femtosecond electron bunches from an rf-gun

ARTICLE IN PRESS

0168-9002/$ - se

doi:10.1016/j.ni

�Correspondi222-776.

E-mail addre

(S. Rimjaem).

Nuclear Instruments and Methods in Physics Research A 533 (2004) 258–269

www.elsevier.com/locate/nima

Femtosecond electron bunches from an RF-gun

Sakhorn Rimjaema,�, Ruy Fariasb, Chitrlada Thongbaia, Thiraphat Vilaithonga,Helmut Wiedemannc

aFast Neutron Research Facility, Physics Department, Chiang Mai University, P.O. Box 217, Chiang Mai 50202, ThailandbLaboratorio National de Luz Sincrotron, LNLS, Campinas, Brazil

cApplied Physics and SSRL,/SLAC Stanford University, Stanford, CA, USA

Received 8 December 2003; received in revised form 3 May 2004; accepted 27 May 2004

Available online 29 July 2004

Abstract

Sub-picosecond electron pulses become a tool of increasing importance to study dynamics at an atomic level. Such

electron pulses can be used directly or be converted into intense coherent far infrared radiation or equally short X-ray

pulses. In principle, sub-picosecond electron pulses can be obtained in large, high-energy electron linear accelerator

systems by repeatedly applying an energy slew and magnetic compression. Another process is the production of short

electron pulses at low energies from an RF-gun with a thermionic cathode together with a bunch compressing a-magnet. In this paper, we present a systematic analysis of capabilities and limits of sub-picosecond electron pulses from

such a source. We discuss particular parameter choices as well as the impact of geometric and electric specifications on

the 6-dimensional phase space electron distribution. Numerical beam simulations with the computer code PARMELA

are performed including effects and limitations due to space charge forces. While the production of femtosecond

electron bunches is of primary concern, we also consider the preservation of such short bunches along a beam transport

line.

r 2004 Elsevier B.V. All rights reserved.

PACS: 41.75.Lx; 29.27.Fh

Keywords: fs electron pulses; fs X-ray pulses; Far infrared radiation; Electron source; RF-gun

e front matter r 2004 Elsevier B.V. All rights reserve

ma.2004.05.135

ng author. Tel.: +66-53-943-379; fax: +66-53-

ss: [email protected]

1. Introduction

Experimental opportunities based on particlebeams are frequently determined by the particles’distribution in six dimensional phase space.Excellent progress has been made in the past 15years to reduce the transverse phase space

d.

www.elsevier.com/locate/nima

ARTICLE IN PRESS

rf input

thermioniccathode

full cell electron beamhalf cell

Fig. 1. RF-gun cross-section and 3D-view.

S. Rimjaem et al. / Nuclear Instruments and Methods in Physics Research A 533 (2004) 258–269 259

distribution of particle beams especially in thepursuit of high brightness third generation syn-chrotron light sources. Only recently has it becomepossible to significantly reduce the longitudinalphase space distribution and to produce intenseelectron pulses of very short duration withoutrelying on high-energy accelerators and extensivebunch compression systems. Sub-picosecond elec-tron pulses at low energies of a few tens of MeVare desired, for example, for direct applications inresearch of physical, chemical and biologicalmaterials [1–3]. Other applications are based onthe transformation of the electron pulses intophoton pulses by way of, for example, single passfree electron lasers (SASE) [4], Compton scattering[5], Parametric and other methods to producefemtosecond X-ray pulses [6], or for the generationof coherent far infrared radiation [7–9] with aphoton brightness far exceeding that availablefrom conventional and synchrotron radiationsources.

In large, high-energy linear accelerator systems,sub-picosecond electron pulses can be obtained byrepeated application of RF beam-conditioningand bunch compression. At low energies, suchbunches can be produced on a laboratory scalefrom an 11

2-cell RF-gun with a thermionic cathode

and an a-magnet for bunch compression, albeit atlower charge intensities [10]. This type of electronsource provides three essential features whichallow efficient bunch compression. First, the highacceleration to near relativistic energies within afew centimeters minimizes detrimental spacecharge effects. Second, the energy-time phasespace distribution of the electrons produced in aRF-gun is specially well suited for bunch compres-sion as will be discussed in more detail. Third, asimple, reliable and easy to use thermionic cathodecan emit a particle flux up to and beyond anintensity where space charge effects becomeuncontrollable at the low electron energies con-sidered here. Utilizing such an RF-gun with athermionic cathode at the Stanford SUNSHINEfacility [9,11], it has been possible to produceelectron pulses as short as 120 fs rms [9,12] and abunch intensity of 100 pCb. Fig. 1 shows aschematic cross-section and a 3D-view of theelectron source as installed at SUNSHINE.

