Design and test of low emittance electron beam for

Smith-Purcell backward wave oscillator

free electron laser

A dissertation submitted in partial satisfaction

of the requirements for the degree

Doctor of Philosophy in Physics

by

Kittipong Kasamsook

Tohoku University

2008

i

ABSTRACT OF THE DISSERTATION

Design and test of low emittance electron beam for Smith-Purcell backward

wave oscillator free electron laser

by

Kittipong Kasamsook

Doctor of Philosophy in Physics

Tohoku University, Sendai, 2008

This thesis presents design, the implementation, the experiment and analysis of beam quality

of a low emittance compact DC gun developed at Laboratory of Nuclear Science, Tohoku

University. This developed DC gun as shown in figure 1 will be used for the Smith-Purcell

Backward Wave Oscillator Free Electron Laser (S-P BWO FEL) application. We have chosen a

single crystal of LaB6 as the thermionic cathode, which can provide higher current density with

good homogeneity electron emission. The DC gun employs a high voltage of 50 kV to extract

electrons, which is suitable to drive S-P BWO FEL. We achieved the maximum electron beam

current more than 300 mA. A very small normalized rms emittance less than 1 mm mrad was

achieved by applying the special negative bias voltage between the cathode electrode and the

wehnelt electrode to manipulate the transverse beam emittance. The transverse phase space of

this small value of emittance is shown in figure 2. Particularly by applying additional bias

voltage between the cathode and the wehnelt, the transverse distribution of electrons is possibly

becoming to be an ideal Kapchinskij-Vladimirskij (K-V) beam, so that the space charge effect

will be minimized.

Up to the present, it should be noted that the thermionic DC electron guns with an emittance

below 1.0 π mm mrad are presently not available. It seems our developed thermionic DC gun

achieved the smallest emittance at this moment. Furthermore, a 3-D numerical simulation for S-P

BWO FEL using our DC beam parameters gave a good prediction to generate the sub-terahertz

radiation by an emittance lower than 1 mm mrad. Average power is expected to be 1 kW/mm2

as shown in figure 3.

ii

Figure 1: A low emittance compact DC gun developed at LNS

Figure 2: The transverse phase space of a

normalized rms emittance less than 1 mm

mrad after applying a special negative bias

voltage between cathode and wehnelt

.

Figure 3: Evolution of the radiation power

simulation resulted from a 3-D numerical

simulation for S-P BWO FEL by using an

emittance of 1.0 π mm mrad.

1

Contents

ABSTRACT OF THE DISSERTATION ............................................................. i

Chapter 1 Introduction ....................................................................................................5

1.1 Motivation for this research .......................................................................................................5

1.2 Overview of this research ........................................................................................................10

Chapter 2 Application of low emittance electron beam for Smith-

Purcell Backward Wave Oscillator Free Electron Laser (BWO FEL)

........................................................................................................................................................11

2.1 Smith-Purcell radiation and FEL .............................................................................................11

2.1.1 Basic principles of an FEL .................................................................................................12

2.1.2 Basic principles of Smith-Purcell radiation .......................................................................17

2.2 Prediction for Smith-Purcell BWO FEL ..................................................................................19

2.2.1 Simulation of S-P BWO FEL ............................................................................................20

2.2.2 Summary and prospect .......................................................................................................27

Chapter 3 Development of a low emittance compact DC gun ...............28

3.1 Design parameters ....................................................................................................................28

3.2 Cathode consideration ..............................................................................................................32

3.2.1 Thermionic cathode ...........................................................................................................33

3.2.2 LaB6 cathode ......................................................................................................................34

3.2.2.1 Thermal emittance of LaB6 cathode ............................................................................35

3.2.2.2 Measurement of cathode temperature ..........................................................................36

3.2.3 One dimensional model of space-charge limited current ..................................................37

2

3.2.4 Emission current density ....................................................................................................40

3.3 Emittance compensation ..........................................................................................................42

3.4 Characteristics of a low emittance compact DC gun ...............................................................43

3.4.1 V-I characteristics ..............................................................................................................43

3.4.2 Gun brightness and lifetime ...............................................................................................46

3.4.3 Gun high voltage ................................................................................................................47

3.5 Gun simulations .......................................................................................................................48

3.6 Support systems .......................................................................................................................51

3.6.1 Power supply system..........................................................................................................51

3.6.2 Ultra high vacuum system .................................................................................................53

3.6.3 Solenoid lens ......................................................................................................................54

3.6.4 Current transformer ............................................................................................................57

3.6.4.1 Method to solve the charge-up problem at FCT ceramic ............................................58

3.6.5 Corona ring ........................................................................................................................61

3.7 Cathode alignment and assembly.............................................................................................62

Chapter 4 Beam quality measurements of the low emittance

compact DC gun .................................................................................................................64

4.1 Beam optic review ...................................................................................................................64

4.1.1 Emittance definition ...........................................................................................................64

4.1.2 Twiss parameter .................................................................................................................73

4.2 Beam size measurement ...........................................................................................................76

4.2.1 Overview of measurement system .....................................................................................76

4.2.2 Slit scan method for beam size measurement ....................................................................77

4.2.2.1 Manufacturing of slit and problems .............................................................................77

4.2.2.2 Measurement results ....................................................................................................78

3

4.3 Solenoid scan method ..............................................................................................................82

4.3.1 Overview of measurement system .....................................................................................82

4.3.2 Thin lens approximation ....................................................................................................83

4.3.3 Error deduction of a solenoid scan technique ....................................................................93

4.4 Double slit measurement..........................................................................................................95

4.4.1 Overview of measurement system .....................................................................................95

4.4.2 Principle of double slit measurement .................................................................................97

4.4.3 Design consideration for the slits .....................................................................................100

4.4.4 Measurement results of double slits .................................................................................104

4.4.5 Resolution of double slit measurement ............................................................................111

Chapter 5 Beam quality analysis of the low emittance compact DC

gun ............................................................................................................................................112

5.1 Beam current dependence ......................................................................................................112

5.1.1 Experimental and simulation results ................................................................................112

5.1.2 Discussion ........................................................................................................................117

5.2 Bias voltage dependence ........................................................................................................118

5.2.1 Experimental and simulation results ................................................................................119

5.2.2 Discussion ........................................................................................................................125

Chapter 6 Conclusion ....................................................................................................133

6.1 Summary and achievement ....................................................................................................133

6.2 Future prospect and suggestion ..............................................................................................135

Acknowledgment ..............................................................................................................136

Appendices ...........................................................................................................................138

A: HV circuit diagram of a low emittance compact DC gun ..............................................138

4

B: CT calibration ....................................................................................................................139

C: The data performed by SUS 316L slit with width of 50 m .........................................140

D: Equations of motion in charged particle beam dynamics ..............................................142

References .............................................................................................................................151

5

Chapter 1 Introduction

1.1 Motivation for this research

The terahertz radiation is electromagnetic waves sent at terahertz frequencies. There are

many terms to call this radiation known as sub-millimeter radiation, terahertz light, terahertz

waves, T-rays, T-light, T-lux and THz. The terahertz radiation is in the region located

between the upper end of the microwave range (mm wavelength) and the far infrared

(hundredths of m). Like infrared radiation or microwaves, these waves usually travel in line

of sight. Unlike X-rays, the terahertz radiation is non-ionizing. It shares with microwaves the

capability to penetrate a wide variety of non-conducting materials.

