Subnanosecond Pulsed-DC Ultra-High Gardient Photogun for Bright Relativistic Electron Bunches

Subnanosecond pulsed-DC ultra-high gardient photogun for bright relativistic electron bunches

Citation for published version (APA): Vyuga, D. A. (2006). Subnanosecond pulsed-DC ultra-high gardient photogun for bright relativistic electron bunches. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR612076

DOI: 10.6100/IR612076

Document status and date: Published: 01/01/2006

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Subnanosecond Pulsed-DC ultra-high gradient photogun for bright relativistic electron bunches

PROEFONTWERP

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 donderdag 31 augustus 2006 om 16.00 uur

door

Dmitry Vyuga

geboren te Sint-Petersburg, Rusland

Dit proefontwerp is goedgekeurd door de promotoren: prof.dr. M.J. van der Wiel en prof.dr.ir. J.H. Blom

Copromotor: dr.ir. G.J.H. Brussaard

This research was financially supported by the Foundation for Fundamental Research on Matter FOM (PR55LWFA)

CIP- DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

Vyuga, Dmitry

Subnanosecond pulsed-DC ultra-high gradient photogun for bright relativistic electron bunches / by Dmitry Vyuga. – Eindhoven : Technische Universiteit Eindhoven, 2006. – Proefschrift. ISBN-10: 90-386-2072-1 ISBN-13: 978-90-386-2072-5 NUR 926 Trefwoorden: vrije-elektronenlasers / laserpulsen / elektronstralen / relativistische elektronen / deeltjesversnellers / hoogspanningsschakelaars / hoogspanningspulsen / foto-emissie Subject headings: pulsed power sources / electron accelerators / Tesla transformer / pulse forming line / vacuum diodes / spark gaps / photoinjectors / pulsed-DC acceleration / free electron lasers

All rights reserved. No part of this book may be reproduced, stored in database or retrieval system, or published, in any form or in any way, electronically, mechanically, by print, microfilm or any other means without prior written permission of the author.

Printed by Printservice Technische Universiteit Eindhoven, Eindhoven, The Netherlands Cover design by Dmitry Vyuga and Paul Verspaget

Contents

1 Introduction…………………………………………………………………………….1 1.1 Introduction………………………………...... 1 1.2 TU/e project…………………………………………………………………...3 1.3 Outline…………………………………………………………………………4

2 High voltage relativistic vacuum diode……………………………………………….8 2.1 Introduction……………………………………………………………………8 2.2 Space Charge Limited Current………………………………………………...9 2.2.1 Continuous Emission…………………………………………………...9 2.2.2 Pancake regime………………………………………………………..10 2.3 Emission in the presence of a strong electrical field…………………………12 2.4 Average and local field (field enhancement)………………………………...19 2.5 Vacuum breakdown………………………………………………………….21 2.6 Conclusions…………………………………………………………………..23

3 Sub-nanosecond high voltage techniques…………………………………………...26 3.1 Introduction…………………………………………………………………..26 3.2 Bandwidth considerations in a pulse forming line…………………………...26 3.3 Pulse sharpening. Commutation time of dischargers………………………...28 3.4 Pulse shortening. Different types of pulse forming systems…………………30 3.4.1 The short-circuited lines system………………………………………30 3.4.2 System with cut-off discharger………………………………………..31 3.4.3 Short storage line based system……………………………………….32 3.5 Vacuum diode for ultra-short pulses…………………………………………33 3.6 Tesla type resonant transformer……………………………………………...35 3.7 Sub-nanosecond high voltage pulse measurements………………………….39

4 TU/e pulser……………………………………………………………………………42 4.1 Introduction…………………………………………………………………..42 4.2 Pulse forming line……………………………………………………………44 4.3 The Tesla transformer………………………………………………………..48 4.4 TU/e Pulser…………………………………………………………………..52

5 Beam line setup……………………………………………………………….………54 5.1 Introduction…………………………………………………………………..54 5.2 The beam line general overview……………………………………………..54 5.3 Acceleration gap……………………………………………………………..56 5.4 Focusing magnet……………………………………………………………..56 5.5 Phosphor screen……………………………………………………………...59 5.6 Bunch charge measurements. Faraday cup…………………………………..60 5.7 Spectrometer…………………………………………………………………61 5.8 Linear photodiode array……………………………………………………...63

v 6 Synchronization………………………………………………………………………65 6.1 Introduction…………………………………………………………………..65 6.2 The laser system and timing sequence……………………………………….65 6.2.1 The lasers……………………………………………………………..65 6.2.2 Timing sequence……………………………………………………...66 6.3 Laser triggered spark gap operation………………………………………….68 6.3.1 Statistical method of breakdown consideration………………………69 6.3.2 Experimental results…………………………………………………..71 6.3.3 Analyses………………………………………………………………76 6.4 Conclusions and discussion………………………………………………….79

7 Commissioning………………………………………………………………………..81 7.1 Introduction ………………………………………………………………….81 7.2 The pulser operation…………………………………………………………81 7.2.1 Tesla transformer operation…………………………………………..81 7.2.2 The pulse forming line operation……………………………………..82 7.2.3 Reliability of the system……………………………………………...85 7.3 Optical high voltage pulse diagnostic in the pulse forming line……………..86 7.3.1 Kerr effect measurements in Carbogal……………………………….87 7.3.2 Optical voltage probe test…………………………………………….89 7.4 Electron emission measurements…………………………………………….91 7.4.1 Dark current measurements…………………………………………...92 7.4.2 Interpretation of the dark current measurements……………………...96 7.4.3 Photoemission measurements…………………………………………97

8 General discussion…………………………………………………………………..100 8.1 Introduction…………………………………………………………………100 8.2 Conclusions…………………………………………………………………100 8.3 Recommendation for further research……………………………………...102 8.3.1 Pulser………………………………………………………………..102 8.3.2 Electron bunch production…………………………………………..103

Summary 105

Sammenvatting 107

Acknowledgements 110

Curriculum Vitae 111

Chapter 1

1.1 Introduction

Developments in science and technology require more and more accurate instruments for diagnostics, material research and technological applications. Electron beams are widely used for intense radiation production in the range from radiofrequency (RF) to gamma rays. Since the first experiments with conversion of electron energy to radiation have been made, electron beam based radiation sources play an important role in many applications. In many different applications the issues for such sources are: • Energy or wavelengths of the radiation quant. • Coherence of radiation. • Brilliance (Brightness). X-ray sources occupy a particular place in this field. Owing to the high penetrability and small wavelength, X-ray analysis allows us to obtain data which is inaccessible by other methods. The brightness of a source is a one of the most important requirements, since the exposure time needed for a measurement is inversely proportional to the intensity of the radiation.

Since the 1970s the highest brightness is achieved with synchrotron radiation sources. These sources led to break through in many areas of research in solid state physics, chemistry, biology and medicine. Already the 3rd generation of synchrotron light sources is now in operation. These 3rd generation synchrotron sources can deliver peak brightness of up to 1026 (ph/s mrad2 mm2). But the science never stops and the required brightness keeps rising.

The synchrotrons needed to generate this kind of light are more than a few hundred meters in circumference. For example the Swiss Light Source (SLS) which utilizes 2.4 GeV electrons has a circumference of 288 meters [1]. Spring8 (in Japan) which uses 8 GeV electrons has a circumference of 1 km [2]. Further improvement in brightness for synchrotron based light sources is also difficult because of fundamental reasons (electron beam brightness in a storage ring reaches fundamental limit).

A likely candidate for the next generation of intense radiation sources is the free electron laser. The idea of the free electron laser (FEL) was proposed as far back as 1955 by Motz at Oxford. Already in 1960 Phillips at the General Electric laboratory at the demand of the US Air Force developed the UBITRON [3] (undulating beam interaction). During this time he also developed a major part of the FEL theory. However, this work was classified and mostly forgotten. In 1970 Madey at Stanford proposed and built a working device [4] based on what he initially called ‘stimulated bremsstrahlung’ and also proposed the powerful name: free electron laser. It stimulated many other scientists and laboratories around the world to investigate this new research area.

There are several advantages of the FEL compared to conventional lasers. The main advantage is the absence of an active medium. The electron energy is directly converted into radiation. This means that no atomic or molecular levels are involved, which makes the FEL easily tunable in a wide range of output wavelengths. Another

1 advantage is the possibility to create XUV and X-ray lasers which are impossible with standard techniques. In FELs in synchrotron storage rings an undulator transfers the energy from an electron bunch to electromagnetic waves in an optical cavity. The optical cavity acts as an amplifier. For an X-ray FEL such an amplifier is practically impossible because of X-ray optics is needed. The solution is to use the spontaneous generation and self amplification regime (Self Amplified Spontaneous Emission, or SASE). In this regime the electron beam passing through an undulator generates electromagnetic wave in the direction of propagation of the electrons. This puts rigid requirements on the quality of the electron bunches. For the SASE-FEL the required electron bunch brightness can not be reached with synchrotrons due to beam instabilities. Therefore a linear accelerator (LINAC) must be used.

The quality (brightness) of the output bunch from a LINAC is mainly determined by the electron injector which is used in the system. Thus, it is necessary to achieve high brightness in the injector section of the accelerator complex. The standard devices for injection are RF guns with thermionic emission cathodes. In such a gun a linearly chirped electron bunch is formed (there is a linear dependence of electron energy and position in the bunch). After the RF gun dispersive elements are installed where phase space manipulation occurs and as result the bunch is compressed. Immediately after this compressor the bunch is injected into a booster, where it is accelerated to a few tens of MeV. Usually compression by this scheme has several stages, which has its effects on the price and sizes of the system.

Even with a few levels of compression, the electron bunch from a conventional RF gun is not good enough for SASE-FEL. Therefore, instead of thermionic cathodes a photocathode is used. These RF guns with photocathode have greatly improved the brightness (the initial brightness of the bunches is significantly higher), but still bunch compressors are needed to reach the requirements of the SASE-FEL.

The main goal of the research in this thesis is to decrease the size of the system and achieve the high brightness required for SASE-FEL without the use of compressors. This is in fact possible if an initially short bunch can be accelerated in such a strong field that the space charge forces are compensated by the growth of the Lorentz factor, . In other words, the electron bunch expansion in its own rest frame due to internal Coulomb field must be comparable with the change of the length of the bunch frame in the laboratory frame.

Very short initial bunch can be quite easily created with a metal photo-cathode (copper, gold) illuminated by a femtosecond laser pulses. In this case the initial length is practically the same as the excitation laser pulse length, and the number of emitted electrons is proportional to the laser intensity. In this way it is possible to control the current or density of the initial bunch. The higher the current at the cathode the more field is needed to retain this current during acceleration. The maximum field achievable with RF structures is limited by the breakdown field strength and is of the order of 100 MV/m for a perfect system. Usually it is around 30-50 MV/m. With this field the maximum achievable current is roughly up to 100 amperes, which is already 100 times smaller than required for SASE-FEL. In [5] it was shown that the acceleration field needed is 1 GV/m. This is well beyond the capabilities of even the best RF structures.

The question is how to create such a strong field without breakdown. In order to create a field of more than 1 GV/m the time in which this field can be present must be much shorter than the characteristic time of breakdown formation. This is of the order of a few nanoseconds. Pulsed accelerators operating in the nanosecond and subnanosecond regime are a suitable option. Accelerators of this type are widely used with explosive emission cathodes [6]. Electron bunches are produced with electron energy of 1-2 MeV and a current of a few kiloamps with a duration of less than 100 ps. However, the required duration of a bunch for the SASE-FEL and LWFA is 100 fs, i.e. 1000 times shorter. In [7] it was proposed to use such a pulsed accelerator in a different regime. Instead of using an explosive or a field emission cathode, a metal photocathode excited with a femtosecond laser pulses is used. The voltage across the acceleration gap is constant during the transition time of the electron bunch. Therefore acceleration occurs in the DC regime. Hereafter we will call this type of accelerators pulsed-DC. In this regime, the duration of the bunch just after acceleration will be less than 100 fs and the corresponding current approximately 1 kA. But with electron energy of the bunch of 1-2 MeV (Lorentz factor 3-5) a kA bunch in a drift space will expand rapidly due to Coulomb forces and as result the current will drop. It was shown that space charge forces for the bunch will be effectively compensated when the Lorentz factor is approximately 25 or more, which means that. the electron energy must be about 10 MeV. The bunch from the pulsed-DC accelerator should therefore be immediately injected into an RF booster, where it will be accelerated to 10 MeV. The complete DC-RF accelerator will be very compact and much cheaper than existing systems, with superior output parameters. The research in this thesis concerns the pulsed-DC accelerator for such a hybrid DC-RF system.

The price of an X-FEL will be determined mainly by the price of the accelerator complex. With LINACs as the main accelerators the length of the whole system will be from a few hundred meters to several kilometers. Such a system still will be inaccessible for many users, and experimental time will be expensive. There is therefore a need to develop “table-top” systems. Theoretically this is possible using a Laser Wakefield Acceleration (LWFA) instead of LINACs. In LWFA, the acceleration process occurs in the wakefield of a powerful laser in a plasma channel [REFS]. The acceleration field gradient in this case can be up to 1000 GV/m. For controlled LWFA the injected electron bunch length must be shorter then the wakefield wavelength, typically 100 fs. For LWFA, the required electron bunch can be produced with the hybrid DC-RF accelerator described above. The LINACs can then be replaced by a plasma channel of the order of 1-10 cm. This really opens a way to create a ‘table-top’ system.

1.2 TU/e project

The idea to use a GV/m acceleration field with photoemission cathodes was initially proposed in Brookhaven National Laboratory (BNL) by Smedley and Srinivasan-Rao [8]. The idea was based on vacuum breakdown studies conducted by Juttner et. al. [9] and Mesyats et. al.[10]. These investigations showed that metals could withstand field gradients of a few GV/m if the duration of the applied field is only a few ns. For high voltage pulses with pulse duration less than 10 ns, both cathode initiated and anode initiated breakdowns become less probable and the breakdown voltage becomes relatively insensitive to the cathode and anode materials. The formation of

3 microscopic craters due to explosive emission becomes less frequent and the erosion of the electrodes decreases significantly.

In order to create such strong field a 1 MV, 1 ns pulser was developed and built [11]. Experiments conducted in this installation showed absence of significant dark current from copper cathodes in fields up to 1.7 GV/m with pressure in the acceleration gap below 10-4 Pa. Further numerical calculation have shown that in order to create the required electron bunches for the SASE X-FEL a field of 5 GV/m is needed. Thus based on the 1 MV pulser a 5 MV apparatus was built [12]. But investigations in this direction at BNL seem to be halted and no recent results (publications) are available from the 5 MV pulser.

In 2001 a FOM (Foundation for Fundamental Research on Matter) program was started in the Netherlands to develop a laser wakefield accelerator [13]. The program has its main focus on two parts: electron injector development and plasma channel development. The development of the electron source takes place at Eindhoven University of Technology and is the basis for the research in this thesis. The hybrid RF/pulsed-DC scheme was proposed by Van der Wiel et. al. [5] to meet the requirements for injection into a laser wakefield accelerator. Numerical calculations by Van der Geer et. al. [14] showed that if a fs electron bunch is initially accelerated to 2 MeV in a DC field of 1 GV/m and is then immediately inserted into a high performance RF booster these bunches will be suitable for injection into the plasma channel. The RF part of the hybrid accelerator was developed and built by Kiewiet [15]. Excellent results were achieved with this RF accelerator, and several new ideas were put into practice. Synchronization of the RF power system with a femtosecond laser – vital for injection into a laser driven wakefield - was improved to a few tens of femtoseconds. The next step, the pulsed DC part of the accelerator is the topic of research in this thesis.

In order to create the required 1 GV/m pulse a 2.5 MV, 1 ns pulser was developed and built at the Efremov Institute in St.Peterburg Russia for the TU/e. The design of the power supply is practically the same as the system at BNL. The only difference is in the pulse transformer which is used. The TU/e transformer has a maximum output voltage of 2.5 MV compared to BNL’s 1 MV. Upon delivery however, the system was far from requirements and suffered from serious reliability problems. Thus during the four years of operation many parts were redesigned and replaced.

1.3 Outline.

The thesis describes the development of the TU/e Pulser and its components. The contents of each chapter are briefly described hereafter. A schematic picture of the pulser is shown in figure 1.1. More detailed drawings can be found in the respective sections.

The first two chapters are devoted to some theoretical problems. Chapter 2 has been dedicated to the theory of high voltage diodes. It describes the principle limitations of a current for the purely DC case (relativistic Langmuir law) and for the case with an initially short bunch from the photocathode excited with a femtosecond laser pulse. The simple models give insight into the emission processes

1 7 8 4

3 2

Figure 1.1 Schematic picture of the pulser setup. 1-Tesla transformer, 2- storage capacitors, 3- DC charger of the primary capacitances, 4- air spark gap of the primary, 5- triggering unit of the primary air spark gap, 6- main liquid spark gap, 7- pulse forming line with sharpening and cut off dischargers, 8- vacuum diode for acceleration. which can occur in the cathode in a very strong field. In addition, the ratio between pure photoemission current (if the photon energy of the laser is higher than the work function of the cathode) and photostimulated field emission (if the photon energy is lower than the work function, but the cathode is in a strong field) has been derived. Finally, the maximum time a field may be applied to the surface of a copper cathode was calculated as a function of field strength. From these considerations, the requirements for the pulsed power supply were formulated.

In Chapter 3 different methods are described for the creation of sub-nanosecond megavolt level pulses. The pulse transformer is described and the reasons to use this kind of source are shown. The theory behind the pulse forming line (PFL) is described including a short overview of the sharpening and cut-off dischargers which are incorporated in the pulse forming line is given. The vacuum diode is described as a part of the forming line, and the possibility for doubling of the applied voltage across the acceleration gap due to reflection in the open end is shown.

Initially the pulser was far from the requirements. During the first start up phase many design and manufacturing errors came to light that affected the output pulse stability (time and amplitude). To increase the life time of the PFL the inner conductor of the whole line was rebuilt, all support insulators inside the PFL were redesigned and replaced with new ones. The vacuum diode in the initial setup was not optimized in order to reach minimum distortion on the incident pulse. Therefore we completely redesigned the vacuum diode. The Tesla transformer output voltage stability is one of the main issues that affect the operation of the main liquid spark gap and in turn the output of the whole pulser. Initially the primary of the Tesla transformer was formed by two circuits, one for each of the windings. Two spark gaps were used on the primary which impacted on the waveform of the Tesla transformer output. As a result, the output voltage variation was more than 20 % and the time jitter of the output with respect to the master clock was more than 100 ns. The variation in the duration of the first half wave (the working point the output) of the Tesla transformer was also more than 100 ns. To improve this, one of the air spark gaps was removed and the whole primary circuit was changed to be powered through one spark gap. The air spark gap

5 was rebuilt with some minor changes to create a stable single channel of commutation of the capacitors of the primary. The high-voltage trigger generator was redesigned to minimize the jitter of the air spark gap and we achieved jitter of the trigger pulses (120 kV) of less than 1 ns. The actual setup of the TU/e pulser is described in Chapter 4.

To produce and diagnose the electron bunches a beam line setup was designed and assembled. All available diagnostics are suitable for single shot measurements. The spectrometer was improved from an earlier design for better energy resolution mainly by using a linear photodiode array as the detector. Chapter 5 describes the complete beam line setup.

Chapter 6 gives the experimental results of the operation of the pulser with emphasis on the synchronization of the Pulser with the rest of the system. The timing system consists of two lasers: an Nd:Yag laser used for triggering of the main spark gap of the high voltage pulser and a femtosecond laser used to produce an electron bunch by photo-emission. The main issue in synchronization is accurate laser triggering of the main 2.5 MV liquid spark gap. Analysis of the data will show the practical and fundamental limitations of synchronization of the present system.

In Chapter 7 the results concerning the actual acceleration of electrons are presented. The pulser operation with signals from the capacitive probes in the different parts of the installation are presented. The electromagnetic noise produced by the pulser during operation influences the measurements of the high voltage pulses in the PFL. We propose the use of an optical method of detection in order to measure the waveforms without distortions. The method is based on measuring the change of polarization of a laser beam by the Kerr effect. The Kerr effect is present in every liquid but the Kerr constant of the insulation liquid used in the PFL was unknown. We built a polarimeter and have measured the Kerr constant. The optical high voltage diagnostic was built with an expected resolution of 70 ps, but a laser with the required beam parameters was not available. The feasibility of the measurements with this device was shown. Finally, measurements of the field emitted electrons (dark current) and photoemission experiments are presented and discussed. The dark current measurements indicate the presence of electrons with energy of 3.6 MeV. This is the highest energy reported for this type of accelerator.

In the final chapter overall conclusions regarding this project are drawn. Recommendations for ways to improve the pulsed DC photo injector are given and discussed.

References.

[1] see the website of the Swiss Light Source: http://sls.web.psi.ch/view.php/about/index.html

[2] see the website of Spring 8: http://www.spring8.or.jp

[3] R.M. Phillips, US patent 3,129,356 granted April 14, 1964

[4] J.M.J. Madey, J. Appl. Phys., v. 42 (1971), p. 1906

[5] M.J. de Loos, S.B. van der Geer, F.B. Kiewiet, O.J. Luiten, M.J. van der Wiel, A high-brightness pre-accelerated rf-photo injector, in Proceedings 7th European Particle Accelerator conference (EPAC); Editors: -, Paris, France, 1831, (2002)

[6] . . . , 1991 ISBN 5-283-03978-1 K.A. Zheltov. High current picoseconds electron accelerators.

[7] K. Batchelor, V. Dudnikov, J. P. Farrell, T. Srinivasan-Rao, and J. Smedley; A Novel, High Gradient, Laser Modulated, Pulsed Electron Gun; BNL 65895; [pres. 17th Int'l. Conf. on High Energy Accelerators, Dubna, Russia, 7-12 September (1998); Proc. XVII Int'l. Conf. On High Energy Accelerators - p.33-35]

[8] T. Tajima and J. M. Dawson. Laser Electron Accelerator. Phys. Rev. Lett. 43, 267–270 (1979)

[9] T.Srinivasan-Rao and J. Smedley, Advanced Accelerator Concepts, AIP Conf. Proceedings 398 (1996) 730-738

[10] B. Juttner, V.F. Puchkarev, W. Rohrbeck, preprint ZIE 75-3 (Akad.Wiss.,Berlin, GDR 1975), B. Juttner, W. Rohrbeck, H. Wolff, Proc. III International Symp. On Discharge and Electrical Insulation in Vacuum, Paris, France, 1968, p. 209

[11] G.A. Mesyats, D.I. Proskurovsky, Pulsed electrical discharge in vacuum. (Springer-Verlag, Berlin) ISBN 3-540-50725-6

[12] K. Batchelor, V. Dudnikov, J. P. Farrell, T. Srinivasan-Rao, and J. Smedley; A Novel, High Gradient, Laser Modulated, Pulsed Electron Gun; BNL 65895; [pres. 17th Int'l. Conf. on High Energy Accelerators, Dubna, Russia, 7-12 September (1998); Proc. XVII Int'l. Conf. On High Energy Accelerators - p.33-35]

[13] Laser Wakefield Accelerator, FOM-programme 55.

[14] S. B. van der Geer and M. J. de Loos, J. I. M. Botman, O. J. Luiten, and M. J. van der Wiel; Nonlinear electrostatic emittance compensation in kA, fs electron bunches, Phys. Rev. E 65, 046501 (2002)

[15] F. Kiewiet; Generation of ultra-short, high-brightness relativistic electron bunches. Thesis, Technische Universiteit Eindhoven, 2003. ISBN 90-386-1815-8

Chapter 2

High voltage relativistic vacuum diode.

2.1 Introduction

In this chapter we will derive the basic limitations of the accelerated electron bunches. Because the acceleration takes place in a quasi-homogenous electrical field we will use a simplified 1-dimensional model. The accelerator is represented by a 1- dimensional vacuum diode. Using this model, in section 2.2 the limitations of the diode current caused by space charge are shown. In the case of unlimited emission from a cathode in a DC field, the current density limit is given by the (relativistic) Child-Langmuir law. It will be shown that the target for the current of 1 kA can only be reached if a field much larger than 1 GV/m is applied. Even then, an additional beam line section would be needed to slice out part of this beam to create short bunches. In the case of photoemission by a short pulse (25 fs) laser, the current can be much higher. In that case the current is limited by expansion of the bunch due to internal space charge forces in the bunch. For this pancake regime, an initially short bunch is required, which is then accelerated to relativistic energies fast enough to keep the bunch short (<100 fs) and consequently the current high enough.

The relation between the initial charge, the applied voltage and the minimum required field is derived in section 2.2.2. The initial bunch can be made by the third harmonic of a femtosecond Ti:Sapphire laser, which has a wavelength of 266 nm. In this case the photon energy exceeds the work function. Good experimental data is available for this process (see, for example [1]). However because we operate in the presence of a strong electrical field, it is also possible to use the second harmonic of this same laser (400 nm) due to lowering of the work function by the Schottky effect. The use of 400 nm laser pulses in stead of 266 nm has several technical and experimental advantages. The expected efficiency of 400 nm photons compared to 266 nm will be derived as a function of applied electric field to establish the regime in which it is possible to operate the accelerator with just the second harmonic. Depending on the available photon flux at the different wavelengths, this puts an additional restriction on the minimum electrical field needed.

The maximum electric field that can be used is determined by two factors: breakdown and dark current (field emission). For all practical applications, the dark current or spontaneous field emission current must be much smaller than the (controlled) photoemission current. In section 2.3, the ratio of photo-emission (or, to be more precise, photo-stimulated field emission at 400 nm) to spontaneous emission is derived to determine the maximum field strength. Finally, in section 2.5 electrical breakdown in vacuum is treated. The spontaneous field emission current will heat up the cathode surface. If the strong electrical field is present long enough, the surface will reach evaporation temperature and breakdown will occur. The analysis will give the maximum pulse duration for different field strengths on the surface.