The SUNSHINE RF-gun, however, has beenoriginally designed for a different application andwas not optimized to generate femtosecondbunches. Specifically, the accelerating field wasnot optimized for bunch compression as will bediscussed later. Furthermore, the geometry of theRF-gun produces transverse focusing forces whichproduce a convergent electron beam at the exit ofthe RF-gun. This and subsequent focusing gen-erates a spread of total path length for individualparticles and limit the shortest achievable bunchlength at SUNSHINE to 120 fs rms. Specificoptimization of the RF-gun to minimize thisfocusing and produce femtosecond electronbunches is therefore expected to result in shorterbunches. In this note, we report on the results of asystematic investigation and discussion of optimi-zation procedures, choice of parameters andlimitations in producing femtosecond bunchesfrom an RF-gun. Specifically, we study the impactof particular geometric and electric parameterchoices on beam performance including theinfluence of space charge. Following this optimi-zation a new RF-gun has been built at Chiang MaiUniversity for the SURIYA facility, soon to becommissioned [13].

2. Method

The electron source consists mainly of a 112-cell

RF-cavity, operating at 2856MHz with a ther-mionic cathode and followed by an a-magnet for

ARTICLE IN PRESS

S. Rimjaem et al. / Nuclear Instruments and Methods in Physics Research A 533 (2004) 258–269260

bunch compression. Electrons emerging from thecathode (Fig. 1) travel first through the half andthen the full RF-cell reaching a kinetic energy ofabout 2:5 MeV. Later, we will discuss in moredetail the optimum choice of the acceleratingfields.

2.1. Numerical beam simulations

The dynamics of particle motion in the RF-gunhas been simulated with the code PARMELA [14]to determine the dependence of expected beamcharacteristics on external parameters as well as onspace charge forces. In this section, we show thefinal results of those studies followed by moredetailed discussions in subsequent sections. Thesesimulations exhibit a particle distribution at theRF-gun exit (Fig. 2) with a high correlationbetween momentum and time as is desired foreffective bunch compression.

The distribution shown is that of a single S-bandbunch repeating at 3GHz. Adjacent bunches areseparated by half a RF-period during which noparticles can be accelerated. This temporal gapdefines a definitive beginning (head) of the bunchwhen the microwave field at the cathode just startsto become accelerating. Although it is assumedthat electrons are emitted in a uniform streamfrom the cathode, we notice an increased long-itudinal particle density at the RF-gun exit asindicated in the histogram showing the number of

time (ps)0

klin

etic

ene

rgy

(MeV

)

0.0

0.5

1.0

1.5

2.0

2.5

hist

ogra

m (

part

icle

/ps)

0

1000

2000

3000

4000

20 40 60 80 100

Fig. 2. Particle distribution in energy-time phase space for a

single S-band bunch at the RF-gun exit with histogram. The

units of the histogram are macroparticles (each representing

6:34� 104 electrons) per picosecond.

macroparticles per picosecond. Unless otherwisenoted, we use for this study a uniform cathodeemission current of 2.9A represented by 100,000macroparticles per 2856MHz RF-period. Eachmacroparticle represents a charge of 10.15 fCb orne ¼ 6:34� 104 electrons. The uniform current of2.9A corresponds to 285.6 macroparticles perpicosecond at the cathode, yet at the RF-gun exit,we observe a much higher particle density duringthe first few picoseconds at the head of each bunch(see Fig. 2). The dynamics of this concentrationderives from the temporal variation of the micro-wave field. The first electrons accelerated encoun-ter initially only a very small field which increasesas the electrons travels through the 1

2-cell. Particles

emerging somewhat later from the cathode intothe raising RF-field gain speed more quickly. Theyactually are able to partially catch up with earlierparticles. This bunching of a CW beam from thecathode is due to the time variation of the RF-fieldyielding short pulses of about 10 ps duration.From now on, we concentrate therefore only onthis part of each bunch.

2.2. Bunch compression

The concave shape of the phase space distribu-tion in Fig. 2 matches especially well to bunchcompression in an a-magnet [15] shown in Fig. 3.

α magnet

energy filter

e- beam

rf-gun

49.29°

49.29°

Fig. 3. Rf-gun and a-magnet layout (schematic).

ARTICLE IN PRESS


This magnet is half a quadrupole with a mirrorplate in the yz-plane to close the magnetic fieldlines. Generally, a beam would travel through aquadrupole along the z-axis, but in an a-magnetthe electron beam enters the magnet in the xz-plane at an angle of 49:29� with respect to themagnet axis or yz-plane. As indicated in Fig. 3,particles follow a closed loop similar to the letter aand exit the magnet again exactly at the entrancepoint independent of the particle momentum, yetin a different direction. The a-magnet is thereforean achromat, while the path length s of the particletrajectory in the magnet exhibits a large disper-sion, depending on the particle momentum cp andmagnetic field gradient g like s /

ffiffiffiffiffiffiffiffiffifficp=g

p[16].

