SINGLE BUNCH BEAM LOADING EXPERIMENT ON THE OSAKA UNIVERSITY ELECTRON LINAC
Seishi Takeda, Norio Kimura, Kunihiko Tsumori,
Masaharu Kawanishi, Koichiro Hayashi and Hiroshi Sakurai
Radiation Laboratory,
The Institute of Scientific and Industrial Research,
Osaka University, Suita 565, Japan
Abstract
Experimental study on single bunch beam loading in an accelerating waveguide has been performed. The energy loss of a single bunch passing through an
L-band cavity is estimated to be 1.225 keV InC from the experimental results.
Introduction
When charged particles are accelerated in a linear accelerator, there isnecessarily a transfer of energy from the accelerating field to the particle
beam. This results in a reduction of the total accelerating field in the waveguide. Consequently subsequent bunch of particles travelling down the waveguide will experience less energy gain than the previous bunch of particles
accelerated. This effect, the resultant reduction in the energy gain of laterbeam bunches, is known as beam loading.
For the travelling wave linear accelerator, the beam loading problem should
be considered from the standpoint of superposition theo~em, in which the fields
in the accelerating waveguide can be composed of the following two parts; thefield from the external rf power source, and the field excited by the beam itself. These two fields and their phases can be treated quite independently.
Therefore the energy gain of the beam from the rf power source and the energy
loss due to beam loading can also be treated independently. When a bunch ofcharge Q travels along an accelerating waveguide, total energy gain of the bunch
per one cavity takes the form

U = EgQ - BQ 2 ,(l )where E is the average applied field along the bunch trajectory, g is the effective accelerating length, and BQ 2 is the radiation loss by the interaction ofbeam with waveguide. B is a proportionality factor, the dependence of which ison the geometrical parameters of the accelerating waveguide and the bunch.
Because of the quadratic increase of the radiation loss with the charge Q,
the interest in an accurate evaluation of the loss factor B suddenly rises withthe advent of "the high current single bunch electron linear accelerators" forradiation physics and chemistry. The energy loss to the higher modes of theaccelerating waveguides and of any other st~ucture such as vacuum vellows, vacuum valves, beam monitor devices, should be taken into consideration. The average gain of energy of electrons in a single bunch would reduce linearly withincreasing charge. If the charge of the single bunch is so intense that theradiation loss excesses the energy gain from the accelerating field, it is impossible to accelerate the single bunch to high energies.
Osaka University Electron Linac-301-

-----------------------------The Osaka University L-band Electron Linac has been constructed for studies on picosecond phenomena in radiation physics and chemistry.
The choiceof L-band was mainly determined by the requirement for high current, whichmakes it possible to measure even the weak interaction of beam with material.
A pulsed beam generated by an electron gun is modulated at the sixth subharmonic frequencies of 216.7 MHz by a single gap cavity ( SHPB ) and the beamelectrons are bunched at the end of their drift distance. About half theamount of the injected charge of that cyclic period would be bunched into one
cycle of the basic machine frequencies of 1300 MHz.
In order to produce asingle bunch, the gun pulse should be less than half cyclic period of the SHPB.
A linac injector can generate a pulsed beam of 6A for 3 nS pulse duration.
As a result, a single bunch, the charge of which is up to 14 nC without satellite, or up to 16.5 nC with a satellite ( 7.8% ), can be accelerated to 30MeV.
Sigle Bunch \~aveform
In order to determine the single
bunch waveform, a Cerenkov light radiated from a cell filled with Xe gas ismeasured by an ultrafast streak camera( Hamamatsu C979 and Cl098).
Figure1 shows a typical bunch waveform obtained at the pulse repetition rate of
1.111 pps to avoid the effect of time
jitter. The length of the single
bunch is estimated to be 38 ps at FWHM.

. 30 MEV
12 .. 8 NCOUl.OMB

1.111 PPS

1 DATAtHTUC0.9HS)

T

Energy Spectrum of Bunch
The energy spectrum of the electrons in a bunch is measured by a 90°
PICOSECOND
analyzer magnet, the momentum resolution of which is better than 10- 3 •Fig. 1. Single bunch waveform.
The magnetic strength of the analyzer
magnet is detected with a fluxmeter,
and the current transmitted throughthe exit slit is collected with a
0 0--+-+--+----4-+--t---t-+----t
Faraday cup.
Figure 2 shows threeenergy spectra: the first is for asingle bunch of 12 nC; the second isfor two bunches of 12 nC ( each bunchis 6 nC); the third is for a single.bunch of 6 nC. The spectra show thatthe average energies of the first andthe second bunch are estimated to be
28.6 MeV and 28.3 MeV respectively.
The second bunch gains energy at areduction of l %. The reduction in~nC3.
the energy gain of second bunch is~~considered to be due to beam loading.
770 psIn fact, the total energy stored in
the accelerating waveguide is 18 J,
and the total energy gain of thefirst bunch is evaluated to be 0.17 J .
. The spectra of the single bunch also
Fig. 2. Energy specra of a single
show the difference between the twobunch and two bunches.
cases. When a single bunch has
higher charge, the spectrum shifts toIt seems that the single bunch loses its energy by thelower side of energy.
radiation loss in proportion to quadratic increase of the charge in a bunch.
-302-Single Bunch Beam Loading
If a bunch of electrons excites the waveguide, the average energy of theelectrons in a bunch should be linearly reduced with increasing charge. The
radiation loss was investigated by varying charges. The charge of a. single ·bunch can be easily controlled by adjusting the voltage·of grid-cathode.pulse
and it is measured by means of current integration. Fig~re 3 and 4 show energy spectra of the single bunch for various charges in a bunch. In thesefigures, it is shown that the energy spectrum shifts to the lower side of the·energy with increasing charge.
.n Ef£RCVSI'£CTRU1 UnBe" G.f16 14: B: 7