Terahertz radiation can be used in a variety of ways because a number of natural

phenomena are associated with the radiation frequency in this spectrum. There are many the

prospective benefits of terahertz radiation. The theoretical and technological uses under

development are summarized below:

- Scientific use and imaging: Terahertz time-domain spectroscopy (THz-TDS) is a

spectroscopic technique where a special generation and detection scheme is used to probe

material properties with short pulses of terahertz radiation. The generation and detection

scheme is sensitive to the effect of a material on both the amplitude and the phase of the

terahertz radiation. In this respect, this technique can provide more information than

conventional Fourier-transform spectroscopy that is only sensitive to the amplitude. The

radiation has several distinct advantages over other forms of spectroscopy: many materials are

transparent to THz, terahertz radiation is safe for biological tissues because it is non-ionizing

(unlike for example x-rays), and images formed with terahertz radiation can have relatively

good resolution (less than 1 mm). Also, many interesting materials have unique spectral

fingerprints in the terahertz range, which means that terahertz radiation can be used to identify

them. Examples which have been demonstrated include several different types of explosives

as well as several illegal narcotic substances.

6

- Medical imaging: Imaging techniques for terahertz radiation have obtained considerable

attention in the last few years. Advances in generation and detection of ultrashort terahertz

pulses and the interest for non-ionizing radiation for medical and material-probing

applications have triggered a fast development of imaging techniques. Because terahertz

radiation is non-ionizing, it does not damage DNA like x-rays and might someday be used as

a safer alternative for certain types of medical and dental imaging such as detecting skin and

breast cancer; identifying dental caries; assessing the magnitude and depth of skin burns; and

determining tissue hydration levels. Some frequencies of terahertz radiation can penetrate

several millimeters of tissue with low water content and reflect back. Terahertz radiation can

also detect differences in water content and density of a tissue. Such methods could allow

effective detection of epithelial cancer with a safer and less invasive or painful system using

imaging. Some frequencies of terahertz radiation can be used for 3D imaging of teeth and

may be more accurate and safer than conventional X-ray imaging in dentistry.

- Security: Terahertz radiation is inevitable as a key technology for security and safe

society, so it can be used in surveillance, such as security screening, to uncover concealed

weapons on a person because terahertz radiation can penetrate fabrics and plastics. Firstly,

application to non-destructive and non-invasive inspection of banned drug and dangerous

object is expected. As detection of cocaine packed in envelope is possible, for example,

development of postal inspection is being worked on. Secondly, it is quite useful for water-

related inspection, and application to administration of food and agricultural crops is

considered. In Europe, the application of THz-TDS and terahertz camera to airport frisking,

outdoor detection of dangerous objects, and development of personal authentication

technology is performed.

- Manufacturing: Terahertz sensing and imaging can be possibly used in manufacturing,

quality control, and process monitoring. These generally exploit the traits of plastics and

cardboard being transparent to terahertz radiation, making it possible to inspect packaged

goods.

- Communication: The RF communication is an exploding area in wireless communication

industry. The complex spectrum allocation methods have to be taken because of the limitation

of spectrum. The THz spectral rang has very wide bandwidth and is very little utilized. It is an

7

attractive area to use this frequency band for communication. The THz region offers huge

potential for communication research.

Up to date, the viable sources of terahertz radiation are the backward wave oscillator

("BWO"), the far infrared laser ("FIR laser"), the gyrotron, photomixing sources, quantum

cascade laser, the free electron laser (FEL), synchrotron light sources, and single-cycle

sources used in terahertz time domain spectroscopy.

The first images generated using terahertz radiation date from the 1960s; however, in 1995,

Binbin Hu and Martin Nuss at Bell Labs created a terahertz imaging system using time-

domain spectroscopy, and they coined the term T-ray for these, broadband terahertz pulse [1].

They showed that the absorption characteristics for terahertz radiation vary greatly from

material to material, and that this characteristic can be used to create images. Moreover,

because the T-ray pulse is so short, it can be used in a reflective, time-of-flight mode to create

three-dimensional transparent reconstructions of various objects reflected from different areas

within the object.

In 2003, an experiment conducted with Jefferson laboratory Free-Electron Laser located in

Newport News has shown how to make a highly useful form of terahertz radiation. They

reported the production of high power (20 W averages, ~1 MW peak) broadband THz light

based on coherent emission from relativistic electrons. This research gave many merits to the

way toward better detection of concealed weapons, hidden explosives and land mines;

improved medical imaging and more productive study of cell dynamics and genes; real-time

"fingerprinting" of chemical and biological terror materials in envelopes, packages or air;

better characterization of semiconductors; and widening the frequency bands available for

wireless communication [2]. In the same year, physicists at the BESSY synchrotron radiation

source in Berlin have generated a steady-state beam of coherent terahertz radiation. They

adjusted the magnetic fields in the storage ring to produce a special “low-alpha” mode in

which the length of the bunches was comparable with the wavelength of terahertz radiation.

The electrons in each bunch now behave as one giant particle and emit a beam of coherent

rays [3].

8

In 2006, the University of Liverpool planed to construct Europe's most intense terahertz

(THz) radiation source to further the development of cancer research. Physicists constructed

an ultra-high intensity THz beamline and attempted to destroy skin cancer cells specially

grown in a new tissue culture facility. The experiments will help scientists understand how to

use this technology in future treatments for the disease in humans [4].

In 2007, news from the conference on Lasers and Electro-optics/Quantum Electronics

Laser Science Conference reported the first real-time terahertz imaging system that obtains

images from 25 meters away. The technique takes advantage of the fact that there are a few

"windows," or frequency ranges, of the terahertz spectrum that do not absorb water very

strongly. The MIT-Sandia group designed a special, semiconductor-based device known as a

"quantum cascade laser" that delivers light in one of these windows (specifically, around 4.9

THz). They shine this light through a thin target with low water content (for example, a dried

seed pod), and a detector on the other side of the sample records an image [5].

In this year, 2008, engineers and physicists from Harvard University have demonstrated

the first room-temperature electrically-pumped semiconductor source of coherent terahertz

(THz) radiation. The breakthrough in laser technology, based upon commercially available

nanotechnology, has the potential to become a standard terahertz source to support

applications ranging from security screening to chemical sensing [6].

With the rapid and continuing growth of new sources in the terahertz (THz) region of the

spectrum, a novel coherent light source project at Laboratory of Nuclear Science (LNS),

Tohoku University, in terahertz wavelength region has been designed. The project may

involve development a high brightness RF gun employing cathode of a single crystal LaB6 for

production of a very short bunch length less than 100 fs for boardband radiation. The light

source has been designed based on isochronous ring optics to preserve the short bunch length

[7].

Of particular interest to use of high brilliant electron beam, the Smith-Purcell radiation

seems to be a candidate of intense terahertz radiation source for the narrow band. The interest

has expanded in the spectroscopy and imaging of materials in the so-called „THz gap‟. Smith–

Purcell (S-P) radiation, especially coherent S-P radiation, promises to be a useful tool for

9

frequency-domain spectroscopy and imaging in this spectral region since it is narrow band

and can be tuned by varying the electron energy or the angle of observation. In this sense, the

RF gun is inappropriate for the S-P FEL because it requires a continuous beam. Hence, there

is a need of a high quality DC electron beam for an injector of the S-P radiation. Most of the

S-P radiation researches are theoretical work with the simulation. For the experiment with a

driver of S-P FELs, one can be found by using the DC beam from Scanning Electron

Microscope (SEM) [8].

Because they lacked reliable sources of S-P radiation, the low emittance compact DC gun

at LNS has been develped. We designed this DC gun without a grid electrode to avoid

emittance growth by through the grid mesh. The single crystal LaB6 cathode has been chosen

to produce the high current density [9]. According to recent theoretical work of Smith-Purcell

Backward Wave Oscillator FEL (S-P BWO FEL) [10], to secure sufficient gain a very low

emittance is required in a direction perpendicular to the grating surface. Beam energy should

be less than ~ 100 keV because of overlapping with negative group velocity of the evanescent

mode supported by the grating. Thereby, the DC gun developed at LNS seems to be very

much suitable for a driver of S-P BWO FEL. Since the diameter of the single crystal LaB6

cathode is 1.75 mm and the gap between cathode and the anode is only 15 mm to obtain high

accelerating field strength, the normalized rms beam emittance less than 1 mm mrad was

obtained by applying the special negative bias voltage between the cathode electrode and the

wehnelt electrode to manipulate the transverse beam emittance. An idea of applying negative

bias makes our DC gun outstanding and differs from conventional DC guns. We have chosen

a low applying voltage of 50 kV to reduce the size of the entire system to be compact.