These features make the a-magnet a convenientand simple bunch-compressor for low-energybeams. One may change the magnet strength andthereby the compression without changing thedirection of the beam path outside the a-magnet. Itis interesting to note that the largest compressionis obtained for a weak a-magnet strength becausebunch compression of relativistic particles ismostly based on path length rather than velocitydispersion. The phase space distribution of Fig. 2rotates clockwise as the beam travels through thea-magnet.

Although the electrons are generated as a CWbeam from the thermionic cathode, they eventuallyemerge from the RF-gun in bunches with theperiodicity of the RF frequency. No electrons areaccelerated during half a RF-period, followed by ahalf-period of acceleration. From Fig. 2 we notethat the highest energy electrons exit the RF-gunfirst and follow a longer path through the a-magnet than lower momentum electrons exitingthe gun later. Even for moderately relativisticelectrons, the velocity dispersion is small, althoughnot negligible, and consequently lower momentumelectrons following a shorter path can catch up tosome degree leading to bunch compression. Still,to avoid excessive bunch lengthening due tovelocity dispersion counteracting bunch compres-sion, the beam energy should not be less thanabout 1MeV and a short distance between RF-gunand a-magnet is desirable. An energy filter insidethe a-magnet, where the momentum dispersion islarge, is used to select the desired part of the beam.

Downstream of the a-magnet, there may be alinear accelerator and/or some transport lineguiding the beam to an experimental station. Tocompensate for the velocity dispersion, the valueof the a-magnet field-gradient must be chosen suchas to generate the shortest bunches at theexperimental station. Although we think of thea-magnet as being a bunch compressor, we have ashort bunch within the a-magnet only for a veryshort time during the phase space rotation. Toobtain the shortest bunch at the experimentalstation, we need to overcompress the bunch suchthat the lower momentum particles exit the a-magnet first and leaving higher energy particlesbehind. This phase space orientation together withthe velocity dispersion due to the energy spreadleads to the shortest bunch at the experimentalstation. This is a fortunate circumstance, since thebunch is most of the time long while the particleenergy ahead of the linear accelerator is low andtherefore space charge effects are negligible. Onlyfor a very short time of a few ps does the bunchreach a very short length inside the a-magnet.Since the transverse beam dimensions are ratherlarge due to the energy dispersion in the a-magnet,we only need to consider longitudinal space chargeeffects. Such space charge effects cannot besimulated with the PARMELA code (or any othercode we know) in a beam line with an a-magnetand we must therefore use analytical methods todeal with this issue.We calculated the energy gain a single particle

would encounter being pushed from behind by allother particles. It was assumed that all particlesare concentrated on a thin disk with the actualtransverse radius as given by beam optics and thesingle particle ahead of this disk by half a bunchlength or 15mm. Such a particle would experiencea relative energy gain of 7� 10�5, which translatesinto a velocity spread and hence into an increase inbunch length. Calculations show that an rmsincrease of 6 fs must be expected from this spacecharge acceleration, which is negligible for ourconditions. The effect is even smaller noting thatthis increase in energy spread occurs just at thetime when the bunch is the shortest and the ðt;EÞ

phase space distribution of the useful beam isspread along the energy coordinate. Due to the

ARTICLE IN PRESS


energy change within the a-magnet a smalltransverse effect must be expected. The energychanging particle suffers a distortion of the a-typepath leading to a transverse displacement of theparticle trajectory at the a-magnet exit of some2mm or less than 0.1% of the beam size.

The numerically simulated particle distributionof Fig. 2 is shown in Fig. 4 after compression andacceleration in the linear accelerator to 26MeV.Note that the temporal particle distribution isshown with respect to the initial momentum at theRF-gun exit. The particle distribution in phasespace and the histogram exhibit some character-istics which we will discuss in more detail. Bunchlengthening due to path length dispersion causedby focusing in the beam transport line has beenkept to a minimum in the particular design of thebeam transport line (Fig. 5) and shows up as asmall broadening of the Gaussian tails. Further-more, the oscillatory temporal perturbation of thedistribution is the result of an instability, theshock-wave instability, arising from the fastchange of particle intensity at the front of eachbunch [10] and is ultimately limiting the shortestachievable bunch length. This perturbation isestablished in the first half-cell persisting over afew oscillations. When space charge forces areignored, this instability does not appear and thelongitudinal phase space is determined only bycathode geometry, RF focusing and thermalenergy distribution. The period of the perturbation

time (fs)

