in good agreement with equation (5.3). In addition, from Figure 5.7, 2 the matching value of C L (where C L=n CH) is approximately 59 µF, which is slightly less than the theoretical value of 60.3 µF (the stray capacitance of the transformer was taken into account). This is due to the fact that the high-voltage capacitors used for C H are slightly voltage dependent, and the capacitance may become slightly smaller at a high voltage.

Fig. 5.8 Typical voltages on C L and C H during one charging cycle under steady operation when C L=60.6 µF and C H=10.37 nF in Fig. 5.6

2 The experiments with the value of CL=60.6 µF (C L>n CH) were used to evaluate the transformer. Figure 5.8 shows the voltages on C L and C H during one charging cycle under steady operation. The low-voltage capacitor C L was charged to 965 V from an initial voltage of 16 V. After closing thyristor Th 2, the voltage on C L dropped to 16 V again and the high-voltage capacitor C H was charged up to 70.3 kV. Then spark gap switch S is triggered and high-voltage capacitor C H discharges into the load. In contrast to the 2 situation shown in Figure 5.2, the voltage on C L does not become negative since C L>n CH.

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1600 1200

1400 1000 1200 Voltage Current 1000 800

800 600

600 400 400

200 Primarycurrent[A] Primaryvoltage[V] 200

0 0 79s 200 200 400 80 100 120 140 160 180 200 220 240 260 Time[s]Time[s]

Fig. 5.9 Typical voltage and current on the primary winding of the transformer

when C L=60.6 µF and C H=10.37 nF in Fig. 5.6

Fig. 5.10 Swing of the flux density ∆B inside the transformer core in Fig. 5.6

Ten-switch prototype system 85

Figure 5.9 shows the typical voltage and current on the primary winding of the transformer when C L=60.6 µF. It can be seen that the peak value of the primary current is 1.14 kA. This is about 57% of the current rating of thyristor Th 2, which indicates that the design of the transformer ensured the switch is used safely. Furthermore, according to the current waveform shown in Figure 5.9, the charging time is about 79 s. The leakage 2 2 inductance of the transformer L 1(1-k )/k is about 17.8 H, thus the stray inductance L S in the present test system is approximately 2.9 H. By integrating the primary voltage shown in Figure 5.9, the swing of the flux density inside the core can be estimated, and the result is shown in Figure 5.10. It can be found that when the charging is finished, the increased flux density inside the core is 0.23 T, which means that the design of the transformer ensured the core became unsaturated. This value is in good agreement with the theoretical value of 0.232 T given by equation (5.6). The further increase of the flux density after the charging has been finished is caused by the voltage oscillation between the primary and the secondary (as shown in Fig. 5.9).

Fig. 5.11 The values of E in and E out when C L=60.6 µF under steady operation in Fig. 5.6

The total energy conversion efficiency η of the transformer was evaluated by the following equation: V (t)I (t)dt E ∫ H H η = out = (5.11) E in V (t)I (t)dt ∫ pri pri

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where E in and E out refer to the energy input into the transformer and the energy output from the transformer, namely the energy that flowed out of diode D 2. V Pri (t), V H(t), I Pri (t) and I H(t) refer to the voltage across the primary of the transformer, the voltage on C H, the current in the transformer primary winding, and the current flowing out of the transformer secondary winding respectively. These four parameters were measured simultaneously when C L=60.6 µF under steady operation. The calculated values of E in and E out are given in Figure 5.11. When the charging is complete, the values of E in and E out are 26.9 J and 24.7 J respectively, thus the energy efficiency is 91.8%. The losses are mainly caused by the resistance of the primary and secondary windings, the secondary stray capacitance, and the transformer core (magnetizing energy E M and eddy current). The losses caused by them were estimated to be about 1.9%, 2.4%, 2.1%, and 1.8% respectively. One can see that there is a slight drop in the E in after the charging is complete. This is due to the recovery process of thyristor Th 2 after the charging is complete.

5.4 Ten-switch system

5.4.1 Charging inductors

The nineteen inductors L 1-L19 , shown in Figure 5.1, are used to charge the ten high- voltage capacitors C H1 -CH10 in parallel during the resonant charging process. During the synchronization process of the ten spark gap switches they provide high impedance to block the discharging of the high-voltage capacitors. To ensure proper synchronization, the value L of the inductors must be: Z ⋅ T L >> s s (5.12) 2 where ∆Ts is the time interval for the synchronization of all switches. For instance, when Zs=2 k and ∆Ts=30 ns, the inductance should be much larger than 30 H.

Within the present setup, rod-type air-core inductors were used. The length and the diameter of the rods are 152 mm and 80 mm, respectively. Each inductor has 142 windings of copper wire with a thickness of 1.07 mm. Aluminum plates with round edges were connected to the ends of the inductors to control the electric field. The inductance value L of each inductor is 605 H.

5.4.2 Spark gap switches

High-pressure spark gap switches (S 1-S10 ) were used for the present system. Compared with atmospheric-pressure spark gaps, the advantages of a high-pressure spark gaps are: (i) smaller conductive resistance, (ii) smaller inductance, and (iii) a faster switching time due to the shorter gap distance and higher field strength. For a uniform or nearly uniform gap filled with air, the breakdown voltage V B is a function of the air pressure p and the gap distance d, and can be expressed as:

Ten-switch prototype system 87

VB = 24.4 pd + 6.53 pd (5.13) where p and d are the air pressure in bar and the gap distance in cm respectively.

Switch S 1 was constructed as a triggered spark gap switch, while the other nine switches S 2-S10 are self-breakdown switches. The electrodes of each switch are made of brass, and the diameter of each electrode is 20 mm. They were designed to have the same breakdown voltage in accordance with equation (5.13). For the self-breakdown switches, the gap distance is 4 mm. For the triggered switch, the distances of the trigger gap and the gap between the trigger electrode and the cathode are 1 mm and 2.8 mm respectively. With such gap distances, all the switches have approximately the same breakdown voltage, as shown in Figure 5.12.

Fig. 5.12 Breakdown voltage of the ten spark gap switches (breakdown voltage is calculated according to (5.13))

5.4.3 The TLTs

The TLT plays an important role in synchronizing the multiple switches and in transferring the energy from the capacitors to the load. To ensure the synchronization and to block the discharging of the high-voltage capacitors during the synchronization process, the secondary mode impedance Z s must be much larger than the characteristic impedance Z0 of the coaxial lines, namely: Z s >>Z 0 (5.14) Moreover, to avoid reflections of the high-voltage pulse between the outer conductors of the TLT, the transit time between the outer conductors of the TLT should be longer than

88 Chapter 5

0.5 ∆Ts, where ∆Ts is the time interval for the synchronization of the multiple switches. Therefore, the length l of the coaxial cables covered by magnetic cores needs to be: l 1 ≥ Ts (5.15) υ s 2

In the above equation, υs is the velocity of the high-voltage pulse between the outer conductors of the TLT.

From discussions in Chapter 2, the overvoltage induced by the closing of the first switches is important for the synchronization of multiple switches. Suppose that the number of applied switches is m and the first several switches (quantity j) have been closed. Then, under the assumption that the secondary mode impedances between the adjacent stages of the TLT are the same, the maximum overvoltage V(m-j) over the (m-j) switches that are not yet closed can be given by: j ⋅V ∆V = 0 (5.16) (m− j) m − j where, V 0 is the initial charging voltage on the high-voltage capacitors. It can be seen that the overvoltage V(m-1) induced by the closing of the first switch to close the switches that are not yet closed is equal to V 0/(m-1). When a large number of switches are used, the small overvoltage V(m-1) may be too small to close the second switch. This will cause the failure of the synchronization of multiple switches. Two solutions can be used to prevent this: (i) using different magnetic cores with different µr; or (ii) putting similar magnetic cores around specific stages of the TLT. Both these solutions will give different secondary mode impedances and provide the second switch with a higher overvoltage. Once the first few switches have been closed, more and more overvoltage can be added to the switches that are not yet closed during the synchronization process. This will result in proper synchronization.

In addition, to ensure the high secondary mode impedance, saturation of the magnetic material must be avoided. Thus equation (5.17) must be observed: V B > 0 r p (5.17) s l m Zs where B s is the saturation flux density of the magnetic material, ℓm is the mean length of the magnetic path of the magnetic toroid, and Vp is the voltage over the secondary mode impedance Z s.

The model shown in Figure 5.13 can be used to evaluate the secondary mode impedance of the TLT and the wave velocity between the outer conductors of the TLT; D is the distance between the magnetic cores, D0 is the diameter of the outer conductor of the cable, D1 and D 2 are the inner and outer diameters of the magnetic toroid respectively. Suppose that the current is distributed uniformly around the outer conductor. Then, the secondary mode impedance and wave velocity can be written as:

Ten-switch prototype system 89

2D + D0 D2 2(D + D0 ) − D1 2D + D0 Z2s = 120 {ln + ( r −1)[ln + ln ]}ln (5.18) D0 D2 2(D + D0 ) − D2 D0

2D + D0 1 D2 2(D + D0 ) − D1 2D + D0 Z1s = 120 {ln + ( r −1)[ln + ln ]}ln (5.19) D0 2 D2 2(D + D0 ) − D2 D0

2D + D0 D2 2(D + D0 ) − D1 1- 2D + D0 υ2s = υ0 {ln + ( r −1)[ln + ln ]} ln (5.20) D0 D2 2(D + D0 ) − D2 D0

2D + D0 1 D2 2(D + D0 ) − D1 1- 2D + D0 υ1s = υ0 {ln + ( r −1)[ln + ln ]} ln (5.21) D0 2 D2 2(D + D0 ) − D2 D0

In the equations shown above, Z 2s and υ2s are the secondary mode impedance and the wave velocity when magnetic cores are placed around both coaxial cables. Similarly, Z 1s and υ1s are for the situation when only one coaxial cable is covered with magnetic cores. µr is the relative permeability of the magnetic material. υ0 is the wave velocity in air. The same model was used by Win( 2007 ) to evaluate a two-stage TLT, and it was observed that the model agrees well with experimental results.

