Nuclear Instruments and Methods in Physics Research A318 (1992) 765-771North-Holland

Compact far-IR FEL designY.C. Huang, J. Schmerge, J. Harris, G.P. Gallerano ', R.H. Pantell and J. FeinsteinDepartment ofElectrical Engineering, Stanford Unirersity, Stanford, CA 94305, USA

A compact size far-infrared free-electron laser (FIR FEL) is currently being built at Stanford . A microwave gun produces 1-3.3MeV electrons, which are sent into a 50 cm long wiggler of 1 cm period through a hole on the upstream mirror to generateradiation at a wavelength of 100 to 1000 Wm . A superconducting solenoid along with an array of permeable material is used togenerate a 9.6 kG rms wiggler field with a 2.0 mm gap . The electron beam consists of 10 ps micropulses with 10 A peak current, I%energy spread and unnormalized emittance for 90% of the particles of 27.- mm mrad. A 10 dB small signal gain has been calculatedwith the parameters mentioned above . An overview of the design details as well as a discussion on the uniqueness of our wigglerare presented .

1 . Introduction

The far-infrared free-electron laser (FIR FEL) pro-ject is valuable in several senses. Today, there are notunable, high peak power, conventional lasers availablein the FIR spectrum. However, the electron energyrequired is low and the beam quality is not critical atthis wavelength for an FEL. With reasonable designparameters, the peak brightness of a FIR FEL over apicosecond time interval can be fifteen orders of mag-nitude greater than that of a black body radiator at 200K [1]. For these reasons, the FIR free-electron laser isa good candidate for a low cost, compact-size lasersource .A compact size far-IR FEL is currently under con-

struction at Stanford University. Fig . 1 illustrates thelayout of this device. A 7.8 cm long microwave gundriven by an S-band klystron at 2.856 GHz produces1-3.3 MeV electrons, which are sent into the wigglerafter passing through a 1% energy selection slit . Theoverall dimensions of the device are estimated to be1.5 x 2 m2.A solenoid derived wiggler [2] is employed. Such a

wiggler has several advantages over conventional wig-glers : high wiggler fields can be obtained with a shortwiggler period ; wavelength tuning can be achieved byvarying the solenoid field ; electron trajectories are lesssensitive to dimensional and alignment errors; and thelongitudinal field provides additional focusing for theelectron beam.

The microwave electron gun has been designed andtested at the Stanford Synchrotron Radiation Labora-

I Permanent address : ENEA, INN-SVIL, P.O . Box 65-00044,Frescatti, Italv.

0168-9002/92/$05 .00 0 1992 - Elsevier Science Publishers B.V . All rights reserved

tory (SSRL). According to the experimental data col-lected at SSRL, low emittance, low energy spread, andhigh output current are obtainable. This electron gun,along with the solenoid derived wiggler and a 2 mmwave guide gap, should result in a 10 dB small signalFEL gain across the FIR band.

With 50 wiggler periods and 1% assumed efficiency,the peak optical power over 10 ps is 0.33 MW. Whenaveraged over a 3 Rs macropulse, the correspondingoutput power is about 10 kW. At a 10 Hz repetitionrate for the macropulse, this results in 0.3 W of aver-age power. Although the slippage between the groupvelocity and the electron velocity gives a reductionfactor of 2.5 on the small signal gain, the effective

sphericalmirror

irüririnnniiinnûioüvivüûni

nnnnnnonunuuuuunnuun

Solenoid-DerivedWiggler

ou Ouadrupoles

:sowing

FT

NUCLEARINSTRUMENTS8rMETHODSIN PHYSICSRESEARCH

SectionA

Fig. 1 . The compact far infrared free-electron laser layout .After electrons are emitted from the rf gun, they are trans-ported to a solenoid derived wiggler via a hole on the upstream mirror . The slit between BM1 and BM2 defines a 1%

energy spread.

IX. UNCONVENTIONAL SCHEMES

766

wiggler length will also be reduced due to the slippage .Therefore, an efficiency increase by a factor of three isestimated at saturation .