All together, chapter 2 will give the main practical limits that were used in the design of the pulsed DC accelerator also gives the range of expected output parameters.

5 ]

2 m

/ 4 A 9 0 1

[ 3 y t i s n e d

t 2 n e r r u c 1

0 0 1 2 3 4 5 6

E [ GV/m ]

Figure 2.1 Space charge limited current density J as a function of the acceleration field E for the interelectrode distance of the diode 0.002 m.

2.2 Space Charge Limited Current

2.2.1 Continuous Emission

In case of continuous emission, the current density is limited by space charge. The maximum achievable current density from a relativistic diode is given by the relativistic case of Child-Langmuir’s law [2]. A 1-dimensional acceleration gap of length d, with an applied voltage difference U0 has been considered. The cathode potential is zero and positioned at z=0. Then, if the acceleration voltage is in the range 0.5 MV to 10 MV, a maximum current density is given by [2]:

2 3 ≈ 1/ 2 ’ ≈ ε m c ’∆≈ eU ’ ÷ j ≈ ∆ 0 0 ÷ ∆1+ 0 ÷ − 0.847 (2.1) ∆ 2 ÷∆∆ 2 ÷ ÷ « ed ◊«« m0c ◊ ◊

with. ε 0 , m0 , c , e respectively are the permeability of vacuum, the rest mass of an electron, the speed of light and elemental charge, U 0 is acceleration voltage in the diode, d is acceleration gap length.

In figure 2.1 the current density as a function of acceleration field for interelectrode distance in the diode of 0.002 m is presented. For example, if an acceleration voltage of 2 MV, the maximum (continuous) current density according to (2.1) is j ≈ 7.3⋅108 A/m2. For a typical 1 mm2 opening in the diode, this corresponds to a maximum emitted current of 0.7 kA.

Equation (2.1) was derived for (quasi-)continuous flow. This means that emission takes place for times longer than the transit time of particles through the acceleration gap. In the case of a interelectrode distance of 0.002 m, this transit time is around 6 ps. The expression is applicable to field emission. In the case of explosive emission ions form a background of positive charge and the current density can be a few orders of magnitude higher.

Even with 1 kA current from the diode, extra equipment is needed to slice beam into the required bunches (100 fs) [3]. This will increase the size of the injector setup and it will not be quite a table top system anymore. A better way to generate short bunches is ‘controlled’ photoemission from the metal cathode.

2.2.2 Pancake regime.

In the case of photoemission, only one bunch per laser pulse is accelerated. The charge and the initial duration of the bunch are completely determined by the excitation laser pulse duration, photon energy (wavelength) and intensity. Here we will consider the case when we have photo emission from a metal surface by an ultra- short laser pulse (25 fs) and there is no other source of electrons or other emission processes are negligible. For metal surfaces it has been shown that the emission process is practically without inertia [4]. This means that immediately after the laser pulse has arrived, an electron bunch with approximately the same length as the laser pulse is formed close to the cathode. We assume that the initial density is constant and that all electrons have the same energy. We will again consider the simple one- dimensional case, which means that the transverse size of the beam is infinite compared to the longitudinal size. Then the bunch will be accelerated in the electric field and at the same time will expand in the longitudinal direction due to space charge forces (Coulomb force). Simultaneously the Lorentz-factor of the bunch will increase and the bunch length in the lab frame will decrease proportionally.

We consider a layer of electrons of thickness ∆z0 at the point z = 0 , with constant electron density. For the transition time of the electron bunch, accelerated over a distance z under action of a constant field E0 we find [5]:

2 2m0 z z t(z) = + 2 (2.2) eE0 c

Since the longitudinal size of the bunch is infinitely small compared to the transverse size, only the self field in the z direction is taken into account. The self field in a 2 bunch with constant charge density, ρ = Q /πR ∆z0 with Q, R, L are accordingly the bunch charge, the bunch radius and length, is then given by:

ρz' σz' Ebunch (z') = = (2.3) ε 0 ε 0 ∆z0

120 140 (b) ]

(a) 120 ]

100 s f s

[ [

h 100 h t t

g 80 g n n e e l l 80

h h c c 60 n n

u 60 u b b 40 40

20 20 0.5 1.0 1.5 2.0 0 100 200 300 400 500 E [ GV/m ] Q [ pC ]

] 5 2 m / (c) A 4 9 0 9 1

[

y 3 t i s n e d

2 t n e r r

u 1 c

0 1 2 3 4 5 E [ GV/m ]

Figure2.2 The bunch length after 2 mm for 100 pC, 0,5 mm radius and 25 fs initial duration(solid line), 50 fs (dotted line) as function of acceleration field (a); the bunch length for a 25 fs (solid line) and 50 fs (dotted line) initial bunches accelerated in a field of 1 GV/m as function of initial charge (b); current density of the 100 pC and 25 fs (dotted line) , 50 fs (solid line) initial duration bunches as function of an acceleration field. with z’ the position within the bunch, σ = Q /πR 2 is the surface charge density associated with an extremely flat bunch. Electrons at the front of the bunch, at initial 1 position 2 ∆z0 therefore experience an additional accelerating field from the rest of the bunch:

1 ρ∆z0 σ Ebunch (2 ∆z0 ) = = (2.4) 2ε 0 2ε 0

Because we do not take radial forces into account, ρ∆z0 is constant, and therefore, the additional accelerating field remains constant and can be added to the applied electric field E0.

The difference in time needed to traverse a distance z for the front and the back of the bunch can now be calculated, using (2.4) with the appropriate field strength. The total bunch length is then given by:

∆t(z) = ∆t0 + tback (z) − t front (z) (2.5)

with ∆t0 the initial bunch length (the duration of the laser pulse). From (2.4) we see that the rear of the bunch is effectively accelerated in the field lower than the front by 1 an amount 2Ebunch (2 ∆z0 ). Taking to account the fact that Ebunch << E0 , we find:

≈ ’ ∆ m0cσ γ −1 ÷ ∆t(z) = ∆t0 ∆1+ 2 ÷ (2.6) « eε 0 E0 ∆t0 γ +1 ◊

eE0 z withγ = 1+ 2 , the Lorentz factor of an electron accelerated in the field E0 , over m0c the distance z. Equation (2.6) is valid only for the pancake regime (bunch length<< the bunch radius). Figure 2.2(a) shows the dependence of the bunch length as a function of accelerating field, for a 0.5 mm initial radius and initial length of 25 and 50 fs, a charge of 100 pC and an acceleration distance of 2 mm. In figure 2.2(b) the bunch lengths of bunches with initial duration 25 fs and 50 fs are shown as a function of the initial charge for 1 GV/m acceleration field (the other parameters are kept constant). The current density as function of the acceleration field for the same parameters is presented in figure 2.2(c). From the graphs it follows that for stronger fields the duration of the bunch after acceleration is smaller.

Comparison of the space charge limited current densities for an acceleration field of 1 GV/m in the case of DC acceleration with the pancake (photoemission) regime case shows that for the required (100 fs) bunch, the current density can be more than 2.5 times higher.

2.3 Emission in the presence of a strong electrical field.

As was shown in the previous chapter, in order to get an electron bunch with duration of 100 fs and a charge of a 100 pC we should apply an acceleration field of around 1 GV/m for 50 fs initial duration of the bunch. In the presence of such a strong field cold emission processes from the cathode play an important role. In our case, for example, significant field emission is a parasitic effect. From this we can determine the upper limit for the acceleration field.

Cold field emission is emanation of electrons from a conducting body under the action of a strong external electrical field. The term “cold” means that no additional energy is needed to excite the electrons. A theoretical description of this process was first given by Fowler and Nordheim [6] in 1929, based on tunneling. The mechanism of the process is the following:

z=0 z=0 0 z z -h Vmax +h h ) )

z ( V

metal vacuum vacuum

Wa Wa (b) (a) Figure 2.3 Potential energy of an electron near the metal surface in a presence of an external field (a) for clear field emission (b) a part of electrons are excited with photons of the energy hν .

In the presence of a strong external electric field, electrons can pass the potential barrier at the interface via tunneling through the barrier, which is deformed by the external field, see figure 2.3. As the field rises, the height of the barrier above the Fermi level drops and at the same time its length decreases. As a result the barrier transmittance D (the probability for electrons to pass the barrier) rises and consequently, the field emission current rises.

The field emission current density (Fowler Nordheim current) can be used for calculations in a convenient form given in [7]:

3 / 2 2 9 ϕ ≈ ’ −1 / 2 −2.82⋅10 −10 ε 4.39ϕ j = 1.4 ⋅10 ∆ ÷ ⋅10 ⋅10 ε (2.7) « ϕ ◊ with ε the external electric field in V/m, ϕ is work function of the metal in eV. This current is always present when the voltage pulse is applied. Figure 2.4 shows this dependence for copper. The effect of field enhancement by local surface roughness will be discussed in section 2.4. To determine the useful range of operation of the applied field, photoemission current and bunch charge must be higher than this field emission current.

In section 2.2 two different regimes were compared and it was shown that the pancake (photoemission regime) has several advantages: • No additional beam line section is needed to slice out part of the beam to create a short bunch. • Lower acceleration field is needed to get the same current from the diode. Therefore, we will only consider the photoemission process as the source of the bunches and compare the photoemission current to the cold field emission current.

4 ] 2 0 m / A , j [

) -4 j ( g o l -8

-12

1 2 3 4 E [ GV/m ] Figure 2.4 Log of the field emission current density as a function of applied field.

Photoemission is the process in which, by the photoelectric effect, electrons are emitted from the emitter surface due to light irradiation. This effect is described by the Einstein equation:

E = hν − eϕ (2.8) where E is the energy of the emitted electron, h is Planck’s constant, ν is the frequency of the incident light, and ϕ is the work function of the material. Consequently, if the energy of the photon is higher than the work function, an electron can leave the surface.

Initially it was considered that this effect carries a surface character, but in the 1950s it was shown experimentally that there is volume dependence [8]. Later, by Spaiser [9] a three-step emission model was proposed: volume optical absorption, excitation and transport of electrons, and escape. In [4] it was shown that the efficiency of photoemission is mainly dominated by electron-electron collisions in the material. In these collisions, an excited electron can lose a considerable portion of its energy, and may not be able to pass the surface energy barrier. Therefore, for metals the effective photoemission depth (the effective depth from which electrons are able to leave) is of the order of the mean free path of the electron for electron-electron collisions. For copper this length is approximately 4 nm. This is much smaller than the optical absorption depth and shorter than the penetration depth of the external field. This allows us to use a simple surface model for photoemission.

Using expression (2.8) for the energy of emitted photoelectrons (figure 2.3 (a)) in the presence of an external field on the surface ε and taking into account the image charge force we find:

e3ε E′ = hν + − eϕ (2.9) 4πε 0

e3ε The term is equal to Vmax in figure 2.3, which is equal to the lowering of the 4πε 0 barrier by the external field. This is effect is known as the Schottky effect [10]. From (2.9) and figure 2.3 it is possible to see that if the local field is high enough, photoemission becomes possible when the photon energy is lower than the work e3ε function. But even for photon energies smaller than − eϕ emission is still 4πε 0 possible due to the tunneling effect. In that case we have tunneling of photo-excited electrons which is termed photostimulated field emission.

Most common femtosecond laser systems are based on Ti:Sapphire. Three harmonics can be generated in a straightforward manner: the fundamental at 800 nm with corresponding photon energy of 1.55 eV, the second harmonic at 400 nm with corresponding photon energy of 3.11 eV and the third harmonic at 265 nm with energy 4.65 eV. As was noted above only photoemission from the metal cathodes does not have significant inertia, in other words, the duration of the photoemission current will be practically the same as the duration of the laser pulse. Thus for the pancake regime a metal cathode should be used. In our case copper is used for this purpose. The work function of copper is 4.45 eV, thus the third harmonic of the Ti:Sapphire laser can be used for clear photoemission. However, as was noted above, emission is also significant at 400 nm due to tunneling. Using of the second harmonic (400 nm) for cathode excitation has several advantages compared to the third harmonic (265 nm), mainly because for beam transport of the third harmonic special UV optics are needed, which reflects on the price and reliability of the laser beam transport system. It is therefore useful to compare the clear photoemission current (265 nm) to photostimulated field emission. Current measurements from the copper cathode by a 265 nm ultra short laser pulse as a function of intensity have been done by Kiewiet [1]. For comparison we will derive expressions for the current for both cases in a similar fashion.

Inside a metal there is an electron gas which obeys Fermi-Dirac statistics. When an ultra short (shorter than the relaxation time of the excited electrons) photon pulse arrives at the surface, the photons interact with the electron gas and are partly absorbed. As a result a distribution of excited electrons is created. A part of this distribution can escape the material by tunneling through the barrier. So, in order to find the current density it is necessary to find the energy distribution of the electrons which absorbed photons (it should be noted that although this distribution is not in equilibrium, it can be considered static on the femtosecond time scale).

Let the surface be irradiated by mono-energetic photons. Then the energy distribution is a delta function. The new (nonequilibrium) distribution will be a convolution of the original Fermi-Dirac distribution with this delta function. The energy distribution of the excited electrons becomes:

1 8π (2m3 ) 2 A ξ dξ nˆ(ξ )dξ = (2.10) h3 exp((ξ − µ − hν )/ kT )+1

15 where A is a proportionality constant, ξ = E + hν the energy of the excited electrons, E,hν the initial energies of electrons and photons respectively, and µ the Fermi level. The work function ϕ = −µ (see figure 2.3).

The number of particles impinging on the surface with the normal energy between w and w + dw and total energy ξ to ξ + dξ will be:

4πmA dwdξ nˆ(w,ξ )dwdξ = − (2.11) h3 exp((ξ − µ − hν )/ kT )+1

The full energy distribution of photoemitted electrons is found from:

ξ P(ξ )dξ = — nˆ(w,ξ )D(w)dwdξ (2.12) w=0 where D is barrier transmittance. In the case of pure photoemission, we can assume a rectangular barrier with:

D(w) = 1, when w > Wa (2.13)

D(w) = 0 , when w < Wa

Using (2.11) we find:

4πmA ξdξ P(ξ )dξ = (2.14) h3 exp((ξ − µ − hν )/ kt)+1

The emission current density j is given by:

∞ 4πmeA ∞ ξdξ j = e — P(ξ )dξ = 3 — (2.15) −∞ h 0 exp((ξ − µ)/ kT )+1

When µ >> kT using the method described in [11] we have:

2πmeA j = (hν −ϕ) 2 (2.16) h3

If we assume that the number of excited electrons is independent of the energy of the photons (in other words, all electrons of the electron gas have the same probability of photon absorption for photon energy in the range 1-5 eV) then the proportionality factor A for 400 nm photons will be the same as for 265 nm. Then we can compare the photocurrent for direct photoemission given by (2.16) with the photo-stimulated field emission current that will be calculated next.

In accordance with our assumption, we can use (2.11) for the normal energy distribution of the electrons impinging on the surface.

The potential of the surface is determined by (see figure 2.3 (b)):

V (z) = 0 , when z < 0 (2.17)

e 2 = − eεz , when z > 0 4z

where ε is the external field. Then for w < Vmax and for emission in the range w ~ µ + hν , the transmittance can be presented in the form [12]:

D(w) ≅ exp(− c + (w − µ − hν ) / d ) (2.18)

1 4(2m(ϕ − hν )3 ) 2 c = ϑ(y) 3>eε

>eε d = 1 2(2m(ϕ − hν )) 2 t(y) where ϑ(y) and t(y) are slowly varying functions of the argument e3ε y = approximated by [13]: 4πε 0 (ϕ − hν )

t 2 (y) ≅ 1.1 (2.19)

ϑ(y) ≅ 0.95 −1.03y 2

Then using (2.12) we obtain:

ξ 4πmeA ≈ µ − hν ’ e d dξ P(ξ )dξ = d exp∆− c − ÷ (2.20) h3 « d ◊ exp((ξ − µ − hν )/ kT )+1 and finally for the current density for µ >> kT using again the method in [11]:

4πmeA j = d 2 exp(− c) (2.21) h3

Substituting d and c, equation (2.21) becomes:

1 3 2 ≈ 2 ’ Ae ε ∆ 4(2m) 2 (ϕ − hν ) ÷ j = ⋅ exp − ϑ(y) (2.22) 2 ∆ > ÷ 8πh ⋅t (y) (ϕ − hν ) « 3 e ε ◊

0.35 500 )

o 0.30 ] t 400 o J h 6 - p (

0.25 0 1 Q [ J /

)

y 300 d l 0.20 g r e i e f - n o e t 0.15 r o 200 e h s p ( a 0.10 l Q 100 0.05

0.00 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 3.0 3.5 4.0 4.5 5.0 ε [ GV/m] ε [ GV/m ]

(a) (b)

Figure 2.5. The ratio of photo-stimulated field emission charge (photon energy is 400 nm) and pure photo emission charge (265 nm) from the copper cathode as function of surface (local) field (a); calculated laser energy at 400 nm needed for 100 pC charge of the initial bunch as a function of surface field (b).

Now we can find the ratio of currents (charge of the bunches), and compare it. Thus we can find the intensity of the laser pulse we need for a known field strength to get the same current from photo-stimulated field emission as from pure photo emission.

1 2 2 2 ≈ 2 2 ’ I field − photo Q field − photo e h ε ∆ 4(2m) (ϕ − hν ) ÷ K = = = ⋅ exp − ϑ(y) j 2 2 3 ∆ > ÷ I photo Q photo 16π m ⋅t (y) (ϕ − hν ) « 3 e ε ◊ (2.23)

In figure 2.5(a) this ratio K j is shown for electric fields in the range 0.1-4 GV/m for a copper cathode illuminated by 400 nm light (3.103 eV). It has been measured that with 53 J of UV (265 nm) for a pulse duration of approximately 50 fs, the output charge is 300 pC [1]. Then for the required bunch of 100 pC, 16.6 µJ is needed in the case of pure photoemission. In figure 2.5(b) the laser power at 400 nm needed for 100 pC of initial charge is shown as a function of the field on the cathode. The measurements for 265 nm were used in the calculations for Figure 2.5(b). From the graph it follows that for normal operation of the photocathode with reasonable laser power (less than 1 mJ) the field on the surface must be around 2.6 GV/m.

Another limitation is imposed when we look at the total or integrated charge. The charge produced by the dark current during the duration of the acceleration voltage pulse must be smaller than the photoemitted charge. The field emission process occurs homogeneously from the entire surface of the cathode. The ratio of the extracted current to the full current from the cathode will be equal to the ratio of the cathode and anode opening areas, For a cathode surface with a radius of 3 mm and a radius of the opening of the anode of the diode of 1 mm (our case) this means that approximately 10% of the field emitted current is emanated from through the anode opening. The emission area in the case of photo emission (or photostimulated field emission) is determined by the laser spot on the cathode and can be much smaller than

1E-6 0.001

1E-5 (a) (b) 0.01 1E-4 h p h p Q 1E-3 I / /

c 0.1 c d d I Q 0.01 1 0.1

10 1 1 2 3 4 5 6 2 4 6 8 10 E [ GV/m ] E [ GV/m ] Figure 2.6 The ratio between dark charge integrated for 1 ns (Faraday cup) and 100 pC photoemission charge (a), and the ratio between dark current I dc and 2 kA photoemission current (100 pC initial charge and duration of 50 fs) (a). the anode opening, so that the extraction of the photocurrent can be around 100%. Using these considerations we can estimate operation range of the field. In figure 2.6(a) the ratio of the field emitted bunch charge (see eq.2.7) to the photoemitted bunch is shown as a function of the field on the surface for a 100 pC (photoemitted) bunch. From the graph it is possible to see that up to 4.2 GV/m, the field emitted current contains less then 100 pC.

In figure 2.6(b) the current produced by field emission is compared to the initial current of 2 kA produced by photoemission to get a charge of 100 pC (100 pC and initial duration of 50 fs). At electric fields up to 10 GV/m the field emitted current is less than the photoemitted current. Because the laser pulse for photoemission is much shorter than the voltage pulse that generates the electric field on the surface (in this case 50 fs for photoemission and 1 ns for field emission), the limitation imposed by total charge is much stronger.

The operating range of the field on the cathode must be no less than 2.6 GV/m in order to get sufficient charge with the 400 nm laser pulse and no more than 4.2 GV/m to keep the field emitted charge in a 1 ns pulse below the photo-emitted charge. We now have the following considerations concerning the field strength for emission from the cathode: • the field must be as small as possible in order to minimize the cold field emission current. • the higher the field the lower the laser power needed to get a high enough current (which reflects strongly on the life time of the cathode). These requirements give the range of the field when the diode will be still suitable for applications such as XFEL or LWFA.

2.4 Average and local field (field enhancement).

In the previous section we determined the range of the field on the surface of the metal cathode suitable for generation of bunches in the pancake regime (described in section 2.2.2). From this consideration the surface field must be between 2.6 and 4.2 GV/m. From consideration of the acceleration process in section 2.1 it was shown that the acceleration field gradient, the average field between cathode and anode must be about 1 GV/m to compensate the space charge blow up of the bunch and keep it below 100 fs. Although closely related these are two different fields: the average field in the gap in which the acceleration process occurs and the surface field responsible for the emission processes. The surface field is determined by the average field and the quality of the surface. On an ideal smooth surface case the surface field is equal to the average field. A real surface normally has finite roughness and as a result the field is locally enhanced by a roughness factorβ:

El = βE (2.24) with El the surface, or local field.

In [14] the relation between β and nonuniformities is described. For a wide range of applications it is possible to use an approximate dependence on the ratio h / r , where h is the height and r is radius of the top of a micro nonuniformity. For example, for a cylinder with a spherical top with radius r and height h :

h β = + 2 (2.25) r

For diamond turned copper measurements of the surface give typically h ≈ 1 m and r ≈ 0.1 m so that β ≈ 12 .

Experiments have been performed to determine the influence of the surface quality on the electrical strength [15]. In the experiments on chemically cleaned copper surfaces the first emission site occurred at an applied field of around 120 MV/m. At higher fields more sites start emitting and at 200 MV/m around 90 sites per square centimeter were found to be emitting. For diamond turned copper only one rather weak and unstable emitter appeared in the range of 90 MV/m to 200 MV/m. The size of the site was measured and found to be between 0.1 and 1 µ m. The factor for the emitting sites was between 20 and 100. This local factor, determined for individual sites, is mainly of interest to determine the field at which breakdown starts. To find the field emission current it is necessary to use the average enhancement over the entire surface. In [16] a method is described and was used to determine the surface enhancement factor of a flat metal photocathode. The field on the surface is determined by the macroscopic field (acceleration field) and the enhancement factor of the surface. In the experiments described in [17] a field was applied, far below the breakdown field and a laser was used to extract electrons from the surface. The photon energy was kept below the work function of the material and the current was measured as a function of the applied voltage. A Magnesium cathode fabricated from a solid rod and polished using diamond powder slurry was used. The surface

20 roughness was about 3 µ m. The surface factor found in this way was between 5 and 7. In the case of diamond turned copper, which we use in our experiments, the surface roughness is much better, about 0.1 µ m. The expected surface enhancement will be smaller than in the experiments described above and could be practically equal to 1. For calculation purposes for the cathode surface of diamond turned copper we will take into account a surface field enhancement (for the entire surface) of approximately 1 plus a finite number of emission sites with local enhancement factor between 20 and 100 and emission areas between 0.1 to 1 µ m. The density of these sites is estimated to be a few sites per square centimeter. Due to the small emission areas these sites will not contribute significantly to the average current. However, they play an important role in the breakdown formation, which determines the electrical strength of the acceleration gap.

2.5 Vacuum breakdown.

In section 2.5 we referred to experimental work in which it was shown that even on a perfectly turned surface sites exist with a local field enhancement factor of up to 100. These sites are emitting a small current due to the small emission area. But the current density from these sites can be very high (up to 108 A/cm2). This can lead to explosion of the micro tip when the temperature of the site, due to Joule heating, exceeds the critical value determined by the material of the cathode. The explosion delivers enough material to the interelectrode space to start a spark, which leads to breakdown. The energy deposited on the tip is determined by the local field strength (Fowler- Nordheim current) and exposure time. It is possible to estimate a critical duration of the applied voltage pulse for a certain field strength to prevent breakdown.

We assume that field emission current from the local sites leads to breakdown. Here we will consider a cylindrically shaped site with h = 1 m and r = 0.1 m ( β ≈ 12 ). The thermal conductivity is assumed to be constant in time. In a 1D approximation, the thermal conductivity equation becomes

∂T (z,t) ∂ ≈ ∂T (z,t) ’ ρc = ∆λ ÷ + j 2 r (2.28) ∂t ∂z « dz ◊ where ρ,c,λ,r and are density of the cathode metal, specific heat, heat conductivity and specific resistance, respectively. The dependence of the specific resistance on temperature is approximated by (with 20% accuracy for most metals in the range of 300 K to melting):

r = r0T (2.29) with r0 the specific resistance at 300 K. For long pulses when dT / dt ≈ 0 , we can solve the stationary case of equation (2.28). We assume that emission occurs from a thin layer close to the top of the cylinder and the cathode is massive so that at the base of the cylinder the temperature is constant. Furthermore we assume no heat exchange between vacuum and metal. Then the solution of Eq.(2.28) is:

≈ ’ ∆ r0 ÷ cos∆ j z÷ « λ ◊ T (z) = T (2.30) 0 ≈ ’ ∆ r0 ÷ cos∆ j h÷ « λ ◊ with T0 the temperature at the base of the cylinder, at z = h (z = 0 at the top of the cylinder). The temperature goes to infinity on the top of the cylinder as the current density approaches:

π λ j = (2.31) 2h r0

For a copper cylinder with a height of 1 µm , from (2.31) the limited current is j = 3⋅1012 A/m2. Solving the Fowler-Nordheim equation, Eq.(2.7), for copper (work function is 4.6 eV), gives a corresponding field strength of 9 ×109 V/m. This is in reasonable agreement with measurements in [17] of 1×1010 V/m, and a measured factor between 75 and 250.