Up to the present, it should be noted that the thermionic DC electron guns with an

emittance below 1.0 π mm mrad are presently not available. It seems our developed

thermionic DC gun achieved the smallest emittance at this moment. Furthermore, a 3-D

numerical simulation for S-P BWO FEL using our DC beam parameters gave a good

prediction to generate the sub-terahertz radiation which is suitable for many applications as

we mentioned above [11].

10

1.2 Overview of this research

For guidance to the reader, this thesis is ordered by priority of work what we have done.

Chapter 2 covers the history of FEL development, the basic theoretical aspects of FEL and S-

P FEL including our simulation predictation of S-P BWO FEL by using 3-D simulation code.

The parameters used in the simulation were design parameters of our low emittance compact

DC gun. The summary and prospect of the simulation were given in this chapter.

Chapter 3 covers the design considerations of our DC gun such as what the parameters that

we have to take into account for the design or how to choice the cathode. We gave the

prominent points of LaB6 material what we have chosen to be an electron source and

introduced basic theories to derive charecteristics of LaB6. The conceptual design of

emittance compensation has been introduced as well in this chapter. All of supporting systems

and problems during the fabrication have been discussed.

The next chapter, chapter 4, reviews the beam optics along with presentation of theoretical

details of emittance definition and twiss parameters. Many of experimental data of beam

quality measurements have been reported involving analytical methodes and many technical

problems in the experiment.

Chapter 5 goes on to detail the beam diagnostics comprised of beam current dependence

and bias voltage dependence. We gave some assumtions and physical meanings to explain

space charge dominated beam and emittance compensation. The simulations have been

performed to compare with the experimental results. Much of the analysis of emittance in

Chapter 5 relies on analytical method from Chapters 4.

Chapter 6 concludes the experimental description with an overview of beam diagnostics,

and presents a summary and some prospects including suggestions to the thesis. A cumulative

list of references is included in back of the thesis while various Appendices are included at the

end of this thesis, and are referred to throughout the text.

Finally, the progression of this research work has been reported in many conferences [12-

17].

11

Chapter 2 Application of low emittance electron

beam for Smith-Purcell Backward Wave Oscillator

Free Electron Laser (BWO FEL)

In this chapter, we highlight the major milestone of a historical study and basic principles

of Smith-Purcell radiation and FEL development. The simulation prediction of Smith-Purcell

BWO FEL using design parameters of our low emittance compact DC gun will be described

onward.

2.1 Smith-Purcell radiation and FEL

In 1970 the Free Electron Laser (FEL) was invented by John Madey [18]. Anyhow, the

starting point of this field begins much earlier. The definitive history of Free Electron Lasers

has yet to be written, but a number of documents have described portions of the attractive

events surrounding these devices [19-23].

In the early 1950’s, H. Motz proposed and experimented with magnet configurations

similar to present day undulators [21]. He showed that an electron beam propagating through

periodic magnet configurations can be used to amplify radiation. Indeed, H. Motz is often

credited with inventing the precursor to the FEL [23]. Many theoretical and experimental

investigations of undulator radiation have been carried out since then.

During the 1960’s, a particular microwave tube developed by D. Phillips. He called it, the

Ubitron. D. Phillips has interest in producing high power microwaves. His Ubitron was

remarkably similar to an FEL (or, more accurately, an FEM — Free Electron Maser).

Unfortunately, the Ubitron was not an economical means of producing microwaves compared

to the already available traveling wave tubes, and, so, the Ubitron research was not pursued.

The extension of the Ubitron to the FEL did not seem to be fully recognized by D. Phillips.

12

In early 1960, a paper of K. Robinson, an accelerator physicist with the Cambridge

Electron Accelerator at Harvard University, was published posthumously, and reveals that he

had formulated a classical theory of the FEL and the optical klystron [24].

In 1970 J. Madey, having experience with ―insertion devices‖ (undulators and wigglers)

for light sources, realized that a laser–like amplifier or oscillator could be constructed by

combining a high quality electron beam, a wiggler or oscillator cavity mirrors. While the

experimental aspects of the first FEL may seem like a straightforward extension of the then

available technology, the theoretical framework produced by J. Madey was a quantum

analysis in the frame of relativistic electrons. Soon after experimental plans were being

conceived, it was realized that the experimental challenges posed by the FEL were

considerable. The FEL was first operated in 1976 at Stanford, California by J. Madey and

coworkers [25]. The first FEL was configured as an amplifier with a CO2 laser used as an

input source. An important step in FEL development came in 1976. The numerous FELs have

operated in a variety of configurations: ranging from microwaves to the UV; some driven by

electron linacs, others by storage rings; some operated as oscillators, others as amplifiers.

2.1.1 Basic principles of an FEL

A free-electron laser, or FEL, is a laser that differs from conventional lasers in that they

use the electron beam as the lasing medium rather than a gas or a solid, but an FEL still shares

the same optical properties as conventional lasers. In the conventional lasers such as

semiconductor lasers, electrons are excited in bound atomic or molecular states, but FELs use

a relativistic electron beam as the lasing medium which move freely through a magnetic

structure, hence the term free electron. An FEL does not have the restrictions of conventional

lasers on operating wavelengths, and is constrained only by the phase-matching condition for

strong interactions between the electrons and laser field. That is for a given wiggler, the

wavelength is determined only by the energy of the electron beam. Current FEL’s cover

wavelengths from millimeter to ultraviolet and are nudging into the vacuum-ultraviolet. New

facilities designed specifically to produce X-rays has been constructed for example: SCSS

project [26].

13

Because the brightness of FELs can be up to one billion times higher than the ordinary

synchrotron light source, FEL’s applications are dramatic increasingly. FELs are usually

based on the combination of a linear accelerator which is used for electron acceleration up to

relativistic speeds, and the electrons enter a high-precision insertion device, known as a FEL

oscillator in the form of a periodic, transverse magnetic field, produced by arranging magnets

with alternating poles within a laser cavity along the beam path. This kind of array magnets is

sometimes called an undulator, or a "wiggler", because it forces the electrons in the beam to

assume a sinusoidal path. The accelerated electrons along this path result in the release of a

photon (synchrotron radiation or spontaneous emission). Since the electron motion is in phase

with the field of the light already emitted, the fields add together (coherently) and since light

intensity is dependent upon the square of the field the light intensity is increased. Instabilities

in the electron beam, which result from the interactions of the oscillations of electrons in the

undulators and the radiation they emit, leads to a bunching of the electrons which continue to

radiate in phase with each other in contrast to conventional undulators where the electrons

radiate independently [27]. The wavelength of the light emitted can be readily tuned by

adjusting the energy of the electron beam or the magnetic field strength of the undulators. A

simple schematic view of FEL is shown in figure 2.1.

14

Figure 2.1: A simple schematic view of FEL.

To calculate the radiated wavelength of an FEL, we consider the radiation of an electron in

an undulator in figure 2.2. The electron has a velocity v=c, where c is the speed of right.

When the electron travelling down the undulator magnets it passes the magnets in a time:

(2.1)

where

(2.2)

is the undulator length, and u is the length of one period of the undulator.

,v

Lt u

,uuu NL

15

Figure 2.2: The electron orbit in Nu of undulator periods and generated wave packet (the plane

of electron orbit and wave packet is perpendicular to magnetic fields of the undulator).