To simplify the transportation of the electron beam,an optical resonator with a hole on the upstreammirror will be used. Because of the large small signalgain, the output coupling loss due to the hole (about20%) and the finite size of the mirror is not expectedto significantly affect the buildup time of the oscilla-tion .

2. icrowave electron gun

In the far-IR FEL design, we employ an S-bandmicrowave electron gun [3) with a thermionic cathodedeveloped by SSRL and Varian Associates. The cross-sectional view of this rf gun is shown in fig . 2. Basically,it consists of a 7.8 cm, a half and a full cell standingwave cavities and a side coupled cavity. The side cou-pled cavity is used to introduce the correct phase andamplitude relationships between the half and the fullcell such that an electron will receive the maximumacceleration. With 5.4 MW of input power from theklystron, this electron gun is capable of producing 3.3MeV electrons which is sufficient for our FIR FEL andno further acceleration is necessary. Approximately

Halfend cell

YC. Huang et al. / Compact FIR FEL design

Side coupled cavity(rotated 90° for ciority)

Fig . 2. Cross-sectional view of the rf gun with thermioniccathode . The output beam energy is 1-3 .3 . MeV, which issufficient for FIR oscillation, no further acceleration is neces -

sary .

W

A

cW

Edm

0.2

0.4

0.6

0.8

10Wavelength (mm)

Fig. 3. Electron beam energy versus wavelength. If a 9.5 kGwiggler field and a 1 .0 cm wiggler period are assumed, the

tuning range is from 160 to 1000 wm.

30% of the particles are contained in a 1% energyspread over a 10 ps micropulse . Tuning of the FIRFEL from 160 to 1000 Rm is achieved by varying theelectron energy from 3.3 to 1 MeV as shown in fig . 3assuming a 1 .0 cm wiggler period and a 9.5 kG rmswiggler field . The wavelength range from 100 to 160Wm can be tuned by adjusting the wiggler field in thesolenoid derived wiggler.A high-performance, impregnated-tungsten dis-

penser cathode is installed in the rf gun. The cathodehas a wide current density tuning range up to 140A/cm-. Although the designed peak current at y = 7.5for our FIR FEL is 10 A at a microwave power of 5.4MW, which corresponds to 13 A/cm- on the cathode,one can easily double or triple the peak current bypumping in more klystron power. The input power isnot necessarily proportional to the output current sincethe cavity loss stays the same for a given acceleratinggradient . For example, 7.3 MW of klystron power issufficient to double the current. A 5 dB coupler isemployed to couple out 8 MW of power from a 25 MWklystron into the gun. Therefore, the small signal gain,which is proportional to the current, can be expectedto be well above 10 dB .

Computer simulations show that the unnormalizedemittance for 90% of the particles after the energyselection slit is about 2 -rr mm mrad, and the energyspread is less than 0.8% with a 10 A current over the10 ps micropulse . Since the required beam quality isinversely proportional to the optical wavelength, themaximum unnormalized emittance and energy spreadwhich can be tolerated for a 100 p,m FEL can becalculated to be around 30 -rr mm mrad and I%, whichare considerably higher than those of the availablebeam . In view of ?.his, it is not necessary for our FIRFEL to use a laser-driven photocathode which greatlyincreases the system complexity and cost without signif-icant improvement in the performance of the device .

3 . Transport line design

The design goals for the transport line are : confinethe electron beam on axis and minimize the secondorder aberration ; filter the beam down to 1% energyspread with good energy resolution between the twobending magnets BM I and BM2 (refer to fig . 1); andintroduce electrons at the appropriate entrance anglesand positions into the solenoid wiggler .

As soon as the electrons are emitted from the gun,a FODO array, QF1 to 0134, is used to confine thebeam. A monochromatic beam is focused horizontallyby forcing the beam to enter and exit perpendicular tothe edges of the first bending magnet (BM 1). Thehorizontal (x) dispersion reaches its maximum at QF5,where an energy selection slit is placed in order tofilter the beam to a 1% energy spread .