For short voltage pulses the current can be larger. In [14] equation (2.28) was solved h 2 ρc for the non-stationary case. For times much shorter than , the temperature at the λ top of the cylinder (z = 0) is given by:

≈ 2 ’ ∆ j r0t ÷ T = T0 exp∆ ÷ (2.32) « ρc ◊

If we assume that the explosion occurs when the surface temperature reaches a certain critical valueTc , then from (2.32) obtain:

2 ρc Tc j td = ln (2.33) r0 T0

As the critical temperature we take the evaporation temperature of copper (2360 K). For the cases under consideration here, the field emitted current is limited by space charge. Therefore the Child-Langmuir current must be used for the current density in (2.33) The(one dimensional) space charge limited current (non-relativistic) is given by [18]: 3 4 2e U 2 j = ε 0 2 (2.34) 9 m0 d eff

6 ]

s n

[ d t 4

0 0 1 2 3 4

E [ GV/m ] Figure 2.7. The breakdown delay time of the copper tip with enhancement factor = 100 as a function of the average field in the gap (cathode-anode).

with U the applied voltage and d eff is the effective gap distance. In this equation the field enhancement by non-uniformities is taken into account through the effective gap d distance: d ≈ , where d is the acceleration gap distance. Substituting (2.34) in eff β (2.33) shows that the delay time is approximately inversely proportional to the third −3 power of the fieldtd ~ E .

The calculated delay time for copper with equation (2.33) and (2.34) is shown in figure 2.7. The constants needed to plot td as a function of the average field, U/d, are: −10 2 3 3 β = 100 , d = 3mm, r0 = 0.63×10 Ω m/K, c = 380 J/kg c , ρ = 8.9×10 kg/m ,

Tc = 2360 K.

2.6 Conclusions.

In this chapter the requirements on field strength for the vacuum diode were discussed. It was shown that we need a field strength of the order GV/m or higher in order to compensate the space charge forces which expand the bunch.

It was also shown that it is possible to generate proper bunches at 400 nm laser wavelength (where the photon energy is less than the work function of the cathode) if the surface field is higher then 2.6 GV/m.. Comparison of the required photoemission current and the dark current (cold field emission) shows that the surface field should not exceed 4 GV/m (for a 1 ns voltage pulse). For these cases the surface field can be derived from the applied average field by taking into account an enhancement factor of 1-5.

To prevent breakdown, the maximum exposure time for an applied field of 1 GV/m must be less than 40 nanoseconds.

References

[1] F. Kiewiet; Generation of ultra-short, high-brightness relativistic electron bunches. Thesis, Technische Universiteit Eindhoven, 2003. ISBN 90-386-1815-8

[2] S. Humphries, Principles of charged particle acceleration,. John Wiley and Sons, Inc. 1997.

[3] Kazuhisa Nakajima Laser-Plasma Accelerator Developments in Japan, http://www.slac.stanford.edu/econf/C010630/papers/T803.PDF

[4] W. Spicer and A. Herrera-Gomez, Modern theory of photocathodes , Tech. Rep. SLAC-PUB-6306, SLAC, 1993

[5] O.J. Luiten, Beyond the RF photogun, in The physics and applications of high- brightness electron beams; Editors: James Rosenzweig, Luca Serafini & Gil Travish, 108-126, World Scientific Publishing Co. Pte. Ltd. , Book Chapter ISBN 981-238- 726-9 (2003)

[6] R.H. Fowler and L. Nordheim, Proc. Roy. Soc. Lond., A119, 173 (1928)

[7] . . . ! " # . . $ . % , 1974 V. N. Shrednik Field emission theory. Cold cathodes. Sov.Radio,1974

[8] W.E. Spicer, C. Coluzza, R. Sanjines, and G. Margaritondo, eds. “Photoemission from the past to the future”, Repro, Ecole Polytechnique Federale de Lousana, Switzerland, p. 1, 1992.

[9] W.E. Spicer, Phys. Rev. Vol. 112, p. 114,1958.

[10] W. Schottky, Ann. der Phys. 57, 541 (1918)

[11] L.D. Landau and E.M. Lifshitz, Statistical physics, volume 5 of Course of Theoretical Physics, Pergamon Press, Paris, 1958

[12] Russell D. Young, Theoretical total-energy distribution of field-emitted electrons, Phys. Rev. Vol. 113, p 110-114

[13] R.H. Good and E. W. Muller, Handbuch der physic, Springer-Verlag, Berlin, 1956, Vol. 21

[14] G.A. Mesyats, D.I. Proskurovsky, Pulsed electrical discharge in vacuum. (Springer-Verlag, Berlin) ISBN 3-540-50725-6

[15] E. Mahner, G. Muller, H. Piel, and N. Pupeter, Reduced field emission of niobium and copper cathodes, J. Vac. Sci. Technol. B 13(2), Mar/Apr 1995

[16] Zikri Yusof, Manoel Conde, Wei Gai, Determination of the field enhancement factor on photocathode surface via the Shottky effect, Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee

[17] P. Kranjec, L. Ruby, Test of the critical theory of electrical breakdown in ultrahigh vacuum, J. Vac. Sci. and Technol. 1967 V.4 & 2, p 94-96

[18] J.P. Barbour, W.W. Dolan, J.K. Trolan, E.E. Martin, Space charge effect on field emission, Phys. Rev. Vol. 92, p 45-51 (1953)

Chapter 3

Sub-nanosecond high voltage techniques.

3.1 Introduction

It was shown in chapter 2 that in order to keep the initial size of the intense bunches formed by femtosecond laser pulse below 100 fs, the acceleration field strength must be in order of 1 GV/m. The energy of the electrons must be a few MeV. To get such fields a megavolt electrical pulse must be applied to a gap of a few mm. Also in chapter 2 it was shown that the duration of this pulse must be a few ns, which is shorter than typical formation time of breakdown of the acceleration gap. The production of such extremely short megavolt pulses requires special techniques. In this chapter we will describe the basic principles of sub-nanosecond pulse formation. In general, an initially long (microsecond range) pulse is ‘cut’ in several stages by a series of dischargers during its propagation in a pulse forming line. The design of this pulse forming line determines the shape of the output pulse.

This chapter therefore starts with the general considerations required for the design, to fulfill the requirements above. The two main issues are pulse sharpening and pulse shortening. Pulse sharpening to decrease the rise time of the front of the pulse occurs by dischargers. The bandwidth of the pulse forming line and the commutation time of the dischargers ultimately determine the minimum rise time. For pulse shortening, described in section 3.4, three different techniques are presented. The design of the load, in this case the vacuum diode (i.e. the accelerator), forms an integral part of the pulse forming line and is described in section 3.5. Once the pulse forming line together with the diode has been designed it is possible to determine the requirements of the charging power supply. In section 3.6 we will briefly describe the Tesla type transformer which is the simplest form of a resonant transformer and it is the transformer used in our system. To tune the system and adjust the dischargers in the pulse forming line, the short high-voltage pulses in the system will need to be measured. This is done by miniature capacitive probes, which are described in the last section. Overall this chapter describes the basic principles and considerations that have gone into the design of the actual experimental system.

3.2 Bandwidth considerations in a pulse forming line

The bandwidth of a coaxial line is defined by the critical frequencies of TM and TE modes, above which the fields are not transverse. In lines with gas or liquid insulation, the critical frequency, determined by the TE waves is [1]:

2c fTE ≅ (3.1) (D + d)π ε where D and d are the diameters of the external and internal conductors, respectively, and ε is the permittivity of the insulation, c is the speed of light.

200

180

160 s p ,

e 140 m i t 120 e s i r 100

60 20 40 60 80 100 Z ,

Figure 3.1 Minimum rise time ( pulse duration) vs impedance of the line for U = 2 106 V, E = 109 V/m and = 1.87

Expression (3.1) determines the minimum rise time and consequently the minimum pulse duration, τmin, that can be transmitted by the line [1]:

τ min ≅ 0.4 / fTE (3.2)

To find the working range of impedances for which the rise time is minimal, we have to write Eq.(3.1) in terms of the electrical properties of the line. For an ideal coaxial line without ohmic losses Z is expressed in terms of the distributed inductance L and capacitance C as:

Z = L / C (3.3)

C and L depend on the geometrical size and permittivity of the insulation. We can express Z in these parameters as:

60ln(D / d ) Z = (3.4) ε The electrical field on the inner conductor is given by:

2U E = (3.5) d ln(D / d) with U the amplitude of the pulse.

To find the minimum rise time as a function of Z we can combine ((3.2) with (3.4) and (3.5) to find:

−10 U ε Z τ min ≅ 10.8 ⋅10 π (1+ exp( )) (3.6) EZ ε 60

4 1

2 3

Figure 3.2. Typical sharpener discharger electrode shape for fast multi channel commutation; 1- external conductor of the transmission lines, 2- the internal conductor of the lower frequency line, 3- the internal conductor of the higher frequency, 4 the spark gap. The pulse that has to be sharpened arrives from line 2. Due to this design the maximum of the field is around the edges (ring shaped area with homogeneous field).

For a given (or required) voltage U and the maximum allowable electric field E, Eq.(3.6) gives a direct relation between the impedance Z and the rise time. This relation is plotted in Figure.3.1 for U = 2 MV and E = 1 GV/m (the typical parameters of interest to us). It shows that the optimal interval of the impedances lies in the range 20-60Ω.

3.3 Pulse sharpening. Commutation time of dischargers.

Pulses with a length in the sub-nanosecond range and amplitude ranging from hundreds of kV to a few MV are formed by sharpening of nanosecond pulses by pulse front sharpening and pulse shortening elements (the latter will be discussed in section 3.4). Usually, sharpening occurs in several stages via sharpening dischargers with short switching times (commutation time). The commutation time is the time it takes for a spark gap to become conductive. Since this time and the spark gap geometry are the critical parameters for the pulse rise time, the commutation time should be as small as possible. To achieve this, the interelectrode distance of the gap must be as short as possible and the discharge must have minimal possible inductance. Therefore, multi channel dischargers (i.e. dischargers in which a number of independent arcs is created simultaneously) are used. In principle, either gas or liquid can be used as an insulator in the pulse forming line. Pressurized gas is preferred in view of bandwidth considerations, but the realization of such a system for very high voltages is more difficult than systems with liquid insulation. In our pulse forming line only liquid insulation is used. Therefore we will discuss the principles of multi-channel commutation in liquids.

The process of multi-channel commutation was initially discovered by Martin [2]. It was shown that the commutation time in a liquid dielectric, t k , is the sum of two components, an inductive and a resistive component:

t k = tr + tl (3.7)

28 with the resistive component: 230 t = (3.8) r Z 1/ 3 N 1/ 3 E 4 / 3 and the inductive component:

L t = (3.9) l NZ where Z is the impedance of the external circuit, E is the electric field in the breakdown area, N the number of discharge channels and L the inductance of a single channel. For a range of impedances 20-60 Ω, the inductive component in the case of multi-channel commutation is negligible compared to the resistive component and usually omitted. Thus, the minimum achievable rise time with multi-channel dischargers is much shorter than in the single spark discharger case due to the lower inductance.

After the sharpening gap, the rise time of the pulse is lower than before. This means that the bandwidth of the line behind the gap must be larger. The second line must be smaller in accordance with section 3.2, Eq.(3.1). The first line therefore has a conically shaped end.

To avoid reflections, the impedance of the two lines must be matched. The multi- channel discharge connects the edges of the first and second line and therefore also provides a better matching than a single channel discharge

To increase the probability to start breakdown simultaneously from different sites in the spark gap area and thus create a multi channel discharge, the maximum field needs to occur over a specific area. The discharger electrode must be shaped to get a smooth field in this area. Usually a half spherical (concave) shape is used. With such a shape, the maximum field is located along the edges of electrodes, as is shown in figure 3.2.

Another requirement to achieve multi-channel discharge is that the voltage still rises during formation of the channels. Finally, the propagation time of the electromagnetic distortion between neighboring channels must be shorter than the characteristic time of the channel formation to allow the channels to develop into conductive arcs.

The formation of multi channel breakdown in a ring-shaped gas-filled gap was studied in [3]. The number of channels was found as:

πD ε 1 dU N = (3.10) cσ U dt where D is the diameter of the ring-shaped electrode, and ' is an experimentally determined constant.

It was shown in [3], for the ring-shaped gaps that σ ≅ 2 ⋅10 −2 and the number of channels is given by:

5⋅10 −7 D ε N ≈ (3.11) t f with tf is the rise time of the applied voltage pulse.

It was shown in the same work that the number of channels in a gap filled with liquid dielectric (in their case transformer oil) can be estimated with the same equation (3.11).

To create a 1 MV pulse after the sharpening gap with a rise time of 100 ps for a transmission line of Z = 20 Ω and N=20 using Eq.(3.11) the rate of change of the voltage across the gap must be about 1015 V/s.

3.4 Pulse shortening. Different types of pulse forming systems.

In order to create a (sub-)nanosecond pulse we need to sharpen the pulse as described in the previous section, but we also need to limit the duration. This requires shortening of the, initially long, pulse. Different schemes can be applied for sub nanosecond pulse formation. These schemes can be roughly divided into three categories with different formation principles. First, systems based on short-circuited lines, second, systems with cut off dischargers, and third, pulse forming devices based on short storage lines.

3.4.1. The short-circuited lines system.

A schematic view of a short-circuited line is presented in figure 3.3. The device consists of three lines, connected in series and separated by spark gaps. The first line (forming line FL) is fed by a low frequency power supply (microsecond timescale). Because the pulse is long, the transverse size of this part is large in order to prevent breakdown. At the maximum output voltage, the spark gap SG1 is switched slowly at a few ns risetime. In the second line (TL1) the pulse length is determined by the length of the line, usually of the order of a few nanoseconds. Because the duration of the traveling pulse in this part is of the order ns, the electrical strength (breakdown voltage) is significantly larger than in the low frequency part. Therefore the cross- section of the second line can be decreased and, as a result, the bandwidth is higher. When the traveling pulse reaches the second spark gap SG2, its amplitude increases due to reflection from the open end (the line capacitance is significantly higher than the capacitance of the spark gap). At the maximum voltage, the sharpening gap SG2 is switched and a pulse is transferred to the third line (TL2). This pulse has a rise time, which is determined by the commutation time of SG2 which can be of the order of 100 picoseconds as discussed in section 3.3. The duration of the transferred pulse is approximately twice the length of the first transmission line, TL1. Two identical short-circuited coaxial lines with impedances equal to the impedance of the main line are connected to the main transmission line. The reflected pulses from the short- circuited lines will have the opposite polarity and extinguish the pulse in the main line. As a result the pulse which propagates into the third transmission line will have a

SG1 SG2 Short-circuited lines Load

FL TL1 TL2 Figure 3.3. The schematic view of forming line with the short-circuited lines. FL- forming line; TL1, TL2 – transmission lines; SG1, SG2 – spark gaps. duration equal to twice the length of the short-circuited line and half the amplitude of the initial pulse.

The advantage of this set up is that the duration of the formed pulse is very stable, since it is determined by the length of the lines. The disadvantage is the low efficiency (voltage conversion). The output pulse amplitude is approximately four times lower than the initial charging voltage.

3.4.2. System with cut-off discharger.

A schematic view of a pulse forming device with a cut off discharger is shown in figure 3.4. As in the previous case, the installation consists of three coaxial lines, separated by two spark gaps SG1 and SG2. As in the system with short-circuited lines, here the front of the output pulse forms after two stages of sharpening on SG1 and

SG2. A cut off discharger is installed at a distance lcut from the sharpening gap SG2.

The cut off discharger can be a simple tungsten rod mounted on the outer conductor of TL2 with a micrometer screw. The screw can be used to tune the voltage level at which breakdown occurs. Another variant that can be used is a ring shaped discharger, mounted on the external conductor. The ring shaped discharger has the advantage that it can create a low inductance multi-channel discharge (see section 3.2). This reduces reflections in the discharger and consequently fewer oscillations behind the main pulse. The disadvantage is that it is in general much more difficult to tune the discharger.

The pulse duration is determined by the operating voltage of the cut off spark gap and the rise time of the incident pulse.

The disadvantage of the system with a cut off discharger is the instability in the duration and amplitude of the output pulse due to variations of the switching voltage of the cut off discharger. The cutoff discharger also induces oscillations behind the main pulse due to the capacitance of the transmission line combined with the inductance of the discharge. These oscillations are reduced if the distance of the cut

Cut off discharger SG1 SG2 Load

l TL FL TL cut

Figure 3.4. Schematic view of the forming line with cut-off discharger. FL-forming line; TL – transmission lines; SG1, SG2 – spark gaps. In the drawing two different types of cut-off discharger are shown: the ring shape discharger and the single channel discharger, lcut is the distance between the SG2 and the cut-off discharger. off discharger from the sharpening gap, SG2, is longer than the duration of the pulse front.

The advantage of the use of a cut off discharger is the complete decoupling from the primary (low frequency) power supply because the line before the cut off discharger is grounded through the discharge channel.

3.4.3. Short storage line based system.

A sketch of an installation based on the short storage line principle is shown in figure3.5. When the storage line (SL) is charged and subsequently discharged through the SG2, it produces pulses with a length which is equal to twice the length of the storage line. The result is a very stable pulse length. The main requirement for this type of pulse forming device is that the storage line needs to be effectively decoupled from the power supply, in this case the forming line (FL). This is accomplished by using a transforming line (TR) with a high impedance output.

For fast commutation of the sharpening gap it is still necessary to charge the storage line rapidly (see section 3.2). This is achieved by keeping the capacitance of the storage line low and the length of the inductive part of the transformer line short.

A problem for this setup is the relatively high background behind the main pulse. This is caused by the fact that the forming line is not completely decoupled from the rest of the system. The background level U bd is given by:

U SL ZTL U bd = (3.20) (ZTrL + ZTL )

Cut-off discharger TrL Load

FL SG1 SL SG2 TL

Figure 3.5 The schematic view of the short storage line based forming setup. FL- forming line; TL – transmitting line; SG1-slow discharger; SG2 – fast spark gap; TrL is a two level transforming line.

The amplitude of the pulse in the transmission line TL is half the voltage to which the storage line is charged, so that the relative background level is given by:

U 2Z bd ≈ SL (3.21) U TL ZTrL

In practical systems the high impedance decoupling can not be more than around 400

Ω, because of the limits on the charging time mentioned earlier. With ZTL = Z SL = 20 Ω the background level is still around 10% of the final pulse amplitude. Therefore additional measures must be used to decrease the background. The standard way to decrease the background level down to a few percent is filtering. A small capacitance can be formed by making a small gap in the inner conductor of the line. Another method is to use a thin wire connecting the inner conductor to the external part of the line.

As an alternative to the inductance-based filtering, it is possible to use a miniature discharger just after the sharpening spark gap, similar to the cutoff discharger discussed in section 3.4.2. This will work, if the impedance of the transforming line is relatively low. In that case, the background voltage will be high enough to create a breakdown of this cutoff discharger.

The pulse forming line used in the actual setup is based on the short storage line principle. The main issues involved in this choice were the output voltage and reproducibility of the output waveform. The short storage line based PFL gives the best trade-off for these parameters. The setup is described in more detail in Chapter 4.

3.5. Vacuum diode for ultra-short pulses.

We will now turn back to the high voltage vacuum diode that was described in chapter 2. In this chapter we will look at it as a part of the transmission line. The design of the diode is important, since it is a nonuniformity in the line. The acceleration voltage and its duration in many respects are defined by correct matching of the diode with the pulse forming line.

TL VTL

acceleration gap insulator (vacuum diode) Figure 3.6. Cut view of the vacuum diode. TL is a transmitting line with liquid insulation, VTL is a vacuum transmitting line.

A schematic view of the diode is presented in figure 3.6. The diode represents a short vacuum transmission line (VTL) with a length comparable to the length of the output pulse of the forming line. The vacuum part is separated from the liquid-filled part of the transmission line by a solid insulator. The impedance of the vacuum line is matched to the impedance at the end of the transmission line, ZTL . The end surface of the inner conductor and part of the external conductor form the acceleration gap as is shown in figure 3.6.

The acceleration voltage and output electron energy can be found from an equivalent circuit of the diode. The equivalent circuit is shown in figure 3.7. The load in this circuit is the vacuum diode.

It has two components, an active load (the electron beam) RVD and passive

(capacitance of the gap)CVD . Such a circuit with lumped elements is valid only for the quasi-stationary case. The quasi-stationary condition holds true if the gap between anode and cathode is much smaller than the length of the pulse and the radius of the diode is much smaller than the length of the pulse.

The incident signal (U inc in the schematic) can be approximated by:

≈ π ’ U = U sin 2 ∆ t÷ (3.22) max « 2T ◊

with U max the incident pulse amplitude and T the half-height duration of the pulse.

The step response of the equivalent circuit H (t) , for the case when RVD >> Z L is given by:

≈ ≈ ’’ RVD ∆ ∆ t ÷÷ H (t) = ∆1− exp∆− ÷÷ (3.23) RVD + Z L « « Z LCVD ◊◊

2Uinc CVD RVD

Figure 3.7 The equivalent circuit of the line loaded by the vacuum diode. ZL- impedance of the transmitting line, CVD-capacitance of the acceleration gap, RVD- electron beam loading (ratio of the experimentally determined electron beam current and the acceleration voltage).

Then the acceleration voltage is determined by the Duhamel integral:

U VD (t) = — H(t −τ )2U i′nc (τ )dτ (3.24) 0 with U i′nc (τ ) the time derivative of the incident signal. After substitution and integration we obtain:

2 ≈ πt ’ Rd U VD (t) = 2U max sin ∆ ÷ « 2T ◊ Rd + ZTL t (3.25) » πα ≈ πt ’≈ ≈πt ’ ≈πt ’ − ’ÿ … −2 ∆ ÷∆ ∆ ÷ ∆ ÷ Tα ÷Ÿ 1+ 2 2 sin ∆cos + sin − παe ÷ … 1+ π α « 2T ◊« « T ◊ « T ◊ ◊⁄Ÿ

where Rd is the resistance (determined by the electron beam), Z L is the impedance of the last stage of the transmission line, andα = Z LCVD /T withCVD the capacitance of the diode. This parameter ( is the ratio between the time constant of the vacuum diode’s capacitance and the half height duration of the incident pulse. When ( is smaller than 1, then the vacuum diode capacitance is charged in a time shorter than the pulse duration. If ( approaches zero, the reflected pulse becomes equal to the incident pulse and the voltage in the diode is twice the amplitude of the incident pulse. In figure.3.8, the ratio of the acceleration voltage to the incident pulse amplitude is R shown for (=1, 0.5 and 0.05 with d = 1. Rd + Z L

From the graphs it is possible to see that a larger capacitance leads to a decrease of the amplitude and widening of the acceleration voltage pulse.

3.6 Tesla type resonant transformer.

The pulse forming line must be charged by a pulse in the megavolt range with a rise time of a few nanoseconds. The line is charged through a spark gap, so that Eq.(3.8) gives the requirement for the field in the spark gap at the moment of breakdown. For a pulse forming line (after the spark gap) with impedance in the range of 20-60 Ω,

2.0

1.6 =0.05 x

a =0.5

m 1.2 U / D V

U =1 0.8

0.4

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

t/T Figure 3.8. The acceleration pulse normalized by incident pulse amplitude U VD /U max for (=1, 0.5 and 0.05.

8 N = 1, and tk is 1-2 ns, we find that the field in the gap must be of the order 10 V/m. The breakdown delay in transformer oil at this field strength is of the order 100 ns (see for example [4]). The output of the power supply must therefore provide pulses in the megavolt range, with a total pulse duration of the order 1 s.

In pulsed accelerator systems often Marx generators are used. However, such systems are very large for the required megavolt pulses. Also, because these systems contain multiple spark gaps, it is practically impossible to synchronize them.

The most commonly used type of power supply that can meet the requirements is the resonant transformer [5],[6]. The classic Tesla transformer (which is here we describe in chapter 4), which is a double resonant transformer.

The operation of a Tesla transformer can be described as two inductively air-coupled damped resonant circuits (see, for example [7]). In figure 3.10 the equivalent circuit of a typical Tesla transformer is presented. The primary circuit is formed by a capacitor C1, an equivalent inductance L1 and equivalent resistance R1 and a (spark gap) switch, SG. L1 represents the sum of the inductance of the primary winding and the parasitic inductances (of the capacitor, conductors and the switch). The capacitor C1 is charged by a DC power supply and discharged through the switch SG. The secondary circuit consists of the secondary coil inductance L2, its equivalent resistance R2 and the secondary capacitance C2.

The practical optimization procedure usually starts at the secondary circuit. The expected or desired output voltage (V2 ) and waveform determine the design of the secondary circuit. The primary circuit is then designed to match the secondary. In most cases the transformer is optimized for energy transfer. In our system the output voltage is the main requirement.

C1 C2

SG L1 L2

R M R 1 2

Figure 3.10. The equivalent circuit of the double resonant transformer (Tesla type transformer). SG-spark gap; R1,R2-resistances of primary and secondary of the Tesla; C1,C2 -capacitances of accordantly primary and secondary of the Tesla, L1,L2- inductances of the primary and secondary coils, M - mutual inductance.