1 0 2 D D D D 2 1 0 D D D

Fig. 5.13 Schematic diagram of two parallel coaxial cables covered with magnetic material

Within the present system, the same magnetic cores were used. Figure 5.14 gives an overview of the input side of the TLT and the specific coaxial cables covered with magnetic cores. Magnetic cores are not put around the cables of stages nos. 3, 6 and 8. The secondary mode impedances between two adjacent stages covered or not covered by magnetic cores are different. Thus the overvoltage induced by the closing of the first switch will be nonuniformly added to the switches that are not yet closed (e.g. the overvoltage added to switch S 2 is larger than that over switch S 3). The switch with more overvoltage will close shortly after the closing of switch S 1. Once the second switch has been closed, the synchronization can be accomplished properly.

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Fig. 5.14 Configuration of the magnetic cores around the coaxial cables of the TLT in Fig. 5.1

The magnetic material used within the present system is metglass MP4510. Its relative permeability r is 245. The values of D 0, D 1 and D 2 are 18.3 mm, 19.6 mm, and 48.4 mm respectively. Calculated values of the secondary mode impedance and the wave velocity versus distance D are shown in Figures 5.15 and 5.16 respectively. It can be seen that a secondary mode impedance Z s>2 k can be obtained. Upon increasing the value of D from 10 cm to 100 cm, the ratio of Z 2s to Z 1s is 1.4. For a value of D less than 100 cm, the 7 7 values of υ2s and υ1s are less than 4.47×10 m/s and 6.25×10 m/s respectively. If the length covered by magnetic material is 100 cm, the two-way transit times corresponding to υ2s and υ1s are 45 ns and 32 ns respectively. In addition, the values of B s and ℓm of metgalss MP4510 are 1.56 T and 10.55 cm respectively. It can be kept far below the saturation, for instance, when Z s =2 k and V p=40 kV the flux density inside the toroid is only 0.058 T.

Ten-switch prototype system 91

Fig. 5.15 Calculated secondary mode impedance Z 1s and Z 2s versus D based on equations (5.18) and (5.19)

Fig. 5.16 Calculated wave velocity υ1s and υ2s versus D based on equations (5.20) and (5.21)

92 Chapter 5

5.4.4 Integration of components into one compact unit

To obtain a fast rise-time, the structure must be as compact as possible. Within the present work, the ten switches S 1-S10 , the ten high-voltage capacitors C H1-CH10 , and the TLT connections are integrated into one compact structure, as shown in Figure 5.17 (for the mechanical sketch, see Appendix D). The ten switches are installed in one single compartment. Consequently, they “see” each other’s UV and other discharge products, which will improve the switching process. The ten switches are put into two arrays, with five switches per array. A compressed air flow can be used to flush the spark gap switches for the high-voltage and high-repetition-rate operation. This unit is able to hold a pressure up to 10 bar.

Fig. 5.17 3-D overview of the compact structure at the switch side of the TLT in Fig. 5.1 (Nos. 1, 3, 5, 7, and 9 indicate the stage numbers of the TLT)

5.4.5 The load

At the output side of the TLT, all the coaxial cables are connected in parallel, thus the output impedance is low (i.e. 5 ). Due to the low output impedance, the stray inductance of the connections to the load must be as low as possible for good matching between the

Ten-switch prototype system 93

TLT and the load. For instance, if the stray inductance is 20 nH, then effective impedance corresponding to a 10 ns pulse is about 4.4 , which is very close to the resistance of the load. To obtain a small stray inductance, the load is constructed coaxially, as shown in Figure 5.18. The load is made from five 1 hard disc resistors. A single-turn Rogowski coil (shown in Figure 5.18) is integrated into the load construction for the current measurements. Additionally, air can be flushed through the structure to cool the load.

Fig. 5.18 Overview of the load construction (the construction also contains a single-turn Rogowski coil for current measurement)

Figure 5.19 gives a total overview of the constructed 10-switch pulsed power system, and pictures of the switch compartment and the output configuration of the TLT.

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Fig. 5.19 Total overview of the ten-switch pulsed power system in Fig. 5.1

5.5 Characteristics of the system

5.5.1 Repetitive operation by the LCR

As shown in Figure 5.1, the present system was operated repetitively by means of an LCR trigger circuit [Yan(2003)]. This circuit automatically triggers the first spark gap switch S 1. It consists of an inductor L, a capacitor C and a resistor R. It is designed to have

Ten-switch prototype system 95

1/2 R>>2(L/C) and C H>>C. During the charging of the high-voltage capacitors, the voltage VH(t) on the high-voltage capacitors and the voltage V T(t) on the trigger electrode can be expressed as:

V  max 1[ − cos( ωt)] when 0 ≤ ωt ≤ π VH (t) =  2 (5.22)  Vmax when ωt ≥ π

Vmax γ t  2 [γ exp( − ) − γ cos( ωt) + sin( ωt)] when 0 ≤ ωt ≤ π  2 1 + γ τ V (t) =  (5.23) T V γ 2 π t − ∆T  max [exp( − ) + ]1 ⋅ exp[ − ] when ωt ≥ π  2 1 + γ 2 γ τ where V max is the voltage on the high-voltage capacitor when the charging is finished, ω is the charging frequency of the resonant charging circuit, ∆T is the charging time and is equal to π/ω, τ is the time constant of the LCR trigger circuit and equal to RC, and the coefficient γ is equal to ωτ . Within the present work, the values of C and R are 323 pF and 429 k respectively.

Fig. 5.20 Typical waveforms of V H and V T when C L=37 µF and C H=10.69 nF

Figure 5.20 gives the typical waveforms of V H(t) and V T(t) during one pulse cycle when C L=37 µF and C H=10.69 nF.. It can be seen that during the charging process the voltages V H and V T increase simultaneously. After the charging has been finished, voltage

96 Chapter 5

VH almost remains constant, while the voltage V T on the trigger electrode decreases exponentially because capacitor C will be further charged by C H via the LCR circuit. Consequently, the voltage across the trigger gap (between the anode and the trigger electrode), increases exponentially until the trigger gap breaks down at 42 µs after the charging has been finished. Now an overvoltage will appear over the gap between the trigger electrode and the cathode, which subsequently causes the switch to close.

The switching behavior of the triggered switch can be divided into pre-firing and normal switching. In the case of pre-firing, the switch closes before the charging is finished, while in the case of normal switching, the switch closes after the charging is finished. Figure 5.21 gives the averaged value of VH from 128 shots and the value of V H from one single shot, where the system was operated at a repetition rate of 20 pps and the input and output pressure of the switch compartment were 4.25 bar and 1.8 bar respectively. It can be seen that no pre-fire occurred and the switch was operated within the normal switching region. In Figure 5.21 it can be seen that the time delay and the jittering of the triggered switch were 61-131 µs and 106 µs respectively.

Fig. 5.21 The averaged value of V H from 128 shots and the value of V H from one single shot in Fig. 5.1

The present system was operated reliably at different repetition rates from 20 pps to 240 pps when C L=37 µF. Figure 5.22 shows the averaged charging voltage at different repetition rates. It can be seen that the average charging voltages at different repetition rates are almost the same, which indicates that the spark gap switches operated within the

Ten-switch prototype system 97 normal switching region. Moreover, one may find that the average charging voltage decreases slightly as the repetition rate is increased. This is due to a small drop in the voltage on the storage capacitor C 0 (see Fig. 5.1) at the high repetition rate.

Fig. 5.22 The charging voltages at different repetition rates when C L=37 µF in Fig. 5.1

5.5.2 Output characteristics

Figure 5.23 shows typical waveforms of output voltage and current when the setup was operated at a repetition rate of 20 pps. For the ten-switch compartment, the input and output pressure were 3.4 bar and 2.4 bar respectively. The low-voltage capacitor C L has a value of 37 µF and the high-voltage capacitors were charged up to 43.8 kV under steady operation. The voltage on the high-voltage capacitors when the switches closed was 42.8 kV. The peak values of the output voltage and current are 48.4 kV and 6.46 kA respectively. The rise-times (10-90%) of the output voltage and current are 11.0 ns and 12.2 ns respectively. Compared with the four-switch pilot setup, no bipolar oscillation occurred in the output pulse and the rise-time of the output pulse is much faster.

98 Chapter 5

Fig. 5.23 Typical output voltage and current when CL=37 µF in Fig. 5.1 (the rise-time of the output voltage and current are 11 ns and 12.2 ns respectively)

Fig. 5.24 Typical output power and energy when C L=37 µF in Fig. 5.1 (the peak output power and the output energy are 312 MW and 9.31 J respectively)

Ten-switch prototype system 99

From Figure 5.23, one can see that a small step with a duration of about 10.4 ns occurs within the rising part of the output pulse (see magnified view in Figure 5.23). This, in fact, implies that the ten spark gap switches are closed in sequence within about 10 ns. Moreover, it was observed that the output pulse forms are exponential. For an exponential pulse, the 10-90% decay time is ideally equal to 2.2 τ. From the discussions in Section 2.1, after all switches have closed, the ten high-voltage capacitors will discharge in parallel into the TLT. The total capacitance of the high-voltage capacitors and the input impedance of the TLT are 10.7 nF and 5 respectively. Thus, the theoretical 2.2 τ is equal to 117.7 ns. The actual 10-90% decay time of the ten-switch system is about 121 ns, and is in good agreement with the theoretical value.