For matching purposes, we have used the computercode MAD [4] for a preliminary beam line design . Wehave approximated the fringe field of each quadrupoleby breaking it into ten constant gradient sections in theMALE si:nula=ions. This approximation is as good asbreaking the fringe field into 50 sections [7]. In thecomputer simulation, a 12 cm bending magnet, BM1,focuses ß .r (the Twiss parameter) into a waist at the slit(right before QF5), where horizontal dispersion Dxreaches its maximum . A good energy resolution(EBA) 1,1-/Dr = 0.04% [8] can be achieved, if the unnor-malized emittance E = 20 ir mm mrad is assumed forthe whole beam before passing through the slit. Afterextracting data from a gun code MASK [5], particlesare then propagated through the lattice designed inMAD by using a tracking/integrating code ELEGANT[6] . Approximately 30% of the particles emitted fromthe gun pass through a 3 mm slit producing a beamwith 0.8% energy spread and no second order aberra-tion is observed . Immediately after the slit, QF5 fo-cusses the dispersion to zero at the end of BM2; thesymmetrical properties of the beam with respect to xand y (vertical dimension) coordinates are thus pre-served . QD4 also introduces a waist in the verticaldimension at QF5 such that the beam size in the ydimension will not grow dramatically after QF5. QD6and QF7 are placed right before the solenoid to intro-duce the proper entrance angles and positions on theelectrons . This issue will be discussed in section 5 .

4. Solenoid derived wiggler

Rather than use the conventional hybrid wiggler, weemployed a solenoid derived wiggler for our FIR FEL.As shown in fig . 4, high permeability iron blocks andnonmagnetic materials are arranged alternately insidea superconducting solenoid . The center of each ironpole on the top array is aligned to the center of each

Y.C. Huang et al. / Compact FIRFEL design

B fiela

2 ,Trkw =

A,

w

nonmagneticmaterial

2BO sin(f-rr)B1

sinh(g-rr/A w)

fzr

'

767

Fig. 4. Iron poles in a staggered array deflect the longitudinalfield in a superconducting solenoid . There are two majorcomponents of field in this wiggler: longitudinal field and

wiggler field.

nonmagnetic spacer on the bottom array. The wigglerfield is derived by deflecting the solenoid field towardthe staggered iron poles so as to produce an alternat-ing transverse field . With this particular design, thereare two major field components existing in the wiggler:the longitudinal field and the wiggler field .

In addition to the betatron focusing, the longitudi-nal field is useful in providing additional focusing toconfine electrons in a small vertical dimension . There-fore, the gap can be significantly smaller than in theconventional hybrid wiggler and hence the small signalgain is greatly enhanced.

The B field inside the staggered wiggler can beobtained by solving the Laplace equation subject toappropriate boundary conditions . The solution [2], tofirst order, is

Bo is the solenoid field, g is the waveguide gap, Aw isthe wiggler period, and f is the ratio of the nonmag-netic spacer length to A,,, .

As one can see, the amplitude of the wiggler field,B1, increases monotonically with decreasing f. How-ever, the saturation on real iron poles will set a limiton the maximum achievable wiggler field . By simulat-ing our wiggler with 1010 steel poles in the computercode POISSON [9] for a wiggler period of 1 cm and awaveguide gap of 2.0 mm, the peak wiggler fields onthe axis as a function of f are plotted in fig. 5 . Whenthe iron poles are partially saturated, there is an opti-

1X . UNCONVENTIONAL SCHEMES

B,.= -B1 sin(kwz) cosh(kwy), (1)

Bz = B(I - Bl cos(kwz) sinh(k,, y), (2)

where

768

-2sed

-5000

-10000

-125ee

Fig . 5. Wiggler field versus f for 101() steel with solenoid field7.5 kG. When the pole pieces are partially saturated atf = 0.4, B. reaches the peak value of 11.4 kG. With Vana-

dium Permendur. the peak field should reach 13.7 kG .

mal value of f= 0.4 corresponding to a rms wigglerfield of 8.0 kG. However, a 9.6 kG rms wiggler field,corresponding to a wiggler parameter of 0.9 for a 1 .0cm wiggler period, can be expected for VanadiumPermendur, whose saturation field is about 20% higherthan that of 1010 steel .