By the total time the electron has moved to the end of the undulator, the front of the wave

packet which was emitted by the electron at the beginning of the undulator has moved a

distance ct. The back of the wave packet is just the end of the undulator, so the length of wave

packet is (c-v)t. From this reason, we can express the radiated wavelength of FEL by

(2.3)

where the wave packet contains Nu oscillations. If the electron velocity is closely to the speed

of light (c) we can simplify:

(2.4)

,)1()(

u

u

FELN

tvc

.2

1

2

)1)(1()1( 2

16

By the Einstein’s law for the relativistic energy of electron:

(2.5)

where is the ratio of energy of electron with respect to electron rest energy. Then, the

equation (2.3) can be expressed by

(2.6)

In the case of strong magnetic fields, the undulator can significantly increase the path

length of the electron trajectory through the undulator. This slows the average velocity of the

electrons through the undulator and increase the radiated wavelength. When this effect takes

into account, we yield

(2.7)

where K is the ratio of the average deflection angle of the electrons to the typical opening

angle of the synchrotron radiation. If Bu is the rms average magnetic field in the undulator:

(2.8)

The interference condition means that in travelling one period along the undulator the

electrons slip one period of the radiation wavelength (because the electromagnetic field

moves faster than the electrons). So, we can rewrite equation 2.7 in the form of

,1

1

2

.2 2

uFEL

,)(12

2

2KuFEL

.2 cm

eBK

e

uu

17

(2.9)

2.1.2 Basic principles of Smith-Purcell radiation

In 1953, the Smith-Purcell radiation was studied by Steve Smith, a graduate student from

Harvard University under the supervision of Edward Purcell [28]. Actually, the Smith-Purcell

radiation is a precursor of FELs. In the experiment, they sent an energetic beam of electrons

by passing above gratings of conducting material, the image charge of the electron beam

oscillates then electromagnetic wave in visible light region occurs. Smith showed there was

negligible effect on the trajectory of the inducing electrons. Essentially, this is a form of

Cherenkov radiation where the phase velocity of the light has been altered by the periodic

grating [29].

Many theoretical and experimental studies about Smith-Purcell radiation have been carried

out [10, 30-60], but they have not been completed yet. However, we describe about the basis

principle of Smith-Purcell radiation. When an electron passes close to the metallic surface of

grating shown in figure 2.3, the electromagnetic wave is radiated at the wavelengths that can

be determined by following expression

(2.10)

In equation (2.10) g is the grating period, is electron velocity relative to the speed of light

(c), is the angle of radiated electromagnetic wave measured from a direction parallel to the

grating’s surface, and m is the spectral order. This prediction has been confirmed by

experiments [28]. The angular and spectral intensity of Smith-Purcell radiation is described by

the theory of van den Berg and Tan [34].

).cos.1(//

m

g

.2

12

2

2

cm

eB

e

uuuFEL

18

Figure 2.3: 2D schematic diagram of Smith-Purcell FEL.

In the case of Smith-Purcell backward wave oscillator free electron laser (S-P BWO FEL),

the radiated electromagnetic wave is happened by interaction between the beam and the

evanescent wave supported by grating. The group velocity is negative, so it is a backward

wave. This radiation of Smith-Purcell has been performed by scanning electron microscope

(SEM) with low energy (~35 keV) [49,54,57]. The Terahertz radiation can be obtained by the

low energy of electron beam using grating period around 100-200 m. Figure 2.4 shows

Backward Wave Oscillator Smith-Purcell FEL by courtesy of K-J Kim and V. Kumar.

19

Figure 2.4: Backward Wave Oscillator Smith-Purcell FEL.

2.2 Prediction for S-P BWO FEL

After the first observation of the superradiant from the electrons passing above the metal

grating [54], coherent Smith-Purcell radiation has been paid much attention experimentally

and theoretically [33,48]. Particularly for the low energy electrons (E < 100keV ), it was

pointed out that the Smith-Purcell free electron laser (FEL) is a backward wave oscillator

(BWO) by taking a look at the dispersion relation of the surface mode [10,59]. The BWO

FEL employing a grating having the period length less than 1 mm seems to be very much

attractive tool for high power radiation source in Terahertz (THz) and sub-Terahetz frequency

region.

As for the electron beam traveling just above the grating, when the phase velocity of the

evanescent wave synchronizes with the electrons the beam amplifies the evanescent wave.

The evanescent wave itself is not radiative, however at least one mode can escape from the

surface of the grating and becomes radiative [10]. The synchronized electrons are

microbunched due to the longitudinal component of the evanescent wave, and then, the

surface mode is enhanced. Since the group velocity of the mode is negative, the amplified

evanescent wave propagates to backward and then the fresh electrons getting into micro-

bunching.

20

This system is essentially same as oscillator FELs. Although the theoretical approach was

already reported [10], there has been no numerical simulation with realistic configuration.

Since a very low emittance DC electron gun has been developed at Laboratory of Nuclear

Science, Tohoku University [17], simulation study is pretty valuable for development of the

Smith-Purcell BWO FEL. We describe results of three-dimensional simulation of interaction

between the electrons and the evanescent wave supported by a metal grating and investigates

evolution of the BWO radiation for various beam parameters.

2.2.1 Simulation of S-P BWO FEL

Smith-Purcell backward wave oscillator free electron laser has been studied via a time

dependent three-dimensional particle-in-cell simulation code employing finite difference time

domain method (FDTD) [11]. This simulation code is employed as Maxwell’s equations

solver and developed in our research group. Nonlinear behavior of the S-P radiation was

already observed [54]. That was coherent and is presumed to result from the beam bunching

effect due to interaction with the evanescent mode [60]. From the Fourier transform analysis

for the surface mode, the dispersion relation of the evanescent wave supported by a grating is

well predicted by Andrew-Brau formula [41]. We found the interaction between the electron

beam and the evanescent wave is enhanced by surrounding the grating with conductor plates.

Non-radiative evanescent mode is excited by the beam traveling on just the surface of the

grating, and the modes are reflected due to periodic structure of the grating and the reflected

wave at a certain frequency can be propagated and carry the energy away.

We have chosen a model grating for the simulation as indicated in figure 2.5, and the

parameters used in the simulation are shown in table 2.1. The sheet DC beam, which has the

normalized emittance of 1 mm mrad for the both directions, is generated by very low

horizontal and vertical beta functions of 62.5 cm and 4 mm, respectively. Since the

evanescent wave is exponentially decreasing as the distance b from the grating surface

increases (see figure 2.6), the sheet beam has to travel just above the surface in order to have

sufficient overlapping (here we have chosen 100 m).

21

Table 2.1: Parameters used in the simulation

Beam energy 50 keV

Beam current 150 mA

Grating period (g) 400 m

Groove width (W) 200 m

Groove depth (d) 300 m

Grating full width (L) 2 mm

Number of periods 50

Beam-grating distance (b) 100 m

Figure 2.5: A model grating for FDTD simulations and scales of a model grating (left).

22

Figure 2.6: The Gaussian beam cross section and relative location against the grating. A

conductive plate is put above the beam. However using absorbing boundary condition, there

was no difference in the BWO FEL.

Dispersion relation of the evanescent wave is derived from the FDTD simulation. A fixed

frequency current oscillator is put in a groove at the grating upstream end. After the

evanescent wave is excited for a while, the wave reaches the downstream end. Mode

appeared above the surface of the grating is analyzed by Fourier transform method, and the

wave numbers are deduced (two wave numbers are actually generated).

23

Figure 2.7: Dispersion relation of the evanescent wave supported by the grating indicated by

figure 2.5. The grating wave number kg= 2/g.

Since the group velocity of the beam frequency is same as phase velocity, the frequency

where the beam line intersects the dispersion curve may be the radiation frequency. As one

can see in figure 2.7, d/dk < 0 at the intersection point, which means the group velocity of

the radiation is negative (-0.107c) so that this is the backward-wave.

The S-P BWO FEL is unlike conventional FELs because it is not driven by a periodic

transverse magnetic field produced by wigglers. The microbunching is occurred by the

longitudinal electric field (Ez) in the evanescent wave, and the conventional S-P radiation

becomes coherent. The evanescent mode is much more excited by the bunched beam, so that

the gain is yielded. The FDTD simulation was performed with a DC beam current of 150

mA. To avoid beam brow-up the strong external longitudinal field (Bz ~ 1 T) was applied.