0 120 160 200 240 280 320 360

hist

ogra

m (

part

icle

s/fs

)

0

1000

2000

3000

4000

kine

tic e

nerg

y (M

eV)

1.9

2.0

2.1

2.2

2.3

2.4

2.5

40 80

Fig. 4. Particle energy-time phase space distribution after

bunch compression and transport to the experimental station

with histogram. The histogram can be fitted by a Gaussian with

a standard width of 52.8 fs and a charge of 94 pCb.

is varying in time from some 0.5 ps to about 7 psafter one period. This is much shorter than theRF-period, and the perturbation therefore cannotbe caused by the 3GHz RF-fields. Furthermore,the nonlinearity arising from bunch compressionin the a-magnet causes only a slow monotonicvariation of compression with particle momentum.The buildup of the perturbation, on the otherhand, matches the rise time of the particledistribution while the perturbation amplitudeincreases with space charge. Indeed, in this study,the maximum beam charge is not limited by thecathode but rather by these oscillatory perturba-tions, which, at some level, prevent efficient bunchcompression. The theory of this instability in [10]describes qualitatively the observations in beamsimulations, but more quantitative studies arerequired and will be reported later.In reality, we expect this shock wave instability

to be somewhat reduced because the particledensity in each bunch will rise less than assumedhere due to the Langmuir–Child effect during thefirst few picoseconds. On the other hand, it is notquite clear how this effect manifests itself in a timevarying field. According to the Langmuir–Childlaw no current should be emitted at zero field, butin our case there is no electron cloud yet in front ofthe cathode as theory assumes. Beam observationand measurements will hopefully shed more lighton the beam construction in the presence ofoscillating fields, space charge effects and shockwave instability.The beam transport line used in this study is

shown in Fig. 5 and has been designed forminimum bunch length broadening due to pathlength dispersion. While this is not the onlysolution possible, we use it as an example todemonstrate the dynamics of the electron beam.Focusing, being the source of path length disper-sion, should be minimized as much as possiblewhile still compensating the unavoidable strongfocusing in the a-magnet.The phase space distribution of Fig. 4 represents

the result of an optimization study which we willuse in this report as a reference for more detaileddiscussions. It shows the particle distribution atthe end of the beamline which is the location ofoptimum bunch compression (Fig. 5). The most

ARTICLE IN PRESS

9876543210

76543210

-1-2-3-4-5-6-7-8-9

-10 Q Q α Q Q Linac Q Q

σ

σ

x

y

σx,

y(m

m)

z (m)

Experiment

Fig. 5. Beam transport line from RF-gun to experimental station (QF1 - QD1 - QF2 - a-magnet - QF3 - QD2 - linac - QF4 - QD3).

Note: a-magnet is shown as a thin element.

Table 1

Optimized S-band RF-gun and beam parameters

Max.beam momentum, cp 2.91 MeV

Velocity, b ¼ v=c 0.9851

Avg./max. field in 12-cell 23.9/29.9 MV/m

Avg./max. field in full-cell 45.0/67.6 MV/m

Cathode emission current 2.9 A

Cathode radius 3.0 mm

Charge/bunch 94 pCb

Peak current 707 A

Bunch length (rms) 52.8 fs

Norm.beam emittance, rms 3.8 mmmrad


obvious feature of the distribution is the oscillatoryvariation in time. This oscillation is believed to becaused by an instability (shock wave instability [10])caused by the sudden increase in the charge intensityat the head of each bunch. That leads to anoscillatory of energy due to space charge forcesalong the bunch which in turn gives rise to temporaloscillations after compression in the a-magnet. Thiseffect is presently under intense quantitative studyand is expected to ultimately limit the bunchcompression of low-energy beams. From the tem-poral oscillations of about�50 fs we derive a relativemomentum ripple of �10�4. The expected bunchlength, including transverse path length dispersion, is53 fs rms at a total charge of 94pCb. Some of themain beam characteristics from this optimized RF-gun are compiled in Table 1 with explanations giventhroughout this note. The geometric features of theRF-gun are compiled in Table 2 and described in alater section of this report.