One can also apply similar boundary conditions,and calculate the magnetic energy contained in thewiggler for different configurations. The shear force

r

5 10 IS 20 25 33z (rruU)

YC Huang et at. / Compact FIR FEL design

Fig. 6 . The distorted magnetic field profile due to the manu-facture error on one iron pole of the stagered wiggler. Ingeneral, no matter whether the pole is shifted horizontally orvertically, the field profile is affected symmetrically in a fullwiggler period as long as it is operated at the flat portion ofthe B,y vs f graph . The electron phase an trajectory are not

sensitive in this symmetrical field profile .

along z is the gradient of this energy with respect tothe lateral displacement 4 in the z direction . Theforce is given by,

aw

/Aw=a= 2B1;

w ~sinz(nf )AO rr

where 1 is the iron pole width, and W is the totalstored magnetic energy .

Coincidentally, the lowest energy configuration is atA = 0, the desired position . This is evident from thefact that F, is opposite in sign with 4 . Therefore, afterthe current being supplied to the solenoid, the top andbottom arrays will align properly .

Another interesting feature associated with thisnovel design is that the electron phase and trajectoryare not sensitive to manufacture errors on the polepieces . Fig . 6 shows that if there were one defect ironpole somewhere inside the staggered wiggler, the fieldprofile would in general be affected symmetrically withrespect to the Bw = 0 line ; whereas, this is not the casefor the hybrid wiggler as shown in fig . 7 . This phe-nomenon is not only true for shifting the pole verticallyor changing the pole size symmetrically with respect to

:Z~30

laraa

-Sae

SZ90

.! ~1cO

3

-a5aa-5000

-leeaa

-1 ;5a0

Stn(2nTr4/A w ) Sln(t1w )X

sinh(g2n rr/Aw ) '

z (mm)

n

Fig . 7. In a hybrid wiggler, if one pole is shifted vertically orthe size is changed evenly with respect to the center of thepole, the field profile is changed mainly in a half wigglerperiod . If there is a lateral shift on the pole, the field profilenearby will be distorted . It is evident that the first and secondintegral of the wiggler field along z will not be zero; in otherwords, phase slippage and walk-off will occur with this type of

error.

the center position of the pole, but also true for smalllateral movement, provided that the wiggler is oper-ated at the flat portion of the wiggler field versus fcurve . As one can see from fig. 5, at f= 0.4, smallvariations in f produce similar decreases in the fieldstrength . Since the field profile changes symmetricallyfor a full wiggler period, whatever the unbalancedforce electrons see on the first half period will becounterbalanced by the next half period. As a result,the first integral of the wiggler field with respect to zwill be zero . With this superior property, there will notbe any phase slippage caused by fabrication errors, andthe electron trajectories are considerably less sensitivethan those in conventional hybrid wiggler.

In addition, one can easily change the wiggler fieldby tuning the current in the solenoid. A 2 T supercon-ducting solenoid, capable of maintaining magnetic fieldfor two months with very low power consumption, hasbeen fabricated for our project . For y = 3.0, about50% wavelength tuning can be achieved without de-grading the small signal gain .

5. Electron trajectories

As mentioned previously, there are two major com-ponents of magnetic field inside the stagered wiggler :one is the longitudinal field in z direction and theother one is the wiggler field in the y direction . The xand y trajectories can be described by

in -yd'-x

d__y

d-y

dx11. 7

, = -9B~- .'.t -

dtTo simplify the trajectory analysis the following

conditions are imposed :1) The electrons stay close to the axis such that B_

in eq . (2) approximately equals B0~, and B,. is expressedas in eq . (1).

2) V,

the

longitudinal

velocity,

is

a

constant,namely, the velocity of light .

Then, the x trajectory is the superposition of thecyclotron motion and the wiggler motion, and the ytrajectory is the cyclotron motion, ifA c >> Aw,

where A c = 27rV_/w,, and w c is the cyclotron fre-quency. In other words, if B0 does not induce toomuch transverse motion on the electrons, the two mo-tions (cyclotron and wiggler motions) can be decou-pled . Since the induced rotational energy and hencethe equivalent energy spread are undesirable, usually,this approximation holds by introducing proper anglesand positions to the electrons entering the wiggler.