24

A time dependent evolution of radiated power observed at the grating upstream end and

just above the surface is shown in figure 2.8 (a). The radiation begins to increase significantly

around 1 ns. After saturation, the intensity is fluctuated and the fluctuation is slowly damped.

We notice that for the normalized emittance of 1 mm mrad case, the power increased up

to several hundreds W/mm2 and a damping oscillation was excuted after saturation.

Meanwhile a larger normalized emittance case, such as 5 mm mrad shown in figure 2.8 (b),

the FEL oscillation was not occurred. The results show the beam emittance is very crucial for

the Smith-Purcell BWO FEL.

Figure 2.9 (a) shows the frequency spectrum obtained Fourier transform of the power

evolution of figure 2.8 (a). An FFT analysis using the data after 1ns presents the frequency of

radiation is 0.18 THz corresponding to a wavelength of 1.6 mm. This result is quite

acceptable in accordance with the dispersion curve shown in figure 2.7. In this grating case,

an intense sub-Terahertz radiation may be obtained.

25

(a)

(b)

Figure 2.8: Evolution of the radiation power simulation resulted from the FDTD Smith-

Purcell BWO FEL. The normalized beam emittances are 1 mm mrad (a), and 5 mm mrad

(b), respectively.

26

(a)

(b)

Figure 2.9: (a) Frequency spectrum of the radiation, (b) Longitudinal phase space of the

electrons traveling above the grating.

27

The microbunch is established by interacting with Ez component of the evanescent wave.

In figure 2.9 (b), microbunches trapped in the longitudinal potential of the evanescent wave

are clearly seen in a phase space plot at a time of 5 ns.

We have examined simulations for different beam currents. Even a lower current of 60

mA, the lasing is started, so that there seems to be no significant threshold current for the

BWO FEL, which was, however, theoretically predicted [10]. At higher beam current, the

temporal evolution of the FEL power is strongly fluctuated, which is almost same as a

previous study of S-P radiation [60].

2.2.2 Summary and prospect

By using parameter of a model grating and an ideal electron beam from a low emittance

compact DC gun approximately 1 kW/mm2 radiation power is obtained for mm-wavelength

region, and it is found out that the normalized emittance of less than 1 π mm mrad is crucial

for lasing according to our simulation.

The beam from the DC gun seems to be suitable as a driver of Smith-Purcell Backward-

Wave Oscillator FEL. According to the FDTD simulation of the S-P BWO FEL, no clear

threshold for lasing is observed. At higher beam current, the temporal evolution of the

radiation intensity is chaotic. However there seems to be proper beam currents to obtain

stable lasing. The simulation predicts the peak energy flow of BWO FEL reaches 1 kW/mm2

or more at the upstream end of the grating.

28

Chapter 3 Development of a low emittance compact

DC gun

3.1 Design parameters

Nowadays, the demand for high-brightness electron gun has increased dramatically to

achieve many applications employing the electron beam technology. The low emittance

compact DC gun at Laboratory of Nuclear Science (LNS), Tohoku university, is one of the

candidates. This DC gun will be used for free electron lasers (FELs) such as Smith-Purcell

backward-wave oscillator FEL (S-P BWO FEL) in the THz wavelength range [15], injector

for advanced accelerators and other applications. Following of this section we describe design

parameters for a low emittance compact DC electron gun.

The constituents of an electron gun logically divide themselves into two categories: (1) the

elements necessary for the generation of free electron, or cathode elements, and (2) the field-

shaping elements necessary for the production of a useful beam, the various electrodes such as

the cathode electrode, anode, grid or modulating electrodes, and wehnelt electrode.

In conventional electron guns, the cathode elements are subdivided into groups by

functions. The most importance factor is the cathode proper which serves as the source of

electrons. The cathode may be a current carrying, self-heating filament, or a solid block

indirectly heated by radiation from the filament, or in some cases, by an electron beam from

another cathode. From among various possible sources, we particularly focus on the

thermionic cathode (Lanthanum Hexaboride, LaB6 in our case) [see section 3.2.1 and 3.2.2]

because it has advantages, such as high reliability and a long cathode lifetime [see section

3.2].

After the cathode can be specified, we can consider the design of the rest parameters of the

gun. The next considerations are frequently the energy and current requirements of the

electron beam. If the voltage is not limited by an available power supply, the choice of a

suitable voltage may make the design simpler. Then, we would like to choose a high voltage

29

level of -50 kV with respect to grounded anode and variable pulse duration from 1 to 5 sec

because this low voltage choice can make the entire system to be compact and air can be a

satisfactory insulator. Once the high voltage has been chosen, the current may be determined,

either independently or though a functional relation such as the total beam power requirement.

One of the basis parameters of the gun may now be calculated. It is called the pervance P and

is defined as the relation of beam current and accelerating high voltage [see section 3.4.1]. By

this parameter we are able to consolidate the two variables into one constant for the particular

gun.

In order to produce low emittance beam, the cathode size should be small. Since a higher

beam current of the macropulse is required in general, a cathode should have higher emission

current density, while the smaller size of the cathode is preferred for lower emittance. The

overveiw of total system is shown in figure 3.1. The design parameters and the drawing of the

low emittance DC electron gun are shown in Table 3.1 and figure 3.2, respectively.

In addition, the prominant point of our gun is that this DC gun has no grid which would

degrade beam emittance [13], but it has been designed with a special bias between wehnelt

electrode and cathode electrode to manipulate electric field arround the cathode as shown in

figure 3.3.

30

Figure 3.1: Schematic diagram of a low emittance compact DC gun.

Figure 3.2: Drawing of DC gun.

31

Table 3.1: Design parameters of the electron gun.

Beam energy 50 keV (Max.)

Peak current >300 mA

Pulse width (FWHM) 1-5 sec

Repetition rate 50 pps

Normalized emittance < 1 mm mrad.

Normalized thermal

emittance

0.25 mm mrad*

*theoretical

Cathode diameter 1.75 mm.

Figure 3.3: The schematic diagram of DC gun power supply with the special bias voltage.

32

3.2 Cathode consideration

The primary design considerations are that a cathode supply an adequate useful emission

current over some period of time. Secondarily, it is desired to have a small power input and a

cathode which is simple to construct. In addition, the cathode must operate in the gun

environment of ultra high vacuum. It is usually to fulfill all these requirements completely.

Hence, the choice of cathode material becomes a compromise which will be most satisfactory

in the application being considered in the designer’s judgment. Thus, in our idea the cathode

should have these properties:

Low work function

High beam current density

Low operation temperature

Long lifetime

Rapid recovery from contamination

Such all of those above properties can be realized by some cathode materials such as a

single crystal of LaB6 or CeB6 [61]. Consequently we have chosen single crystal LaB6 [see

section 3.2.2] as the cathode, which can provide higher current with good homogeneity

emission.

Other cathodes have been considered before such as dispenser cathode which is widely

used in the field of accelerators, but this cathode type has emission current density lower than

a single crystal of LaB6 roughly about one order. Thus, the bigger size of cathode is required

to get the same order of emission current with a single crystal of LaB6. This is inappropriate

for our research work because the intrinsic thermal emittance depends on the size of cathode

[see section 3.2.2.1]. Moreover, the surface flatness of cathode is preferable to obtain a low

emittance. Comparing with dispenser cathode, a single crystal of LaB6 cathode with

extremely flat surface and low porosity is superior in this point [9].

In many cases the vacuum condition places severse limitations on the choice of cathode

materials. If the gun is expected to operate in the pressure region of 1 x 10-5

torr or higher, the

33

choice is restricted to the factory metals. If below that level, dispenser cathodes may be

considered [62].