2.3. RF-gun field

The choice of the electric accelerating fieldemployed in each cell of the RF-gun greatly

controls the efficacy of bunchcompression. InFig. 6, we show the particle distribution in phasespace at the RF-gun exit for different values of theaccelerating fields in the half- and full-cell,respectively. The field ratio between half- andfull-cell is kept constant to about 1:2 for thisdiscussion.In Fig. 6 we note that particles in the bunch

head are virtually quasi-monoenergetic for electricfields of about 45MV/m in the half-cell. Thisrenders the beam unfit for bunch compression, yetexhibits a very desirable quasi-monochromatic

ARTICLE IN PRESS

Table 2

Geometry of half (left) and full (right) cell for optimized RF-gun

Segment (units mm) x y Segment (units mm) x y

Origin 0.00 0.00 Origin 0.00 5.20

Line to 0.00 41.90 Line to 4.35 5.20

Line to 5.00 41.90 arc,�90�; r ¼ 5:00mm to 9.35 10.20

arc,90�; r ¼ 24:64mm to 29.64 17.26 Line to 9.35 10.50

Line to 29.64 15.00 arc,�90�; r ¼ 2:50mm to 6.85 13.00

arc,90�; r ¼ 2:00mm to 27.64 13.00 Line to 4.46 13.00

Line to 26.50 13.00 arc,0�; r ¼ 2:00mm to 2.46 15.00

arc,90�; r ¼ 2:50mm to 24.00 10.50 Line to 2.46 17.26

Line to 24.00 10.20 arc,180�; r ¼ 24:64mm to 51.74 17.26

arc,90�; r ¼ 5:00mm to 29.00 5.20 Line to 51.74 15.00

Line to 32.10 5.20 arc,90�; r ¼ 2:00mm to 49.71 13.00

Line to 47.35 13.00

arc,�90�; r ¼ 2:50mm to 44.85 10.50

Line to 44.85 10.20

arc,�90�; r ¼ 5:00mm to 49.85 5.20

Line to 58.00 5.20

time (ps)

700 725 750 775 800 825 850

klin

etic

ene

rgy

(MeV

)

0

1

2

3

4

5

6

45/90 MV/m

35/70 MV/m

23.9/45 MV/m

15/30 MV/m

Fig. 6. Energy-time phase space distributions for different

accelerating fields in the RF-gun. Parameters are averaged half/

full-cell accelerating fields.


beam to drive, for example, a Free Electron Laser.In this high field case, particles pass through thehalf-cell in less than one half-RF-cycle and theintegrated acceleration turns out to be about thesame for particles emerging from the cathodeduring about the first 25 ps in the RF-cycle.

For lower fields, a monotonic correlation ofparticle energy with time appears as desired forbunch compression. In this situation, particlesemerging at zero phase from the cathode will not

quite reach the cavity exit before the field directioninverts and particles exiting the cathode atincreasing RF-phases experience increasing nega-tive acceleration before they reach the end of thehalf-cell. This becomes more true as the field isfurther reduced and is determined purely by thecavity dimensions, the RF-field amplitude and itstemporal variation.At this point, we need to get some guidance on

the choice of the electric field strength foroptimum bunch compression. With the knowledgeof the beam line downstream of the RF-gun (forexample Fig. 5), we may determine an ideallydesired particle distribution at the gun exit.

2.4. Ideal phase space distribution

For a given beam transport line, an idealelectron phase space distribution at the RF-gunexit can be defined. The first particle to exit theRF-gun in each cycle at time T0 ¼ 0 is thereference particle, which also happens to be theparticle with the highest momentum, will arrive atthe experimental station at time T ref . An electronwith lower momentum travels to the experiment ina time DT and must therefore exit the RF-gun at atime dT compared to the reference particle such

ARTICLE IN PRESS


that DT þ dT ¼ T ref and in this case, bothparticles arrive at the experimental station at thesame time. Calculating the ideal gun exit-times dT

for all particle momenta, we obtain the ideallydesired particle phase space distribution at the RF-gun exit as shown in Fig. 7 in comparison with anactual particle distribution.

For this particular simulation we used the beamtransport line of Fig. 5 although another beamtransport line could be used as well. The distribu-tion within the bunch head of the ideal distributionhas the same convex curvature as those we observein Fig. 6. A proper choice of the electric fieldstrength can therefore match the actual to the idealdistribution at least over a finite range of particlemomenta. For too low-energy particles, bothdistributions diverge greatly because particlestravel too slow to be able to catch up and,extremely, should have left the cathode when theaccelerating field was still negative, which, ofcourse, is nonphysical. The range of almost perfectmatch extends over about the first 10–15 ps of eachbunch where most of the charge is concentrated. Asimilar, but much smaller dynamic effect occurs inthe second, full-cell cavity and must therefore beincluded as a correction in the overall optimizationprocedure. For the RF-gun under discussion thisoptimization leads to a perfect match if theaverage accelerating field in the half-cell is23.9MeV and in the full-cell 45MeV.

-20

1

1.5

2

2.5

∆ t (ps)

kine

tic e

nerg

y (M

eV)

idealdistribution

actual particledistribution

-10 0 10 20 30 40 50

Fig. 7. Ideal and actual phase space distribution at the RF-gun

exit.