The primary and secondary coils are inductively coupled with mutual inductance M. In accordance with Kirchoff’s laws for this circuit we obtain:

1 di1 di2 R1i1 + — i1dt + L1 + M = 0 (3.28) C1 dt dt

1 di2 di1 R2i2 + —i2 dt + L2 + M = 0 C2 dt dt

The solution of this system for V2 (secondary voltage) can be found analytically only in the ideal case without damping (all resistances are zero) [7]:

2 2kV1 (1− k ) L2 ≈ ω1 + ω2 ’ ≈ ω1 − ω2 ’ V2 = sin∆ t ÷sin∆ t ÷ (3.29) (1− T ) 2 + 4k 2T L1 « 2 ◊ « 2 ◊ with: M k = (3.30) L1L2

(1+ T) − (1− T ) 2 + 4k 2T ω = Ω (3.33) 1 1 2(1− k 2 )

(1+ T ) + (1− T ) 2 + 4k 2T ω = Ω (3.34) 2 2 2(1− k 2 ) with:

1 Ω1 = L1C pr

1 Ω 2 = L 2 C2 2 Ω1 L2C2 T = 2 = (3.32) Ω 2 L1C pr

k being the coupling coefficient. Ω1 and Ω 2 are the natural resonance frequencies of the primary and the secondary circuits, respectively. T is the tuning parameter. ω1 and

ω 2 are the frequencies of the coupled primary and secondary circuits and usuallyω1 < ω 2 .

From equation (3.29) it follows that the secondary voltage is a high frequency oscillation with frequency (ω1 + ω 2 ) / 2 , with an additional amplitude modulation at the frequency (ω 2 −ω1 ) / 2.

Because we want to achieve maximum voltage at the secondary side, we need to optimize for this case.

The secondary voltage reaches a maximum if the sine terms in equation (3.29) are 1 or -1 simultaneously. Then for the frequencies we obtain:

ω + ω π 1 2 t = + mπ , 2 2 ω −ω π 2 1 t = + nπ (3.35) 2 2

Here m and n are positive integers. Without losing generality, let n = 0, then

ω 1+ m 2 = (3.36) ω1 m

The voltage gain is given by:

2 V2 2k(1− k ) γ = = L2 L1 (3.37) 2 2 V1 (1− T ) + 4k T

Substituting (3.33) and (3.34) into (3.36) we obtain:

α 2 (1+ T) 2 − (1− T ) 2 k = (3.38) 4T

1+ 2m with α = 1+ 2m + 2m 2

Finally, we can represent the secondary voltage in the form:

L2 V2 = V1γ T (3.39) L1

1 (1+ α 2 ) 2 (1+ T) 2 (α 2 (1+ T) 2 − (1− T )2 ) with γ = T 4 α 2T 3

Using equation (3.39) the condition for the maximum voltage gain is achieved whenT = 1. This condition is reached if the natural resonance frequencies of the primary and secondary circuits are equal.

In principle triple (and more) resonance transformers can produce higher gain (see for example [8]), but these systems are more complicated.

3.7 Sub-nanosecond high voltage pulse measurements

For tuning of the different stages of the pulse forming line it is necessary to have information about the pulse shape and amplitude. It is evident that a divider, i.e. capacitive or resistive probe must be small enough to prevent disturbance of the measured pulse shape and must be wideband. The amplitude of the traveling pulse is of the order of a few MV, thus the dividing ratio must be of the order of 10-5-10-6. The traveling pulse rise time is of the order of 100 ps, thus the cut off frequency must be a few gigahertz. These requirements are usually obeyed using miniature capacitive dividers with elements that are a few mm in size. Resistive dividers are generally not suitable for measurements in this regime due to the presence of parasitic inductance and the fact that they have to be physically connected to the inner conductor.

In figure 3.9 two types of capacitive dividers with cylindrical and conical measurement elements (ME) are presented. Both dividers consist of a standard high frequency connector (N-type) placed on the outer conductor of the line. The ME is connected to the inner conductor of this connector as shown in figure 3.9. The ME is separated from the outer conductor by a thin insulating layer (usually Teflon or polyethylene film) of thicknessδ i .

The voltage of the pulse that is to be measured is divided between two capacitances.

The first capacitance,C1 , is formed by the inner conductor of the pulse forming line and the tip of the ME. The second capacitance,C2 , is formed by the surface of the ME and the outer conductor. The dividing coefficient, D, is given by:

D = (C1 + C2 ) / C1 ≈ C2 / C1 (3.26)

For the cylindrical probe, calculating C1 andC2 and substituting into (3.26) gives:

d 3 1

δ 2 h i r1

a b

Figure 3.9 Schematic view of the capacitive dividers with cylindrical (a) and conical measuring elements (ME). 1-measuring element (ME); 2-external conductor of the coaxial line; 3-radiofrequency coaxial cable.

ε hZr ε D = 8 i 2 (3.27) ε d60δ i

With d the length of the ME along the pulse forming line (i.e. the diameter of the top of the cylinder or the cone), ε i andε are the relative permeability of the foil and the insulation of the line, respectively r2 is the radius of the outer conductor of the pulse forming line, h is the length of the ME and Z is the impedance of the measuring line. The length h determines the maximum frequency that can be measured. If h is too large, it works not as a lumped capacitance, but as a transmission line. In that case the pulse in will be deformed in the ME. The length of the ME must therefore be chosen a few times smaller then the assumed length of the measured pulse: h ε i / c << T .

A conical shape of the ME instead of a cylindrical shape allows us to increase the dividing coefficient while keeping the length h small. In this case, the dividing ratio depends on the angle of the cone, 2), the ratio between the height of the ME, h, and the top diameter, d [3]. The dividing coefficient for such a conical shaped capacitive probe is: » h ÿ 4h…1+ sinθ Ÿ d ⁄ D = Zr2 ε (3.28) d60δ ε

References

[1] *.. *+ , ,. . , - - - . . $ , 1973 G.V. Glebovich, I.P. Kovalev, Wideband transmitting lines for impulse signals. Sovetskoe radio, 1973

[2] J.C. Martin, Multichannel gaps. Int. Report SSWA/JC.M/703/27. AWRE, Aldermaston

[3] . . . , 1991 ISBN 5-283-03978-1 K.A. Zheltov. High current picoseconds electron accelerators. Energoatomizdat, 1991

[4] .. + , ./. 01 , .. 2 " - 3 . - . -"3 " # . . , 1971, &7, .55-57 A.A. Vorob’ev, V. Ushakov, V. Bagin Electric strength of liquid dielectrics under the action of nanosecond voltage pulses. Electrotechnika, 1971, &7,p. 55-57

[5] Antonio Carlos M. de Queiroz, A simple design technique for multiple resonance networks, ICECS 2001 - September 2-5, 2001 - Malta - pp. 169-172

[6] John Randolph Reed, Analytical expression for the output voltage of the triple resonance Tesla transformer, Review of scientific instruments 76, 104702, 2005

[7] Paul W. Smith Transient electronics. Pulsed circuit technology. John Wiley & Sons Ltd., 2002

[8] K.A. Zheltov, V.M. Kuzin, V.F. Shalimanov, A generator of ultrashort megavolt pulses, Instruments and experimental technique, V.45, &3, 2002, p. 347-350

Chapter 4

TU/e Pulser

4.1 Introduction

In chapter 2 the requirements of the acceleration field were considered that are needed in order to produce 100 fs long bunches with a charge of 100 pC and energy of around 2 MeV: • the field strength must be about 1 GV/m. • in order to keep such strong field without breakdown the exposure time of the acceleration voltage must be shorter then typical time of the breakdown formation i.e. less than a few nanoseconds • for the production of the bunch a femtosecond laser pulse is needed, which must be on the surface of the cathode within the acceleration pulse (preferably at the maximum of the field). Thus the jitter of the voltage across the gap must be less than a nanosecond. To satisfy these requirements a (sub-)nanosecond, megavolt level pulsed power supply is needed. In chapter 3 some specific sub-nanosecond techniques were discussed and possible ways of the realization of a pulser were shown. In this chapter we will describe the TU/e 1 ns, 2.5 MV Pulser. This installation has been designed and manufactured for TU/e at the Efremov Institute, St.Petersburg Russia. Initially the pulser was far from the requirements. During the first start up phase many design and manufacturing errors came to light that affected the output pulse stability (time and amplitude). To increase the life time of the PFL the inner conductor of the whole line was rebuilt, all support insulators inside the PFL were redesigned and replaced with new ones. The vacuum diode in the initial setup was not optimized in order to reach minimum distortion on the incident pulse. Therefore we completely redesigned the vacuum diode. The Tesla transformer output voltage stability is one of the main issues that affect the operation of the main liquid spark gap and in turn the output of the whole pulser. Initially the primary of the Tesla transformer was formed by two circuits, one for each of the windings. Two spark gaps were used on the primary which impacted on the waveform of the Tesla transformer output. As a result, the output voltage variation was more than 20 % and the time jitter of the output with respect to the master clock was more than 100 ns. The variation in the duration of the first half wave (the working point the output) of the Tesla transformer was also more than 100 ns. To improve this, one of the air spark gaps was removed and the whole primary circuit was changed to be powered through one spark gap. The air spark gap was rebuilt with some minor changes to create a stable single channel of commutation of the capacitors of the primary. The high-voltage trigger generator was redesigned to minimize the jitter of the air spark gap and we achieved jitter of the trigger pulses (120 kV) of less than 1 ns. This chapter describes the pulser after implementation of the changes mentioned above.

The Pulser consists of two main parts: a pulse forming line (PFL) and a transformer. The PFL determines the output of the pulser and sets the requirements for the transformer. We will therefore start with a description of the PFL in section 4.2. The vacuum diode, which constitutes the actual accelerator is treated as part of the PFL. The transformer will be described in section 4.3. The complete system is presented in section 4.4

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4.2 Pulse forming line.

A drawing of the pulse forming line is presented in figure 4.1. The pulse forming line can be considered as 4 transmission lines connected in series. In the drawing these lines are numbered with Roman numerals. The main feature of the line is the short storage line, part III in figure 4.1. The output pulse is mainly determined by the length of this component. The other parts are designed to optimize the working of this short storage line.

In chapter 3 several possible options for pulse forming devices based on coaxial transmitting lines were presented. In the TU/e Pulser we use a short storage line type of forming device, which was described in section 3.4.3. The short storage line produces pulses with a length which is proportional to the double run time over it. This type of forming line was chosen because the output pulse length is completely determined by the length of the storage line and is therefore very stable. The high voltage conversion efficiency is two times higher than for the short-circuited lines (section 3.4.1). The advantage of the short storage line over the cut-off discharger based design (section 3.4.2) is the stability of the output pulse amplitude

Although the short storage line mainly determines the design of the other lines and spark-gaps, we will present the different parts in sequence, beginning at the transformer output. The lines are separated by spark gaps (SG), numbered starting from the forming line. As insulation in the pulse forming line we use a liquid called carbogal (1.3 dimethyl perfluorocyclohexane). This liquid has low viscosity (a few times lower than for transforming oil), which allows quick outgassing of the system after commutation of the dischargers. The relative permittivity is 1.88, and the DC breakdown field is 450 kV/m, which make it more convenient than transformer oil.

The first stage (part I) is formed by the forming line (FL). All lines are named in compliance with section 3.4 The FL is formed by the output electrode of the high voltage transformer (1). The external conductor is mounted on the transformer output insulator (2). On the external conductor three optical windows are installed. The windows can be used for optical diagnostics and for laser triggering. The forming line has the largest cross section of the lines in the system because the voltage pulse at this stage has the longest duration of the order hundreds of nanoseconds. The FL has a impedance of 52 Ω.

The next stage is formed by the two level transforming line TrL (part II) and short storage line SL (part III). The transforming line is needed to decouple the storage line from the forming line. The transforming line has input impedance of 62 Ω and output impedance of 140 Ω. After spark gap 1, SG1, has been switched a short pulse with a duration of 4 nanoseconds and a rise time of about 1.5 ns is formed in TrL. The amplitude of the pulse which is transferred from the FL through SG1 to the transforming line is 0.55 times the amplitude in the FL. Propagating through the TrL it charges the storage line, SL. At the end of the transforming line the pulse has an amplitude of 0.76UFL. Because the length of the short storage line is much shorter than the front of the transforming line output pulse (the length of SL is 0.5 ns and the front is 2 ns) the storage line can be represented as a lumped capacitance; in our case the capacitance is around 30 pF. The amplitude of the storage line pulse is determined

TL 2

SG 1

(b) (a) Figure 4.2 (a) - sharpener discharger, SG are spark gaps, SL is the storage line, TL is the transmitting line. . (b) cut of discharger , 1 is the micrometric screw, 2 inner conductor stainless steel insert, 3 is the tungsten rod. by the time constant ZTrlCSL and can be calculated by equation (3.25) for the case of infinite resistance in the scheme shown in figure 3.7. In our case the voltage of SL becomes 1.3 times the output voltage of the transforming line. Thus the short storage line is charged to a voltage equal to the output voltage of the forming line. At maximum voltage in the storage line, SG2 is switched. In this sharpener discharger the electrodes described in section 3.3 are used. The sharpener gap is shown in detail in figure 4.2(a). The rise time of the applied voltage in the gap is of the order of 1015 V/s and the field in the gap of 500-800 MV/m. This leads to the formation of a multi- channel breakdown. A commutation time of 150-250 ps is achieved in SG2. The sharpener gap length can be varied within the range 0-10 mm. It is adjusted by the rotation of a coupling nut (RN) mounted on the casing of the transmitting line (part IV).

The final stage of the PFL is formed by the transmitting line TL (part IV). After SG2 has been switched the pulse with a rise time equal to the commutation time of the sharpener discharger and a duration equal to the double run time over the storage line (1 ns) is transferred to the transmitting line. Because the impedances of the storage line and transmitting line are practically equal, the amplitude of the transferred voltage pulse is half the incident pulse amplitude. In order to increase the voltage conversion efficiency the transmitting line has a gradually rising impedance (coaxial line transformer). The impedance at the input of the transmitting line is 22 Ω and at the end it reaches 70 Ω. The amplitude of the output pulse of the transmitting line is 0.8 times the amplitude of the storage line pulse.

As was shown in section 3.4.3, to decrease the influence of the primary (slow) power supply on the output pulse it is not enough to just have high ohmic decoupling (formed by the output of the TrL). The duration of the background pulse is determined by the life time of the spark in SG1 and usually it is much longer than required 1 ns pulse. In our case, in accordance with equation (3.21) the amplitude of the pulse transferred into the transmitting line is (only) 3 times higher than the transferred

2 1

Figure 4.3. The capacitive probe, 1 is miniature measuring element ME, 2 is the coaxial RF cable, 3 is the external conductor of the measured line, 4 is the inner conductor of the line. background voltage pulse. This can lead to breakdown in the acceleration gap. Therefore two additional decouplings are used. First is a wire, (LS in figure 4.1) which connects the input of the TrL to the outer conductor of the PFL. This forms an inductive decoupling of the PFL from the forming line for low frequencies.

The second decoupling device is the cut off discharger (CD) with construction analogous to the design of the one discussed in section 3.4.2. The cut off discharger is shown in detail in figure 4.2(b). The discharger is placed after the sharpening discharger, at a distance equal to the traveling pulse length (1 ns, or 20 cm). It is formed by a 1 mm diameter tungsten rod. The rod is installed on a micrometer screw, which is mounted on the outer conductor of the transmitting line (TL). The micrometer screw allows us to adjust the distance from the internal electrode of the transmitting line and with that to change the breakdown voltage level. The distance in the cut off discharger is chosen in such a way to get breakdown at the top of the traveling pulse. Then after a certain time (the commutation time) which is usually of the order of a few hundred picoseconds, a conducting channel is formed and as a result the transmitting line is decoupled from the rest of the PFL.

For the measurements of the traveling pulse three capacitive probes (CP) are installed on the PFL. The theory of measurements of short pulses in the coaxial lines is described in section 3.7. We use capacitive probes with the conical shape sensor. In figure 4.3 the capacitive probe design is shown. The first probe is installed at the end of the storage line (CP1). The second (CP2) is installed just after the sharpener gap and is mainly used to optimize the distance in the gap. The third one is placed after the cut off discharger at a distance equal to the double length of the final pulse (2 ns) from the vacuum diode. This position is chosen in order to separate the incident pulse from the pulse reflected from the load. The probes have not been calibrated and are used mainly as a diagnostic.

vacuum

Figure 4.4 The vacuum diode. 1 - high voltage insulator; 2 - the inner conductor of the vacuum line; 3 - acceleration gap.

To estimate the dividing coefficient of the probes we can use equation (3.28):

» h ÿ …1+ sinα Ÿ ε i d ⁄ D = 8 Zr2 ε ε 60dδ ε

The insulation between the sensor and the outer conductor of the PFL is formed by a

10 µm Teflon film withε i = 4 . For calculations we use δ ε =20 µm because the film does not form a uniform layer (it is actually thin Teflon tape wound around the sensor). The height of the measuring element, h, is 6 mm and the diameter of the top of the cone d, is 3.5 mm. The external conductor radius rext is 1.5 cm for the first probe, 1 cm for the second probe and 1.4 cm for the third probe. The permittivity of the insulation liquid between the probe and the internal conductor of the PFL is 1.88. The calculated dividing coefficients are k1 = 1.94×10 4 , k2 = 1.54×10 4 , and k3 = 4.85×10 4 respectively for the first, second and third probes.

The pulse forming line is loaded by the vacuum line with the acceleration gap at the end. Hereafter we will call all these parts together the vacuum diode. The drawing of the vacuum diode is given in figure 4.4. The vacuum line is separated from the end of the pulse forming line by the high voltage insulator 1. The insulator is made from Macor with relative permittivity of 4. Thus it does not dramatically change the field distribution in the place of connection. The insulator is hermetically mounted on the vacuum flange. The internal conductor of the PFL is glued to the center of the insulator. The end of the vacuum line forms the acceleration gap 3.

The impedance of the vacuum line is chosen higher than the resistance of the end of the pulse forming line. Consequently the amplitude in the vacuum line is higher than the incident pulse amplitude. In our case the impedances of the PFL and the vacuum line are 70 Ω and 117 Ω respectively, which gives a transmission coefficient for the voltage amplitude of 1.25. The capacitance of the acceleration gap can be estimated as

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0.000 0 10 20 30 40 50 60 Z, Figure 4.5. The gap length as the function of the forming line impedance for 2.5 MV output voltage of the forming line and commutation time 1.5 ns.

ε S the capacitance of two parallel platesC = 0 , with ε permittivity of vacuum, S the d 0 surface of the plate and d the distance between the plates. Usually we use a gap of 2 mm, so that the capacitance of the acceleration gap is approximately 0.5 pF. Thus in accordance with section 3.5, ( = 0.058 and the voltage across the gap is 1.99 times the incident pulse amplitude. The acceleration voltage is 2.48 (1.99×1.25 ) the amplitude of the pulse at the end of the transmitting line. The pulse at the end of the transmitting line is 0.8 times the forming line pulse amplitude. Therefore, at the end of the entire PFL, the acceleration voltage is 1.99 times the voltage at the beginning of the PFL. The system has been designed for operation voltages in the range 1.5-2.5 MV, and preferred is 2 MV. In this case the acceleration voltage is around 4 MV.

4.3 The Tesla transformer.

In the previous section the design of the pulse forming line was discussed. The design of the PFL directly determines the requirements on the power supply which charges the forming line. At the time the requirements were specified, the design of the vacuum diode was not yet made. Therefore the line had been designed in order to create at the final stage an impedance of about 70-80 Ω, a pulse amplitude of 2 MV and a duration of 1 ns. As was shown in previous chapter, the output voltage of the pulse forming line is 0.8 times the voltage of the forming line (first stage). Thus the forming line has to be charged to 2.5 MV. The next requirement is that the transforming line has to be charged with a pulse rise time of 1-2 ns and a duration of 4-5 ns.

As was shown in section 3.3 the front of the pulse is determined by the commutation time of of the discharger. In our case it is determined by the commutation time of SG1 (figure 4.1). Then in accordance with (3.14) for the required rise time of 1-2 ns in the

48 case of single channel commutation (N = 1) we can find the field strength or the gap length for a certain output voltage as a function of the forming line impedance. For the output voltage level of 2.5 MV this dependence is presented in figure 4.5. The corresponding field in the gap is of the order 108 V/m. In [1] the breakdown field for transformer oil was measured in sub-microsecond scale of applied voltages. In accordance with this data the duration of the applied voltage was shown to be hundreds of nanoseconds. It was assumed that for Carbogal (the insulation liquid used in the present setup), the breakdown behavior will not be significantly different. Then the requirements for the charging power supply of the forming line can be summarized as follows: • Maximum output voltage is 2.5 MV • Output pulse duration is several hundred nanoseconds.

To meet these requirements, the choice was made to use a Tesla transformer as the charging power supply. The main consideration was that it is probably the most simple device (both in operation and manufacturing) which meets the above requirements.

In chapter 3 the theory of the double resonance or Tesla type transformers was described. Our transformer was designed with the following parameters: • Maximum voltage on the primary side: 50 kV. This requirement is imposed by the availability of high voltage, low inductive (less then 0.4 nH) capacitances. • Maximum output voltage of the transformer: 2.5 MV. • Insulation of the transformer must be standard transformer oil (breakdown field strength 8-14 MV/m). • Duration of the first half-wave must be of the order 500-800 ns.

The design of the Tesla transformer is presented in figure 4.6. The main constructive element of the transformer is a dielectric cylinder 1 (the material is specially prepared electrical pressboard). Inside the cylinder is filled with transformer oil. The primary windings are on the outside of the cylinder and the secondary windings of the transformer are inside this cylinder. The ends of the cylinder are hermetically closed with plexiglas flanges 2 and 3. The flange placed at the high voltage side is also the electrical feedthrough between the transformer and the spark gap SG1 (figure 4.1). At the inner side of this flange (inside the cylinder) a hollow electrode (4) is mounted. The electrode plays the role of secondary (intrinsic) capacitance and smoothens the field in the high voltage area. On the outer side of the high voltage insulator the cone shaped electrode (5) with round top is mounted, which forms the negative electrode of the main liquid spark gap (SG1 in figure 4.1). The secondary winding of the Tesla transformer (6) is formed by a solenoid of copper wire, wound around a Plexiglas spool, which has a conical shape. The base of the conical coil is mounted on the inner side of the main cylinder (1) close to Plexiglas flange (3) on the grounded side. The top of the coil is constructively and electrically connected to the secondary capacitance (4). The primary windings of the Tesla transformer are formed by two flat copper bus-bars (7). In order to prevent corona discharge formation around the edges, the windings are insulated by a thin Teflon layer. The bus-bars tightly fit around the outer surface of the cylinder.

1 2 6 8 3

7 4

Figure 4.6 Cut view of the Tesla transformer.1-insulation cylinder, 2-output (high voltage) insulator, 3-plexiglass flange, 4-intrinsic capacitance, 5-output electrode, 6- secondary coil, 7-primary windings, 8- resistive divider

On the axis of the cylinder between flanges 2 and 3 a resistive divider (8) is placed with an ohmic resistance of 100 kΩ. The low ohmic arm of the divider has a resistance of 0.1 Ohm. The dividing coefficient of the resistive divider is 106.

The electrical scheme of the Tesla transformer is presented in figure 4.7. All elements of the primary excitation circuit are placed under the cylindrical body of the Tesla transformer. The main elements of the circuit are two parallel low inductive storage capacitors, CPR, the triggered air spark gap, ASG, the two single-turn windings which form the primary coil, LPR, the secondary coil, LS, and the secondary capacitance, CS., The primary capacitors have a total capacitance of 400 nF. They are charged through a current limiting resistance R1. The primary coil inductance is 400 nH with intrinsic resistance RP = 10 mΩ. The secondary side of the Tesla transformer is formed by the inductance LS = 1 mH, with intrinsic resistance of RS = 0.1 mΩ and the secondary capacitance CS = 70 pF. The mutual inductance of the Tesla transformer is 3.6 mH and the coupling coefficient is 0.45. The transformation coefficient of this setup is approximately 45.

The discharger in the primary circuit is a so-called field distortion air spark gap ASG (figure 4.7). The geometrical profile of the electrode of the spark gap has been chosen in order to operate reliably in the range of 35-50 kV. The spark gap triggering circuit is formed by the capacitances C1 and C2 and resistances R2 and R3. All elements of the circuit are mounted on a Plexiglas insulation plate, which is installed close to the spark gap. A 25 kV triggering signal UTR is generated by a triggering unit (not shown on the scheme). From this signal, the trigger transformer generates a 120 kV pulse with a rise time of 40 ns. Before the trigger pulse arrives the triggering electrode of the air spark gap is floating. The pulse from the trigger transformer creates a distortion in the gap between the main electrodes. The voltages between the negative electrode

Trigger transformer

25/120 kV R2 C3 RPR M RS

UTR ASG LPR LS CS R3 C2

R2 C1 Tesla transformer

Charger R1

0-50 KV CPR

Figure 4.7 The electrical scheme of the Tesla transformer and the triggering electrode and between the triggering electrode and the positive main electrode are determined by the capacitances C1, C2 and C3. The capacitors are used to decouple the triggering circuit for DC voltages. This decoupling allows the use of a relatively compact transformer. For pulse operation, the capacitors act as resistances, and there is no difference with the standard triggering circuits of field distortion dischargers, see for example [2].

4.4 TU/e Pulser.

The parts described in sections 4.2 and 4.3 together formed the Pulser setup. A drawing of the pulser is shown in figure 4.8. All parts of the Pulser are mounted in a welded frame. The length of the setup is 2.25 m and its height is 1.62 m. For a 2.5 MV system, this installation is relatively compact. The whole system is installed inside a grounded metal cage in order to prevent electromagnetic noise from the spark gaps from interfering with other laboratory equipment. All power supplies used for the Pulser (primary charger, trigger unit, pumps for the insulation liquid) are powered through 1-to-1 transformers in order to reduce the influence of the Pulser on the power network.