Y.C. Huang et al. / Compact FIR FCL design

Typically, A�,/Ac is about 0.1, provided the entranceangle is less than several milliradians .

To suppress the cyclotron motion, it is importantthat electrons follow the magnetic flux lines into thesolenoid . Otherwise, two unfavorable situations willoccur :

1) Electrons at different positions will cut differentamounts of flux and result in an equivalent energyspread .

2) Electrons gain too much transverse velocity andfall out synchronism.

Because the wiggler motion and the cyclotron mo-tion can be approximately decoupled, the second inte-gral of the wiggler field along the longitudinal directionis proportional to the electron walk-off, provided thelongitudinal velocity is much higher than the transversevelocity. By actually using the field data provided bythe manufacturer, we found that the slowly varyingsolenoid field is critical . To achieve the adiabatic entry,we insert a 0.2 cm thick, 5 cm long iron tube into theupstream end of the cryostat. Most of the electronwalk-off can be eliminated by this scheme . However,since the wiggler field is a hyperbolic cosine function inthe vertical dimension, electrons entering off axis willnot see a slowly varying field . The entrance conditionsof I y 15 0.4 mm and y'/y = -10 mrad/mm (corre-sponding to a focal length of 10 cm) on the electronphase diagram at the entrance are necessary to mini-mize the walk-off problems. It is also understandablethat, because the wiggler field is independent of x (aslong as the electrons stay close to the axis), the elec-tron trajectory is less sensitive to the x, x' entranceconditions . Fig . 8 illustrates the x and y trajectoriesfor two off-axis particles with different entrance anglesin the y dimension and the same conditions for y, xand x' . The trajectory (Y,, X,) correspond to entrance

EE 0

_20

~4 ~I y~l ~9 I I

~I I ~~ I

lr1.Aa

i+~i t~~~4 x,

z (-)

solenoidReld

769

Fig. 8 . Electron trajectories for two different entrance condi-tions: (X,, X,', Y,, Y;) = (0.5 mm. 0.0 mrad, 0.5 mm, 0.0rwad), and (X,, X2, Y,, Y,) = (0.5 mm, 0.0 mrad, 0.5 mm,-5.0 mrad). The proper entrance angle Y, =5.0 mrad reme-dies the walk-off problem at Y = 0.5 mm. In general Y'l Y=-10 mrad/mm is desired for removing the electron walk-off.whereas the X, X' entrance conditions are not important,

provided they are small.

IX . UNCONVENTIONAL SCHEMES

770

x (mm)Fig. 9. The computer simulation result of the electron beam atthe center of the wiggler. y is the vertical dimension, and x isthe horizontal dimension . The electron beam diameter in they dimension is squeezed by the solenoid field from 2.0 mm,the waveguide gap, to 0 .-4 mm. However, slight walk-offcausesthe beam to spread in the x dimension, and reduces the spacecharge. The optical mode waist is 4 mm in the x direction.

condition Y'= 0.0 mrad and y, = 0.5 mm; whereas,(Y, X,) entrance condition is y' = 5.0 mrad and y =0.5 mm. It is evident from the plot that the properentrance angle y' = 5.0 mrad at y = 0.5 mm remediesthe walk-off problem.

The total length of the solenoid designed for our farIR FEL is 1 .0 m with the central 50 cm containing theuniform field. Because there is a finite emittance asso-ciated with the rf gun, only part of the electrons can beconfined at the correct region on y, y' phase plot atthe entrance . Slight transverse drifting for some parti-cles unavoidably occurs . Because of the large waist ofthe far-IR mode, computer simulation shows that es-sentially no electron walks out of the optical mode inthe wiggler section . The slight walk-off is actually bene-ficial to reduce the space charge . Fig. 9 illustrates theelectron beam size at the center of the wiggler . It isinteresting to see that the beam radius in the y dimen-sion is squeezed from 1 .0 mm (half of the waveguidegap) down to 0.2 mm by the solenoid field, and theelectrons in the x dimension are well confined in the± 4.0 mm optical mode.