Figure 5.24 shows the output power and energy for the measurement shown in Figure 5.23. The peak output power and the output energy are 312 MW and 9.31 J, respectively. The voltage on the high-voltage capacitors when the switches closed was 42.8 kV. Therefore, ideally (i.e. no energy loss and the TLT with a perfectly matched load), the theoretical value of the peak output power should be 366 MW. The ratio of the experimental value to the theoretical one is about 85%, which is much larger than that of the four-switch pilot setup (20%) (see Section 4.3.4).

To evaluate the reproducibility of the present system, Figure 5.25 gives the comparison of the averaged waveforms of the output current (averaged over 101 shots) and a single shot record when C L=37 µF and the setup was operated at 50 pps. One can see that both signals are in good agreement, which means that the ten-switch system has good reproducibility. However, when the repetition rate was increased to 150 pps, it was observed that a difference between the two signals occurred. Possibly the cooling of the load is insufficient to cool it and keep its resistance stable at a high repetition rate. Consequently, the current will change slightly during operation.

The peak output power is proportional to the square of the switching voltage. Experiments were carried out with different values of C L, varying from 24 µF to 58.2 µF. Figure 5.26 gives the peak output power at different switching voltages. The theoretical value of the peak output power is also given in Figure 5.26, which is calculated under the assumption that the TLT is perfectly matched and the energy loss can be neglected. Apparently, due to energy losses and the reflection, the experimental values are always less than those calculated ones. From experimental results, it can be seen that the peak output power increases as the switching voltage increases. More than 800 MW peak output power was obtained when C L=58.2 µF.

Figure 5.27 gives the typical output voltage and current when C L=58.2 µF and at a switching voltage of 69.7 kV. The peak values of the output voltage and current are 76.8 kV and 10.95 kA respectively. The output power and the output energy for the measurement in Figure 5.27 are shown in Figure 5.28. The peak output power and the output energy are 810 MW and 24.1 J, respectively.

100 Chapter 5

Fig. 5.25 Comparison of the averaged waveforms of the output current and a single shot record when C L=37 µF in Fig. 5.1

Fig. 5.26 Peak output power at different switching voltages in Fig. 5.1

Ten-switch prototype system 101

Outputvoltage 12 80 Outputcurrent

10

60 8

40 6

4 20 2

0 0

100 50 0 50 100 150 200 250 300 350 Time[ns]

Fig. 5.27 Typical output voltage and current at a switching voltage of 69.7 kV (their peak values and rise-times are 76.8 kV and 10.95 kA, and 10 ns and 11 ns respectively)

Fig. 5.28 The typical output power and energy at the switching voltage of 69.7 kV (the peak output power and the output energy are 810 MW and 24.1 J respectively)

102 Chapter 5

5.5.3 The energy conversion efficiency

The energy conversion efficiency η of the ten-switch pulsed power system was calculated according to the following equation. V (t)I (t)dt E ∫ output output η = load = (5.24) Ech arg ing V (t)I (t)dt ∫ H H where, E load and E charging are the energy obtained in the load and the total energy used to charge the system, respectively. They are calculated by integrating the corresponding product of the voltage and the current. Within the present setup, the energy conversion efficiency varied between 93% and 98%.

The main energy losses are caused by the LCR trigger circuit, the spark gap switches, the resistance of the inner conductors of the TLT, and the secondary mode impedance of the TLT.

The losses in the LCR trigger circuit are caused by the resistor R and the capacitor C. The resistor R dissipates energy during and after the charging period until the spark gap switches close; the capacitor C absorbs energy during these processes, and the energy stored in C will be dissipated by the triggered switch S 1 after it has been triggered. The relative contribution to the losses by these factors can be calculated with the following equations: 2 EC C[VH (t) −VT (t)] 2/ ηC (t) = = (5.25) Ech arg ing Ech arg ing

2 VT (t /) Rdt ER ∫ ηR (t) = = (5.26) Ech arg ing Ech arg ing

ELCR EC + ER ηLCR (t) = = = ηC +ηR (5.27) Ech arg ing Ech arg ing

In above equations, ηC, ηR, and ηLCR are the loss ratios for the resistor R, the capacitor C, and the LCR trigger circuit respectively. E C, E R, and E charging refer to the energy absorbed by C, the energy dissipated by R, and the energy used to charge the ten-switch unit respectively.

Figure 5.29 shows the calculated values of ηC, ηR, and ηLCR when C L=37 µF (charging time ∆T=68 us). It can be observed that the LCR loss ratio is a function of time. When t= ∆T, namely the moment when the charging is finished, the values of ηC|t= ∆T, ηR|t= ∆T, and ηLCR |t= ∆T are 0.14%, 0.8% and 0.94% respectively. After a much longer time (t →∞ ), the values of ηC|t→∞ , ηR|t→∞ , and ηLCR |t→∞ are 2.86%, 2.54% and 5.40% respectively. Apparently, if the switches work in the normal switching region (i.e. they are closed at t≥∆ T), the minimal loss caused by the LCR will be less than 1% and the maximum loss can be up to 5.40%.

Ten-switch prototype system 103

C

Fig. 5.29 The calculated ηC, ηR, and ηLCR when C L=37 µF ( T=68 µs) in Fig. 5.1

Fig. 5.30 The typical experimental values of E C, E R and E LCR when C L=37 µF in Fig. 5.1

104 Chapter 5

Figure 5.30 shows typical waveforms for E C, E R, and E LCR when C L=37 µF and the setup was operated steadily. The charging time ∆T and the charging energy E charging were about 68 µs and 10.17 J respectively. It can be seen that, when the charging is finished, E C, ER and E LCR are 0.022 J, 0.066 J and 0.088 J respectively. Thus the corresponding values of ηC, ηR, and ηLCR are 0.22%, 0.65% and 0.87% respectively. From Figure 5.30, one can also see that after the charging has been finished and before the switches have been closed, the energy E C and E R increase continuously because capacitor C is further charged by the high-voltage capacitors, and when the switches closed 66 µs after the charging finished (i.e. at the moment t=1.97 ∆T), E C, E R and E LCR were 0.096 J, 0.167 J and 0.263 J respectively; and thus ηC, ηR and ηLCR were about 0.94%, 1.64% and 2.59% respectively and the theoretical value of ηLCR is 2.67%.

The losses caused by other factors, namely the spark gap switches, the core of the TLT, and the secondary mode impedance Z s of the TLT, were estimated using η- ηLCR . It was observed that when C L=37 µF and the switches worked within the normal region, the losses caused by other factors accounted for roughly 3.4% of the total charging energy.

5.6 Summary

Using the presented multiple-switch pulsed power technology, efficient high pulsed power generation with a fast rise-time and a short pulse width has been realized. The system operated correctly at repetition rates up to 300 pps. The ten spark gap switches were properly synchronized.

A high ratio transformer was developed for charging the system. An equivalent circuit model was introduced to analyze the influence of the coupling coefficient on the swing of the flux density of the core and the magnetizing energy. The transformer was designed on the basis of this model. The core is made from 68 ferrite blocks. Along the flux path there are 17 air gaps, and the total gap distance is about 0.67 mm. The primary and secondary windings are 16 turns and 1280 turns respectively, and the transformer ratio actually obtained is 1:75.4. The coupling coefficient of 99.62% was obtained. The transformer was tested on the resonant charging system. The experimental results show that the model can provide a good guideline for designing a resonant magnetic transformer and that the glued ferrite core works well. Using this transformer, the high-voltage capacitors can be charged to more than 70 kV repetitively (potentially up to 1000 pps). With 26.9 J of energy transfer, the increased flux density inside the core was 0.23 T, which is below the usable flux density swing (0.35 T-0.5 T). The energy transfer efficiency from the primary to the secondary was approximately 92%.

The ten-switch unit consists of ten high-voltage capacitors, ten high-pressure spark gap switches, and a ten-stage TLT. All these components are integrated into a compact structure. Magnetic cores were placed around specific coaxial cables of the TLT for proper synchronization of the multiple switches. The results showed that using a TLT with one

Ten-switch prototype system 105 cable per stage and more switches (compared to the four-switch pilot setup) is an efficient way to achieve high pulsed power generation using the presented multiple-switch technology. Ten switches can be synchronized within about 10 ns. This system is able to produce a pulse with a rise-time of about 10 ns and a width of about 55 ns. It has good reproducibility. An output power of more than 800 MW was realized. The energy conversion efficiency varies between 93% and 98%.