3. RF-gun geometry

Internal geometric features of the RF-guncavities determine greatly the final beam charac-teristics. In Fig. 8, the cross-section of both, thehalf-cell and the full-cell is shown together with theelectric field profile.The actual geometry of the optimized SURIYA

RF-gun used for the simulations presented in thisarticle is documented in Table 2 for both the half-and full-cell. The ratio in the full- to half-cell fieldcan be chosen by practical considerations like RF-power availability and field break-down, whilepreserving optimum matching. Since the full-cellfield affects the ideal particle distribution only littleone might choose the highest practical field tominimize space charge effects. The electric fieldvalues along the cavity axis is shown in Fig. 9. Thegeometrical features can be separated into twogroups; those which affect mainly RF-parametersand have little effect on beam parameters ofinterest and those which affect mostly the beamcharacteristics. Features further away from theaxis (beam) like the wall defining the cavitydiameter determine in particular the resonantfrequency, which in our case should be2856MHz. The length of the effective cavity canbe adjusted either by varying the dimension a orthe iris length by varying dimensions c and e.Close to ideal phase space distributions can be

achieved if the accelerating field and length of thehalf-cell cavity is such that the reference particlecan traverse its effective part within one half RF-period, the accelerating period.

ar=24.64mm, 90°

bc

d e

R

half cell full cell

Fig. 8. Internal RF-gun geometry.

ARTICLE IN PRESS

0

-80

-60

-40

-20

0

20

40

E (

MV

/m)

z (mm)

half cell

full cell

20 40 60 80

Fig. 9. Electric field profile along the cavity axis.

-1 -0.5 0 0.5 1

-40

-20

0

20

40

x,y ( mm)

x',y

' (m

rad)

Fig. 10. Transverse phase space distribution at the exit of the

SUNSHINE RF-gun.


As discussed earlier, internal features in theSUNSHINE RF-gun caused a significant beamconvergence/divergence to seriously affect theachievable bunch length due to path lengthdispersion (Fig. 10). Specifically, a nose cone atthe cathode plate introduced much of the focusing.In the new design this nose cone is eliminated andwe use a flat cathode plate to minimize beamdivergence. For the same reason the iris radii at thecell ends are increased sufficiently to reduce theradial electric fields and it’s effect on the beamdivergence.

4. Transverse particle dynamics

Due to the natural divergence of the beam andunder the forces of focusing elements, particlesfollow trajectories which are oscillatory about theideal beam axis and therefore longer than on-axistrajectories leading to path length dispersion. TheRF-gun used in the SUNSHINE facility creates alarge beam convergence/divergence as shown inFig. 10 which must be compensated with quadru-pole focusing between RF-gun, a-magnet andexperimental station. The slopes of particle trajec-tories being of the order of 10mrad cause asignificant spread of the pathlengths and thus limitthe shortest bunch achievable to about s 120 fs[12].

In the optimized RF-gun design a flat cathodeplate is used and the iris radii are increased to

reduce the effect of radial RF-fields in theirvicinity. Both changes result in a much reducedbeam divergence as shown in Fig. 11 (left)compared to the case for the SUNSHINE RF-gun shown in Fig. 10. Ignoring space chargeeffects, a slightly convergent beam is desired (Fig.11, left) which then becomes a parallel beam (Fig.11, right) when repelling space charge forces areincluded.Bunch lengthening depends quadratically on the

beam divergence and is therefore greatly reducedfor the optimized gun design with less than 1mradof divergence for the core of the beam. Unfortu-nately, the a-magnet introduces strong focusingwhich must be matched by some external quadru-pole focusing causing an unavoidable finiteamount of bunch lengthening. This has beenincluded in the simulation of the particle distribu-tion of Fig. 4 for the transport line in Fig. 5. Thelattice parameters for this transport line arecompiled in Table 3, where the parameters beforeand after the linac section are for an averagebeam momentum of cp ¼ 2:81MeV and cp ¼

27:18MeV, respectively. Special care was takenin the design of this transport line to avoid anyunnecessary focusing which could lead to pathlength dispersion. For the design of the beam lineshown in Fig. 5 we were able to reduce these effectsto a negligible level within the statistical fluctua-tions of bunch length due to the limited number ofparticles in the simulation.To calculate the beam emittance, we take only

the useful part of the beam with particle momenta

ARTICLE IN PRESS

without space charge effects

x, y (mm) x, y (mm)-2 -1 0

x', y

' (m

rad)

x', y

' (m

rad)

-20

-10

0

10

20

with space charge effects

-2 -1-20

-10

0

10

20

1 2 0 1 2

Fig. 11. Transverse phase space distribution of optimized RF-gun without (left) and with (right) space charge effects.