EtiERGV

SPECTRI.JI't a:a Bit/ G.-'16 14t 8: 7...

Fig. 3 and 4.

The energy spectra of single bunches for various charges.

In order to investigate the dependence of radiation loss on the accelerating field, the rf power and the rf phase into the accelerating waveguide arevaried respectively. The average energies of electrons in single bunches are
p1otted with charges ( see- Fig. 5 and Fig. 6 ) •Slw.!E

E~'=IN~LE

BEM l.OADIHC· EXPElUI'IEHT
2~

0/30 15:37:1-4

~

BEAn

tOAD-.fttC EXPERlrEHT
sa... 51"30 1?: s:-.otG

3S

3t;

DEPEI'IDEHC!; 01"

DEPENDENCE 01'~..
E

M

BEM LOADINGE

BEM LOADINGOH RF- IttPIJTEOH RF -PHASE.

POUER.

A
M-·-·-· -·-·--·-·-•--+•-..-+--.J:.,_'v+--+--t--~--t-+-+M'MEE

u.u

Fig. 5.

Dependence of single bunch
beam loading on rf-input
power.

Fig. 6.

Dependence of single bunch
beam loading on rf-phase.

The timing of a beam injection is also varied in order that in the accelerating waveguide the single bunch may travel through the part where the rf
power is empty. Figure 7 shows the dependence of the average energy of electrons in a bunch on the charge.
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Experimental Results and Discussion

SINGLE

From the data described above. itis evident that the single bunch beamloading never depends on the rf power.
rf phase, or injection timing of thebunch. In other words, it is not todepend on the energy stored in theaccelerating waveguide, but only on thecharge of the single bunch itself.
Accordingly, it is reasonable to consider that the beam loading of single bunchis the radiation loss expressed inEq. ( 1).

BUtCH

BEMl.OADUG

EXPERD'£1'1'f3<V c;..-16 141 s: 730 r-+--+--_,__-+--f--+--+ --+-_.....,•! ~·-·-·-·-·--· -•-•-+--+--'M~ -z--s-a:-L-a:-a:
E ·-•-s-s-a:-z--c-z-*-s-

1.84 MICRO SEC

1.S7 I'IICRO SECRGv ~·-·-·-•-•-.

"EIt might be possible to neglect theradiation loss in the waveguides ofbuncher sections, and then loss factor B
per one cavity, total radiation loss ina cavity, is evaluated to be 1.225 keV/nC.
It has also been reported that the single
bunch of 0.16 nC ( 0.9- 19 GeV) loses energies of 33-45 MeV in 81416 cavitiesof SLAC 1 ) . The loss factors in thesecases are estimated to be 2.5-3.5 keV/nC.

---·-·-·~

1.'38 riiCRO SEC

TIPIING""B£M

ItUECTIOH""""

RF It<PUTFig. 7. Dependence of a single
bunch beam loading on the timing of beam injection after rfinput.

bI_j_ ____ _From the modal analyses for radiation loss of a point charge. it is reported that the radiation loss BQ 2 depends on the geometrical parameters of acavity and on the value of~ as follows;
J... .J..
Q2 g2 ~2BQ 2 -- 0.6(2)7reoat(Lawson)
4Fig. 8. Geometri ca 1 parametersof cavities.
g2Q2
BQ 27reo.za
2d(Kolpakov)(3)
4
where a,g and d are geometrical parameters as shown in Fiq. 8. Assuminq thatthe radiation loss is inversely in proportion to the size of a cavity, it is possible to compare the radiation loss between L-band and S-band cavity. When thesingle bunch of 30MeV passes through aS-band cavity, the radiation loss factor
B is eva 1uated to be 2. 7 keV I nC. Accardi ngly it is concluded that the beamloading of single bunch, that is the radiation loss, is not to depend on theenergy between 30 MeV and 19 GeV.
All the data obtained during the experiment were acquired and proceeded bythe Linac Real Time Data Processing System linked with MELCOM 70/35(160kB) andMELCOM 70/25{128kB).
References
1) R.F.Koontz, G.A.Loew, R.H.Miller and P.B.Wilson, Proc. 1977 PaPtiele AeeelePato.r Conf., IEEE Trans. Nucl. Sci. NS-24, no.3 (1977) 1493.
2) J.D.Lawson, Rutherford High Energy Laboratory Report/Ml44 (1968} unpublished.
3 )O.A.Kolpakov and V.I.Kotov. Soviet Phys. Tech. Phys. 9 (1965) 1072.

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