The overall pulser is quite a unique machine. Only two similar devices have been reported in operation, both at Brookhaven National Laboratory [3]. Although the device is based on conventional technology, this technology has been pushed very close to its limits. Because it operates close to critical values (breakdown voltage and output power) careful design is essential for reliable operation. During the course of the work presented in this thesis many parts had to be redesigned. Results of operating the pulser and a more extensive discussion on the issue of reliability will be treated in Chapter 7. Presently the pulser operates to its requirements. It provides 1 ns pulses of 2 MV to the vacuum diode. The vacuum diode was designed to achieve optimal matching between the PFL and the diode and to optimize the acceleration voltage in

2.25 m Tesla PFL 1 . 6 2

m 1.05 m

Figure 4.8 The main view of the TU/e Pulser. the acceleration gap. The acceleration voltage is expected to be around 4 MV in a gap of only a few mm.

References

[1] .. + , ./. 01 , .. 2 " - 3 . - . -"3 " # . . , 1971, &7, .55-57 A.A. Vorob’ev, V. Ushakov, V. Bagin Electric strength of liquid dielectrics under the action of nanosecond voltage pulses. Electrotechnika, 1971, &7,p. 55-57

[2] *.. 5 "6. * 7. . - . 5 . $ , 1974 G.A. Mesyats Generation of high power nanosecond pulses. Moscow. Sovetskoe radio, 1974

[3] K. Batchelor, V. Dudnikov, J. P. Farrell, T. Srinivasan-Rao, and J. Smedley; A Novel, High Gradient, Laser Modulated, Pulsed Electron Gun; BNL 65895; [pres. 17th Int'l. Conf. on High Energy Accelerators, Dubna, Russia, 7-12 September (1998); Proc. XVII Int'l. Conf. On High Energy Accelerators - p.33-35

Chapter 5

Beam line setup

5.1 Introduction

In chapter 4 we considered the vacuum diode as part of the pulse forming line. In this chapter it constitutes the source of electron bunches. To transport and measure the electron bunches, a beam line setup was designed and constructed. The generation and transport system is formed by the acceleration gap, the input of the excitation laser (laser in-coupling) and a focusing magnet. The diagnostics consist of a phosphor screen to measure transverse beam size, a Faraday cup for bunch charge measurements and a spectrometer for energy measurements. Because the pulser operates at low frequency (typically 1 shot per minute) all diagnostics were designed to be suitable for single-shot measurements.

5.2 The beam line general overview.

Electron bunches are created in the acceleration gap of the vacuum diode. In the beam line these bunches are transported and measured by several diagnostic tools. A drawing of the beam line setup is presented in figure 5.1. The bunch formation (generation) takes place in the acceleration gap (2). The gap is formed by the end of the vacuum transmission line (1). The bunch is created via photoemission induced by a 50 fs laser pulse. The laser pulse is inserted into the system by a laser in-coupling assembly (4). The bunch has a divergence of a few degrees after acceleration caused both by the space charge forces and the anode opening of the acceleration gap which acts as a defocusing lens. Therefore a focusing magnet (3) is used in the beam line. For measurements of the transverse size of the bunch a phosphor screen (5) is used. The charge of the bunch is measured with a Faraday cup (6). For measurements of the bunch energy we use a magnetic spectrometer (7) with a linear diode array as detector (8). All diagnostics are suitable for single-short measurements.

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(a) (b) Figure 5.2 (a) Cut view of the acceleration gap. 1: cathode, 2: anode/flange,3: anode opening, 4: pumping holes. (b) field distribution in the gap calculated with Superfish and electron trajectories calculated with GPT [3]

5.3 Acceleration gap.

The electron bunch is created in the acceleration gap via photoemission. A cut view of the acceleration gap is shown in figure 5.2 (a). The cathode of the acceleration gap is formed by the end surface of a copper insert (1) mounted on the inner conductor of the vacuum transmission line. The cathode surface is diamond turned, which gives a surface roughness of approximately 0.1 m. The anode of the gap is formed by the surface of a flange (2) welded to the external conductor of the vacuum transmission line. The anode aperture (3) has a radius ra = 1 mm. Holes (4) are used for pumping. The acceleration gap length is determined by the length of the cathode insert. We use 4 different insert lengths which allow changing the gap from 1 to 5 mm.

In figure 5.2(b) the simplified electrode geometry is shown. The length of the acceleration gap is 2 mm and the radius of the anode aperture is 0.7 mm. The field distribution has been calculated with Superfish [1] for a DC field for an applied voltage of 2 MV. A simulation by the General Particle Tracer code (GPT, [2]) is shown. The simulation shows that the normalized transverse bunch emittance is about 0.4 8 mm mrad at a distance of 4.5 mm from the cathode surface [3]. The divergence of the bunch at this point is a few degrees.

5.4 Focusing magnet.

For the focusing of the bunch in the beam line a focusing magnet has been installed. The magnet is placed just after the acceleration gap. A thin magnet lens is used in order to decrease the influence of the magnetic field on the electrons during acceleration. The magnetic field in this case is concentrated within a small area inside the magnet

3 1

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Figure 5.3. Focusing magnet. 1: solenoid, 2: jacket, 3: gap, 4: posts.

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Figure 5.4. Bz on the axis of the magnet (solid line). The maximum of the field is in the middle of the gap. The dotted line shows the Glaser approximation.

A drawing of the focusing magnet is shown in figure 5.4. Magnetic field is created by a solenoid (1). The solenoid is mounted inside a iron jacket (2). The vacuum beam pipe is placed inside the jacket (not shown in figure 5.3). In the inner surface of the jacket a gap (3) of 1 cm is made. The jacket and the coil are mounted on adjustable posts (4). To change the position of the lens in respect to the acceleration gap the magnet can be moved along the vacuum pipe. The position of the magnet with respect to the axis of the beam line can also be adjusted.

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0.15 T

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, d l e i f 0.10 m u m i x a m 0.05

0.00 0 5 10 15 20 coil current, [ A ]

Figure 5.5 Maximum on-axis field of the focusing magnet as function of the coil current.

In figure 5.4 the field of the magnet measured on the axis of the solenoid (solid line) is shown. The magnetic field is concentrated inside the jacket, thus there is no influence of the field on the bunch during acceleration even if the coil is installed immediately after the gap.

The focal length of the thin magnetic lens in the paraxial approximation is given by [4]:

2 1 e 2 = — Bz dz (5.1) f 4γ 2 m 2 β 2c 2 with e the electron charge, γ the Lorentz factor, m the rest mass of an electron, c the velocity of light and v . β = c

The focal length can be calculated analytically if the magnetic field is approximated by the Glaser approximation [5] (dotted line in figure 5.4):

Bzm Bz = (5.2) ≈ z ’2 1+ ∆ ÷ « d ◊ where Bzm is the maximum value of the field and d is given by: d ≅ 0.48 s2 + 0.45D2 (5.3)

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electron bunch

4 3

Figure 5.6. Phosphor screen assembly. 1: holder, 2: phosphor screen, 3: Al ring, 4: mirror. The beam line (and the propagation direction of the bunch) is perpendicular to the surface of the screen. with s the length of the gap in the magnet and D the internal diameter of the jacket. Then with the Glaser approximation:

1 e 2 ∞ B 2 e 2 πB 2 d = — zm dz = zm (5.4) f 4γ 2 m 2 β 2c 2 ≈ 2 ’ 2 4γ 2m 2 β 2c 2 2 −∞∆ ≈ z ’ ÷ ∆1+ ∆ ÷ ÷ « « d ◊ ◊

The focusing magnet in combination with the phosphor screen can be used to obtain an estimate of the bunch energy. The focal length for a certain electron energy is a function of the magnetic field, which is a function of the coil current. In figure 5.5 the maximum of the on-axis field ( Bzm ) as a function of the coil current is shown. If the current is adjusted to obtain a focused beam on the phosphor screen, then for a known position of the magnet with respect to the acceleration gap and the phosphor screen, using equation (5.4), the electron bunch energy can be found.

5.5 Phosphor screen.

A phosphor screen is a standard diagnostic tool for transverse size measurement of the bunch. In the phosphor screen electron-to-photon conversion occurs which enables direct visualization of the electron bunch profile. The emitted photon energies for commonly used phosphors are in the visible part of the spectra. This allows the use of relatively simple registration techniques such as photo or CCD cameras. However, the phosphor screen is a destructive analysis so it should be easily moved in and out of the system without disturbing the vacuum.

5 2 0.13

1 3

Figure 5.7. The Faraday cup.1: collector, 2: vacuum chamber, 3: flanges, 4: iris, 5: insulators, 6: BNC connector

The phosphor screen assembly used in our beam line has a design similar to the one described in [6]. A drawing of the phosphor screen assembly is shown in figure 5.6. The phosphor screen holder (1) is mounted on a vacuum feedthrough, which allows it to be removed or inserted into the beam line when necessary. The movement occurs perpendicular to the beam line. The phosphor screen (2) is fixed inside the holder by an aluminum ring (3), which is pressed against the surface of the screen. Inside the holder at an angle of 450 in respect to the screen, a mirror (4) is installed. The phosphor screen is imaged on the CCD chip by an objective lens. The phosphor screen and the mirror are mounted inside a four-way vacuum cross. The other components (camera and lens) are installed outside the vacuum. This allows changing the size of the observed area of the screen during experiments if this is necessary.

The phosphor screen is manufactured from P20 type phosphor (ZnCdS:Ag) deposited on glass. The other side of the glass is coated by a 25-50 nm aluminum layer to remove the electron bunch induced charge. The phosphor grain size is 1 m. A Sony DFX-X700 CCD externally triggered camera is used to record the image.

5.6 Bunch charge measurements. Faraday cup.

One of the important parameters of the electron bunch is the charge. A few different schemes are possible to measure the charge. Charge registration can be done by measurement of the current (or rather the magnetic field induced by a current in, for example, a Rogovsky coil) or by a charge collector. The main advantage of the current measurement based devices is that they are not destructive. But the sensitivity of these devices is limited, especially for short bunches.

output face

detector input face

0 50 electron bunch

3 4 2

Figure 5.8. The spectrometer. 1: yoke, 2: coils, 3: poles, 4: chamber

Collector-based charge measurements are the simplest way to obtain information about the bunch charge. There is practically no limitation on the bunch duration, only on the total charge. The main disadvantage of the collector measurements is that it is a destructive diagnostic. Therefore, in our case the charge detector is placed at the end of the beam line. Charge collector or Faraday cup is shown in figure 5.7. The design of the Faraday cup is exactly the same as was used in [7]. A copper collector (1) is mounted inside a vacuum chamber formed by the stainless steel pipe (2) closed with standard CF40 flanges (3). The collector was designed to absorb all electrons with energies up to 10 MeV and to keep very large fraction of secondary electrons inside the collector. The opening of the collector can be reduced with changeable copper irises (4). The collector is insulated from the pipe (2) by six insulation pins (5). The collector is connected to a standard coaxial feedthrough with BNC type connector (6). The capacitance of the Faraday cup is 67 pF. The corresponding time constant with a 50 Ω cable in series is 3.5 ns.

5.7 Spectrometer.

Energy and energy spread are measured using a sector dipole magnet. Figure 5.8 shows a drawing of the spectrometer. The spectrometer is formed by the magnet (1). The poles of the magnet (3) are sectors with an angle of 50° and a radius 122 mm. The distance between the poles of the magnet is 30 mm. Two coils (2) provide a magnetic field in the gap of the dipole. Between the poles a vacuum chamber (4) is placed with two exit ports: one in the propagation direction of the electrons and another making an angle of 500 with respect to this direction. The electron bunch enters into the magnet perpendicular to the face of the poles. The electrons are bent over a 50° angle and leave the magnet perpendicular to the face of the poles at the exit. At the output port a detector is mounted. This can be a Faraday cup (see section 5.5), or a diode array (see section 5.8).

] 16

[

, t

n 12 e r r u C 8

0 0 2 4 6 8 10

Energy [ MeV]

Figure 5.9. Calculated energy of the electrons in the center of the detector aperture as a function of the coil current.

The energy of the electrons that arrive at the center of the detector is calculated as a function of the applied current (field), using a simple ray-tracing program written in Pascal. The measured field map of the magnet is used in these calculations. The field has been measured with a Hall probe with an accuracy of 0.15%. The calculations have been done for single electrons injected into the magnet through the center of the input port perpendicular to input face of the magnet. In figure 5.9 the energy of the electrons arriving on the detector is shown as a function of the coil current. The energy resolution is determined both by the position of the detector and the width of the detector (the size of the detector in the direction parallel to the face of the magnet). The calculated energy resolution for a paraxial beam with a detector width of 8 mm (typical size of the iris of the Faraday cup) is 4 %.

For accurate measurements the magnet has to be carefully aligned with respect to the beam line. Alignment has been done in two steps: first the vacuum chamber (4) (see figure 5.8) has been mounted inside the magnet; second, the magnet with the chamber was installed on a frame and connected to the beam line. The plane defined by the ports of the chamber has an angle with respect to the poles of the magnet of less than 0.1°. All ports and the middle of the chamber have been marked. A special template has been made in accordance with a drawing of the magnet and the chamber. This template was installed in place of one of the poles. Holes were made in the template at the positions where the marks on the chamber should be. Rods with sharp tips are inserted into the holes and when all the tips and marks coincide, the correct position is found. The uncertainty of this procedure (the position of any port with respect to the

5 1

Figure 5.9. The photodiode array detector. 1: casing, 2: flange, 3: slit, 4: Titanium foil, 5: scintillator screen, 6: photodiode array. center of the bending magnet) is less than 1 mm. After this, the spectrometer is mounted on the frame and connected to the beam line. The uncertainty in the position of the chamber with respect to the beam line is less than 0.1 mm. The uncertainty in the angle between the axis of the beam line and the main axis of the spectrometer is 1 mrad. This small alignment uncertainty does not significantly affect the measurements compared to the uncertainty of the magnetic field measurements (about 0.15%).

5.8 Linear photodiode array.

Because we use a very low repetition rate accelerator we should obtain as much information as possible from each shot. Therefore we used a linear photodiode array as the detector for the spectrometer instead of the Faraday cup. The system is based on a Hamamatsu S8865 series silicon photodiode array. The S8865 is a silicon photodiode array combined with a signal processing circuit chip. We use the S8865- 128 detector, which has 128 diodes in a linear array. The active length of each diode is 0.3 mm, the height is 0.75 mm, the spacing between two neighboring elements is 0.1 mm and the total length of the array is 51 mm. The array is mounted on a board together with the signal processing circuit chip. The signal processing circuit chip is a CMOS processor which incorporates an internal clock generator, a charge amplifier array, a clamp circuit and hold circuit.

The detector design is shown in figure 5.9. To prevent influence of the pulser (electromagnetic noise) on the detector it is mounted inside a metal casing (1). The casing is mounted on a standard CF-40 flange (2). A slit (3) of 10 mm wide and 3 centimeters long was made in the centre of the flange. The slit is covered by a 0.125 mm thick titanium foil (4). For electrons with energies in the range of 1-5 MeV this foil is practically transparent (70 % of electrons with energy of 1 MeV pass through

62 it). Just after the foil a scintillator (Applied scintillation technology, MedeX) is placed (5). The scintillation screen is manufactured from Gd2O2S:Tb phosphor deposited on a plastic plate.

The thickness of the scintillator layer is 1.5 mm. The phosphor grain size is 20 m. Electrons with energies up to 10 MeV are completely absorbed by the scincillator. The photodiode array (6) is mounted in the middle of the slit behind the screen.

The energy range observed with the spectrometer with photodiode array as detector is determined by the aperture of the output port of the vacuum chamber. The range is 8%. The energy resolution for a paraxial beam with infinitely small diameter is determined by the width of a single photodiode. The resolution is 0.2%.

The detector can be externally triggered. The integration time of the detector can be varied by the external processing circuit in a range of 0.1-20 ms. The time needed to scan one diode is 16 s. The external control unit scans the diodes in sequence and generates a video signal. This signal is registered by the oscilloscope so that it shows the intensity as a function of diode position.

References

[1] http://laacg1.lanl.gov/laacg/services/download_sf.phtml#ps0

[2] http://www.pulsar.nl/gpt/

[3] S.B. van der Geer, M.J. de Loos, J.I.M. Botman, O.J. Luiten, M.J. van der Wiel Nonlinear electrostatic emittance compensation in kA, fs electron bunches. Physical Review E, Volume 65, 046501 (2002).

[4] S. Humphries, Principles of charged particle acceleration. John Wiley and Sons, Inc.,1997

[5] $.,. 5 #, .9. $1 , - . 5 , , 1991 S.I. Molokhovsky, A.D. Syshkov Intense electron and ion beams. Moscow, Energoatomizdat, 1991

[6] F. Kiewiet; Generation of ultra-short, high-brightness relativistic electron bunches. Thesis, Technische Universiteit Eindhoven, 2003. ISBN 90-386-1815-8

Chapter 6

Synchronization.

6.1 Introduction

For efficient synchronization the electron bunches excited by the laser have to be created at the maximum of the acceleration field. Because the duration of the output pulses of the TU/e Pulser is 1 ns, the femtosecond laser and the Pulser have to be synchronized within 1 ns.

The femtosecond laser is used as the master clock in the system. The main source of jitter is the high voltage pulser. The Tesla transformer produces megavolt pulses with a duration of 800 ns. The main liquid-filled spark gap described in Chapter 4 charges the transforming line. This spark gap determines the timing of the output pulse of the pulser system. To achieve the required synchronization a short laser pulse is used to ignite the breakdown in this gap. The entire synchronization of the system thus involves two lasers (femtosecond laser and spark gap trigger laser) and the high voltage pulser. The timing sequence of this system will be presented in section 6.2. The results of synchronization under different conditions are presented and discussed in section 6.3.

6.2 The laser system and timing sequence.

6.2.1 The lasers.

The main laser is a femtosecond Ti:Sapphire laser system which is used to produce the electron bunches. This system was described in [1], here we will give only a brief overview. The laser consist of a Ti:Saphire oscillator (Femtosource, Femtolasers Produtions Gmbh) and amplifier (Omega Pro, also from Femtolasers Produtions Gmbh). The oscillator produces 5 nJ, 20 fs pulses at 800 nm with a repetition frequency of 75 MHz, determined by the optical cavity. The oscillator repetition frequency is used as the master clock for the whole system. The pulses from the oscillator are amplified to 1 mJ per pulse in the Ti:Sapphire amplifier. Higher harmonics (second and third harmonic) are generated by two crystals. The harmonic generation has an efficiency of 30% and 10% respectively for the second (400 nm) and third harmonics (266 nm). As was mentioned in chapter 2 we decided to use the 400 nm pulses to generate the electron bunches, because the required laser pulse transport system is more simple and reliable.

For triggering of the main liquid spark gap of the megavolt pulser (at the output of the Tesla transformer) a Nd:Yag (Thales, Saga 230/10) laser is used. The laser can deliver per pulse energy up to 2.5 J in a 5 ns pulse at 1064 nm and 1.2 J at 532 nm. The maximum operation frequency of this laser is 10 Hz. The laser is synchronized with the master clock (75 MHz). The jitter of the laser is less 1 ns.

Both lasers are located in a separate laser lab next to the bunker with the Pulser. Laser pulse delivery occurs via two transport systems. The path lengths of the systems are

s l a ) n g m i n s

0 e 0 r d 4 e o i ( g

r e d J g s e i l o µ r t g

r u

r o e g T p o l i 0

m t e

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l r u a e 5 l f n g

n i h m i

p n p / o r t r c

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u e L s s l l l t e l l l o o s m w s s

i g h i e e e s n a e e g a

- i r m l C C C r m i i r 0 m t e F Q e h

s s s h

’ ’ ’ l l l z p p F F l l l g g g 8 ( p p L H L e e e a a a a a k k k J Y Y Y Y Y M : : : : : c c c S S

: m : d d d d d o o o i i

5 T N 7 N P P P 1 N N N T e c n e y u a q l e e y d a s

e e l g d b

n a i e t l s b m u i a j t t d

s r a u j e y d a s l a

a e l s d

o d 0 r g e 2 x P a i 2

Y a s : g µ d

e 7 N 1 m 2 O

z z H H k k 1 1 z z H H 0 0 1 1

Figure 6.1. The time sequence of the optical setup (Nd:Yag and OmegaPro lasers). equal and total about 17 meters (56 ns). Two breadboards are mounted on the same frame as the electron beam line. One of the breadboards is used for the laser which triggers the spark gap and the other for the photoemission laser.

The expected length of the femtosecond laser pulse on the surface of the cathode is longer than at the output from the harmonic generator (HG). The duration of the femtosecond pulse at the output of the HG is approximately 35 fs. The pulse travels a distance of 17 m and is focused by a 1.7 mm thick plano-convex lens with focal length of 1 m. The pulse enters the vacuum system (the beam line) through a 3.3 mm thick window. Due to effect of these three factors the pulse length on the cathode is expected to be around 66 fs.

6.2.2 Timing sequence.

In this section we will consider the timing scheme of the complete experimental setup. The synchronization system can be separated into two parts. First the laser part, which consist of the Ti:Sapphire femtosecond laser for photoemission and the Nd:Yag laser for triggering of the main spark gap. The second part is the Tesla transformer which

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r n r o ) ) a t o t t i c m m c c e n n l e

a l r e 0 0 p e e s 0 0 a s

c 4 4 e r g

e ( ( i s

e e e y r l s l r J J s s g u l l T r u a

µ µ g p u u

i e p

p r

m p p 0 0 t g i e

e r t t m 0 0 n g h i h t h p u u a 5 5 o r t

i c t

f p p L / / t

f e t t

s i

o ) ) p s o h

u u h w i t

t a s

t o o r m m s f

r - g m a a n n l

o e e a t

t r r Q k

F i i 0 0

S r

g S

g h h 0 0 g

. a g n . a i p p y 8 8 a p a z y ( ( g p p Y d s z Y r : Y d

: H a a : J J a r

a d H a i d d S S e h 0 k e : : m m N A

i i

N N 1 R C R 1 T T 1 1 y y a a l l e e d d

l e e l b l b a b t a a t s t s u s j u u j d j d a d

a a s

µ s

µ 6

. 7 5 2 2 2 2 1 T e s l u p e l b a t s u j d a

t r s

a t 4 . S 0 0 T

Figure 6.2. The time sequence of the experimental setup. has to be triggered in time with respect to the laser system. The pulse into the primary of the transformer is triggered electrically.

In figure 6.1 the timing sequence of the lasers is shown. The whole sequence starts with a trigger from the oscillator and is shown in figure 6.1 as T0. After a fixed delay, the flash lamps of the Nd:YLF) laser (the pump laser for the Ti:Sapphire amplifier) are triggered. We have set the delay to 217 s. A photodiode is measuring the output of the Nd:YLF. This photodiode sends an ‘enable’ signal to the Pockels cell driver. A second photodiode is measuring the pulses from the Ti:Sapphire oscillator and

66 triggers the Pockels cell driver. On the Pockels cell driver we can set an adjustable delay with respect to the trigger signal from the Ti:Sapphire oscillator. After the adjustable delay the Pockels cell opens and one of the pulses from the pulse train of the oscillator is amplified. The delay is chosen to give maximum output power of the pulse selected by the Pockels cell.

This whole system (Omega Pro) works at 1 kHz, the maximum repetition frequency of the Nd: YLF laser.

The high voltage pulses in the vacuum diode need to arrive at the same instance as the laser pulse from the Ti:Sapphire system, in order to get controlled photoemission. Therefore the main liquid spark gap at the output of the Tesla transformer (and the beginning of the pulse forming line) needs to be triggered synchronously with the Ti:Sapphire laser. Because the energy in the Ti:Sapphire laser is insufficient for triggering of the liquid spark gap, we use a separate Nd:Yag laser. The maximum operation frequency of the Nd:Yag laser is 10 Hz. Thus from the 1 kHz output of the Ti:Sapphire, every hundredth pulse is selected. From the same time T0, the Nd:Yag laser firing sequence is started. At T0 the flash lamps of the Nd:Yag fired. After approximately 227 s the Q-switch is triggered and we have laser emission. The output power of the Nd:Yag laser is not very sensitive to the exact delay between the start of the flash lamps to the Q-switch trigger in the range 200-250 s. The trigger of the Q-switch is therefore chosen to get the required delay between the breakdown of the liquid spark gap and the arrival of the Ti:Sapphire laser pulse for photoemission in the vacuum diode.

Before we can trigger the main liquid spark gap the Tesla transformer must be started. The timing sequence for the Tesla transformer with respect to the laser system is shown in figure 6.2. To start the transformer we must first charge the capacitors. This takes a relatively long time (at least 0.4 s). Again we start from the trigger signal T0 i.e. the same as . At T0 the delay generator sends a long pulse (0.4 s) to the charger of the primary capacitances. Immediately after the end of charging, an ‘enable’ signal is sent to a second delay generator. During the charging time the flash lamps of the Nd:Yag laser are triggered every 100 ms (10 Hz) but the Q-switch is not triggered. After the ‘enable’ signal from the charging supply is received, the second delay generator is triggered by the next pulse from the 10 Hz sequence (another T0 in the scheme). This signal triggers the primary air spark gap between the main capacitors and the Tesla transformer. The same trigger enables the Q-switch of the Nd:Yag laser so that during the next (10 Hz) firing sequence the Q-switch is fired, according to the scheme of figure 6.1, and the liquid spark gap will be triggered. Because the main liquid spark gap needs to recover after each shot we have added another ‘enable’ signal for the whole system. This signal can be activated manually or automatically with a delay of approximately 1 minute. The whole system operates reliably at a repetition frequency of approximately 0.01 Hz.

