A LINEAR COLLIDE R IN THE TBA SCHEME
USING MICROWA VE FREE ELECTRO N LASERS
J.Kishiro, K.Ebihara, S.Hiramat su, Y.Kimura, H.Kurino* ,T.Monaka, T.Ozaki and K.Takayam a
National Laboratory for High Energy Physics
1-1, Oho, Tsukuba, Ibaraki, 305, Japan(*) Departmen t of Physics, Tohoku University, Sendai, 980, Japan

Abstract
A 500 GeVx2 high energy linear collider in the twobeam accelerator scheme (TBA) has been conceptuallydesigned. The collider can be realized by employing a
multi-stage free electron laser (FEL) as a extremely
high power microwave source. The stability analysis
for a klystron-typ e FEL in the microwave regime isalso described in this article.
Introduction
An accelerator for the high energy physics is requested to increase its energy up to more than 500
Ge V. The size of such a high energy linear collider
might be more than 30 km and the number of rf
sources, such as klystrons, increases to several tens of
thousand, if we take conventional technologies. A linear collider employing the free electron laser (FEL)
in a multi-stage configuration driven by an induction
linac -was proposed by A.M.Sessler 1 , which is called atwo beam accelerator (TBA). A successful single-stage
experiment of the FEL had been carried out for therf frequency of 35 GHz, and the possibility to obtainan 1 GW rf power was also demonstrate d 2 . This indicates that the FEL in the microwave regime is one ofmost promising instruments as a GW order powerful
rf source in a future high gradient linac. The collider
size might be reduced down to 4 km and a high efficiency of the multi-stage FEL enables us to realize
such high energy collider because of the low primaryelectric power requirement.
A new version of the multi-stage FEL, klystron-typ e
FEL (KFEL), has been also proposed 3 to overcome
the difficulties intrinsic in the original version, where
the amplified rf signal is removed out in whole at theend of the each stage and the input small signal is
fed into the stage independently. An intrinsic-featureof the longitudinal stability of the multi-stage KFEL
has been manifested by the macroparticle model 4 •5 ,which enables us to design a 500 GeVx2 linear collider
employing a multi- stage KFEL as a high power rfsource.
How far can be propagated a kilo-ampere FEL driving electron beam in the steady-state regime, that is
an essential key issue of the TBA scheme. The strong
beam break-up instability (BBU) and the resistive wall

instability 6 has to be investigated and overcome tomake the long distance propagation of a high current
electron beam possible. The beam transport in thelaser assisted ion focusing regime (IFR) might be apromising scheme to avoid these instabilities becauseof its strong non- linear focusing force.
A R/D work for the linear collider in the TBA/FEL
scheme started at KEK and the construction of asingle-stage X-band FEL test stand has been completed, which is driven by an induction linac energizedwith two magnetic pulse compressors. The feasibility of the IFR has been also demonstrate d in this test
stand 7 .
Linear Collider in the TBA/FEL
In contrast to the conventional klystron, the FEL
easily generates the rf power of order of GW capable of producing the accelerating field of several hundred MV fm. The breakdown limit is expected to beso higher than 1 GV /m at 30 GHz 8 •9 that we take theaccelerating gradient of 300 MV /m at 17 GHz. The
rf frequency of 17 GHz seems to be adequate by taking into account the local over voltage less than 500
MV /m, because to reduce it the attenuation factor r
should be less than 0.9 and the restriction tor requires
the rf frequency less than 18 GHz.
The filling time T J of the accelerating structure isstrongly limited because of the short pulse duration ofthe FEL driving beam, it takes about 100 nsec so T 1
is assumed to be 90 nsec in this design.
The optimization of the required rf power in thelinac has been done by using the expression developedby Z.D.Farkas 10 , and shows that the peak power in aunit length ofthe structure is minimized and given as
follow:
3~72/3p,( Lo )min = 7.03 1 _ e_,. 2 r,(ns)[Eo(G VfmW (1)yEquation (1) shows the minimum peak power for thecase of a/).. = 0.0939, where a and ).. are the cavity aperture and the wavelength, respectively, and thegroup velocity in the unit of light velocity is taken tobe v9 / c=0.809 %. The smaller is the group velocity,
the shorter accelerating section we have to make, sothat it should be taking into account of the practicalsize of the section.

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•ICOLLISION
POINT

-300m
(--.100 FEL STAGES)(MULTISTAGE FEL)(.vJOO MeV/m)( -12.5 MeV)
2.6 KA

Fig.1

Conceptual illustration of the 500 GeVx2 linear collider in the TBA/FEL regime.

The most significant parameter is af>. which shouldranges from 0.094 to 0.163 in order to minimize thepeak power. According to this range, we take af>. =0.134 which provides the section length of 75 em. Thisdesigi)._fit a practical FEL period length, 3 m. The
output power larger than 2.6 GW should be generated
in each FEL stage and divided into four to energize
the 75 em accelerating structure.
Fig.1 illustrates the conceptual design of the 500
GeVx2 linear collider in the TBA/FEL concept employing the multi-stage KFEL, which is driven by aninduction linac of Eo ""'14 MeV with ""'100 nsec pulsewidth. Since the multi-stage FEL performance is madeefficient by driving a bunched beam, a buncher FEL isplaced at the upstream of the normal FELs. The wiggler field has a constant gradient taper, which provides
either the rf power enhancement and the longitudinalbeam stability. It has to be re- compensated the beamenergy, LlE =1 MeV, which goes into the rf power ineach FEL, by employing a induction accelerator unit.
A period of the FEL stage has the length of 3 m, inwhich 1.3 m is occupied by the wiggler magnet andthe remnant is reserved for both the energy compensation induction unit and the instruments for rf/beammonitors.
Stability of the KFEL