References

[Den( 2002 )] M. Denicolai. Optimal performance for Tesla transformer. Review of Scientific Instruments Vol. 73, No. 9, September 2002, pp. 3332-3336. [Fin( 1966 )] D. Finkelsten, P. Goldberg, and J. Shuchatowitz. High-voltage impulse system. Review of Scientific Instruments Vol. 37, No. 2, February 1966, pp.159- 162. [Lee( 2005 )] J. Lee, C. H. Kim, J. H. Kuk, J. K. Kim, and J. W. Ahn. Design of a compact epoxy molded pulsed transformer. Proceedings of 15th IEEE International Pulsed Power Conference June 2005, pp. 477-480. [Liu( 2006 )] Z. Liu, K. Yan, G. J. J. Winands, E. J. M. Van Heesch, and A. J. M. Pemen. Multiple-gap spark-gap. Review of Scientific Instruments Vol.77, Issue 7, 2006. [Mas( 1997 )] K. Masugata, H. Saitoh, H. Maekawa, K. Shibata, and M. Shigeta. Development of high voltage step-up transformer as a substitute for a Marx generator. Rev. Sci. Instrum. Vol. 68, No. 5, May 1997, pp. 2214-2220. [Nai( 2004 )] S. A. Nair. Corona plasma for tar removal. PhD diss., Eindhoven University of Technology 2001, ISBN-90-386-2666-5. [Tho( 1998 )] R. E. Thoms, and A. J. Rosa. The analysis and design of linear circuits . ISBN-0-13-535379-7, 1998, pp. 485-487. [Win( 2007 )] G. J. J. Winands. Efficient streamer plasma generation. PhD diss., Eindhoven University of Technology, 2004, ISBN-978-90-386-1040-5. [Yan( 2003 )] K. Yan, E. J. M. van Heesch, S. A. Nair, and A. J. M. Pemen. A triggered spark-gap switch for high-repetition rate high-voltage pulse generation. Journal of Electrostatics 57 (2003), pp. 29-33. [Yan( 2001 )] K. Yan. Corona plasma generation. PhD diss., Eindhoven University of Technology, 2001, ISBN-90-386-1870-0. [Zha( 1999 )] J. Zhang, J. Dickens, M. Giesselmann, J. Kim, E. Kristiansen, J. Mankowski, D. Garcia, and M. Kristiansen. The design of a compact pulse transformer. Proceedings of 12th IEEE International Pulsed Power Conference , June 1999, pp. 704-707.

Chapter 6 Exploration of using semiconductor switches and other circuit topologies

In this chapter, exploration of utilizing semiconductor switches in the TLT based multiple-switch circuit is presented. The application of thyristors has been verified on a small-scale testing setup. Through use of a BOD (Break Over Diode), the transient overvoltage is no longer problematic. And the multiple-switch technology provides an excellent current balance among individual devices. A circuit topology for using MOSFET/IGBT is also proposed. In addition, other multiple-switch circuit topologies (i.e. multiple-switch inductive adder and magnetically coupled multiple switches) are presented and analyzed.

108 Chapter 6

6.1 Synchronization of multiple semiconductor switches

As discussed previously, one characteristic of the multiple-switch technology is that the closing of the first switches leads to an overvoltage over the switches that are not yet closed. This is very helpful to the synchronization process when spark gap switches are used. However, when semiconductor switches (thyristor, MOSFET/IGBT) are used, the transient overvoltage can easily damage them. Precautions are needed to protect semiconductor switches against transient overvoltages.

6.1.1 Thyristors Load

Fig. 6.1 Schematic diagram of the testing setup with three thyristors

The synchronization of multiple thyristors has been verified on a small-scale testing setup with three thyristors, as shown in Figure 6.1. Three identical capacitors C 1-C3 are charged in parallel via resistors R 1-R6, and interconnected to a three-stage TLT via three thyristors Th 1-Th 3. The transmission lines Line 1-Line 3 are made from coaxial cables (Z 0=50 ) wound on ferrite toroids. And they are connected in parallel to a resistive load at the output side. Thyristor Th 1 is manually triggered by closing switch S. The other two thyristors Th 2 and Th 3 are used as self triggering switches (like spark gap switches) by putting a break-over diode (BOD) in series with a resistor R T between their anodes and gates [Law( 1988 )]. BOD is a gateless thyristor. It is designed to break down and conduct at a specific voltage in excess of several kVs and is used in protection applications. When the transient overvoltage across Th 2 and Th 3 exceeds the BOD breakover voltage (which is chosen below the voltage rating of thyristors), the BOD becomes conductive and provides a trigger current, which turns on the thyristor. The value of this trigger current is limited by the resistor R T, in series with the BOD. Once the thyristor is turned on, the

Exploration of using semiconductor switches and other… 109 parallel-connected RC snubber will provide the holding current to keep it conductive until all thyristors are closed. Three diodes D 1-D3 are used to complete the energy transfer from the capacitors to the load when oscillation occurs. Within the present testing circuit, two diacs stacked in series were used as BODs, with a clipping voltage of about 90-100 V. C 1- C3 have values of about 1.88 µF; R T is 5 k; R and C are 1 k and 2 nF respectively; the resistance value of the load is about 1.25 ; and the charging resistors R 1-R6 are about 7 k.

Figure 6.2 shows the typical voltages over the thyristors (Th 2 and Th 3) and the switching current in Th 1. They clearly show the working process of the thyristors before, during and after the synchronization. Initially, the capacitors are charged to 60 V. Thyristor Th 1 was closed first by closing switch S manually. As expected, the closing of the first Th 1 leads to an overvoltage across thyristors Th 2 and Th 3, which forces the two BODs to conduct and turn on Th 2 and Th 3 sequentially within a time interval of 5 µs. The voltage over Th 3 when it closed was 100 V, which is below the maximum value of 180 V, since the BOD already broke down before the maximum value has been reached. During the closing process, the switching current in Th 1, as shown in Figure 6.2, was very small due to the large inductance formed by the coaxial cables, which prevents the discharging of the capacitors. After all thyristors have been closed, the cables behave like a current balance transformer and the switching current increases and the capacitors discharge into the load rapidly and simultaneously.

Fig. 6.2 Typical voltages over thyristors Th 2 and Th 3 and the switching current in Th 1 before, during and after the synchronization process in Fig. 6.1

110 Chapter 6

Fig. 6.3 Typical switching currents in thyristors Th 1-Th 3, respectively in Fig. 6.1 (they are shifted from each other for the clarity; actually they are simultaneous and identical)

Fig. 6.4 Relationship between the switching current and the output current in Fig 6.1 (they are shifted from each other for the clarity; actually they are simultaneous)

Exploration of using semiconductor switches and other… 111

Figure 6.3 shows the switching currents in all thyristors Th 1-Th 3. Note that the three curves are shifted in time for clarity; actually they overlap (see small plot within the figure). As can be seen, the time needed for all switches to close is about 5 µs, however, the switching currents are simultaneous and identical. Figure 6.4 gives the relationship between the switching current and the output current. Note that, again, both curves are shifted in time. It can be seen that they are simultaneous, and the output current is three times the switching current, as expected.

It can be seen that by using BODs, overvoltage is no longer a problem for using thyristors in the multiple-switch circuit. Moreover, an excellent current balance can be realized. Today, optical triggered thyristors with integrated BODs are available [Sch( 1996 ) and Prz( 2003 )]. It is believed that by using the multiple-switch technology, pulses on the order of microseconds can be generated that meet various voltage and current requirements, e.g. the large-current (in excess of several hundreds kAs) pulse for electrohydraulic spark plasma [Yan ( 2004 )].

Fig. 6.5 Equivalent circuit of the three-switch circuit in Fig. 6.1 for µs-pulse generation

Although the characteristics of the circuit shown in Figure 6.1 are similar to those of the spark gap switch based topologies discussed in Chapter 2, the equivalent circuit presented in Section 2.1 is no longer valid. This is because for the relatively long pulse duration, the lines act as coupled inductors, as shown in Figure 6.5. The circuit model shown in Figure 6.5 can be used to gain insight into the three-switch circuit shown in Figure 6.1. Here, three stages of the TLT are represented by three identical 1:1 transformers K 1-K3 respectively, and the winding inductance and the mutual inductance are L and M respectively. From the circuit model shown in Figure 6.5, one can derive the following equations for different situations: (i) switch S 1 is closed and S 2-S3 are open; (ii) switches S 1-S2 are closed and S 3 is open; and (iii) all switches S 1-S3 are closed.

112 Chapter 6

(i) Switch S 1 is closed and switches S2-S3 are open

 VC (s) I1 (s) =  2sL + Z  (6.1)  3VC (s)  Z / sL + 1(2 − k 3/)  VS (s) =VS (s) = 1−   2 3 2  2 + Z / sL 

(ii) Switches S 1-S2 are closed and switch S3 is open

 VC (s) I1 (s) = I 2 (s) =  s 2( − k)L + 2Z  (6.2)  2Z / sL 1(2 k 3/)    + −  VS 3 (s) = 3VC (s)1−    2( − k) + 2Z / sL 

(iii) All three switches S 1-S3 are closed  V (s) I (s) = I (s) = I (s) = C  1 2 3 2s 1( − k)L + 3Z (6.3)  I Load (s) = 3I1 (s)

In the above equations, Z is the load impedance; k is the coupling coefficient of the transformers; V C(s) is the Laplace form of the voltage on the capacitors; I 1(s), I 2(s), I 3(s), and I Load (s) are the Laplace forms of the currents in switches S 1-S3 and in the load respectively; V S2 (s) and V S3 (s) are the Laplace forms of voltages on switches S2 and S 3 respectively. Under the assumption that k ≈1, from (6.1-3) one can conclude that: (i) when the first switch S 1 is closed and the other two switches S 2-S3 are open, the current in S 1 will be negligible (as shown in Figure 6.2) when ωL>>Z; the closing of the first switch S 1 will lead to an overvoltage over the other switches (S 2-S3) that are open (as shown in Figure 6.2), and the theoretical voltages on S 2-S3 could by up to about 1.5 times the charging voltage; (ii) when two switches S 1-S2 have been closed and while switch S 3 is open, the switching current in S 1-S2 can be still kept very small (as shown in Figures 6.2- 6.4) provided that ωL>>Z; and the voltage on S 3 will continue to increase (as shown in Figure 6.2), theoretically it can be up to about 3 times the charging voltage; (iii) after all three switches have been closed, the currents in S 1-S3 are identical (as shown in Figure 6.3) and determined by the leakage inductance and the load; and the current in the load is equal to three times the current in each switch, as shown in Figure 6.4; and the discharging of each capacitor can be represented by an equivalent circuit model shown in Figure 6.6, where the capacitor discharges into the load with a value of 3Z via an inductance 2(1-k)L.