3.2.1 Thermionic cathode

Thermionic cathodes (or hot cathode) use heat to expel electrons from a solid. This

phenomenon of emission knows as thermionic emission. They are in contrast to cold (field

emission) cathodes, which use high electric fields to tear the electrons out of the solid. This

cathode is widely used in cathode ray tube (CRT), display monitors, and the advanced gun in

the accelerator technology for examples. One kind of thermionic cathodes is shown in figure

3.4. This cathode is using for an electron gun in the Laboratory of Nuclear Science, Tohoku

University (LNS).

Figure 3.4: Example of a thermionic cathode using in LNS.

Thermionic emission is the emission of charged carriers (typically electrons) from a

conductor at high temperature. At sufficiently high temperature, some significant fraction of

electrons exceed the energy required (the work function) to escape the atom from the Fermi

level. Thermionic emission is governed by the Richardson-Dushman equation [see section

3.2.4]. Actually, the charged carriers can be electrons or ions, and are sometimes referred to

as "thermions". The total charge of the emitted carriers (either positive or negative) will be

equal in magnitude and opposite in sign to the charge left in the emitting region. The most

34

classical example of thermionic emission is the emission of electrons from a hot metal

cathode into a vacuum which was known as the Edison effect [63].

3.2.2 LaB6 cathode

In this section we describe another thermionic cathode which is used in this research work.

To gain the high current density in thermionic cathode, the material with low work function is

required. Rare earth boride materials are known for this property. There are 12 kinds of rare

earth boride materials. Especially, the LaB6 and CeB6 can emit such an intense current over

long lifetimes [64-66]. A single crystal is preferable for obtaining low emittance because of its

extremely flat surface with low porosity after surface material evaporation. The emission

density is more uniform because the crystal orientation is the same over the whole surface. In

recent years, single crystal LaB6 cathodes are widely used for scanning electron microscope

(SEM) and superior stability has been demonstrated. So, we decided to use a single-crystal

LaB6 cathode with a flat crystal surface and the cathode diameter is 1.75 mm shown in

Fig.3.5.

Figure 3.5: LaB6 cathode.

35

3.2.2.1 Thermal emittance of LaB6

Thermal electron emitted from surface of cathode performs rough thermal motion, and

emittance due to this motion is called thermal emittance. Energy (E) that its direction is

parallel to surface of cathode is

(3.1)

where m= m0 is mass of electron, T is cathode temperature ,is the work function, k is

Boltzmann’s constant ,and h is Planck's constant. The number of thermal electron emitted

from cathode is

(3.2)

and

(3.3)

is radius direction energy in cylindrical coordinate system. When we assumed

electron beam is symmetrical distributed in x and y directions, energy in rectangular

coordinate system is

(3.4)

where =1 , the momentum px can determined by

(3.5)

,)(4 )(

3

3

kTeNh

kTmE

,)(4 )(

3

2

kTeh

kTmN

.kTE

,2

kTEx

,2

2

0cm

Ep

x

x

36

and emittacne in horizontal direction x is

(3.6)

where x is standard deviation of beam projection to x axis (r.m.s. cathode size). However, we

have to assume the distribution of electron on the cathode surface is Gaussian, and the

electron distribution cannot be bigger than cathode. Let cathode radius is rc, so x= rc /2 for

rms cathode radius, we can yield

(3.7)

From the above relation, in order to obtain the small emittance less than 1 mm mrad

required for an FEL application, the diameter of the cathode must be in the range of a few

mm. The diameter of our LaB6 cathode is 1.75 mm. The normalized thermal emittance can

calculated to be 0.25 mm mrad when cathode temperature is 1900K.

3.2.2.2 Measurement of cathode temperature

As shown in Figure 3.3, the heater power supply heats the LaB6 cathode. When the

thermionic cathode is used, the cathode temperature is an important parameter that relates to

the thermal emittance and the emission of the current. The radiation thermometer (CHINO

IR-CAS3CS) was used to measure cathode temperature. This radiation thermometer has an

accuracy ±2%, range of use is 900K - 3200K and resolution is 0.5K. The result is shown in

Figure 3.6.

,2

0cm

kTp xxxx

.2 2

0cm

kTrcx

37

Figure 3.6: Heater current vs cathode temperature of a single-crystal cathode of LaB6.

3.2.3 One dimensional model of space-charge limited current

This section describes the space-charge limited current for infinite parallel model of our

DC gun by using the one dimensional model. We start with Poisson equation for electrostatic

potential:

(3.8)

where the boundary conditions of equation 3.8 are:

(3.9)

(3.10)

,0

2

V

.2

1 20 qVvm

,vJ

38

This gives:

(3.11)

where A = -J ε0-1

(-(1/2) m0/q)1/2

is a constant and V' = dV/dx. Substitute dx = dV/V' to obtain

a separable differential equation and solve, while applying boundary conditions V(x=0) = 0,

V(x=d) = Vd, and V'(x=0) = 0:

(3.12)

(3.13)

(3.14)

(3.15)

where A = (4/9)Vd3/2

d-2

(due to V(x=d) boundary condition). Now knowing A, we can solve

for J in the expression for A:

(3.16)

In the case q= -e for electron, we can yield:

(3.17)

,'

21

2

AVdx

dVV

,'' 21

dVAVdVV

,2' 41

21

VAdx

dVV

,2 21

41

dxAdVV

,3

22

14

3

xAV

.)2

1(

9

42

11

0

223

q

mJAdV

,2

9

42

23

0

0d

V

m

eJ

39

where:

Charge density: ρ

Anode-Cathode Potential: V

Current density: J

Velocity: v

Anode-Cathode distance: d

Electron charge: e

Electron rest mass: m0

This equation knows as the Child-Langmuir law or three-halves-power law [67]. The best

known example of the influence of space-charge is the limitation of the current that can cross

a simple diode. The Child-Langmuir law is also express in the term of the potential

distribution:

(3.18)

where:

Potential at point x from cathode: V

Anode-Cathode Potential: Vd

Distance from cathode: x

Anode-Cathode distance: d

The results of space-charge-limited current are shown in figure 3.7. At our designed

parameters, 50 kV and 300 mA, the distance between anode and cathode electrode should be

15 mm.

,3

4

d

x

V

V

d

40

Figure 3.7: Results of space-charge-limited current.

3.2.4 Emission current density

The mechanism by which a metal is able to emit electrons is most accurately explained by

quantum dynamics. In any metal, there are one or two electrons per atom that are free to move

from atom to atom. This is sometimes known as a "sea of electrons". At 0Kthe energy levels

of electrons are well defined band of finite width. When the temperature of material is

increased, the width of these bands also increases. In particular, for metal the upper limit on

the conduction band become fuzzy, and some of the conduction electrons have enough energy

to overcome the potential barrier of the metal surface. The minimum amount of energy

needed for an electron to leave the surface is called the work function. The work function is

characteristic of the material and for most metals is on the order of several electron-volts. The

emission currents can be increased by decreasing the work function of material.

In 1901 Owen Willans Richardson published the results of his experiments: the current

from a heated wire seemed to depend exponentially on the temperature of the wire with a

mathematical form similar to the Arrhenius equation [68]. The modern form of this law

(demonstrated by Saul Dushman in 1923, and hence sometimes called the Richardson-

41

Dushman equation) states that the emitted current density J (A/m2) is related to temperature T

by the equation:

(3.19)

where T is the metal temperature in Kelvin, is the work function of the metal, k is the

Boltzmann’s constant. The proportionality constant A, known as Richardson's constant, given

by

(3.20)

where m and e are the mass and charge of an electron, and h is Planck's constant.

Because of the exponential function, the current increases rapidly with temperature when

kT is less than . (For essentially every material, melting occurs well before kT=)

By the Richardson-Dushman equation the emission current density of the low emittance

compact DC gun can be defined as the graph in figure 3.8.

While A theoretically has a value of 120.173 A cm-2

K-2

, in practice it strongly depends on

material used. The work function of LaB6 cathode is 2.4 eV.