6.3 Laser triggered spark gap operation

The main issue for synchronization of the Pulser with external systems is the triggering of the 2.5 MV liquid spark gap. The sharpening and cutoff dischargers operate with short pulses (1-2 ns) and slew rate of more than 1014 V/s. As a result

67 these spark gaps have a jitter of less then 0.1 ns. In contrast, the main 2.5 MV discharger commutates the long output pulse of the Tesla transformer with a duration of approximately 800 ns. The jitter in this discharger is of the order of one hundred ns (for spontaneous breakdown). In this section the operation of this discharger is investigated with the aim of optimizing the timing. To achieve this, first measurements are made with self breakdown of the gap to obtain data about the formation time of the spark and its dependence on different parameters such as gap length and charging voltage. This data is used to determine the optimal delay time of the triggering laser pulse with respect to the beginning of the output pulse of the Tesla transformer in order to minimize the jitter.

6.3.1 Statistical method of breakdown consideration.

A clear picture of breakdown phenomena in liquid dielectrics does not exist. A lot of work has been reported in the millisecond and microsecond regime (see for example [2]) and theory and experiment agree well. Although also for sub-microsecond and nanosecond time scales a lot of work has been reported (see for example [3]), the physics of the processes in this regime is far from clear. We will therefore employ a mostly empirical approach in which we apply statistical methods to the experimental data to identify the parameters that are of most interest to our specific situation [4].

For the initiation of the discharge process leading to breakdown formation, it is necessary to get free electrons in the cathode region. These free electrons will be accelerated in the electric field, which starts an avalanche. The appearance of these seeding electrons is a random process. The initiation of the discharge therefore has a variable delay, which we will call the statistical breakdown delay. This statistical breakdown delay time, ts , is the time between the moment when the electrical pulse has reached the minimum required breakdown level and the appearance of the initial seed particle that starts the actual breakdown process.

After the start of the breakdown process, some time is needed for the spark gap to become completely conducting. This time is the formation time,t f , which depends on the medium and the electrical pulse parameters. The full time delay from the point when the applied voltage reaches the (self-) breakdown value to a completely conducting channel, tbr , is equal to the sum of the statistical and formation delays.

tbr = tst + t f (6.1)

Although this approach has been tested for gas-filled spark gaps, it can be applied to the breakdown in liquids due to the empirical nature of this approach.

To determine the distribution of the statistical breakdown delay time, we make the following two assumptions: First, the initiation of the discharge in a time interval ∆t is independent from any events earlier in time (statistical independence of events). Second, the probability of the initiation for an (infinitely small) interval dt is proportional to the duration of the interval, that is:

p = µdt (6.2)

where is the probability of events per unit of time. The probability of two or more events in the time interval is assumed to be negligible. A time interval t can be divided into N small intervals, with p the probability of an event for each interval. Then the probability of an event in the full interval is given by:

P(t) = Np(1− p) N −1 (6.2)

When N tends to infinity, the probability distribution of the statistical breakdown delay time is:

f (tst ) = µ exp(−µtst ) (6.3) The average and standard deviation of the distribution are:

tst = 1/ µ

2 2 σ st (tst ) = (t st ) (6.4)

Then the probability that the initiation of breakdown occurs after a time interval larger or equal to tst is:

∞

P(tst ,∞) = — f (t)dt = exp(−tst / tst ) (6.5) tst

In typical experiments, measurements are made of the time delay between the beginning of the voltage pulse and the moment of breakdown. The frequency with which breakdown has occurred in a time interval equal to or longer than t is determined from these measurements using:

N F(t,∞) = t (6.6) N where Nt is the number of shots when breakdown occurred after a time t and N is the full number of shots in a measurement series. If we assume that the formation time delay, t f , is constant we obtain from (6.5) and (6.1):

N t = N exp(−(t − t f ) / t st ) (6.7)

The dependence of ( − ln(N t / N) ) on t is linear and the slope givestst . The intersection with the line − ln(N t / N) = 1 gives the value of tf. This is the basis of Laue’s method of discharge time delay analysis [5].

In a real experiment the formation time, tf, also fluctuates. Because many different processes can play a role in the formation of breakdown, these fluctuations can be regarded as the sum of a large number of independent (or slightly dependent)

69 elementary fluctuations. Each elementary fluctuation has a relatively small effect on the sum. In accordance with the central limit theorem, the distribution of a large number of statistically independent quantities approximately tends to a normal distribution [6]. Measurements of the delay time of breakdown in a strong electric field in some liquid dielectrics (albeit on the sub-microsecond scale) have indeed shown that the formation time is distributed close to a normal distribution [7].

The formation time distribution can thus be approximated by:

» 2 ÿ 1 (t f − t f ) f (t f ) = exp…− 2 Ÿ (6.8) σ 2π … 2σ ⁄Ÿ

with t f the average of the distribution and σ the standard deviation.

The full delay time distribution can now be represented as a superposition of the exponential distribution of the statistical breakdown delay time and the normal distribution of the formation time. Then the probability of breakdown in the interval t,t + dt is given by:

» ÿ » 2 ÿ 1 ts 1 (t − ts − t f ) dP(t,t + dt) = exp…− Ÿdts exp…− 2 Ÿdt (6.9) ts ts ⁄ σ 2π … 2σ ⁄Ÿ

For the probability of breakdown in an interval 0,t we finally obtain: t » ÿÀ t » ÿ ¤ 1 ts Œ 1 (t − ts − t f ) Œ P(0,t) = — exp…− ŸÃ — exp…− 2 Ÿdt‹dts (6.10) t t Œ 2σ Œ s 0 s ⁄Õσ 2π ts ⁄ ›

6.3.2 Experimental results.

The influence of the time jitter of the Tesla output voltage

Expression (6.10) is written for the case of perfect reproducibility of the applied voltage. In our case fluctuations in the applied voltage occur, caused by the air spark gap switch before the primary winding of the Tesla transformer. In figure 6.3 the distribution is shown of the third of the Tesla output pulse (which is the applied voltage pulse on the main spark gap) with respect to the master clock of the entire system. If breakdown occurs, the registered wave form of the transformer output significantly changes. Therefore, to determine the jitter of the Tesla transformer, the measurements were taken in the condition that the maximum output voltage of the Tesla transformer is lower than the breakdown level for the given gap length (0.02 m). The data in figure 6.3 was measured with the charging voltage of 20 kV on the primary side of the Tesla transformer. The corresponding output voltage of 0.9 MV was not enough to start a breakdown. The distribution shown in figure 6.3 can be approximated by a normal distribution with standard deviation of σ = 8 ±1 ns (The

s 5 t n u

o 4 c 3

0 280 290 300 310 320 330 340 time (ns)

Figure 6.3. Delay time of the Tesla transformer output pulse with respect to the master clock. The solid line is a Gaussian fit to the data.

Shapiro-Wilk test shows that the distribution is normal with W = 0.927 and P = 0.2008. The distribution is considered normal if the P value is more than 0.05.)

Taking into account these fluctuations in the air spark gap, the total measured delay time distribution (in respect to the master clock) is the combination of (6.9) and the Tesla output distribution. Then the probability of breakdown in a time interval t,t + dt is given by: » 2 ÿ » ÿ 1 (tU − tU ) 1 t − tU − ts dP(t,t + dt) = exp…− 2 Ÿdtu exp…− Ÿdts σ U 2π … 2σ U ⁄Ÿ ts ts ⁄

» 2 ÿ 1 (t − tU − ts − t f ) … Ÿ exp − 2 dt σ f 2π … 2σ f ⁄Ÿ (6.11)

with tU the time needed to reach the breakdown voltage, tU and σ U are the average and standard deviation of tU.

32 10 (a) 28 (b)

8 24

20 s s t t 6 n n u u 16 o o c c 4 12

8 2 4 0 0 250 300 350 400 450 500 550 600 250 300 350 400 450 500 550 600 t [ ns] t [ ns]

12 (c)

s 8 t n u o c

0 250 300 350 400 450 500 550 600

t [ ns]

Figure 6.4. Delay time for the spontaneous breakdown: (a) interelectrode distance 1.5 cm charging voltage 37 kV; (b) interelectrode distance 1.5 cm charging voltage 40 kV; (c) interelectrode distance 2 cm, charging voltage 38 kV.

Breakdown delay time measurements.

The delay time has been measured for several series of experiments with 100 shots in each series. In figure 6.4 (a), (b) and (c) the histograms and Gaussian fits of the time delay with master clock for the self-breakdown (spontaneous breakdown) are shown. To increase the accuracy, the delay was measured between the master clock and the first capacitive probe (placed at the end of SL, see chapter3 figure 3.1). The real breakdown in the main spark gap is 4 ns before the signal of the capacitive probe by the construction. The absolute value of the output level of the Tesla transformer was impossible to measure correctly using the resistive divider because the occurrence of breakdown changes the waveform. Therefore hereafter we will use the charging voltage (on the primary side of the Tesla transformer) as the setting for each series. The corresponding maximum voltage of the transformer can be estimated with the transformer ratio of 45 (section 4.3).

16 16 (a) (b) 12 12 s s t t n n u u o o 8 c c 8

4 4

0 0 250 300 350 400 450 500 550 600 250 300 350 400 450 500 550 600 t [ ns ] t [ ns ]

24 16 (c) (d) 20 s s t t 12 16 n n u u o o c c 12 8 8 4 4

0 0 250 300 350 400 450 500 550 600 250 300 350 400 450 500 550 600 t [ ns ] t [ ns ]

Figure 6.5. The delay time for the breakdown with the laser (a) 311 ns from the beginning of the Tesla output, (b) 291 ns, (c) 271 ns, (d) 251 ns. The interelectrode distance is 1.8 cm.

In table I the experimental settings and the parameters of the Gaussian fit are summarized.

Table I: Spontaneous Breakdown a b c Charging 37 40 38 Voltage (kV) Gap Length 1.5 1.5 1.8 (cm)

t = tU + tst + t f 423±4.6 408±3.5 424±3.7 (ns)

σ t (ns) 41±4.7 30±3.4 66.2±23

In figure 6.5 the histograms of the delay time of breakdown are shown when a triggering laser was used. All delays are measured with respect to the same time mark (zero point) of the master clock. The triggering laser pulse has a power of about 30 mJ and has been focused by a 200 mm focal length lens perpendicularly to the spark gap axis. The focal spot was near the axis of the spark gap at a distance 3 mm in front of

20 s t

n 16 u o c 12

0 250 300 350 400 450 500 550 600 t [ ns ] Figure 6.6 The delay time distribution for spontaneous breakdown (approximation with normal distribution) 1.8 MV and 1.5 cm gap solid line, 1.66 MV 1.5 cm gap - dashed line, 1.75 MV and 1.8 cm gap – dotted line. the cathode surface. The observed laser spark was actually a line formed by a large number of randomly distributed micro sparks with a total length of 5-10 mm.

The charging voltage for the primary winding of the Tesla transformer was 38 kV in all experiments shown in figure 6.5. In all of these cases breakdown occurred. This implies that the output voltage exceeded the minimum voltage required for breakdown within the duration of the output pulse. The experimental settings and the parameters of the Gaussian fits are summarized in Table II.

Table II: Laser Triggered Breakdown a b c d Charging 38 38 38 38 Voltage (kV) Gap-length 1.5 1.5 1.5 1.5 (cm)

t = tU + tst + t f 455±10 437±6 423±7 411±4 (ns)

σ t (ns) 59±10 54±6 32±8 32±4 Laser delay 311 291 271 251 (ns)

70 ]

n 60

[

n o i t a

i 50 v e d

d r

a 40 d n a t s 30

20 1.0 1.1 1.2 1.3 1.4

E [ MV/cm ]

Figure 6.7 Standard deviation vs. maximum field strength in the gap.

6.3.3 Analyses.

Spontaneous breakdown.

The histograms of the delay times presented in figures 6.4 (a), (b) and (c) have been measured for different gap distances of 1.5 cm ((a) and (b)) and 1.8 cm (c). The charging voltage is 37 kV for (a), 40 kV (b), 38 kV (c). The corresponding maximum output of the Tesla transformer is 1.66, 1.8 and 1.75 MV. In figure 6.6 the Gaussian fits to the delay time distributions are presented. The Shapiro-Wilk test shows that the distributions are normal with W = 0.886 and P = 0.12 for (a), W = 0.878 and P = 0.12 for (c), W = 0.875 and P = 0.051 for (c).

First we will compare the experiments from figure 6.4 (a) and (b) only, because between these experimental series, only the charging voltage was changed. The average time delay increases with lower output voltage: 408 ns for 40 kV charging voltage and 423 ns for 37 kV charging voltage. As explained in section 6.3.1, the measured time delay in respect to the beginning of an applied voltage pulse is given by:

t = tU + tst + t f (6.12)

Because the charging voltage of the Tesla transformer was changed only slightly, we can assume that the shape of the waveform remains the same. In that case, the statistical and formation time are not influenced, so that tst + t f stays the same in both cases, and only the first term, tU , in (6.12) affects the total average delay time.

460 ] 450 s n

[

m 440 i t

y a l

e 430 d

n w

o 420 d k a e r

b 410

400 250 260 270 280 290 300 310 320

laser spark delay time [ ns ]

Figure 6.8. The total average delay time of the breakdown as a function of the laser spark delay time both delays are measured in respect to the beginning of the Tesla output.

If we assume that the minimum breakdown field strength is the same in both cases, we can estimate the breakdown voltage level. The estimate is obtained using a bell shape (sinus squared) approximation for the applied voltage pulse: ≈π ’ U (t) = U sin 2 ∆ t÷ (6.13) out,i max,i « τ ◊

with i the experiment number, U max the maximum output voltage and : the width of the pulse, in our case 800 ns . If we then compare the two sets of experiments we can find the breakdown voltage U br from: ≈ ’ ≈ ’ ∆ U br ÷ τ ∆ U br ÷ τ arcsin∆ ÷ − arcsin∆ ÷ = ∆t (6.14) « U max,1 ◊ π « U max,2 ◊ π where ∆t is the difference in the average delay times between the two series, in our case 14 ns. We solved (6.14) for U br and obtained 1120 kV or 746 kV/cm. Taking into account the uncertainties for the average total delay time in the Gaussian fits we find that U br lies between 670 and 1360 kV, or in terms of the field strength: 450-900 kV/cm. For comparison: the DC breakdown field strength of Carbogal (the insulating liquid used) is given by the manufacturer as 450 kV/cm. The breakdown field in the case of exposure to a short pulse (the 800 ns output pulse of the Tesla transformer) is expected to be somewhat higher.

60 ]

s n

[ 50 n o i t a i v e d

40 d r a d n a t

s 30

20 250 260 270 280 290 300 310 320

laser spark delay [ ns ]

Figure 6.9 The standard deviation (jitter) of the breakdown as a function of the delay time of the laser spark.

Using equation (6.12) we can estimate the delay time caused by the initiation and formation of breakdown, tst + t f for all three series. The time needed to reach the breakdown levels calculated above from the beginning of the applied voltage is 175- 288 ns for case (a), 167-268 ns for case (b), and 190-333 ns for case (c)..The average initiation and formation delay times are 135-248 ns (a), 140-241 ns (b) and 91-234 ns (c). Because of the large uncertainties, very little can be concluded on the influence of the gap length. An important conclusion that we can draw from this analysis is that the delay time, introduced by initiation and formation of breakdown is of the order of a few hundred nanoseconds. This corresponds to literature values of streamer (breakdown) velocities in liquids [3]. The accuracy of these literature values is similar to what we find (approximately 50%).

In figure 6.7 the standard deviation of the delay time distribution is shown as a function of the maximum achievable field strength in the gap for the different settings. This field strength is the output voltage of the Tesla transformer (charging voltage multiplied by 45) divided by the gap length. The graph shows that the standard deviation decreases with increasing field strength. As was discussed before, we assume that the process of breakdown formation starts at some critical field strength, which is the same for all settings. But because the actual breakdown takes 100-300 ns, the voltage across the gap rises during that time. The rise in field strength during breakdown formation depends on the maximum field amplitude. This effect is shown in figure 6.7.

Laser triggering operation.

In the previous section we described the spontaneous breakdown in the main gap. The best achieved jitter of 30 ns has been measured for the gap of 1.5 cm and 1.8 MV maximum output voltage of the Tesla transformer. The jitter is far from the requirements (less than 1 ns jitter). Therefore a laser was used to trigger the breakdown process in the main gap.

In accordance with the theory presented in section 6.3.1 the laser spark in the gap can decrease the statistical time (initiation of the spark) and have some effect on the formation time. In figure 6.5 the delay times for breakdown with the laser are shown using different laser delay times, measured from the beginning of the Tesla output. The interelectrode distance was 1.8 cm and the maximum output voltage of the Tesla transformer was 1.75 MV. These settings are identical to the settings of case (c) for spontaneous breakdown.

Figure 6.8 shows that the timing of the laser influences the average total delay time, as expected. However, in cases (c) and (d) the delay is longer in the presence of the laser than in the case of spontaneous breakdown. In the analysis of the experiments on spontaneous breakdown we found that breakdown starts between 190 and 333 ns after the beginning of the Tesla transformer output. The two cases (c) and (d) in figure 6.5 are close to the end of this range. It is possible that in a large portion of the shots in these cases, breakdown has already started. The distortion caused by the arrival of the laser pulse then somehow destroys the initial spark formation.

In figure 6.9 the standard deviation as a function of the laser pulse delay time with respect to the transformer output is shown. The jitter is decreased for shorter laser pulse delays. The best jitter of 32 ns is reached when the laser pulse arrives in the gap close to the expectation value of the time needed to reach the critical breakdown voltage level calculated for this setting for spontaneous breakdown (270 ns).

The experiments do not show a clear dependence of the variation of the breakdown delay time on the laser timing. This suggests that the laser can initiate the breakdown, but the process of formation determines the variation of the breakdown delay. This formation time does not seem to be greatly influenced by the laser pulse..

6.4 Conclusions and discussion.

The operation of the liquid spark gap determines the synchronization accuracy of the entire system. The measured jitter of the transformer output which is determined by the air spark gap on the primary side of the transformer is 8±1 ns. This is relatively small compared to the length of the output pulse of 800 ns. The output of the Tesla transformer can be considered constant during these 8 ns, so that the jitter in the air spark gap has no significant influence on the operation of the main liquid spark gap.

Spontaneous breakdown of the liquid spark gap leads to a standard deviation in the timing of the output pulse (jitter) of 30-70 ns, depending on the conditions (gap length and field strength in the gap). The results suggest that a smaller jitter is possible if the gap length is reduced further and/or the field strength in the gap is increased.

However, this also means that the delay between the output of the Tesla transformer and breakdown decreases, so that the maximum voltage is not reached. This could be overcome if a shorter transformer pulse output is generated. This would require a different design of the transformer. With a shorter transformer output pulse, it will be difficult to achieve a constant output voltage during the discharge into the pulse forming line.

The results of laser triggering of the main liquid spark gap show that there is a limited effect of the laser on the jitter in the output pulse. The jitter was reduced from 60 ns to 32 ns for the condition that was investigated. There is no clear evidence that changing the timing will cause further reduction of the jitter. It seems unlikely that with the present setup the required 1 ns jitter can be reached. The main reason for this is that the laser pulse mainly affects the statistical (initiation) time but does not influence the formation time of the breakdown. To improve this situation, a preformed channel should be created in the gap between electrodes. This is commonly done by on-axis triggering, where the laser is focused through one of the electrodes. This would require some constructive changes to the transformer. Another important drawback is that it requires optical components near the spark area. Discharge products can easily form an absorbing layer on the optics, which reduces the reliability and lifetime of the system. A possible alternative is to use the laser perpendicular to the axis of the system (the same as it is now), but create a wide, cylindrical focus. Such experiments were reported by [7] (in a gas-filled spark gap) using cylindrical optics. This creates a line focus between the electrodes. If the laser power is high enough, it is possible to create a complete conducting channel in the gap. At present we do not have enough power to form this spark and some constructive changes to the laser input ports would be required.

References

[1] F. Kiewiet; Generation of ultra-short, high-brightness relativistic electron bunches. Thesis, Technische Universiteit Eindhoven, 2003. ISBN 90-386-1815-8

[2] Arii K., Kitani I. // J. Phys. D. 1981. Vol. 14. N 9. P. 1675-1679.

[3] Akiyama, H. Streamer discharges in liquids and their applications. Dielectrics and Electrical Insulation, IEEE Transactions on [see also Electrical Insulation, IEEE Transactions on] Volume 7, Issue 5, Oct. 2000 Page(s):646 - 653

[4] .;. $ " . -+" - -. !;, 2002, 72, -. 9 V.F. Klimkin Statistical investigation of electrical breakdown formation in nanosecond scale. ZTF (journal of technical physics), 2002, vol. 72, issue 9

[5] J.M. Meek and J.D. Craggs Electrical breakdown of gases, Wiley-Interscience, 1978

[6] 2. . * " #. ,- : , 1969 . B.V. Gnedenko Course of probability theory. Moscow, Nauka, 1969

[7] Beddow A.J., Brignell J.E. // Electron. Lett. 1966. Vol. 2. N 4. P. 142-143.

[8] Jimi Hendriks, The physics of photocunductive spark gap switching: Pushing the frontiers. Thesis, Technische Universiteit Eindhoven, 2006. ISBN 90-386-2471-9

Chapter 7

Commissioning

7.1 Introduction.

In previous chapters we described the whole system. In this chapter we will present the results. In section 7.2. the pulser operation will be presented. In order to improve diagnostics on the pulse forming line it was proposed to use the Kerr effect based optical voltage measurements in the line. The Kerr constant for the insulation liquid therefore has been measured. The Kerr constant measurements and the probe design and test will be presented in section 7.3. The spontaneous and photo-excited electron emission measurements will be discussed in section 7.4.

7.2. The pulser operation.

7.2.1 Tesla transformer operation.

It was shown in chapter 6 that the main issue of synchronization of the entire system is the operation of the main liquid spark gap. One of the important parameters to minimize the jitter caused by the main liquid spark gap is the waveform reproducibility and the amplitude stability of the Tesla transformer output voltage. The stability of the output of the transformer is completely determined by the operation of the primary circuit. The stability of the primary side of the transformer in turn is determined by two main parameters: first, the charging voltage of the capacitors on the primary side of the transformer and second, the operation of the air spark gap which discharges the capacitors into the primary windings.

The stability of the primary voltage level affects the transformer output pulse amplitude. Therefore the voltage drop induced by the leakage current in the capacitors must be comparable to the required transformer output voltage stability of 1%. This voltage drop induced by the leakage has been measured. The voltage of the primary capacitors drops less than 1% during 1 second for charging voltages in the range of 25 to 50 kV. During normal operation we have to hold the primary capacitors charged for a few hundred microseconds. The voltage drop during this time is therefore well within the requirements.

breakdown 4

2 ]

V M

[ 0.0

-2

0 200 400 600 800 1000

t [ ns ] Figure 7.1 The Tesla transformer typical output waveform.

The output waveform stability and synchronization depend mainly on the triggering and operation of the (primary side) air spark gap. A measurement of the output waveform of the Tesla transformer with breakdown in the main spark gap is shown in figure 7.1. The first half wave of the output of the transformer has a duration of approximately 700 ns. Breakdown ideally is triggered near the minimum voltage. The moment of breakdown is fixed with respect to the master clock; the jitter of the air spark gap switching with respect to the master clock must be less than 20 ns to obtain an amplitude variation of less than 1 %. Another source of variation in the output voltage level is the inductance of the air spark gap. For an output pulse stability of 1%, the variation of the inductance of the air spark gap must be less than 2% (see also Eq. (3.39)). To minimize the jitter and achieve a constant shot-to-shot inductance the air spark was redesigned to always trigger at the same position and with the single discharge channel. Additionally, the output of the triggering circuit (see section 4.3) was stabilized both in amplitude and time so that the trigger pulse is delivered at the trigger electrode inside the air spark gap with a jitter of less than 300 ps. The final jitter measurements on the output of the transformer were already presented in section 6.3 (as part of the operation of the main liquid spark gap). The time jitter at the output of the transformer was found to be 8 ns. For 25 kV primary (charging) voltage (1.1 MV output, i.e. below the self breakdown voltage of the main liquid spark gap) the pulses were reproducible with less than 1 % variation in amplitude.

7.2.2 The pulse forming line operation.

We have three capacitive probes (the theory is discussed in chapter 4) installed on the pulse forming line (PFL). The first probe is at the end of the storage line, the second

0.75

0.37

0.0 ] ]

V V M M -0.37

[ [ (a)

U -0.75

-1.1

-1.5

102 104 106 108 110 112 t [ ns ]

0.0 ] ]

V V (b) M M

-0.3 [ [

-0.6

40 42 44 46 48 50

t [ ns ]

1 (c) ]

V M

[

0.0 U

-1

40 42 44 46 48 50

t [ ns ]

Figure 7.2. The signals from the probes. (a) – first probe, (b) – second probe, (c) – third probe. Charging voltage on the primary of the Tesla transformer is 40 kV.

83 after the sharpener discharger and the third after the cut off discharger (see figure 4.1). Typical signals from the three probes are shown in figure 7.2. To reconstruct the pulse form in the PFL we can express the measured signal as the Fourier integral:

∞

m(ω) = —U M (t) ⋅ exp(− jωt)dt (7.1) −∞

with U M (t) the measured signal . Then the signal in the PFL, U (t) , is given by the inverse transform:

1 ∞ U (t) = — m(ω) ⋅ h(ω)−1 exp( jωt)dω (7.2) 2π −∞ with h(ω) the transfer function of the probe: C jω(C + C )Z h(ω) = 1 2 1 L (7.3) C2 + C1 1+ jω(C2 + C1 )Z L where C1 is the capacitance to the inner conductor, C2 is the capacitance to the outer conductor and ZL is the impedance of the measuring cable (50 Ω) . Because in our case C1 << C2, the transfer function reduces to:

C jωC Z h(ω) = 1 2 L (7.4) C2 1+ jωC2 Z L

The time constant C2 Z L is approximately 5 ns for all probes, which is longer than the typical pulse length. The (numerically) reconstructed waveform was therefore practically the same as the one registered by the oscilloscope.