Fig. 6.6 Equivalent circuit model for each capacitor after all switches are closed

Exploration of using semiconductor switches and other… 113

The three-switch circuit topology shown in Figure 6.5 can be extended to any number of switches (m). After all m switches have been closed, the current in each switch and the current in the load can be expressed as (according to (6.3)):  V (s) I (s) = C  j 2s 1( − k)L + mZ where j = 2,1 ... m (6.4)  I Load (s) = mI 1 (s)

6.1.2 MOSFET/IGBT

10

C H

8

H C

5 C H

Fig. 6.7 Schematic diagram of the circuit using MOSFET/IGBT

A circuit topology using multiple MOSFETs/IGBTs is shown in Figure 6.7. Diodes are connected between the cathodes of the switches and the negative ends of the capacitors. The closing of the first switches will cause the diodes of the switches that are not yet closed to become forward biased and thus conducting. Consequently, the current will flow via the diodes and the voltage blocked by these switches equals the charging voltage. However, when the switches are closed the corresponding diodes become reversed biased and open, and the discharging of the capacitors starts. So, one can see that by using diodes the overvoltage will never occur over individual MOSFET/IGBTs during

114 Chapter 6 the closing process. However, it is noted that the driving circuits must be synchronized, and isolated gate circuits are required (e.g. optical trigger), since all the switches are at different potentials during the closing process.

6.2 Other multiple-switch circuit topologies

6.2.1 Inductive adder

Fig. 6.8 Circuit topologies of three-switch inductive adders

Exploration of using semiconductor switches and other… 115

The basic idea of the previously described multiple-switch circuits can be also applied for the conventional inductive adder circuit (see Section 1.2.2), thus leading to new multiple-switch inductive adders, as shown in Figure 6.8. Capacitors C 1-C3 are interconnected to the primary windings of transformers K 1-K3 via the switches S 1-S3. At the secondary sides, the secondary windings can be put in series to obtain high voltage as shown in Figure 6.8 (a), or in parallel to produce large current as shown in Figure 6.8 (b).

Fig. 6.9 Simulated results for the circuit in Figure 6.8 (a) (C1=C 2=C 3=1 µF; the load resistance is 20 ; primary and secondary inductances of all transformers are 1 mH, and the coupling coefficient is 1; stray inductance at the primary side is 1 µH per stage; the time delay between two switches is 3 µs)

In principle, the characteristics of the circuits shown in Figure 6.8 are similar to those of the TLT based multiple-switch circuit topologies. Figure 6.9 gives an example of the simulated results of the circuit in Fig. 6.9 (a). Here the values of the capacitors C 1-C3 are 1 µF; the resistance of the load is 20 ; the primary and secondary inductances of all transformers are 1 mH, and the coupling coefficient is 1; the stray inductance caused by the connection loop at the primary side is 1 µH per stage; the time delay between two switches is 3 µs. As expected, the closing of the first switch leads to an overvoltage over the switches that are not yet closed; during the closing process the discharging of the capacitors is prevented due to the interconnection. After all three switches have been closed, the capacitors discharge simultaneously to the load via the pulse transformers. The voltage on the load is equal to three times that on the primary sides of the transformers.

116 Chapter 6

6.2.2 Magnetically coupled multiple-switch circuits

Fig. 6.10 Topologies of the magnetically coupled three-switch circuits

Figure 6.10 shows topologies of magnetically coupled three-switch circuits. Three identical transformers are used to synchronize multiple switches and to ensure the balance of currents among the multiple switches. The primary windings are connected in series with the three switches S 1-S3; the three secondary windings are interconnected in series with each other. The circuit topology can be used to drive independent loads, as shown in Figure 6.10 (a), or to drive a single load, as shown in Figure 6.10 (b). The basic principle of the synchronization of multiple switches is similar to that of the previously described circuits, namely the closing of the first switches leads to an overvoltage over the switches that are not yet closed and forces them to be closed subsequently. After all the switches have ignited, the energy will be transferred into the load(s) via the three switches simultaneously and identically. [Pem(2007)] gives a comprehensive discussion about the characteristics of the topology for driving multiple plasma torches (similar to the situation in Figure 6.10 (a)).

Exploration of using semiconductor switches and other… 117

Suppose that the primary and secondary inductances and the coupling coefficient of the transformers are L 1 and L 2, and k respectively. Then, one can derive the following equations for the circuit in Figure 6.10 (a) under different situations: (i) switch S 1 is closed and switches S2-S3 are open; (ii) switches S 1-S2 are closed and switch S3 is open; and (iii) all switches S 1-S3 are closed.

(i) Switch S1 is closed and switches S2-S3 are open  V (s) I1 (s) = 2  sL 1 1( − k )3/ + Z1  (6.5)  k 2  V (s) = V (s) = V (s)1 +   S2 S3  2    3( − k ) + Z1 sL 1 

(ii) Switches S 1-S2 are closed and switch S3 is open

 V (s) 1+ Z / sL  ()2 1 I1 (s) = 2 2 2 2  sL 1 (()()1− 2k 3/ + 1− k 3/ ()Z1 + Z 2 / sL 1 + Z1Z 2 / s L1 )   V (s)()1+ Z1 / sL 1 I 2 (s) = 2 2 2 2 (6.6)  sL 1 (()()1− 2k 3/ + 1− k 3/ ()Z1 + Z2 / sL 1 + Z1Z2 / s L1 )   k 2 2 + (Z + Z /) sL    ()1 2 1  VS 3 (s) =V (s)1+ 2 2 2 2    3( − 2k ) + 3( − k )( Z1 + Z2 /) sL 1 + 3Z1Z2 / s L1 

(iii) All three switches S 1-S3 are closed

  Z + Z Z Z   2 3 2 3   V (s)1+ + 2 2    sL 1 s L1  I (s) =  1   2k 2  Z + Z + Z  k 2  Z Z + Z Z + Z Z Z Z Z    2   ()1 2 3   ()1 2 2 3 3 1 1 2 3  sL 1 1( − k ) + 1−  + 1−  2 2 + 3 3   3 sL 3 s L s L     1   1 1     Z + Z Z Z   1 3 1 3   V (s)1+ + 2 2    sL 1 s L1  I 2 (s) =  2 2   2k  Z + Z + Z  k  Z Z + Z Z + Z Z Z Z Z  (6.7)   2   ()1 2 3   ()1 2 2 3 3 1 1 2 3   sL 1 1( − k ) + 1−  + 1−  2 2 + 3 3  3 sL 3 s L s L      1   1 1    Z + Z Z Z   V (s)1+ 1 2 + 1 2    2 2   sL 1 s L1  I3 (s) =    2k 2  Z + Z + Z  k 2  Z Z + Z Z + Z Z Z Z Z   2   ()1 2 3   ()1 2 2 3 3 1 1 2 3   sL 1 1( − k ) + 1−  + 1−  2 2 + 3 3   3  sL  3  s L s L    1 1 1   1 L I (s) = k 1 ()I (s) + I (s) + I (s)  sec 1 2 3  3 L2

118 Chapter 6

Fig. 6.11 Typical switching currents in Fig. 6.10 (a) under the condition of ωL1>>Z 1, ωL1>>Z2 and ωL1>>Z3 (this figure is reproduced from [Pem(2007)])

Fig. 6.12 Typical switching currents in Fig. 6.10 (a) when the condition of ωL1>>Z 1, ωL1>>Z2 and ωL1>> Z 3 failed (this figure is reproduced from [Pem(2007)])

Exploration of using semiconductor switches and other… 119

In the equations (6.5-7), Z 1, Z 2 and Z 3 are the impedance of each load respectively; V(s) is the Laplace form of the voltage source; I 1(s), I 2(s), I 3(s), and I sec (s) are the Laplace forms of the currents in switches S 1-S3 and in the secondary windings of the transformers respectively; V S2 (s) and V S3 (s) are the Laplace forms of the voltages on switches S 2 and S 3 respectively. Under the assumption that k ≈1, from (6.5-7) one can conclude that: (i) when the first switch S 1 is closed and the other two switches S 2-S3 are open, the current in S 1 will be negligible if ωL1>>Z 1; the closing of the first switch S 1 leads to an overvoltage over the other switches (S 2-S3) that are open, and the theoretical voltages on S 2-S3 could be up to about 1.5 V(s); (ii) when two switches S 1-S2 have been closed and while the switch S 3 is open, the switching current in S 1-S2 can be still kept very small provided that ωL1>>Z1 and ωL1>>Z 2; and the voltage on S 3 can theoretically be up to about 3 V(s); (iii) after all three switches have been closed, the currents in S 1-S3 are almost identical when the conditions of ωL1>>Z 1, ωL1>>Z 2 and ωL1>>Z 3 are matched.