Figure 3.8: The emission current density of the low emittance compact DC gun.

,2 kTeATJ

,1020173.14 226

3

2 KAm

h

emkA

42

Moreover, we have deduced the work function of LaB6 cathode by measuring the thermal

emission current varying the cathode temperature. From equation (3.19), we can calculate the

work function of LaB6 cathode to be 2.4 eV. This measured value is not far from the previous

value [69].

3.3 Emittance compensation

In general case, the emittance compensation known as a magnetic field (a solenoid) which

is typically used to control the beam divergence. For high–brightness electron–beams, space

charge rapidly becomes a limiting factor. At the low beam energies found near a cathode’s

surface, the beam diverges strongly due to the space charge forces. It is possible to

compensate for a portion of the space charge growth using a technique termed emittance

compensation by using the confining magnetic field and a drift space to rotate the phase space

[70]. The emittance compensation takes advantage of the correlation between particles’

momentum and position [71]. Anyhow, the emittance is still diluted by space charge after the

solenoid exit.

In the case of our DC gun system we have a conceptual design about emittance

compensation and think in the different manner. This manner is about applying a negative

bias voltage to manipulate the initial emission around the cathode’s surface of our DC gun

which is shown in figure 3.9. This idea will be proved and realized by the experimental and

simulation results in section 5.2 of Chapter 5.

43

Figure 3.9: A conceptual design of the new DC gun for emittance compensation.

3.4 Characteristics of a low emittance compact DC gun

3.4.1 V-I characteristics

We measured gun characteristics at the test bench. The first measurement of the LaB6 gun

is V-I characteristics. The measurement was done for various cathode temperatures, which is

shown in Figure 3.10. From V-I characteristic curve, our gun should be operated around 1800

K in temperature limited region to avoid the space charge effect from high emission current.

In this region, the beam current is dominated by Schottky effect rather than Child’s law.

Accordingly, the slope of the current-voltage curve becomes very smooth.

Recall from Child-Langmuir equation in section 3.2.3. We can express this equation in the

term of emission current (I):

44

(3.21)

where S is cathode area. If we divide both sides of Eq. (3.21) by V3/2

, we found that the

quantity (I/V3/2

) depends only on the geometry of the gun. We call this quantity the gun

Perveance (P) which is one of the most important characteristics of an electron gun. This

value can be expressed by

(3.22)

where I is the emission current and V is the anode potential with respect to the cathode. For

guns with flat cathodes, current density inhomogeneity becomes large when the perveance is

high value. However, electron beams with higher perveance are needed in number of

applications where charge or current density is a key parameter. In figure 3.10, we can obtain

0.155 μA/V3/2

for the perveance of the LaB6 gun by fitting function. This result shows that this

DC gun has high emission current density.

,2

3

V

IP

,2

9

42

3

2

0

0 Vd

S

m

eI

45

Figure 3.10: Current-voltage characteristic curve of the LaB6 gun.

46

3.4.2 Gun brightness and lifetime

There are many technical terms to explain about brightness in the field of electron gun. In

our case we focus on maximum brightness which is considered at the cathode surface of an

electron gun. Theoretically, maximum brightness (Bmax) defined as

(3.23)

where

Current density at cathode surface: J

Accelerating voltage: V

Cathode temperature in K: T

Boltzmann's constant: k

Electron charge: e

The maximum brightness of the gun depends on:

- Configuration of the gun

- Gun bias-voltage between cathode and wehnelt

- Distance between cathode and anode

- Cathode temperature

The lifetime of LaB6 cathode varies with operating condition, vacuum level, and heating

current. One case causes by sputtering on the ceramic surface of LaB6 cathode which is

shown in figure 3.11. This cathode was operated in heat run test for 7000 hrs in temperature

1800 K. Indeed, the LaB6 requires good vacuum level 10-7

torr or better for reliable operation.

In the figure, 2 pins of cathode are shorted by the sputter. Thus, this reason brings to the death

of cathode.

,maxkT

JeVB

47

Figure 3.11: Sputter of LaB6 on the ceramic surface of dead cathode.

3.4.3 Gun high voltage

The high voltage power supply with generate a DC pulse voltage was tested by loading

with the electron gun. The beam current was measured by the Faraday plate. The cathode was

heated up to ~1900 K by applying 10 W of heater power and the DC pulsed electron beam

current, 1.5 A, was measured in the test chamber. Figure 3.12 shows the measured waveforms

of the accelerating voltage and beam current. Up to now, the cathode has been operated for

7000 hours without failure.

Figure 3.12: The measurement waveform of the accelerating voltage and electron beam

current.

48

3.5 Gun simulations

At the beginning of this research work, the numerical calculation has been performed using

EGUN code [72]. Nevertheless, it seems EGUN is not suitable for a very small cathode size

which was used in this research [12]. Thereby, we have to use 3 dimensional simulation code

developed in our group [11]. This code is based on the Poisson’s equation including the space

charge effect with boundary conditions given by the gun geometry, the applied voltage, and

the beam current. Magnetic fields are to be specified independently.

This self-developed code is written to calculate electron trajectories in electrostatic and

magnetostatic fields. Poisson’s equation is solved by finite difference equations using

boundary conditions defined by specifying position of the boundary. Electric fields are

determined by differentiating the potential distribution. The electron trajectory equations are

relativistic and account for all possible electric and magnetic field components. Space charge

forces are realized through appropriate deposition of charge on one cycle followed by another

solution of Poisson’s equation which is in turn followed by another cycle of trajectory

calculations.

Electron trajectories may be started at cathode in which electrons are started assuming

Child’s law holds near a surface designated as the cathode. On the first iteration cycle, space

charge forces are calculated from the assumption of paraxial flow. As the rays are traced

through the program, space charge is computed and stored in a separate array. After all the

electron trajectories have been calculated, the program begins the second cycle by solving

Poisson’s equation with the space charge from the first cycle. Iteration cycles can be specified

following the above pattern.

Magnetic fields are read in either as axial strengths or as arrays of coils with specified

coordinates and currents. The preferred technique of defining the magnetic field is to calculate

the axial field from an arbitrary configuration of solenoids. Anyhow, this self-developed code

is another work of this research group.

We performed a computer simulation using the 3 dimensional self-developed code for 50

keV, 300 mA beam current and 15 mm cathode-anode distance in simple model. As shown in

49

figure 3.13, the beam trajectories diverge including the emittance growth due to space charge,

which would result in a rapid increase in beam spot size. In addition, the simulation result

shows the electric field near the cathode surface is very sensitive to the emittance growth,

which means the mechanical positioning of the cathode is very important. So we need special

bias voltage between cathode and wehnelt to manipulate the electric field around cathode

surface.

Figure 3.13: An electron beam extraction and normalized emittance of 300 mA with no bias.

50

Figure 3.14: The bias voltage dependence of normalized emittance.

In another result of the 3D simulation, we applied bias voltage between wehnelt and

cathode to manipulate the electric field around the cathode surface as shown in figure 3.14. At

the low bias voltage, a little focusing action, therefore, the emittance is gradually grow and

become smoothly when the bias voltage was increased from -200 V to -400 V. The minimum

point of emittance was shifted backward to cathode side by increasing of special bias voltage.

In the simulation at bias voltage of -600 V, it seems the emittance does not so much change

while the electron beam propagates in the drift space. This result showed that we can

manipulate the equipotential line near the cathode surface by adjusting the special bias voltage

to optimize the extracted beam emittance [13]. An extremely low emittance less than 1 mm

mrad is obtained by the simulation.

Due to the bias voltage of -600 V, the macro-particle distribution and phase space

distribution at the end point possibly became an ideal Kapchinskij-Vladimirskij (K-V) as

shown in figure 3.15 [73]. In an ideal case, the K-V beam has a perfect linear space-charge

51

force within the beam radius. Therefore, the transverse phase space is kicked by linear space-

charge force proportional to the distance from the beam center like the transverse phase space

in figure 3.15.