Figure 7.2 shows the signals from the three capacitive probes for a charging voltage of the Tesla transformer of 40 kV with corresponding output voltage of 1.8 MV. The signal from the first probe (figure7.2(a)) shows that the pulse in the storage line is about 4 ns, which is in compliance with the design (see chapter 4). The pulse amplitude is about 1.4 MV, which is also in the projected range (0.76 times the output voltage of the Tesla transformer, see chapter 4). The uncertainty in the measurement of the voltage, as determined from the probe signal is around 20%. This uncertainty is mainly due to the uncertainty in the dividing coefficient (mostly C2) of the capacitive probes.

The signal from the second probe, just after the sharpening gap, is shown in figure7.2(b). The interelectrode length of the sharpener discharger was optimized to obtain maximum amplitude of the signal on the second probe while keeping the duration as short as possible (around 1 ns). The optimum length of the gap corresponds to approximately 1 mm per 0.7 MV of the Tesla transformer output voltage (around 2.5 mm for the settings used for these measurements). The amplitude of the pulse is 0.6 MV which is close to the expected value of 0.75 MV (0.55 times the voltage in the storage line), especially when taking into account the 20% uncertainty in the dividing coefficient of the probe.

60 s t o h s

f 40 o

r e b m u n 20

0 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 U [ MV ] Figure 7.3. Variation of the pulse forming line output voltage induced by the main spark gap jitter.

The third probe is positioned approximately 10 cm from the end of the PFL. This probe measures the pulse in the transmitting line. The transmitting line has a continuously increasing impedance to increase the amplitude of the pulse in the line. The signal from the third probe is shown in figure 7.2(c). The length of the pulse is the same as for the previous probe, around 1 ns. The amplitude is approximately 1.7 MV, which is according to design specifications. The amplitude at this point is practically equal to the Tesla transformer output voltage.

The output pulse amplitude stability (third probe signal) has been measured with 40 kV charging voltage on the primary side of the Tesla transformer and 2 cm gap length of the main liquid spark gap. The amplitude variation of the pulse is shown in figure 7.3. The pulses reproduced with an amplitude variation of 11% FWHM. The time variation in the moment of breakdown at similar settings was presented in chapter 6 (section 6.3.2, figure 6.4(c)) and was shown to be approximately 70 ns. This jitter directly results in amplitude variation (the output voltage of the transformer at the moment of breakdown) of about 10%

7.2.3 Reliability of the system

One of the main concerns during operation of the pulser is reliability. The critical parts of the Tesla transformer (up to the main liquid spark gap) are the high voltage capacitors and the trigger pulse circuitry for the primary air spark gap. During four years of operation two high voltage capacitors were replaced. Normally such capacitors have a lifetime of 104-105 shots. The capacitors were already used extensively during the fabrication of the pulser and just reached the end of their lifetime.

The trigger unit for the primary air spark gap initially suffered from self-triggering, due to breakdown inside the system, and inconsistent output voltage. The system was

85 upgraded to improve reliability and has performed without problems for more than two years. The pulse forming line is the most critical part of the whole system. Because the system must allow a very high bandwidth, the dimensions of the PFL are relatively small (see chapter 3). This means that it operates very close to the breakdown limit in many parts of the line. Also, the power density in the line is in the GW range(2 MV pulses in a 100 Ω line). This means that any imperfection in a connection, support insulator or gas bubbles in the insulating liquid results in catastrophic breakdown. During operation several critical parts were identified and redesigned and replaced (see chapter 4). To increase the operation rate the supporting insulators were redesigned. This improves the flow of the insulating liquid and reduces outgassing time. At this moment the pulser can be operated at a rate of 1 shot per 20 seconds and has produced well over 10000 shots.

7.3 Optical high voltage pulse diagnostic in the pulse forming line.

In the previous section the pulses from the different parts of the pulse forming line were presented. Capacitive probes are used to register the traveling pulse. These are relatively simple devices but they have a few drawbacks. The resolution is determined by the length of the sensor (along the tested transmitting line), which is usually in the order of a few mm. But in practice for megavolt-level pulses measurements, the dividing coefficient of the probe must be of the order of 103. Therefore the second capacitance of the divider should be at least 103 times higher. This capacitance is formed by the external conductor of the line and the conical surface of the sensor. To get the required dividing coefficient, a thin dielectric film of a few tens of microns is used as insulation. The insulation film has a limited life time (a few thousand shots). Therefore it should be replaced regularly and the probe has to be calibrated. Another drawback of the use of the capacitive probes is the presence of electromagnetic noise. We have in our setup several dischargers in which significant dissipation of energy takes place. This leads to high electromagnetic noise formation, which influences the signals in the measurement cables. Additionally, the radiofrequency cables used for the measurements have a length about 10 m. The dispersion in the cables gives additional distortion of the registered waveform.

To avoid all the distortions listed above we propose to use optical detection of the high voltage pulses in the PFL. Several optical techniques have been used to measure high voltage pulses, such as Faraday rotation [1] (which uses an optical fiber wound around the inner conductor to measure the Faraday rotation induced by the magnetic field), or the Pockels effect [2] (which measures the change in polarization of a laser pulse in a crystal under the influence of an electric field). Both methods require the presence of material (fiber or crystal) inside the pulse forming line. and the presence of material with a different permittivity will form a nonuniformity in the line. Because the line operates very close to breakdown, this will lead to breakdown formation. To avoid these problems, we propose to use the Kerr effect in the liquid insulator of the pulse forming line. The Kerr effect causes a change in polarization in the presence of an electric field. This effect is present in every liquid. The Kerr constant for Carbogal (the insulation liquid used in the PFL, see chapter 5) was unknown in literature. It was therefore necessary to determine it experimentally. The next section describes the experiment to determine the Kerr constant for Carbogal. Based on this an optical

HV transformer electrodes 0/25kV

PD1 Polarizer /4 WP

He-Ne Laser 633 nm PD2

+ Audio amplifier - I +I I -I HV transformer 1 2 1 2 Kerr cell 0/25kV

Generator Lock-in amplifier Reference frequency

Figure 7.4 Schematic layout of the Kerr constant measuring setup. probe was designed and the feasibility of using the Kerr effect in Carbogal as a means to measure the high voltage pulses in the PFL is discussed.

7.3.1 Kerr effect measurements in Carbogal

The electro-optical Kerr effect results from the birefringence induced in an initially isotropic medium by an externally applied electric field E [3]. Linearly polarized light propagating in such a medium experiences a different index of refraction when its polarization is parallel to E compared to the case when its polarization is perpendicular to E. The difference between the two refractive indices is proportional to E2:

2 ∆n = n|| − n⊥ = KE (7.5)

A light beam which is initially polarized at 450 with respect to an electrical field, propagating in the liquid for a distance L becomes elliptically polarized. The phase shift, ∆φ , between the ordinary and extraordinary components (parallel and perpendicular to the applied electric field) is given by [4]:

2π L 2πL ∆φ = K — E 2 dl = KE 2 (7.6) λ 0 λ

Table I gives the optical Kerr constant, B0 = K / λ , for several liquids.

0.2

] 0.1 . u . a

[

y t

i 0.0 c i t p i l l e -0.1

-0.2

Figure 7.5. Measurements of the Kerr induced phase shift for an applied voltage of 40 kV. The solid line is the measurement for cyclohexane, the dotted line is for Carbogal.

To get an idea of the expected response, and the required sensitivity of the experimental setup, we can make a quick estimation: For a laser beam with 800 nm wavelength, initially linearly polarized at 450 with respect to an electrical field of 10 MV/m which passes through 0.1 meter in cyclohexane, the Kerr-induced ellipticity is 1.85·10-2 rad. With special technique this value of ellipticity can be measured.

Table I Optical Kerr constant of selected pure liquids [5] Liquid Wavelength, < Optical Kerr constant -16 -2 (nm) B0 (K/), (10 mV ) Cyclohexane, C6H12 694 6.8 Ethanol, C2H5OH 694 5.22 Methanol, CH4O 694 4.76 Water, H2O 694 4.6

For the experiment a field modulation polarimeter was designed. The setup is shown in figure 7.4. A beam from a He-Ne laser with output power of 0.5 mW and diameter of 0.5 mm passes a polarizer and passes through the Kerr cell. The Kerr cell is a 30 cm long aluminum pipe with input and output windows. Inside the pipe, two 20 cm long and 6 mm wide electrodes are mounted parallel to the axis of the chamber . The distance between the electrodes is 3 mm. The field between the electrodes is practically uniform. The polarizer is oriented at 450 with respect to the field between the electrodes. The electrodes are connected to two high voltage transformers with maximum output of 25 kV. The transformers operate with a phase shift of 1800 with respect to each other. The voltage in the gap is doubled with a maximum of up to 50 kV. Propagating between the electrodes in the presence of the field, the laser beam

88 becomes slightly elliptical. The applied voltage is modulated which causes the ellipticity of the laser beam to be modulated with the same frequency. After the Kerr cell a quarter wave plate is installed which transforms the slightly elliptical polarized beam into a nearly circularly polarized beam. The polarization beam splitter (Wollaston prism) splits the nearly circularly polarized beam into two linearly polarized beams, which are separately measured by two photodiodes. The intensities of these two beams are given by:

1 I = I (1± sin(∆φ)) (7.7) 1,2 2 0 with I0 the intensity of the laser beam before the prism, ∆φ the phase shift caused by the Kerr effect. We measure these two intensities and take the difference and the sum. To increase the sensitivity a lock-in amplifier is used, which is synchronized to the generator. For small ellipticity, the ratio between the signals from the two diodes is proportional to the Kerr induced ellipticity:

I − I ∆φ ≈ sin(∆φ) = 1 2 (7.8) I1 + I 2

With this method the absorption along the laser beam path length is removed. To remove the influence of the uncertainty in the electric field distribution and amplitude, the system is calibrated using cyclohexane (see Table I). Measurements were made first for the calibration liquid and then with the same settings for Carbogal. The accuracy of the measurements is determined by the extinction ratio of the polarizer optics, in our case about 10-3, the uncertainty in the Kerr constant for cyclohexane, approximately 10%, and the noise level of the measurements.

The results of a measurement is shown in figure 7.5. The measured Kerr induced ellipticity is 4 times higher for cyclohexane than for Carbogal. The corresponding -16 -2 optical Kerr constant for Carbogal at 694 nm is Bo = (1.7±0.3)·10 m V .

7.3.2 Optical voltage probe test.

To use the Kerr effect as a diagnostic technique in the PFL an optical probe was designed as part of the PFL. Fiber incouplings and polarizers are mounted outside the PFL. The drawing of the optical voltage probe is shown in figure 7.6. The probe is mounted at the end of the pulse forming line, just before the output insulator (the insulator of the vacuum diode). The internal diameter of the body (object (1) in figure 7.6) of this setup is matched to the diameter of the pulse forming line at the place of connection. On the sides of the probe body two optical windows (2) are placed in such a way that the optical axis is placed 1 mm below the inner conductor of the PFL. The position of the optical axis of the probe is chosen to get the maximum Kerr induced phase shift. A holder for optical components is mounted outside on the probe body. Two fiber incouplings (3), a polarizer (4) and an analyzer (5) are installed on this holder.

2 1

4 optical axis

fiber fiber

3 Figure 7.6 The optical voltage probe.

The electrical field component perpendicular to the optical axis of the probe setup is given by:

−1 ≈ R ’ Uh ∆ 2 ÷ E(l) = 2 2 ln∆ ÷ (7.9) (h + l ) « R1 ◊

with l the coordinate along the optical path length of the probe beam, h the distance from the optical axis to the axis of the PFL, R2 the radius of the outer conductor of the PFL, R1 the radius of the inner conductor, and U the potential difference between inner and outer conductor of the PFL. Using equation (7.6) for the phase shift at the wavelength 694 nm we find:

L −2 2 2 2 ≈ ’ U h ∆ R2 ÷ ∆φ = 2πBo — 2 2 2 ln∆ ÷ dl (7.10) −L (h + l ) « R1 ◊ 2 with L the path length of the laser inside the pulse forming line. In figure 7.7(a) the phase shift (after integration) is shown as a function of the voltage in the PFL. The light intensity after the analyzer is given by:

≈ ∆φ ’ I = I sin 2 ∆ ÷ (7.12) an 0 « 2 ◊

The ratio between the input light intensity and the light intensity after the analyzer is shown in figure 7.7(b). For 2 MV the light intensity after the polarizer is about 1.8 % of the incident intensity.

0.10

0.6 (a) (b) 0.08 ] d a r

[ 0.4 0.06

/ t f n i a I h s

e 0.04 s a

h 0.2 p 0.02

0.0 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 U [ MV ] U [ MV ] Figure 7.7. (a) The Kerr induced phase shift in the pulse forming line as the function of the voltage. (b) The ratio between the input light intensity and the light intensity after analyzer.

The signal after the analyzer is measured by a fast (7 GHz) photodiode (Thorlabs SUV7-FC). The path length of the laser inside the PFL is approximately 1.5 cm. The maximum time resolution of the setup is therefore around 70 ps.

Two attempts were made to measure the pulses in the PFL using two different lasers. The first test was made with a He-Ne laser with a power of 0.5 mW. Losses due to coupling of the laser to the fibers and absorption reduced the signal by approximately 75%. The (expected) power on the detector for a 2 MV pulse in the PFL was 2 W. The sensitivity of the photodiode (≈ 1 A/W, or 50 V/W at 50Ω output impedance) was insufficient to obtain a measurable output signal. In the second attempt, a laser diode with power up to 4 W was used to get a detectable signal. The expected intensity at the photodiode was 14 mW. However, due to the line-shaped emission area of this laser diode it was impossible to efficiently couple the laser into the fiber optical system.

In order to have a detectable signal on the photodiode the laser must have the following output parameters: • Single mode and linearly polarized. • Output power of 5 W for an output voltage of 100 mV from the photodiode. • Wavelength in the range 600-800 nm (maximum response of the photodiode). • Beam diameter not larger than 0.5 mm and the divergence of the laser beam not more than 0.5 mrad to couple the laser and single mode fiber with standard available fiber optics.

7.4 Electron emission measurements.

In this section we will present the results of the electron emission measurements which have been performed. All measurements were made with the same charging voltage on the primary side of the Tesla transformer of 40 kV, which produces 1.8 MV in the transmitting line.

Figure 7.8. The cathode surface after several thousand shots.

7.4.1 Dark current measurements.

The first measurements of electrons from the setup used spontaneous field emission (dark current). These experiments serve several different purposes. First, before performing photoemission experiments it is necessary to determine if the spontaneous emission will be lower than the expected photoemission. Second, because the capacitive probes installed on the pulse forming line could not be calibrated with sufficient accuracy, measurements of the energy spectrum of the spontaneous emission can be used to determine the acceleration voltage. Finally, the alignment of the system could be checked and improved by measuring the image of the electron bunch on the phosphor screen.

The first experiments were performed with a new diamond turned copper cathode (surface roughness better than 0.1 m). The distance in the acceleration gap was chosen in order to get an acceleration field gradient of about 1 GV/m at 3 MV (the expected acceleration voltage). The emitted charge was measured by the Faraday cup for different settings of the current through the focusing coil (see chapter 5 for a complete description of the beam line setup). The measurements showed that during the first few hundred shots the charge was in the range 20-50 pC for any setting of the focusing coil current. After a few hundred shots the shot-to-shot variation increased and the maximum charge rose up to one hundred pC. Inspection of the cathode surface showed that a crater is formed on the cathode opposite to the anode opening. A picture of the cathode surface after several thousand shots is shown in figure 7.8.

5 6

(a) (b) 5 ] ]

] 4 V V V e e e M M

4 M [ [

[ y y y g 3 g r r g r e e e n n 3 n e e

n n n o 2 o r r o t t r 2 t c c c e e l l e l e e 1 1

0 0 10 20 30 40 50 0 5 10 15 20 25 30 35 40 I [ A ] coil Icoil [ A ] Figure 7.9 The energy of the focused electrons vs the focusing coil current (a) the electrons are focused into the Faraday cup, (b) the electrons focused on the phosphor screen.

The expected photoemission charge is between 100 and 300 pC. Therefore with a new cathode, photoemission can be realized and registered for a few hundred shots, using this simple charge measurement. Once a good time-resolved diagnostic is available.

In order to obtain information about the acceleration voltage we decided to use the “damaged” cathode to measure the energy of the emitted electrons.

To determine roughly the range of the energies, we used the focusing magnet and the Faraday cup. As was shown in chapter 5 the magnet acts as a thin lens and the focal length is a function of the applied current and the electron energy. Therefore for a known distance from the cathode to the lens and from the lens to the Faraday cup opening we can estimate the energy of the electrons collected by the Faraday cup. The distance between the lens and the cathode was 0.15 m and the distance between the lens and the Faraday cup opening was 0.76 m. The corresponding focal length needed to focus the electrons into the Faraday cup was 0.19 m. In figure 7.9(a) the energies of the electrons focused into the Faraday cup is shown as a function of the focusing coil current (calculated using Eq.5.4). In figure 7.10 the measured charge as a function of the focusing magnet current is shown. In the graph a clear peak is present around 11 A, corresponding to energies of around 0.75 MeV. There is also a small increase in the signal around 38 A. This may indicate the presence of electrons with energy around 3.5 MeV.

100

80 ]

C p

[ 60

e g r a h

c 40

0 0 5 10 15 20 25 30 35 40 45

Icoil [ A ]

Figure 7.10. The dark current electron bunch charge vs the focusing magnet current. Error bars represent range of variation over typically 20 shots.

To measure the electron energy more carefully, the bending magnet with linear photodiode array detector was used. A scan was made for the same range as the measurements with the Faraday cup. At each setting for the focusing coil current, the bending magnet current was varied around the corresponding value. For settings of the focusing coil around 10 A (0.7 MeV, see figure 7.9(a)), and for bending magnet currents in the range between 2 and 3 A (0.75-1.25 MeV, see figure 5.9 for the calibration curve), the photodiodes were completely saturated. For settings of the focusing coil around 38 A, the bending magnet current was varied from 5 to 9 A (2-5 MeV), but no detectable signal was registered.

The electron bunches were imaged on the phosphor screen at different settings of the focusing coil current. Some typical images are shown in figure 7.11. The experiments with the phosphor screen have been performed to inspect the position of the bunches after the focusing magnet and to supplement the energy measurements. The images of the bunches on the phosphor screen show that the position changes from shot to shot and is independent from the focusing coil current. With 10-11 Amperes of the focusing coil current, the phosphor screen was completely saturated (not shown in figure 7.11), something that was also seen in the bending magnet results. For currents higher than 30 A the bunch falls outside the phosphor screen (figure 7.11(9)).

12.5 mm

(1) (2) (3)

(4) (5) (6)

(7) (8) (9)

Figure 7.11. The images of the dark current electron bunches on the phosphor screen. the focusing coil currents are : (1) 16.5 A, (2) 17.5 A, (3) 18.5 A, (4) 20.5 A, (5) 21.5 A, (6) 22 A, (7) 26 A, (8) 29 A, (9) 31 A. Visible area has diameter of 12.5 mm.

To estimate the electron bunch energy we used the same procedure as in the case of the measurements with the Faraday cup. The energy of the electrons focused on the phosphor screen as a function of the focusing magnet current is shown in figure 7.9(b). From the images of the electron bunches such as shown in figure 7.11 the spot size was determined by fitting a Gaussian distribution to the image. In figure 7.12 the spot size (sigma) on the phosphor screen as a function of the focusing coil current is shown. For each point (setting of the focusing coil) 10 shots were made. For each series the smallest measured spot size was selected and is shown in figure 7.12. The spot size decreases for low current through the focusing coil (16 A) and for high currents (26 A and 29 A). This is consistent with the measurements from the Faraday cup.

4.4

4.0 ]

m m

[

e 3.6 z i s

t o p s 3.2

2.8

16 18 20 22 24 26 28 30

Icoil [ A ] Figure 7.12. The bunch spot size as a function of the focusing coil current.

7.4.2 Interpretation of the dark current measurements

The maximum energy measured using the Faraday cup is practically the same as was expected We expected that the voltage across the acceleration gap will be two times higher than the Tesla transformer output voltage, around 3.6 MV. However several observations were made in the measurements that need further discussion.

Energy distribution

The large number of electrons with relatively low energy (around 0.75 MeV) may come from the background of the pulse in the PFL. After the pulse is transferred from the Tesla transformer onto the pulse forming line, the pulse duration is shortened, as described in chapter 4. The pulse is steepened by the sharpener discharger and the trailing or afterpulse is cut by the cut-off discharger. It was estimated that without the cut-off discharger the amplitude of the afterpulse would be around 30% of the output pulse amplitude. Because the low frequency afterpulse can not be measured by the capacitive probes, the effectiveness of the cut-off discharger could not be determined. The presence of electrons with energy around 0.75 MeV can be explained if despite the cut-off discharger, a background level of approximately 20% remains.

Emission Process

It was observed during the first measurements with a new cathode, that after a few hundred shots, the emission current increased significantly. Inspection of the cathode after several thousand shots showed significant erosion (see figure 7.8). This erosion shows that we have explosive emission, at least in some cases. Apparently, after several hundred shots, the surface roughness increases which increases the field enhancement factor. For a certain enhancement factor, emission continues during the

96 long afterpulse. The emission site continues to be heated during this afterpulse and can reach the evaporation temperature. As a result the surface will be modified. If this happens towards the end of the applied field or afterpulse, this can actually decrease the enhancement factor. But if this happens long before the end of the applied field, it can lead to explosive emission. Explosive emission leads to ion bombardment which further increases the enhancement factor and the number of emission sites. If the enhancement factor exceeds a certain value, this explosive emission will also take place during the principal (one nanosecond) pulse. In the phosphor screen measurements we observed that the image of the electron bunches varies shot to shot. This is consistent with the assumption that the surface is modified, although other possible explanations for this observation will be discussed below. In the same way, the shot-to-shot variation of the collected charge in the Faraday cup measurements are consistent with surface modification and occasional explosive emission. Furthermore, the high charge at low energy (around 1 MeV) in the Faraday cup measurements can only be explained if emission takes place during the long afterpulse. This supports the assumption that (at least after several hundred shots) the surface roughness is high enough to start the processes described above.

Beam alignment

The phosphor screen measurements show that the position of the bunch on the screen varies from shot to shot, independent of the setting of the focusing coil current. As mentioned above, this may be due to variation of the emission site. Another possible explanation is that the energy varies from shot to shot (around 11%, see figure 7.2). If emission takes place off-axis, and the energy varies, the position of the image on the screen will change. The off-axis emission can be due to surface modification, which can eventually create a preferred site (the edges of the crater). Another factor that can lead to off-axis emission is misalignment of the anode and cathode surfaces. For the bending magnet measurements the alignment is even more critical. Especially for high energy electrons, the settings of the focusing coil and bending magnet must exactly match the electron energy. Because the energy varies, and apparently the pointing of the beam changes from shot to shot, the probability of a good measurement is very small. For low energy electrons, the situation is less critical, because the energy spectrum is much wider. For every setting in the low energy range, there are enough electrons with the correct energy to reach the diode array.

7.4.3 Photoemission measurements.

For good photoemission of electrons it is necessary to have the laser pulse on the cathode surface simultaneous with the acceleration voltage pulse. In chapter 6 we found that the main liquid spark gap has a jitter of about 30 ns in the present setup. The probability of a successful shot within the 1 ns duration of the acceleration voltage pulse, is therefore around 1 %. Moreover, the waveform of the voltage pulse can be approximated by a sine squared (see chapter 3) with a full duration of 1 ns. To get photoemission at the maximum of the acceleration voltage we should hit with the laser within 0.1 ns of the maximum of the acceleration voltage. This means that the probability of a successful shot is about 0.1%.

300

250

200 s t n u

o 150 c

100

0 0 100 200 300 400 charge [ pC ]

Figure 7.13 Histogram of the photoemission experiment.

Thus the idea of the photoemission experiment was to make several hundred shots and then a few of them will be at the correct time. Still there is a high probability that in the case of successful shot the laser will be not at the maximum; therefore the focusing coil current was chosen to be about the value which gives the maximum response in the case of dark current.

The photoemission measurements have been performed with the following settings: • The Tesla transformer primary side capacitors charging voltage of the capacitors for the primary side of the Tesla transformer was 38 kV. The transformer output is 1.7 MV, while the expected acceleration voltage was accordingly up to 3.4 MV. • The acceleration gap length was 3.5 mm to get 1 GV/m acceleration field. • In the experiments a new diamond turned cathode was installed with a roughness better than 0.1 m. During the experiment the pressure in the beam line was around 10-5 Pa. • The 50 fs, 400 nm laser was used for photoemission. The laser pulse energy at the cathode surface was about 0.1-0.2 mJ; this means we are in the regime of photo-stimulated field emission. • The focusing magnet current was set to 10 A.

The timing of the femtosecond laser was measured by a photodiode with respect to the third probe signals. The measuring cable lengths were equal. The distance from the third probe to the acceleration gap is about 2 ns, the path length of the laser pulse from the cathode surface after reflection to the photodiode was about 2.5 ns. Therefore the delay between the third probe and the photodiode signals is 4.5-5 ns if the laser and the high voltage pulse coincide on the cathode.

A series of 360 shots was made. In figure 7.13 the histogram of the registered charge is shown. A fraction of 55% of the pulses yield a collected charge of less than 50 pC and 98% had charge below 100 pC. After 360 shots the charge increased significantly and the experiment was stopped.

