CHARACTERISTICS OF LONGITUDINAL WAKE FIELD
AT THE KEK POSITRON GENERATOR LINAC
M. Takao, *Y. Ogawa, *T. Shidara and *A. Asami
Japan Atomic Energy Research InstituteTokai，Ibaraki 319-11，Japan^National Laboratory for High Energy Physics (KEK)
Tsukuba，Ibaraki 305, Japan
ABSTRACTA detailed experimental study on the longitudinal wake field characteristics of a hignintensity muitトbunched electron beam was carried out at the primary electron section of theKEK positron generator linac. The observed energy spectrum, which indicated the bunch-tobunch energy variation, was explained by the longitudinal wake field effect. In the nnmericalestimation of the energy loss due to the longitudinal wake field, the importance of the indi­vidual bunch length was noted.
1。Introduction
Future e+e 一 linear colliders for high energy experiments in TeV region require highluminosity. For the purpose of achieving the required luminosity, it is intended to increase
the number of particles in a bunch, or to raise the repetition rate of the acceleration. But theincrease of the luminosity by these methods is restricted by the available wall plug power. The
multi-bunch acceleration, where a bunch train is accelerated in a RF pulse, can improve boththe luminosity and the efficiency of the power transfer from RF to a beam. The drawback of
the multi-bunch is the instabilities caused by the wake fields, which are the electromagnetic
fields excited by the interaction between the beam and the envelopment. It the bunch train
travels along the off-axis o f the accelerating structure, it induces the transverse wake field
as well as the longitudinal one. Transversally, the wake field kicks any trailing particles,
and then brings about a cumulative beam breakup. On the other hand, a longitudinal wakefield extracts energy from the accelerating field, leading to a variation m the beam energies.
Although the problems related to the single-bunch phenomena have been studied by several
people [1], there have so far been few investigations on the multi-buncii phenomena of highly
intense bundled beams*
The positron generator linac at KEK [2] has a nigh intensity primary electron beam,
which is bunched and accelerated to 250 Me V" by an RF field. The beam is split into 5-6bunches with the electric charge of a few nano Coulomb, respectively. A series of experimental
studies on the wake field characteristics of the KEK positron generator linac has been carriedout [3]. In tins paper we discuss ihe longitudinal wake field chairacteiistics of the high-intensity,mnlti-bunclied beam. The energy spectrum of such a multi-bunched beam is measured at theenergy analyzing station and compared with numerical analysis by using the computer code
TBCL
2. Results and Discussions
The measurement of a nigh-current multi-bnnched beam at the above-mentioned energy
analyzing station gave the energy spectrum shown in Fig.l. There are several peaks in thespectrum which, correspond to bunches. The bnnch-to-buncli energy difference, which should
be attributed to the longitudinal wake field, was estimated by a numerical analysis according
to the following. The energy gains and charges of bunches were determined from Fig.l andare listed in Table 1.
B efore«starting a numerical analysis, we present the basis of enersty extraction by amulti-bunched beam [4]。The assumptions o f our numerical analysis are as follows.

1 ) An accelerating structure o f length L is fully filled with RF power.
2) The attenuation o f the field is negligible, or the structure has a constant gradient.
3) Since the group velocity o f the fundamental m ode Is a few percent o f the speed o f light,
we neglect the propagation o ffundamental wake field, com pared to the structure
length.

theAfter all the total energy gain o f the n-th bunch is given by.

n—1^En/eL = Sq - kqn — 2 Y,，

(1)

m = l

where

qm is the charge o f the m -th bunch, and k the loss factor, £q the field gradient. Since

the loss factor is a function of the bunch length, aZ} it can assume different bunch-to-bnnch.
values if each bunch possesses its own lengthy respectively.
We now compare the experimental result with, a numerical analysis. W e evaluate thelongitudinal wake field by means of theAlthough the structure of the KEK

TBCI-code.

positron generator linac is a quasi-constant gradient5the evaluation was performed by assum­
ing a constant impedance structure. Figure 2 shows the calculated longitudinal wake field
excited by a bunch of length 7.5 mm, whicn is a probable bunch length ot the KEK positron
generator linac. In order to obtain a loss factor of constant gradient structure, we calculated
the corresponding wake fields o f a constant im pedance structure using various apertures andthen average them. Assuming that all of the bunches have the same bunch length. (7.5 mm)
and using the expression for the energy gain ( 1 ) with the calculated loss factor, we thenobtained the energy spectrum shown in F ig.3(b).
To improve the numerical estimation，we include the higher modes o f longitudinal wakefield. To this end, we computed the loss factors at the positions of the trailing bunches, wmch
are listed in Table 1 . Note that the loss factors at the following bunches are almost double
the single bnncn loss factor, as expected. The difference is ascribed to the Higher modes ofthe longitudinal wake field. Using the modified loss factors, the energy spectrum (c) in Fig.3
is compntedo
T he measured energy spectrum can be partly explained by a numerical analysis. Toobtain a better agreement between the experimental and numerical investigations, we needto obtain the precise information concerning the bunch length. This implies that keeping theenergy o f bunches in Mgh precision requires ns to closely control the bunch lengths o f theismlti-bniLclied beam .

References[1 ]K. Bane，C. Adolphsen, T.L. Lavine, M. Ross, J. Seeman and K. Thompson, Measure­ments oi ijongitudinal Phase Space in the SLC Jbmac.

Proceedings ofthe 1988 Linear Accelerator Con­ference^ Williamsburg, VA, U.S.A., 1988; A. Enomoto, I. Sato, A . Asami, G, Horikoshi[2] A . Asam i and the Electron linac Group, inand J. Tanaka, NucIJnstrum.Metliods. A 2 8 1 ,1(1989).
[3] Y. Ogawa, T. SMdara, H. Kobayashi Y. Otake and G. Horikoshi, KEK Preprint 89-76(1989); Y. Ogawa, T. Shidara, H. Kobayashi and A. Asami, in Proceedings of the 1990
Linear Accelerator Conference^ Albuquerque, NM, U.S.A., 1990.
[4] R. Ruth, SLAC-PUB-4541 (1988).

Bimch123456Table 1 . List of bunch characteristics
Loss Factor
Energy Gains (MeV) Charges (nC)1255.2，6251.17245.3239.49236.244233.9(xlO 13 V /C /m )
1.8
3.4
3.3
3.4
3.5
3.2

Figure 1 .Energy spectrum measured at the energy analyzing station.

22 x
S/O /A
0.6

0.S

Distance from Bunch Center (m)Figure 2. The longitudinal wake field of the KEK positron generator linac excitedby a bunch 7.5 mm long.
'MeV250 •240 -230 -(a)(b)(c)

Figure 3. (a) Energy spectrum measured, (b) Energy spectrum computed notincluding higher modes, (c) Energy spectrum computed with Higher modes.