Table 3

Beam line lattice

# Name l (m) Strength Units

1 D1 0.283 m

2 QD1 0.073 18.750 1=m2

3 D3 0.050 m

4 QF2 0.073 �34.440 1=m2

5 D4 0.200 m

6 a-mag n/a 399.00 G/cm

7 D5 0.189 m

8 QF3 0.073 43.300 1=m2

9 D6 0.164 m

10 QD2 0.073 �39.717 1=m2

11 D7 0.600 m

12 Linac 3.040 8.0 MeV/m

13 D8 0.853 m

14 QF4 0.073 19.664 1=m2

15 D9 0.150 m

16 QD3 0.073 �21.623 1=m2

17 D10 2.480 m


of cpX2:60MeV (Fig. 4). Using the definition

�rms ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihx2ihx02i � hxx0i2

pthe useful beam rms

emittance is �rms ¼ 0:69mm mrad. For an averagevalue of the kinetic energy of 2.35MeV, bg ¼ 5:51and the normalized beam emittance is�n;rms ¼ 3:8mmmrad. The normalized thermal

cathode emittance (at T 1300K and a radiusrcath ¼ 3mm) of �n;therm ¼ 0:28 mmmrad (page 102of [17]) is still small, but has been included in thePARMELA simulations.

5. Effect of source size

The size of the cathode diameter can limit theshortest achievable bunch length. Particles emer-ging at the same time from different cathode radiiwill travel through regions containing differentradial field components. As a consequence, thelength of the trajectories for particles emergingfrom different parts of the cathode at thesame time differ although the particle kineticenergies at the RF-gun exit are almost thesame. Such particles cannot be distinguishedenergetically and therefore resist bunch compres-sion, thus limiting the shortest achievable bunchlength.Reducing the cathode diameter, space charge

effects become increasingly evident. An intensepencil beam, for example, does not remain thinduring acceleration in the RF-gun if space chargeforces are included. With decreasing cathodediameter and constant emission current, spacecharge forces from the bulk of the bunch accel-erate particles in the head of the bunch to anundesirable degree. As a consequence, thebunch head follows a longer path in the a-magnetand the time distribution of the bunch headis tilted towards later times with respect tothe rest of the bunch. Such a distribution cannotbe compressed effectively. The choice of anemission current of 2.9A from a 6mm Ø cathodeseems to be optimum while avoiding suchproblems.

ARTICLE IN PRESS


5.1. Beam emittance and particle energy

The particle phase space distribution from RF-gun has the familiar ‘‘butterfly’’-shape due to time-dependent focusing in the RF-field as evident fromFig. 11 [18]. If high bunch intensities are desired, acommensurate increase of the overall beam emit-tance must be accepted. Closer inspection of theparticle phase space distribution in other dimen-sions reveals, however, a significant amount ofcorrelation with particle energy. In Fig. 12 weshow again the results of Fig. 11 (right) but thistime including the finite effect of the thermalcathode emittance. Furthermore, we plot thetransverse phase space distribution only for selectenergy bins of �0:5% to show clearer thecorrelation. Since particles of different energiesare also separated in time, this correlation providesan opportunity for emittance compensation. Acavity excited to produce radial fields (TM011-mode cavity) seems suitable to eliminate, in firstapproximation, the emittance correlation andthereby significantly reduce the overall beamemittance.

The unnormalized slice-emittances for 95% ofthe beamlet intensities including (ignoring) ther-mal cathode emittance are � ¼ 0:35ð0:11Þ;0:42ð0:21Þ, and 0:45ð0:34Þmmmrad for the 2.44,2.36 and 2:29MeV beamlets, respectively, asshown in Fig. 12. A compensation of the apparentemittance increase due to the RF-field in the RF-gun seems very desirable and may be possible withthe use of a TM011-cavity. This possibility is

x (mm)-2 -1 0 1 2

-3

-2

-1

0

1

2

3

2.44 MeV +/- 0.5%

2.36 MeV +/- 0.5%

2.29 MeV +/- 0.5%

thermal emittance not included t

x' (mrad)

Fig. 12. Transverse phase space distribution for 1% energy slices of

included (right). Parameter: kinetic particle energy.

presently under detailed study. In case of such asuccessful emittance compensation one couldexpect an overall normalized beam emittance of2mmmrad compared to 3:8mmmrad withoutcompensation.