and phase may cause the difficulties in the desired linac
performance.
To manifest essential features of the longitudinalstability4 and output rf phase's sensitivity against injection errors 11 , we have developed extensive computer
simulations and the macroparticle analysis where thegain of a KFEL has been proved to be dominated by
the universal gain equation:y 11 = -ve- 2Y- (y')2 + e- 2Y- 2(y') 2(2)where y is proportional to e. (normalized signal field)
and primes represent the derivative with respect tothe normalized wiggler distance s. Following themacroparticle approach in Ref. 4, the spatial evolution of beam energy, pondermotive phase, and output
rf phase are described in recursion forms from period
to period:n+l _Ian _- Ia~[eZoJ] a!(O) exp [2y(ib(l~)iLw)] Ll
4 mc2 (1:;)2ib(l:;)i2+ It/J~+l = t/J~ -ib(l~)iLw + fl</>.

i(</>.)~ut = (n-1)Ll¢>.+ 0(3)(4)

lbiL ..
e-Y(•)J1- (y'(s))e 2Y(•)ds(5)
The capability of the multi-stage FEL as a rf source
for linac is strongly dependent on the stable rf generation in each stage. The fluctuations in the rf power

where J is a beam current density, Zo is the resistivity
in vacuum, aw is a normalized wiggler field-strength
divided by the wavenumber, Lw is a wiggler length,-188-.D.:y is the energy gain,- lb('Y~)ILw is the beam phaseadvance through the n-th wiggler,respectively. Andeq.(5) has initial conditions:y(o)eye.(O)ex -J-'(O) _ sin .,P~- eY(O)shows that the bunch subject to the periodic transient
process is not destroyed. Thus the intrinsic stabilityof the KFEL has been established.
However, the transit process between the buncher
FEL and the normal FELs is demonstrated only by
a computer simulation, and which shows that a fractional part of the beam is lost due to phase-space mismatching caused from the long tail generated in thebuncher F~;:.::L::....:..:(F:...:i~l!:-:..:::3.!..:)._ _ _ _ _ _ __,'"'

Assuming a current error .t:..J where f:..J = J0 - J,
the recursion formula (3) for a small deviation fromthe designed value 'Yo is written in a linearized form
of:

100•.
80··.

.. ...

60········I

IIIIII

I~0(6)

20(on= 'Yn- 'Yo)8

162~32<O<aS&&4

72 Sloge No.

Fig.3 Trapping efficiency of the driving beamin the multi-stage KFEL

with:

(7)
Its solution is:
On+l = (1-Jlt+l[c5o+(.6.."'{)(.6..J))-(.6..1 )(.6..J) (8)JoJlJoJlThe small deviation is known to reach an equilibrium
6 1 when 0 < Jl < 2. This yields a shot-tostate, - ~JJ 1 0shot fluctuation in the output rf power of lJJ 61 01 . Fig.2
demonstrates how the energy deviation is damped for
f:..J = 0. The output rf power is stabilized in thesimilQ.r. way. Although the fluctuations in the pondermotive phase and rf phase tend to decrease associatedwith stabilizing of 'Y~, the shift in the rf phase ¢. is inevitable due to a combination of eq.( 4) and the initialconditions; however, the shift is less sensitive to injection errors and itsmagnitude is tolerable for a typical~xample. These characteristics have been confirmedwith multiparticle computer simulations.

These loss have to be stational in order to get a
constant rf power in the regular FELs and maintainthe constant phasing of the rf signal. Eventually, theconversion efficiency from the beam power to the rf
power will reach more than 84% for 100 stage KFEL.
Summary
A linear collider of 500 GeVx2 is designed by beeing encouraged by the stability analysis for the beam
bunch in FEL. The linac size can be reduced to about 2km by employing six FEL complexes as the high powerrf sources. The high power of 2.6 GW at 17 GHz is notdifficult to generate if we take FEL, which is driven by
an induction linac of 14 MeV. A combination of theinduction linac and the energy recovery units are energized with the magnetic pulse compressors at a repetition rate of more than 1 kHz and promises a luminosityof ~lx10 33 cm- 2sec 1 in a single bunch operation.
R~FERENGES

1. A.M.Sessler, AlP Conf.Proc. No.91(1982)154.
2. T.J.Orzechowski et a/., Phys. Rev. Lett. 57(1986)2172
3. A.M.Sessler et a/., Proc. lOth Int. Conf. Appl. Ace. inReg. and Ind., Nucl. lnstr. and Meth. 840/41(1989)1064
4. K.Takayama, Phys. Rev. Lett. 63(1989)516
5. A.M.Sessler et a/., Proc. of the XIV Int. Conf. on HighEnergy Accelerator, 1989, Tsukuba, Japan6. K.Takayama, Phys. Rev. A39(1989)184

24.5

7. H.Kurino et a/., Proc. of the XIV Int. Conf. on HighEnergy Accelerator, 1989, Tsukuba, Japan;;.--..........,,!;;-'
1000 ~..,;!

..~~. .
24.o 0!----~20~......;,;
STAGE Ha

Fig.2 Energy deviation damping
in the multi-stage KFEL.

8. P.B.Wilson, SLAC-PUB-2674, 1985

Meanwhile, stability of the bunch shape itself isalso studied by investigating a motion of microparticle
moving around the macroparticle 12 . The motion of themicroparticle around the macroparticle is described bya kind of Hill's equation, and the exact solution of it

10. Z.D.Farkas, SLAC-PUB-4722, 1988

9. R.B.Palmer, SLAC-PUB-4295, 1987

11. K.Takayama, to be published.
12. K.Takayama and S.Hiramatsu, Proc. 11th Int. FEL. Conf.

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