Figure 3.15: The macro-particle distribution including phase space distribution at the end

point according to a simulation.

3.6 Support systems

3.6.1 Power supply system

A high-voltage DC power supply for the electron gun was developed for 0~-50 kV with

300 mA, a pulse width of 1-5 sec, pulse droop 0.1%, and maximum repetition rate of 300

pps respectively [see Appendix A for circuit diagram]. For high efficiency of the system we

have chosen the Insulated-Gate Bipolar Transistor (IGBT) as an inverter. This IGBT is a

three-terminal power semiconductor device, noted for high efficiency and fast switching. The

IGBT combines the simple gate-drive characteristics of the MOSFETs with the high-current

and low–saturation-voltage capability of bipolar transistors by combining an isolated-gate

FET for the control input, and a bipolar power transistor as a switch, in a single device which

is shown a typical cross section in figure 3.16 . The wehnelt DC voltage can be adjusted from

http://en.wikipedia.org/wiki/Power_semiconductor_devicehttp://en.wikipedia.org/wiki/Power_MOSFEThttp://en.wikipedia.org/wiki/Bipolar_junction_transistorhttp://en.wikipedia.org/wiki/Field-effect_transistorhttp://en.wikipedia.org/wiki/Transistor

52

0~-1 kV. In the case of the heater power supply, we use 1 Vdc and 12 A maximum current to

feed the LaB6 cathode. All of modules are combined together in figure 3.17. This system can

be operated on control panel.

Figure 3.16: A typical cross section of IGBT.

Figure 3.17: The power supply module.

53

3.6.2 Ultra high vacuum system

The Ultra High Vacuum (UHV) is required for our gun system. To increase the pumping

speed and quick recovery when the system opens to normal pressure two vacuum pumps were

added to the system. One is turbo-molecular pump [PFEIFFER TSU071] with pumping speed

60 l/s and the other is ion pump [ANELVA] with pumping speed 60 l/s. This UHV system

requires the use of special materials in creating the vacuum system, extreme cleanliness to

maintain the vacuum system, and baking the entire system to remove water and other trace

gases that are accumulated due to the difficulties of maintaining a UHV. Figure 3.18 shows

vacuum condition of a low emittance compact DC gun. Moreover, a good vacuum level must

be a high insulator to prevent electrical breakdown of high voltage system as well.

Figure 3.18: Vacuum condition of a low emittance compact DC gun.

54

3.6.3 Solenoid lens

Figure 3.19 (a) shows a shape of the solenoid lens used for this experiment with a 300

turns coil and pure iron yoke. The coil with 14 mm width was covered by yoke and cutting

off the edge of yoke at the surface in both sides like a slant to concentrate the magnetic

flux. There is no influence of fringe field reach outside the solenoid lens, in particular on

the cathode surface.

Figure 3.19 (b) shows the distribution of magnetic field from solenoid lens. The

calculation of magnetic field of solenoid lens was done by POISSON. This code was

developed by Los Alamos Accelerator Code Group (LAACG) for two-dimensional magnetic

field analysis [74].

As example, a distribution of Bs (strength of magnetic field in the direction of beam axis on

s axis) where the current of solenoid electromagnetic lens was set at 1 A, is shown as Figure

3.20. The center of solenoid lens was set to the origin. At the approximately distance of 35

mm from the center of the solenoid lens, the magnetic field’s strength in both the negative and

the positive poles is 0.4 G or less, according to the result of POISSON.

Based on this result, the effective length of magnetic field was calculated. If Bs(s) is the

strength of magnetic field in a certain position s, and that Bs0 is the strength of magnetic field

at the center, the effective length of magnetic field leff is generally expressed as:

(3.24)

According to the result of Figure 3.20, the effective length leff is:

(3.25)

.)(

0s

s

effB

dssBl

.2.201)(

0

mmB

sBl

s

n ns

eff

55

(a) (b)

Figure 3.19: (a) Shape of Solenoid lens, (b) Distribution of magnetic field from solenoid lens

resulted POISSON.

56

In addition, as the strength of magnetic field is 184 G, according to Figure 3.20, when s

(the center position of solenoid lens) equals 0, the strength of magnetic field at the center

position, Bs0I (I: current value), is:

(3.26)

Figure 3.20: Distribution of magnetic field of Solenoid electromagnetic lens.

].[184][0 AIGB Is

57

3.6.4 Current transformer

For the measurement of beam current the in-flange fast current transformer (FCT) was

installed at the downstream of the solenoid lens. Figure 3.21 shows the FCT. The operating

principle is very easy to understand by figure 3.22. In this figure the induced current from the

coil inside the FCT was terminated by the resistor, 50 ohms, and the signal was measured in

the form of voltage across the resistor. We can calculate the beam current by voltage across

the resistor and the sensitivity of FCT.

Figure 3.21: The in-flange fast current transformer (FCT) attached at the down-stream of

solenoid lens.

Figure 3.22: The operating principle of the in-flange fast current transformer.

58

3.6.4.1 Method to solve the charge-up problem at FCT ceramic

In some cases of electron optic system we face the charge up problem at the ceramic part

of FCT. This problem causes by sputtered electron on the FCT ceramic. When electrons hit

and accumulate charge at the ceramic part shown in figure 3.23 (A), sputtered electrons have

enough force to repel the beam. This makes electron beam fluctuation and brings to

measurement problems. So, the Al sleeve had been attached at the inner diameter of FCT

shown in figure 3.23 (B).

To confirm this Al sleeve does not affect the signal which is generated by the FCT. We

calibrated the FCT by feeding square wave from function generator to resistor 50 ohms. The

diagram of calibration is shown in figure 3.24. The induced voltage from FCT was measured

by oscilloscope. The voltage signals measured by oscilloscope in both cases shown in figure

3.25 and 3.26 are same value. Figure 3.27 shows the beam current measured by FCT

comparing between 2 cases [see Appendix B for FCT calibration].

(A) (B)

Figure 3.23: (A) Show the ceramic part of FCT, and (B) Assembly of FCT and Al sleeve.

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Figure 3.24: Circuit diagram of FCT calibration.

Figure 3.25: Voltage signal of FCT without Al sleeve.

60

Figure 3.26: Voltage signal of FCT with Al sleeve.

Figure 3.27: Comparing of beam current measured by FCT in 2 cases.

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3.6.5 Corona ring

The corona ring had been installed at the joined position between ceramic feedthrough

and wehnelt supporter shown in figure 3.28. This point has high tension of electric field.

Therefore, we could not drive the HV for a long time in early stage of our experiment because

of discharging. After we installed the corona ring, the problem had been solved. We

succeeded to drive the HV up to 50 kV without discharge.

Figure 3.28: The position of installation of corona ring.

62

3.7 Cathode alignment and assembly

The alignment of LaB6 cathode were performed by using a non-contact laser measurement

system that comprised a laser sensor (Keyence LK-G80), a controller (Keyence LK-G3000V),

and a 2 axis stage. The laser sensor which was used having resolution 0.01 μm and its

accuracy is ±5%. The alignment was performed by scanning the cathode by the stage and

measuring the depth of the surface to observe the flatness between the cathode and wehnelt

surface. In this alignment, the flatness between the cathode and wehnelt in the range of 50 μm

is acceptable. Figure 3.29 shows a non-contact laser measurement system and Figure 3.30

shows the cathode fixed on wehnelt electrode. The inserted picture in figure 3.30 shows the

cathode viewed by a microscope. The cathode is located at the center of wehnelt electrode

with positioning error of ±100 μm by using microscope.

Figure 3.29: A non-contact laser measurement system.

63

Figure 3.30: The cathode position after alignment and the inserted picture shows the cathode

viewed by a microscope.

64

Chapter 4 Beam quality measurements of the low

emittance compact DC gun

An overvie