6. Summary

Based on PARMELA simulations, we havesystematically investigated the effect of geometricand electric features of an RF-gun with athermionic cathode on electron beam parameters.Specifically, we were interested in the generation offemtosecond electron pulses. Beam characteristicsare greatly influenced by RF-gun design andoperational parameters. By proper design, thephase space distribution can be matched to anideal distribution for the core of the beam, limitedonly by space charge forces. A compromisebetween cathode radius and space charge effectscan be found which produces femtosecond elec-tron bunches of significant intensity. These opti-mization methods have been applied to the designof an RF-gun specially optimized to producefemtosecond electron pulses. Such an electronsource has been built at Chiang Mai Universityand will be being commissioned in 2003 [13].Results from PARMELA simulations show, thatfor this S-band RF-gun, electron pulses with abunch length of s ¼ 52:8 fs rms and a bunchcharge of 94 pCb can be expected. This value doesinclude effects of path length dispersion in the

x (mm)-2 -1 0 1 2

-3

-2

-1

0

1

2

3

2.36 MeV +/- 0.5%

2.29 MeV +/- 0.5%

2.44 MeV +/- 0.5%

hermal emittance included

x' (mrad)

the full beam (Fig. 11). Thermal emittance ignored (left) and

ARTICLE IN PRESS


beam transport line leading from the RF-gun tothe experiment (Fig. 5).

A rms transverse beam emittance of �rms ¼

0:69mmmrad at an average kinetic energy of W ¼

2:35MeV or bg ¼ 5:51 can be achieved for the fullintensity of 94 pCb per bunch. This corresponds toa normalized emittance of �n;rms ¼ 3:17mmmrad.The transverse phase space distribution is corre-lated with the particle energy or time opening apossibility for correction with the use of a TM011-mode cavity.

Acknowledgements

We would like to acknowledge the financialsupport of the Thai Royal Golden Royal JubileeScholarship Program 3.F.CM/41/B.1 (Rimjaem);FAPESP, The State of Sao Paulo ResearchFoundation 97/7523-4 (Farias); the ThailandResearch Fund (Thongbai, Vilaithong) and theUS Department of Energy, BES DE-AC03-76SF00515 (Wiedemann).

References

[1] M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M.M.

Murnane, H.C. Kapteyn, Phys. Rev. Lett. 87 (2001)

025501-1.

[2] D.A. Reis, M.F. DeCamp, P.H. Bucksbaum, R. Clarke, E.

Dufresne, M. Hertlein, R. Merlin, R. Falcone, H.

Kapteyn, M.M. Murnane, J. Larsson, Th. Missalla, J.S.

Wark, Phys. Rev. Lett. 86 (2001) 3072.

[3] H. Ihee, V.A. Lobastov, U.M. Gomez, B.M. Goodson, R.

Srinivasan, C.Y. Ruan, A.H. Zeweil, Science 291 (2001)

458.

[4] R. Bonifacio, C. Pellegrini, L.M. Narducci, Opt. Commun.

50 (6) (1985) 313.

[5] A.H. Chin, et al., Phys. Rev. Lett. 83 (1999) 336.

[6] H. Wiedemann (Ed.), Electron-Photon Interaction in

Dense Media, Kluwer, Dortrecht, 2002.

[7] T. Nakazato, et al., Pattern Recogn. Lett. 63 (1989) 1245.

[8] E.B. Blum, U. Happek, A.J. Sievers, Nucl. Instr. and

Meth. A 307 (1992) 568.

[9] P. Kung, D. Bocek, H.C. Lihn, H. Wiedemann, Phys. Rev.

Lett. 73 (1994) 967.

[10] P.H. Kung, Generation and Characterization of Sub-

Picosecond Electron Bunches, Ph.D. Thesis, Stanford

University, 1996.

[11] H. Wiedemann, D. Bocek, M. Hernandez, C. Settakorn,

J. Nucl. Mater. 248 (1997) 374.

[12] H. Lihn, P. Kung, C. Settakorn, H. Wiedemann, Phys.

Rev. E 53 (1996) 6413.

[13] T. Vilaithong, N. Chirapatpimol, M.W. Rhodes, C.

Settakorn, S. Rimjaem, J. Saisut, P. Wichaisirimongkol,

H. Wiedemann, Proceedings of the Second Asian Particle

Acceleration Conference APAC01, Beijing, China, 2001,

p. 91.

[14] L.M. Young, J.H. Billen, Los Alamos National Labora-

tory, Tech Note LA-UR-96-1835, July 2002.

[15] H.A. Enge, Rev. Sci. Instrum. 34 (1963) 385.

[16] M. Borland, A High-brightness Thermionic Microwave

Electron Gun, Ph.D. Thesis, Stanford University, 1991.

[17] A.W. Chao, M. Tigner (Eds.), Handbook of Accelerator

Physics and Engineering, World Scientific, Singapore,

2002.

[18] Kwang-Je Kim, Nucl. Instr. and Meth. A 275 (1989) 201.

femtosecond electron bunches from an rf-gun

Documents