During the series of 360 shots, for only three shots the delay between the third probe and the photodiode signal was within the desired range (4-5 ns). One more shot produced a charge of 150 pC, the two other shots produced charge between 350 and 400 pC. Unfortunately we were not able to verify that photoemission occurred during these shots. The focusing coil current was set to 10 A. This means that predominantly electrons were collected with around 1 MeV of energy. Electrons with 1 MeV energy are probably produced during the afterpulse. To get 50 pC of charge during the afterpulse of approximately 10 ns, the field on the surface needs to be in the 3-4 GV/m range. This means that the (average) field enhancement factor is 10-15 and the 0.1 mJ laser pulse would then produce around 100 pC of charge (see chapter 2). This 100 pC photoemitted charge would be (just) detectable.

References

[1] Yeh, P. and Gu, C. "Optical Activity and Faraday Rotation." §3.6 in Optics of Liquid Crystal Displays. New York: Wiley, 1999.

[2] Optics, Eugene Hecht, Addison Wesley, 4th edition 2002, chapter 8.11.2

[3] R. W. Munn, in Principles and Applications of Nonlinear Optical Materials, edited by R.W. Munn, and C.N. Ironside, Blackie Academic and Professional, London, 1993, Ch. 2.

[4] A.O. Sushkov, E. Williams, V.V. Yashchuk, D. Budker, and S. K. Lamoreaux, Kerr effect in liquid helium at temperatures below the superfluid transition, arXiv:physics/0403143 v2 20 Jul 2004

[5] Marvin J. Weber Handbook of Optical Materials, CRC Press LLC, 2000

Chapter 8

General discussion.

8.1 Introduction

The goal of the research described in this thesis was development of a pulsed DC photo injector in the context of the FOM Laser Wakefield Acceleration project. This type of accelerator was proposed because of its ability to create acceleration field gradients which are an order of magnitude higher than conventional RF accelerators. Such strong fields can be applied without breakdown if the exposure time of the voltage across the acceleration gap is shorter than the typical formation time of vacuum breakdown. Therefore the required parameters of the acceleration voltage pulse is as follows: • Pulse duration must be a few nanoseconds or less. • Amplitude of the pulse should be in the megavolt range. In order to determine the requirements for the pulse forming system, the theory of acceleration and emission processes that occur in strong fields were considered. A model was developed for photostimulated field emission. To determine the requirements of the acceleration voltage pulse, the breakdown formation in vacuum was investigated. The typical time of breakdown formation was calculated as a function of the surface quality and the field in the acceleration gap. A pulsed power supply was designed and built for the TU/e but was initially far from requirements and the system was not reliable. Several components of the system were redesigned and replaced. At present the pulser has been operated without any changes for more than 10000 shots. An optical voltage monitor based on the Kerr effect has been designed and the Kerr constant of the insulation liquid of the pulse forming line was measured. For the diagnostics and transport of the accelerated electron bunches, a beam line setup was designed and built.

This concluding chapter links the previous chapters. It gives a short overview and discussion of the results achieved. Recommendation are given to improve the system and for future investigations.

8.2 Conclusions.

The pulser used throughout this thesis was ordered in 1999 in St.Petersburg. The design was based on a pulser that had already been made for Brookhaven National Laboratory two years earlier. The requirements for the new system were different compared to this first setup. The requirements were: output voltage (acceleration voltage) of 2.5 MV (compared to 1 MV for the Brookhaven setup), pulse duration of 1 ns and output pulse stability is not worse than 1%.

From the start of operation several critical design mistakes were detected: • The design of the primary of the pulse transformer was not suitable for our purpose. In the original construction, the two primary windings was powered by two independent circuits. Two air spark gaps were used that discharged two separated capacitors into each winding. As a result the amplitude of the output pulse of the Tesla transformer was unstable, with variations of more than 20%.

100

In addition, the instability in the duration was around 70 ns and the jitter of the output pulse of the transformer was more than 100 ns. • The trigger pulse generator of the triggering circuit of the primary of the Tesla transformer had jitter of 10 ns and sometimes the pulse generator discharged spontaneously due to insulation problems (corona discharge formation on the supports of the thyratron and breakdown on the surface of the insulator of the thyratron). • In the pulse forming line (PFL) we found several critical sites: First, The transforming line where the diameter of the internal conductor of the line decreases down to 1.5 mm. High currents flow through this wire and this limits the life time of the transforming line. Initially the life time was no more than a few hundred shots. Second, the support insulators of the transmitting line are located in places with very high fields. The lifetime of these supports was limited by breakdown, due to incorrect design. Third, the repetition rate of the system was less than 1 shot per minute. This was due to the recovery time of the insulation liquid of the PFL and the main spark gap. The recovery time is determined by the outgassing process after each shot. In the original design the flow of the insulation liquid through the critical parts was the limiting factor. It was not possible to operate the whole pulser without any replacements for more than a few hundred shots.

To improve the original design and to make the system close to the requirements the following parts were redesigned: • The primary of the Tesla transformer was redesigned. The two air spark gaps were replaced by a single spark gap. The spark gap was improved to stabilize the number and the position of the breakdown channels. As a result the required output pulse stability of 1 % and a constant pulse duration were reached. • The trigger pulse generator for the air spark gap was improved. This reduced the jitter to less than 1 ns and the operating voltage increased to 30 kV without spontaneous triggering. • The complete inner part (conductors and support insulators) of the PFL was redesigned and replaced. The reliability of the PFL improved to more then 10000 shots. A new pumping system was installed to circulate and filter the insulation liquid. The support insulators were designed to minimize the flow resistance. The repetition rate improved to 1 shot per 20 seconds.

At this moment the pulser can be operated for more than 10000 shots without any problem. The required output voltage waveform stability of the Tesla transformer was achieved.

In order to determine the operation range of the field in the acceleration gap, the electron emission and electron bunch formation processes were considered theoretically. This consideration showed that in the case of single photon, photostimulated field emission at 400 nm the surface field must be more than 2.6 GV/m, but less than 4 GV/m to prevent significant dark current. It was shown that for a typical surface roughness of 0.1 m the corresponding acceleration field (average field in the gap) must be around 1 GV/m. This consideration was confirmed by the experiments that were performed.

101

To prevent the effect of the electromagnetic noise produced by the pulser on the high voltage measurements, an optical measurement of the pulses in the PFL was proposed. The diagnostic is based on the Kerr effect in the insulation liquid used in the PFL. The expected resolution of the designed probe is about 70 picoseconds. A polarimeter was designed and built to measure the Kerr constant of the insulation liquid (Carbogal). The optical Kerr constant for Carbogal at 694 nm was found to be -16 -2 Bo = (1.7±0.3)·10 m V .

The vacuum diode was not a part of original design. It was treated theoretically with a simple model, which showed the possibility of doubling of the voltage across the acceleration gap. Using this data the actual device was manufactured. The doubling of the voltage was conformed by measurements of the energy field emitted electrons. Electrons with energy of 3.6 MeV were measured. This is the highest energy measured for this type of accelerator.

8.3 Recommendation for further research.

8.3.1 Pulser.

At present it is impossible to produce the electron bunches that we want with this system. First of all, the time jitter of the output pulses is 30 ns or more, even with laser triggering. Because the pulse duration is only 1 ns, this makes it impossible to perform photoemission. Related to this time jitter is the variation in amplitude of the output pulses, so that the energy of the electrons that are produced varies by around 10%. Both these problems are directly linked to the operation of the main liquid spark gap.

It was shown in chapter 6 that the jitter of the main spark gap is related to the gap length. To reduce the jitter, the gap distance must be decreased. In order to decrease the distance but still operate with the same output voltage amplitude, the output pulse duration from the transformer must be smaller. The minimum duration of the applied voltage is determined by the fact that the preferred pulse shape at the end of the PFL is rectangular. During the charging of the short storage line (4 ns), the applied voltage amplitude should be constant. Therefore the duration of the output pulse from the transformer can be decreased to around two hundred nanosecond, without changes in the design of the PFL. For a two hundred nanosecond pulse, the gap length can be decreased to less than one centimeter. This will lead to a decrease of the variation of the spontaneous breakdown delay time to around 10 ns. It is expected that with laser triggering the overall jitter will be around 5 ns.

To further improve the jitter we need to replace the liquid insulation in the spark gap by pressurized gas. In liquids, the breakdown formation process is complicated and depends on many parameters (purity of the liquid, flow distribution in the gap at the moment of breakdown, pressure and so on). In gases, the breakdown formation process is more predictable. Relatively simple models can be used to determine gas mixture parameters and operation pressure to meet the requirements of the spark gap. Gas mixture and pressure can be used as two additional tuning parameters for the proper operation of the system. An important extra advantage is the much shorter recovery time of gas which allows a significant increase of the repetition rate.

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As mentioned earlier, to implement the improvements of the spark gap, we need to produce shorter output pulses from the transformer. This can be achieved if a triple resonant transformer is used instead the double resonant Tesla type transformer. Such a triple resonant transformer with MV output amplitude and output pulse duration of 200 ns is described in [1]. Such a triple resonant transformer has to be more carefully designed and manufactured to optimally tune the different resonant circuits. But such a system has number of significant advantages. The voltage gain in a triple resonant system can be higher. This means that the voltage on the primary can be lower, around 20 kV, which allows the use of semiconductor switches. Because the voltage increases in two steps, in stead of one, it is possible to use metal cores. This greatly improves the efficiency, so we can use smaller capacitors and the electromagnetic noise produced will be significantly reduced.

A final matter that is worth investigating further is the presence of the afterpulse in the PFL. From the data presented in chapter 7 we found evidence for a low voltage (≈ 1 MV) afterpulse. This afterpulse leads to low energy electron emission and since the duration of the afterpulse may be tens of nanoseconds it can lead to breakdown formation in the gap. To remove this afterpulse an active (real) load must be installed in the PFL. A resistive coating can be made on the internal side of the output insulator of the PFL. This layer must be capable to withstand very high power (order 10 GW during 1 ns) and absorb a significant amount of energy (order 10 J). Some engineering will be needed to produce a suitable layer for this purpose.

8.3.2 Electron bunch production.

For the applications for which this pulsed DC accelerator was designed (LWFA and X-FEL) the main requirements for the electron bunches are reproducibility of duration, current and energy. With the recommendations given in the previous section it is possible meet the requirements for reproducibility in energy and, with a stable laser, bunch duration. The (variation in) current, however, depends on the cathode surface condition. In our experiments we showed that the cathode surface erodes significantly in a few hundred shots. This can lead to vacuum breakdown formation and limits the life time of the cathode. Also, the surface roughness will not be constant during the operation and therefore the photoemission current is not constant from shot-to-shot. To increase the life time both cathode and anode surfaces should be diamond turned. But even then, the photocurrent in the presence of the strong field on the surface strongly depends on the surface condition. Small changes in the field enhancement factor will lead to significant changes in the photoemitted current.

A possible way to avoid cathode erosion is to use a recoverable surface, such as a liquid metal cathode. In principle, the surface quality can be controlled externally. However, to implement such a liquid cathode the diode design will be drastically more complicated.

Another possible solution is to use reproducible explosive emission instead of photoemission. Such reproducible explosive emission can be created from a surface of, for example, carbon nanotubes [2]. In that case an electron bunch with (sub-) nanosecond duration will be created. The current of such a bunch can be up to several kilo amperes. Immediately after electron gun the electrons will have to be injected

103 into a bunch slicer, where the bunch will interact with a 25-50 fs high power laser pulse. Part of the electron bunch will be excited by the laser pulse. The length of this part is approximately the same as the length of the laser pulse. After the slicer this part can be extracted by a bending magnet. Such a slicer system was proposed in [3]. With the proper design the peak current of the output bunch will still be in the kA range which meets the requirements for the X-FEL and LWFA.

References

[1] K.A. Zheltov, V.M. Kuzin, V.F. Shalimanov, A generator of ultrashort megavolt pulses, Instruments and experimental technique, V.45, &3, 2002, p. 347-350

[2] S. Iijima, Nature, 354 56 (1991)

[3] Kazuhisa Nakajima Laser-Plasma Accelerator Developments in Japan, http://www.slac.stanford.edu/econf/C010630/papers/T803.PDF

104

Summary

This work is devoted to a novel method for the production of bright, relativistic electron bunches for Laser Wakefield Acceleration. The production of high brightness, ultrarelativistic electron bunches to be used, for example, in X-ray Free- Electron-Lasers is a big challenge for accelerator physicists. Utilization of classical schemes of acceleration leads to significant size of the bunch forming system (injector) and requires large accelerators. This makes it impossible to have such a system available in the laboratory. The only option is to use large facilities shared between many users, and even then, the price of experiments will be high. Therefore novel methods of acceleration and bunch compression have been explored during the last few decades. One of these methods is Laser Wakefield Acceleration, where the acceleration process occurs in a plasma channel. For LWA an injector is needed which produces ultrashort (less than 100 fs) electron bunches.

The method investigated in this thesis is based on acceleration of an initially short (25 fs) photo-emitted electron bunch in an extremely high DC field (1 GV/m). To avoid breakdown the acceleration field should be applied for a time shorter than the typical formation time of vacuum breakdown, which is in the range of one nanosecond. For this project it was proposed to use an electrical pulse with a duration of 1 ns and an amplitude of up to 2.5 MV. For production of such a short and high voltage pulse conventional pulsed high voltage generators are not suitable due to many problems related to synchronization, electrical insulation and output pulse reproducibility. Therefore sub nanosecond pulse forming techniques were used in order to create the required output pulse. The main element of this technique is a pulse forming line (PFL), where pulse sharpening and shortening occurs. A Tesla type pulse transformer produces 2.5 MV pulses with (sub-) microsecond duration. The output of the pulsed transformer is switched in a liquid filled spark gap. The PFL is then charged in 5 ns to the 2.5 MV level. The PFL consists of a short storage line and a sharpener discharger to produce pulses with a risetime of around 200 ps. After the sharpener discharger, a cut off discharger reduces the duration to around 1 ns.

The pulser was designed and built specially for TU/e at the Efremov institute, St. Petersburg, Russian Federation. During first start up of operation after the system was installed in Eindhoven, we identified several critical points in the design of the pulser. Together these points seriously affected the life time of the entire pulser system. During the first two years of this work the pulser setup was considerably improved. Many parts of the pulser were redesigned and remanufactured. Finally the pulser could be operated for several thousand shots without replacement of the components. In addition, the reproducibility of the output pulses from the transformer was improved from around 20% to about 1%. Variations of the output of the transformer cause instabilities in the breakdown formation in the main liquid spark gap between the transformer and the pulse forming line (PFL). The overall voltage reproducibility achieved at the end of the PFL, i.e. the output of the system, was better than 10%.

An acceleration section consisting of a vacuum diode and a beam line setup was designed and built, including several diagnostics. Consideration of the vacuum diode as a part of the PFL showed that the voltage across the acceleration gap can be practically two times higher than the amplitude of the incident pulse (the output pulse of the PFL). This was confirmed later by dark current energy spectra measurements.

105

The maximum registered energy of the electrons was 3.6 MV at 75% of the practical maximum output of the PFL (100% is 2.5 MV), this is the highest registered electron energy for this type of accelerators.

For the successful realization of the pulsed DC acceleration concept, a femtosecond laser pulse should arrive on the cathode surface within the applied voltage pulse duration. This imposes strong requirements on the jitter of the whole system, which must be less than 1 ns. For synchronization of the pulser to the laser system we used a laser pulse for the triggering of the main liquid spark gap. The experiments performed showed that even with laser triggering of the liquid spark gap it is impossible to achieve jitter less than the requirements. This is due to the fact that random processes which occur after triggering determine the final breakdown jitter. The best synchronization that was achieved with laser triggering is 29 ns.

Photoemission was attempted in a series of several hundred shots. In this series, only two shots with possible photoemission result were detected. The registered charge of these (two) bunches was around 350 pC, close to the expected value.

On the basis of this work we identified several critical points of the existing device which must be improved in order to get a suitable setup. Most of them are related to the pulser. As was motioned before, the main issue for stable operation is synchronization, which is mainly determined by the liquid spark gap operation.. To improve the existing situation we propose to use a gas filled spark gap, shorter applied voltage pulses (higher operation frequencies of the pulse transformer), and cylindrical optics for the triggering laser pulse to ionize a larger part of the gap directly by the laser. Another problem is related to the lifetime of the cathode. In our setup the output pulse from the PFL has a long after-pulse with an amplitude up to 1 MV. During this after-pulse the probability of vacuum breakdown in the diode is significant. This significantly decreases the lifetime of the cathode and the reproducibility of the charge of the bunches. To improve this, an active (ohmic) load should be installed in the final part of the PFL. Another possible way to stabilize the current is to use a self- recovering cathode, such as a liquid metal cathode.

In conclusion we can state that the concept of pulsed DC acceleration can be used for the production of ultrashort relativistic electron bunches, but it requires considerable additional engineering research.

106

Samenvatting

Dit proefschrift betreft onderzoek aan een nieuwe methode om ultra-korte wolkjes van elektronen te maken. Dergelijke groepjes elektronen met een hoge dichtheid zijn nodig voor bijvoorbeeld Röntgen vrije-elektronen-lasers. Het maken van hele korte intense elektronenwolkjes vormt één van de grootste uitdagingen op het gebied van elektronenversnellers. Om met conventionele technieken elektronen te versnellen tot hoge energie en te comprimeren zijn zeer grote experimentele opstellingen nodig. Gedurende de afgelopen decennia bestaat daarom steeds meer belangstelling voor nieuwe versneltechnieken. Eén van de meest veelbelovende technieken op dit gebied is de Laser Plasma Versneller. In zo’n versneller worden elektronen op de hekgolf van een laser in een plasma versnelt. Om deze techniek te kunnen beheersen is het nodig om elektronen op de hekgolf in het plasma te injecteren. De elektronenwolk dient dan wel zeer kort (ongeveer 100 fs) te zijn. Het hier beschreven werk onderzoekt of het mogelijk is om met een gepulst DC (gelijkstroom) elektrisch veld dergelijke elektronenwolkjes te maken.

De techniek die in dit proefschrift wordt onderzocht is gebaseerd op het versnellen van elektronenwolkjes van 25 fs die zijn gemaakt via foto-emissie op een metalen oppervlak. De elektronen moeten worden versneld in een veld van minimaal 1 GV/m om te voorkomen dat de lengte van de wolk groter wordt dan ongeveer 100 fs. Onder normale omstandigheden zorgt een veld van 1 GV/m voor elektrische doorslag in het vacuüm. Om dit te voorkomen moet het veld worden uitgeschakeld voordat de doorslag plaatsvindt. Dit betekent dat de puls die het elektrisch veld maakt niet langer dan ongeveer 1 nanoseconde mag duren. Om de elektronen tot relativistische energie te versnellen moet de amplitude van de puls enkele megavolts (2.5 MV in deze opstelling) zijn. Conventionele hoogspanningspulsapparatuur is niet geschikt voor het maken van deze pulsen. Dit ligt vooral aan de eisen die worden gesteld aan de synchronisatie, het isolatiemateriaal (doorslag) en de reproduceerbaarheid van de pulsen. In het huidige onderzoek wordt gebruik gemaakt van een (conventionele) Tesla transformator om de 2.5 MV te genereren. Vervolgens wordt de puls, die enkele honderden nanoseconden lang is, geschakeld op een puls-vormende coaxiale lijn. In deze lijn wordt met behulp van capacitieve en inductieve secties (zogenaamde korte- opslaglijn techniek) en enkele vonkbruggen de puls ingekort tot 1 ns.

De pulser is specifiek voor het onderzoek op de TU/e ontworpen en gebouwd in het Efremov instituut, St.Petersburg, Rusland. Tijdens de installatie en eerste ingebruikname van het apparaat kwamen al een aantal kwetsbare aspecten aan het licht. Als gevolg van de tekortkomingen in het ontwerp en vooral de uitvoering van het apparaat was het onmogelijk om reproduceerbaar pulsen te genereren en ontstonden regelmatig defecten. Gedurende de eerste twee jaar is het apparaat verbeterd en is vrijwel de hele puls-vormende lijn opnieuw opgebouwd. Uiteindelijk is de betrouwbaarheid zover verbeterd dat zonder aanpassingen of reparaties enkele tienduizenden schoten konden worden gemaakt. Door verbeteringen in de aansturing is de stabiliteit aan de uitgang van de Tesla transformator verbeterd van 20% tot 1%. Dit betekende een zeer belangrijke vooruitgang, aangezien kleine variaties aan de uitgang van de transformator zorgen voor variatie van het moment van schakelen (tussen transformator en puls-vormende lijn) en daarmee de reproduceerbaarheid van de uiteindelijke versnelpulsen sterk beïnvloeden. Uiteindelijk is een stabiliteit aan het

107 einde van de pulsvormende lijn bereikt van ongeveer 10%, zowel in amplitude als in pulsduur.

Om de versnelde elektronen te kunnen analyseren is een bundellijn gebouwd met diverse diagnostieken. De versneller zelf wordt gevormd door een vacuüm diode. Door de versneller te ontwerpen als een integraal onderdeel van de puls-vormende lijn is het mogelijk gebleken om een versnelspanning te genereren van bijna 2 maal de amplitude van de puls in de lijn. Dit is later bevestigt door metingen van de energie van spontaan vrijkomende elektronen (donkerstroom). De maximale energie die is gemeten bedraagt 3.6 MeV, bij een puls amplitude in de lijn van 1.9 MV.

Om korte elektronenwolkjes te maken wordt gebruik gemaakt van een 25 fs laser puls. Om op het juiste moment (tijdens de aanwezigheid van het maximale veld in de diode) elektronen vrij te maken moet de pulser worden gesynchroniseerd met de laser. De variatie tussen de pulser en de laser moet dan minder dan 1 ns zijn. Om dit te bereiken is gebruik gemaakt van een tweede laser om de met vloeistof gevulde vonkbrug tussen de transformator en de pulsvormende lijn te schakelen. Uit het onderzoek is gebleken dat de intrinsieke processen die plaatsvinden tijdens het schakelen van de vonkbrug leiden tot variaties van enkele tientallen nanoseconden. Deze processen kunnen niet worden beïnvloedt met de laser die gebruikt wordt om het schakelproces op gang te brengen. De beste synchronisatie tussen de laser(s) en de pulser die is bereikt bedroeg 29 ns. Door deze veel te grote variatie is het niet mogelijk gebleken om op betrouwbare wijze elektronen te genereren met behulp van foto-emissie. Gedurende een serie van enkele honderden schoten is het slechts bij een tweetal schoten gelukt om de femtoseconde laserpuls samen te laten vallen met de versnel-puls. De lading die in deze twee gevallen werd vrijgemaakt was ongeveer 350 pC, hetgeen overeenkomt met de op grond van het aanwezige laser vermogen te verwachten lading .

Op grond van het onderzoek zijn diverse kritieke punten aangedragen die verbeterd dienen te worden om de huidige apparatuur toe te kunnen passen als onderdeel van bijvoorbeeld een plasma-versneller. De voornaamste verbetering betreft de synchronisatie tussen de pulser en de femtoseconde laser. Het gebrek aan synchronisatie wordt vooral bepaald door de schakelaar tussen de transformator en de pulsvormende lijn. De vloeistof in de schakelaar zorgt voor veel intrinsieke variatie en dient daarom vervangen te worden door een gasgevulde (hoge druk) schakelaar. Daarnaast is het beter om een transformator te gebruiken met hogere resonantie frequentie, waardoor een hogere veldsterkte kan worden bereikt in een kleinere schakelaar. Ook kan gebruik gemaakt worden van cilindrische optiek om een groter deel van het medium in de schakelaar direct met de laser te ioniseren. Een tweede belangrijk probleem heeft te maken met de levensduur van de kathode. In het huidige apparaat wordt de nanoseconde puls gevolgd door een veel langere (ca. 10 ns) puls met een amplitude van ongeveer 1 MV. De aanwezigheid van deze lange puls verhoogt de kans op doorslag in de diode. Dit zorgt voor verkorting van de levensduur en verslechtering van de reproduceerbaarheid van de hoeveelheid versnelde lading. Om dit te voorkomen moet een actieve (reële) belasting worden geplaatst aan het einde van de pulsvormende lijn. Een andere mogelijkheid is om een zelfherstellend (vloeibaar metaal) kathode oppervlak te gebruiken.

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Op grond van het onderzoek in dit proefschrift kan worden geconcludeerd dat het concept van een gepulste DC versneller haalbaar is, maar dat voor betrouwbare toepassing van dit concept nog een aanzienlijke hoeveelheid technisch onderzoek noodzakelijk is.

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Acknowledgements

This is the time to say thanks to the people with whom I worked during the last four years, who supported me in my work and in daily life.

First I want to say great thanks to Seth Brussaard. Only due to his help and perseverance was this thesis finished in time. Seth, you are one of the best scientists and persons I have ever met.

Marnix van der Wiel is another person I have to thank as a perfect group leader and physicist.

Only due to the great support of the technical staff of the group was this work possible. Many thanks to Eddy Rietman, Harry van Doorn and Wim Kemper for the technical support. I think they are the best technicians I could have wished for.

Thanks also to Ad Kemper for a lot of discussions and advice.

I am happy that I was working together with these people. I will have fond memories of these four years my whole life.

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Curriculum vitae

15 July 1977 Born in Leningrad, the Soviet Union

1984-1991 Middle school, Leningrad, the Soviet Union

1991-1994 Physics-mathematics gymnasium 30, St. Petersburg, Russia

1994-2000 St. Petersburg State Polytechnic University, Russia

1998-2000: NIIEFA (Efremov Institute), St. Petersburg, Russia

2000-2002 NIIEFA (Efremov Institute), St. Petersburg, Russia

2002-2006 Ph.D. research project, FTVgroup, Technische Universiteit Eindhoven, Eindhoven, the Netherlands

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