6. Optical cavity

For satisfactory performance, several considerationsare made for the interferometer design . High gain, lowloss and easy extraction of the optical power are themain concerns ; simplifying the electron transportationand saving space is also desirable . Although the longwavelength of the FIR provides a large mode area forthe electrons, the large diffraction angle, which walls if

Y.C. Huang et al. / Compact FIR FEL design

care is not taken . Therefore, it is advantageous toplace a cylindrical mirror with a hole at the beginningof the waveguide . The hole serves to both allow theelectron beam into the wiggler and to couple theoptical power out .

The top view and side view of the resonator setup isdepicted in fig . 10 . The waveguide geometry gives riseto a Guassian mode in the x dimension and a cosinemode in the y dimension [10] . The presence of thehole requires a superposition of the Guassian modes inorder to null the field at the hole [11] . The taperedwaveguide on the downstream side is mainly for pre-venting electrons from hitting the guide walls after theyemerge form the solenoid field. It also eliminates thediffraction losses in the y dimension and allows the useof a spherical mirror if the correct angle for the taperis chosen. It should also provide radiative loss for thesynchronous low frequency mode which occurs nearthe A = 4 mm cutoff of the guide.

In addition, placing a hole on the mirror can savethe extra cost of two bending magnets, reduce themirror damage due to the high peak power, and canincrease the small signal gain [11] . A detailed study forour interferometer is being carried out . Further work isnecessary for optimizing the field inside the wiggler byvarying the Rayleigh length, the hole size, and themirror diameter .

6. Summary

A compact FIR FEL with tuning range from 100 to1000 p.m is being constructed at Stanford.

With the design parameters mentioned above, a 10dB small signal gain is calculated . If 3.0% efficiency isassumed, the peak optical power is expected to be 1MW.

sideview

topview

wiggler/waveguide

Fig . 10 . The side view and the top view of the optical cavity. Acylindrical mirror with one hole is placed at the upstream endfor propagating electrons directly into the wiggler, and ex-tracting optical power . Since the electron beam size blows upat the downstream end, a spherical mirror is provided after a

short tapered waveguide .

The overall dimension from the electron gun to theend of the optical cavity is estimated to be about1.5 x 2 m2. The total cost of the er tirc system isexpected to be less than $300000 . Currently, we arebuilding the beam line up to the slit position for testingthe beam properties in October, 1991 . Completion ofthe FEL is scheduled for the following year.

Acknowledgement

The work reported in the paper is supported by theCalifornia Competitive Technology Program, and Var-ian Associates . The authors are especially appreciativeof Michael Borland for consulting on the beam linedesign .

References

[Il R.H . Pantell, Radiat . Eff. Def. Solids 122&123 (1991)571 .

Y. C. Huang et al. / Compact FIR FEL design 771

[2] A.H . Ho, R.H . Pantell. J . Feinstei n and Y.C. Huang.IEEE J . Quantum Electron . QE-27 (1991) 2650.

't3] E. Tanabe . M . Borland, M.C. Green, R.H. Miller, L.V.Nelson, J.N. Weaver and H. Wiedemann, SLAC Publica-tion 5054, SLAC, August, 1989.

[4] F.C . Iselin and J. Niederer, Technical ReportCERN/LEP-TH/88-38, CERN, July, 1988.

[5] A.T. Drobot et al., IEEE Trans . Nucl . Sci . 32 (1985)2733 .

[6] M . Borland . ELEGANT: a matrix/integrating code forthird-order tracking. to be published.

[7] M. Borland, Ph.D . Dissertation, Stanford University.Stanford, CA, 1991, p. 263 .

[8] H . Wiedemann, Lecture notes of course given in Fall1987, Stanford University, Applied Physics Department,1987 .

[9] Los Alamos Accelerator Code Group, User's guide forthe POISSON/SUPERFISH group of codes, LosAlamos, NM. January 1987.

[10] L . Elias and J. Gallar, Appl. Phys. B3 (1983) 229.[11] R.H . Pantell, J. Feinstein and A.H . Ho, Nucl. Instr. and

Meth. A296 (1981) 638 .

IX . UNCONVENTIONAL SCHEMES