Figures 6.11 and 6.12 give examples of the typical switching currents when three independent plasma torches were used [Pem( 2007 )]. As shown in Figure 6.10, when the conditions of ωL1>>Z 1, ωL1>>Z 2 and ωL1>>Z 3 are met, the currents are almost identical despite the fact that the impedance of the three plasma torches will probably not be the same. However, when the impedances of the torches become relatively high and this condition failed, a current imbalance occurred, as shown in Figure 6.11. When the three loads have an identical impedance (i.e. Z 1=Z 2=Z 3=Z) the current in each switch will be always the same, and from (6.7) one can derive: V (s) I1 (s) = I 2 (s) = I 3 (s) = 2 (6.8) s 1( − k )L1 + Z From the above equation, one can represent the discharging of each switch by the circuit shown in Figure 6.13.

Fig. 6.13 Equivalent circuit for each switch of the circuit in Figure 6.2.3 (a) after the synchronization under the condition Z 1=Z 2=Z 3=Z

With regard to the circuit topology in Figure 6.10 (b), the characteristics are similar to those of the circuit in Figure 6.10 (a). When the impedances of the three switches are much smaller than the impedance ωL1, the currents in the three switches will be almost the same. Especially when the impedances of the three switches are negligible, the currents in the three switches can be expressed as:

120 Chapter 6

V (s) I1 (s) = I 2 (s) = I 3 (s) = 2 (6.9) s 1( − k )L1 + 3Z

References

[Law(1988)] H. M. Lawatsch, and J. Vitins. Protection of thyristors against overvoltage with Breakover Diodes. IEEE Transactions on Industry Applications Vol. 24, No. 3, May/June 1988. [Pem(2007)] A. J. M. Pemen, F. J. C. M. Beckers, L. J. H. van Raay, Z. Liu, E. J. M. van Heesch, and P. P. M. Blom. Electrical characteristics of a multiple pusled plasma torch. Proceedings of IEEE Pulsed Power and Plasma Science Conference June 2007. [Prz(2003)] J. Przybilla, R. Keller, U. Kellner, C. Schneider, H. -J. Schulze, F. -J. Niedernostheide, and T. Peppel. Direct light-triggered solid-state switches for pulsed power applications. Proceedings of 14th IEEE Pulsed Power Conference June 2003, Vol. 1, pp. 150-154. [Sch(1996)] H. –J. Schulze, M. Ruff, and B. Baur. Light triggered 8 kV thyristors with a new type of integrated breakover diode. Proceedings of 8th International Symposium of Power Semiconductor Devices and ICs May 1996, pp. 197-200. [Yan(2004)] K. Yan, G. J. J. Winands, S. A. Nair, E. J. M. van Heesch, A. J. M. Pemen, and I. de Jong. Evaluation of pulsed power sources for plasma generation. J. Adv. Oxid. Technol. Vol. 7, No. 2, 2004.

Chapter 7 Conclusions

7.1 Conclusions

The main aim of the investigation is to gain insight into the mechanisms and characteristics of a new multiple-switch pulsed power technology and to realize efficient (>90%) generation of large pulsed power (500 MW-1 GW) with a short pulse width (~50 ns) and a fast rise-time (~10 ns) using this technology. Based on the investigations, the following conclusions can be drawn.

7.1.1 TLT based multiple-switch circuit technology

(a) By interconnecting multiple spark gap switches via a transmission line transformer (TLT), multiple spark gap switches can be synchronized automatically. The synchronization process is quite unique, and typically has two distinctive phases. Once one of multiple spark gap switches is triggered, the first phase starts. The synchronization process is as follows: the closing of the first switch(s) leads to an overvoltage over the switches that are not yet closed. This overvoltage forces them to close sequentially within a nanosecond time scale (typically 10-50 ns). During the first phase, the energy storage components (e.g. capacitors or PFLs) can hardly discharge. When all the switches have been closed, the first phase ends and the second phase starts. And now all stages of the TLT are used in parallel equivalently, and the capacitors discharge simultaneously and identically into the load(s) via the TLT.

(b) The secondary mode impedances Z s of the TLT play an important role in the synchronization of multiple spark gap switches. It must be much larger than the characteristic impedance Z 0 of each stage of the TLT (i.e. Z s>>Z 0), to guarantee a high overvoltage over the switches that are not yet closed and to prevent the leak of the energy storage capacitors during the synchronization process.

When a large number of spark gap switches, the overvoltage induced by the closing of the first switch can be too small for a fast and proper closing of the second switch. To ensure proper synchronization in this case, a higher secondary mode impedance can be used for specific stages of the TLT. In this way, a higher overvoltage will be provided to the second switch, causing it to close more easily. This can be realized by using magnetic cores around specific stages of the TLT, as successfully applied in the ten-switch system.

122 Chapter 7

(c) The synchronization of multiple spark gap switches does not depend on the different configurations that can be realized at the output side of the TLT. The output of the TLT can be connected to a load in a series configuration (to obtain a high voltage pulse), or in a parallel configuration (to obtain a large current). The outputs can also be connected to multiple independent loads. Moreover, the synchronization is independent of the type of the load. This was confirmed by experiments on matched resistive loads and on a more complex non-matched load, namely a corona plasma reactor.

(d) An interesting feature of the analyzed topology is that the rise-time of the output pulse is mainly determined by the last switch that will close. This implies that only one of the multiple switches has to be optimized for very fast switching (e.g. by applying a multiple-gap spark gap switch), provided that the order of switching of the switches can be controlled (e.g. by using varying values for the secondary mode impedances).

(e) The peak output power of the multiple-switch circuit is a nonlinear function of the damping coefficient (i.e. stray inductance) of the input connection loop of the TLT. The higher the damping coefficient, the larger the peak output power becomes. The low output power of the four-switch pilot setup (using a TLT with four parallel coaxial cables per stage) is mainly caused by the low damping coefficient of the input loop of the TLT.

(f) Compared with using a TLT with multiple parallel coaxial cables per stage (and thus a relatively low characteristic impedance per stage, as for the four-switch system), using a TLT with one single coaxial cable per stage is more effective in generating large pulsed power, due to the following advantages: (i) it is easier to realize compact connections; (ii) each stage has a larger characteristic impedance Z 0, thus the damping coefficient ξ is higher; (iii) a low input impedance Z in can also be obtained when a large number of stages are used.

(g) Through use of the present multiple-switch technology, an efficient repetitive large pulsed power generation with a short pulse and a fast rise-time has been achieved on a ten-switch prototype system. This prototype consists of ten high-voltage capacitors, ten high-pressure spark gap switches, and a ten-stage TLT with a single coaxial cable per stage. Experiments show that the ten switches can be synchronized within about 10 ns. This system is able to produce a pulse with a rise-time of about 10 ns and a width of about 55 ns. It has a good reproducibility. More than 800 MW output power was realized. The energy conversion efficiency of more than 90% has been obtained.

(h) Not only spark gap switches but also semiconductor switches can be applied for the multiple-switch circuits analyzed in this dissertation. Either short pulses (ns, by using spark gaps or MOSFET switches) or longer pulses ( µs, by using thyristors) can be generated this way. Precautions must be taken to limit the overvoltages on the semiconductor switches, for instance by applying break-over diodes across the semiconductor switches.

Conclusions 123

7.1.2 Multiple-switch Blumlein generator

The synchronization of multiple switches was also successfully applied for the widely used Blumlein configuration. Using this circuit, square pulses can be generated over a matched load with an amplitude that is equal to the charging voltage of the lines. The characteristics of the synchronization of the multiple switches in a Blumlein configuration are the same to those of the TLT based multiple-switch circuit. This has been successfully used to generate an efficient corona plasma. In addition, the investigated multiple-switch Blumlein circuit is highly flexible in allowing the choice of different output configurations and polarity of the output pulse (positive, negative or bipolar).

7.1.3 Repetitive resonant charging system

(a) When the low-voltage capacitor C L of the resonant capacitor charging circuit has a 2 value lower than the matching value of n CH, the charging voltage on the high-voltage capacitor C H can be linearly tuned by adjusting the value of C L (here n is the 2 transformation ratio of the pulse transformer). For the situation that C L≥ n CH, the high- voltage capacitor C H will be charged to a constant value, which does not depend on C L.

(b) When a magnetic core transformer is used in a resonant charging circuit, the energy conversion efficiency from the low-voltage capacitor C L to the high-voltage capacitor C H can be as high as 99%. The required minimal volume of magnetic material to keep the core unsaturated (for a given energy per pulse) is determined by the coupling coefficient of the transformer, and is independent of the number of turns of the primary winding.

(c) We successfully applied a pulse transformer with a magnetic core that was constructed from many small ferrite blocks, glued together with epoxy resin. This allows a high degree of freedom in core size and shape. The multiple air gaps that are present due to the gluing of the blocks could be kept very small. Doing so, a high coupling coefficient of over 99.6% could be obtained.

7.2 Outlook

By using this technology, an efficient pulsed power source has been realized with specifications that are far beyond the state-of-the-art. Very high peak power has been obtained within a nanosecond time scale, and at high repetition rates. The low output impedance of the ten-switch system provides very large output currents. Multiple switches are successfully used, which share the heavy switching duty and are synchronized within nanoseconds. Based on literature [Dic( 1993 ), Don( 1989 ), Leh( 1989 )], the erosion rate was observed to be a nonlinear function of the transferred charge per shot (i.e. switching current). When the transferred charge per shot is reduced by a factor n, the erosion rate can be reduced by a factor over n 2. Thus, the lifetimes of the discribed multiple-switch

124 Chapter 7 systems are expected to be extended to over n 2 times, compared with a single-switch system with the same switching duty.

In terms of the characteristics of the technology, it can be used in many applications such as large-scale plasma generation [Win( 2007 )], plasma generation with a high volume density of streamers or for the generation of EUV (Extreme UV, typically 13.5 nm wavelength) [Kie(2 006 )]. Particularly the ten-switch system as described in this dissertation is very suitable for these applications, as well as for other applications, due to its capacity for delivering a large current. An example is the generation of very large currents (several hundreds of kA) in electrohydraulic discharges for high-resolution seismic imaging or water treatment [Yan( 2004 ), Sat( 2006 )]. It can also be used for a plasma reactor with a large capacitance [Yan( 2001 )] due to its capacity for a low output impedance. Of course, it can also be used for loads with a higher impedance (e.g. broadband EM-sources) since this technology allows a high degree of freedom in choosing different output impedances.

From an industrial application point of view, the system can be made more cost- effective. Within the present prototype system, the spark gaps were flushed with a pressurized air flow for operation at higher repetition rates. Replacing the present spark gap switches with multiple gap switches filled with a gas with a light molecular weight (e.g. H 2), no expensive compression and flushing system is required, and the system will become cheaper, while fast switching, a high repetition rate and a high energy conversion efficiency can be obtained as well.

References

[Dic( 1993 )] J. C. Dickens, T. G. Engel, and M. Kristiansen. Electrode performance of a three electrode triggered high energy spark gap switch. 9th IEEE International Pulsed Power Conference 21-23 June, 1993, pp. 471-474. [Don( 1989 )] State-of-the-art insulator and electrode materials for use in high current high energy switching. IEEE Transactions on Magnetics Vol. 25, Issue 1, pp. 138-141. [Kie(2 006 )] E. R. Kieft, Transient behavior of EUV emitting discharge plasmas a study by optical methods. PhD diss., Eindhoven University of Technology (available at http://alexandria.tue.nl/extra2/200512577.pdf). [Leh( 1989 )]F. M. Lehr, and M. Kristiansen. Electrode erosion from high current moving arcs. IEEE Transactions on Plasma Science Vol. 17, No. 5, October 1989. [Sat( 2006 )] B. R. Locke, M. Sato, P. Sunka, M. R. Hoffmann, and J. -S. Chang. Electrohydraulic Discharge and Nonthermal Plasma for Water Treatment. Ind. Eng. Chem. Res. 2006, 45, pp. 882-905. [Win( 2007 )] G. J. J. Winands. Efficient streamer plasma generation. PhD diss., Eindhoven University of Technology. 2007, ISBN-978-90-386-1040-5. [Yan( 2001 )] K. Yan. Corona plasma generation. PhD diss., Eindhoven University of Technology, 2001 (available at http://alexandria.tue.nl/extra2/200142096.pdf ).

Conclusions 125

[Yan( 2004 )] K. Yan, G. J. J. Winands, S. A. Nair, E. J. M. van Heesch, A. J. M. Pemen, and I. de Jong. Evaluation of pulsed power sources for plasma generation. J. Adv. Oxid. Technol. Vol. 7, No. 2, 2004, pp. 116-122.

Appendix A. Coupled resonant circuit

Fig. A.1 Coupled resonant circuit

A coupled resonant circuit, as shown in Figure A.1, is frequently used in pulsed power systems to increase the charging voltage. Initially, the low-voltage capacitor C L is charged to a voltage of V 0. By closing switch S, the high-voltage capacitor CH will be charged by CL via the transformer TR. From the circuit in Fig. A.1, one can derive the following equations: t  d d 1 L I (t) + M I (t) + I (t)dt = V 1 1 2 ∫ 1 0  dt dt CL 0 (A.1)  t  d d 1 M I1 (t) + L2 I2 (t) + I 2 (t)dt = 0 dt dt C ∫  H 0 where L 1, L 2 and M are the primary, secondary, and mutual inductance of the transformer Tr. The Laplace expressions of the above equations can be written as:

 1 V0 (sL 1 + )I1 (s) + sMI 2 (s) =  sC s  L (A.2) 1 sMI (s) + (sL + )I (s) = 0  1 2 2  sC H From (A.2), one can derive:  2 2 kV 0 1 ω1 ω2 I 2 (s) = ⋅ ⋅ ( − ) 2 (ω2 −ω2 ) s2 + ω2 s2 +ω2  L1L2 1( − k ) 2 1 1 2  (A.3)  kC HV0 L2 I 2 (t) = ⋅ ⋅[ω1 sin( ω1t) − ω2 sin( ω2t)]  2 2 L  1( − T ) + 4k T 1

128 Appendix A

1 1( + T ) m 1( − T )2 + 4k 2T L C M where ω2 ,ω2 = ⋅ , T = 2 H and k = . And then 1 2 L C 1(2 − k 2 ) L C 2 H 1 L L1L2 the voltage V H(t) on C H can be calculated as: t 1 kV 0 L2 VH (t) = I 2 (t)dt = ⋅ ⋅[cos( ω2t) − cos( ω1t)] (A.4) C ∫ 2 2 L H 0 1( −T ) + 4k T 1

A.I Complete energy transfer ∗

The voltage V H on C H has the maximum value when the following conditions are matched. cos( ω t) = ±1 2 , namely  m cos( ω1t) = 1 ω t = (m + 2n + )1 π  2 where m, n = ,0 ,1 ,2 3... (A.5) ω1t = mπ From the equation above, one can derive the following equations:  ± 2kV 0 L2 VH (t) = ⋅ max 2 2  1( − T ) + 4k T L1   (α − T )( αT − )1 k = 2 (A.6)  1( + α) T  m + 2n +1 α = ( )2  m 

For the complete energy transfer, the energy stored in C H when V H reaches its maximum peak value should be equal to the initial energy stored in C L, i.e. 1 2k 2C V 2 L 1 C [V (t) ]2 = H 0 ⋅ 2 = ⋅ C V 2 (A.7) H H max 2 2 L 0 2 1( − T ) + 4k T L1 2 From (A.7), one can obtain T=1, namely

L1CL = L2CH (A.8)

Under the situation of L 1CL=L 2CH, the voltages V L(t) and V H(t) can be expressed as:

 V0 ωt ωt VL (t) = − [cos( ) + cos( )]  2 1 + k 1 − k  (A.9) V C ωt ωt V (t) = 0 L [cos( ) − cos( )]  H  2 CH 1 + k 1 − k

∗M. Denicolai. Optimal performance for Tesla transformers. Review of Scientific Instruments Vol. 73, No. 9, September 2002, pp. 3332-3336.

Coupled resonant circuit 129

1/2 1/2 where ω=1/(L 1CL) =1/(L 2CH) . With specific values of the coupling coefficient k, the complete energy transfer will be realized. And k is determined by α −1 k = (A.10) α +1

The voltage on CH, when the complete energy transfer is finished, will be C L V (t) = V L = V 2 (A.11) H Max 0 0 CH L1

From the discussion above, it can be seen that completely transferring energy from C L to C H requires both L 1CL=L 2CH and specific values of k. The specific values of k are determined by the numbers m and n. Different m and n will give different values of k; therefore, there are a lot of usable values of k. As an example, Table A.1 gives some specific values of k for complete energy transfer. Table A.1 some specific values of k for complete energy transfer

Fig. A.2 (a) k=0.117 when m=8 and n=0; complete energy transfer is realized after 4.5 primary oscillations

130 Appendix A

Fig. A.2 Typical examples of complete energy transfer in Fig. A.1 when L 1CL=L 2CH; and L1=2 mH, L 2=200 mH, C L=1 µF, CH=10 nF, and V 0=1 kV; V H(t) |max =10 kV

Moreover, the number of primary oscillation cycles required for complete energy transfer is dependent on k, namely m and n. And it is equal to (m+2n+1)/2. For instance, when k=0.117, 0.6 and 0.969, the numbers of primary oscillation cycles required for complete energy transfer are 4.5, 1, and 4 respectively, as shown in Figure A.2. It is noted that when k=0.6 (m=1 and n=0), only one primary oscillation cycle is needed for complete transfer. And it is the minimal one. This is why k=0.6 is normally adopted for air-core Tesla transformers.

Coupled resonant circuit 131

A.II Effect of the coupling coefficient k on the first peak value of V H

From Figure A.2, one can see that the first peak value of V H varies with the coupling coefficient k. To further evaluate the effect of k, the first peak value of V H was numerically calculated according to (A.9) at different values of k, under the condition of

L1CL=L 2CH. And the values of ωt, efficiency η, and V L at the moment when V H reaches its first peak value were calculated as well. All the calculated results are shown in Table A.2 and plotted in Figures A.3 and A.4. Here the efficiency η is defined as the energy absorbed by C H to the energy stored in C L initially.

Table A.2 Numerical calculations at different values of k under L 1CL=L 2CH (in Fig. A.1)

132 Appendix A

Fig. A.3 Effect of k on the values of V L and V H in Fig. A.1 at the moment VH reaches its first peak value

Fig. A.4 Effect of k on the conversion efficiency η in Fig. A.1 at the moment VH reaches its first peak value

Figures A.3 and A.4 clearly show that the voltage V H and the efficiency η increase as k increases. The higher the coupling coefficient k, the higher the first peak value of V H and the efficiency η. When k is close to 1, almost all the energy stored in C L can be transferred to C H at the moment when V H reaches it first peak value.

Coupled resonant circuit 133

A.III Efficient resonant charging

Fig. A.5 Resonant charging circuit with a magnetic-core transformer

Figure A.5 shows the resonant charging circuit used in this dissertation, where a diode D is used on the secondary side. In this way, the voltage on C H when the charging finishes is the fist peak value of V H in the circuit in Fig. A.1. From the above discussions, one can conclude that for efficient energy transfer using the circuit in Figure A.5, the coupling coefficient k needs to be as high as possible. When a magnetic-core transformer is used, the coupling coefficient k of over 0.996 could be obtained. Thus, the feasible energy conversion efficiency of the circuit in Figure A.5 could be up to about 99%. In addition, by means of the circuit in Figure A.5, the voltage on C H is unipolar, which makes it easy to use semiconductor or magnetic switches. With regard to how to design a magnetic transformer for such a resonant circuit, please see Section 5.3.

Appendix B. Repetitive resonant charging

Fig. B.1 (a) Main circuit of the resonant charging system; (b) Equivalent circuit model, 2 where C H is transferred into the primary side of TR and C’=n CH

Figure B.1 shows the main circuit of the resonant charging system used within this dissertation and its equivalent circuit. Initially, the storage capacitor C 0 (C 0>>C L) is charged up to a voltage of V 0, and it remains constant. The circuit accomplishes one charging cycle through four steps as described in Section 5.2. As discussed in Section 5.3.2, by representing the transformer TR as an ideal transformer with a ratio of n and two uncoupled inductors and transferring the component on the secondary side of TR to the primary side, one can derive the equivalent circuit as shown in Figure B.1 (b). Here n is 1/2 equal to k(L 2/L 1) ; L 1 and L 2 are the primary and the secondary inductance of the TR 2 respectively; k is the coupling coefficient of the TR; and C’=n CH.

Assuming the coupling coefficient is large enough (e.g.>0.996), L 1 will be much 2 2 larger than the inductance L 1(1-k )/k and most of the energy (>99%) stored in C L will be

136 Appendix B

transferred into C’ and only a very tiny part (<1%) will be absorbed by L 1 during one charging cycle. Ignoring L 1 and energy losses during the charging cycle, one can derive 2 the following expressions for the situation of C L≥C’=n CH under the assumption that the voltage on C H is completely discharged before each charging cycle starts.

C0 C0 − CL CL − C' VL ( j) = ⋅ 2V0 − ⋅ ⋅VL ( j − )1 (B.1) C0 + CL C0 + CL CL + C'

CL − C' ∆VL ( j) = ⋅VL ( j) (B.2) CL + C'

2 ⋅ CL VC' ( j) = ⋅VL ( j) (B.3) CL + C'

VH ( j) = n ⋅VC' ( j) (B.4)

In the above equations, j refers to the charging cycle sequence number; V L(j) is the voltage on C L when the charging from C 0 to C L is finished during charging cycle j; VL(j) and V C’ (j) are the voltages on the C L and on the C’ when charging from C L to C’ is complete; V H(j) is the obtained voltage on C H during charging cycle j. Since C 0>>C L, (B.1) can be approximately expressed as:

CL − C' VL ( j) ≈ 2V0 − ⋅VL ( j − )1 CL + C'

= 2V0 + ε ⋅ 2( V0 + ε ⋅ 2( V0 + ... 2 3 = 2V0 ⋅ 1( + ε + ε + ε + ... (B.5) C − C In the above equation, ε = − 2 3 , and ε < 1 . When the charging cycle sequence C2 + C3 j→∞ , one may have:

1 CL + C' lim VL ( j) = 2V0 ⋅ = ⋅V0 (B.6) j→∞ 1 − ε CL According to (B.2-4), one can derive the following equations:

CL − C' CL − C' lim ∆VL ( j) = lim ⋅VL ( j) = ⋅V0 (B.7) j→∞ j→∞ CL + C' CL

2 ⋅ CL lim VC' ( j) = lim ⋅VL ( j) = 2V0 (B.8) j→∞ j→∞ CL + C'

lim VH ( j) = lim n ⋅VC' ( j) = 2nV 0 (B.9) j→∞ j→∞

From the above equations, one can see that the voltages on C L and C H will become stabilized. Actually, after 3-5 shots they already approach the steady values.

Appendix C. Calibration of current probe

Fig. C.1 (a) Schematic diagram of the current probe; (b) equivalent circuit; (c) simplified circuit model, where the transmission line T is represented by a resistor Z and by a voltage source 2V in series with a resistor Z at both sides respectively

Figure C.1 shows the current probe used on the ten-switch prototype system. It is based on a Rogowski coil and an integrator. The Rogowski coil is connected to an integrator via a transmission line T, which is terminated with a resistor R 1. The integrator is composed of a resistor R i and a coaxial capacitor C i and connected directly to the oscilloscope with an 1 M input impedance. Figure C.1 (b) shows the equivalent circuit of the current probe where M is the mutual inductance between the current I and the coil and L represents the self inductance of the coil. Representing the transmission line T by a resistor Z at the left side of T and by a voltage source 2V in series with a resistor Z at the right side of T, one can derive the simplified circuit model as shown in Figure C.1 (c), where Z and V are the characteristic impedance of T and the voltage across T at the left side respectively.

138 Appendix C

From the simplified circuit shown in Fig. C.1 (c), one can derive the following expression: dV k L I = kV + k ⋅τ ⋅ out + ⋅ V dt when R C >> & R ≈ Z (C.1) out 1 ∫ out i i 1 dt τ 2 Z

In the above equation, k ≈RiCi/M, τ1≈L/Z and τ2≈RiCi. There are three terms at the right side of (C.1). The first term represents the ideal system; the second term is a correction factor for the high frequency; the third term is a correction factor for low frequency. To obtain the actual current, first the obtained signal V out must be corrected by (C.2); then, by multiplying by the corrected V corrected and the coefficient k, one can derive the actual current I, as expressed by (C.3). dV 1 V = V +τ ⋅ out + ⋅ V dt (C.2) corrected out 1 ∫ out dt τ 2

I = k ⋅Vcorrected (C.3)

Fig. C.2 Calibration of the current probe; current I was measured with a Pearson probe (model 6600), V out is the actual signal obtained by the designed probe, Vcorrected is corrected signal according to (C.2)

Within the designed current probe, a single Rogowski coil, as shown in Figure 5.18, was adopted. Its self inductance L and mutual inductance M are estimated to be about 0.5 nH. Thus the second term in (C.2) was ignored when the signal V out was corrected. The calibration of the designed current probe was carried out on a small pulse generator.

Calibration of current probe 139

The pulse is generated by discharging a 1.3 nF capacitor into a 40 resistive load. The current I of the pulse was measured with a Pearson current probe (model 6600, bandwidth

120 MHz), and it has a rise-time of 9 ns. The V out was corrected with τ2=4 µs. Figure C.2 shows typical results of I, V out and V corrected . From the plots shown in Figure C.2, it can be seen that the tail of the actual signal V out is negative and does not fit with the current I; however, after the correction, the signal V corrected is in perfect agreement with the current I. Based on the reference current I and the corrected signal V corrected , the coefficient k was determined according to (C.3), and its average value is about 5475 A/V. Its statistic deviation, mean error, and maximum error are 37.68 A/V, 0.69%, and 1.76% respectively.

Appendix D. Schematic diagram of high-pressure spark gap switches

Acknowledgements

First of all, I would like to express my sincere gratitude to Dr. A.J.M. Pemen, my thesis co-promotor. His constant support and supervision has played a significant role in the completion of the work. Without his guide and efforts, it is impossible to have the dissertation in the present form. I also wish to express my sincere thanks to Prof. J.H. Blom, my first promotor, for his solid support, interest, and valuable remarks.

I am deeply grateful to Prof. K. Yan, who was closely involved in the present work in the first two and half years. The present work has greatly benefited from his deep insight into the subject, extensive knowledge and experience, and advices. My sincere thanks to Dr. E.J.M. van Heesch for inspiring talks and encouragements, which always helped me to have a deeper understanding of problems I met during the project.

I do very appreciate my second promotor Prof. M.J. van der Wiel, and core committee members Prof. A.J.A. Vandenput and Prof. J.A. Ferriera, for spending their valuable time reading the manuscript of the thesis. The present dissertation has greatly benefited from their valuable remarks and corrections.

I am very indebted to Mr. Ad van Iersel, one of the best engineers in our group. Without his special talent contribution, it is impossible to convert ideas into practical systems such as the pulse transformer and the ten-switch system, which are indeed essential for completing the work. I would also like to express my sincere gratitude to Mr. R.T.W.J. van Hoppe, for his great help with the calibration of the current probe, installation of the pulse counter, and experiments carried out on the ten-switch system. My sincere thanks also go to Dr. L.R. Grabowski for his help with measuring the concentration of the dye solution. I would also like to thank Dr. E.M. van Veldhuizen and Mr. A.H.F.M. Baede for sharing their knowledge and experiences on light measurement.

Throughout the project, I have benefited a lot from my colleagues within EPS group. I would like to thank all of them. In particular I would like to tank Dr. G.J.J. Winands, Dr. P.A.A.F. Wouters, Ms. D.B. Pawelek, Mrs. L. Cuijpers, Mr. H.M. van der Zanden, Mr. Huub Bonn ÷, and Mr. Arie van Staalduinen for sharing their knowledge and experiences, common research and assistances.

Curriculum Vitae

Zhen Liu was born on June 06, 1978, in Xiang Cheng, China. In 2000, he completed his bachelor study at the Department of Electronic Science from Xi’an Jiaotong Univeristy, China. In 2003, he received his master degree at the Electrical Department from Tsinghua University, China. His master thesis was awarded as one of the best master theses by Tsinghua University in 2004. Since November 2003, he started his Ph.D project in the EPS (Electrical Power Systems) group, TU/e (Technische Universiteit Eindhoven), the Netherlands. The subject is to develop an efficient large pulsed power supply using a transmission line transformer based multiple-switch technology.