The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Beam Loading hi. JHF 50 GeV Proton Synchrotron
Ma.<!anobu YAMAMOTO: Tomonori UESUGI! Chihiro OHMORI, Kazuyoshi SAITOt Manabu SOUDM
Shin'ya SAWADA, TetsumiTANABEt, Yoshio TANABE§, Hitoshi NAKAYAMA, Yoshinori HASHIMOTO,Miho FUJIEDA~Shinji MACHIDA, Yoshiharu MORI, Taixuan YAN\1Eiji EZURA 1 , Akira TAKAGI 1 , Makoto TODA 1 , Ma.<!ahito YOSHII 1
KEK-Tanashi, 3-2-1 Midori-cho, Tanashi, Tokyo 188, Japan
1 KEK, 1-1 Oho, Tsukuba, Ibamki 305, Japan
Abstract

Longitudinal particle motion in JHF 50 GeV proton synchrotron have been investigated by computer simulation.
We found that emittance blow up Wa.<! not so serious even
without a beam loading compensation at the present design intensity, but more stable operation becomes possible applying the fundamental and 2nd harmonic rf mode
compensation.
1

quency w component, and Zcav(w) is an impedance ofthe rf cavity.
In eq.(1), Ib(w) is obtained by a Fourier transformation based on a 'revolution frequency. The cavity impedance Zcav(w) is obtained from LCR parallel
resonant circuit. Assuming a peak value of a shunt
impedance of 500 n per cavity, the magnitude of theimpedance IZI is shown in Fig. 1 for various Q values.

Introduction·

FT Cavity Impedance

In JHF(Japan Hadron Facility) proton synchrotron [1],heavy beam loading of rf system is a very severe problem
in rf acceleration because its circulating beam current islarge (Average beam current is 7 A in 50 GeV main ring).
The broad band rf cavity [2, 3] loaded new magnetic
alloy material(MA rf cavity), 'FINEMET', [4] ha.<! beendeveloped and achieved high accelerating voltage of morethan 10 kV /m.
This type of rf cavity is useful to suppress the coupled bunch instability [5] because its quality factor islow(Q "' 1). But, on the other hand, the beam induced voltage is composed of not only fundamental but
also higher order components of the wake field, contrary
to the ferrite loaded rf cavity which only fundamental component is dominant because its quality factor ishigh(mostly, Q > 10).
We have developed a simulation code of the longitudinal motion to investigate the feasibility of the beam
induced voltage compensation.

il=~tOO

soI···

I!

o'-'-"~-'-s-'--'--'--'-t"-o~'-'--"~~2f_,_l_,__._~zs'--'--''--'--'-:'3CJ

Frequency (MHz)Figure 1: The impedance of the broad band rf cavity.
There are seven rf stations each of which consists of2

Beam Loading Simulation

The beam induced voltage is obtained with a frequency
domain calculation.
Vb(w) = Zcav(w) X h(w),four cavities are installed in the 50 Ge V main ring. Thetotal impedance seen by the beam is 14 kn.
The beam induced voltage Vb(w) in eq. (1) is transformed to the time domain voltage Vb(t) through an inverse Fourier transformation.

(1)Vb(t) = LVb(Nwrev}e-iNwrevt

where Vb(w) is the beam induced voltage on the frequency w component, his the beam current on the fre• Also Research Center for Nuclear Physics, Osaka U niv.
t Also Center for Nuclear Study, Univ. of Tokyo.
t Also Hitachi Co. Ltd.
§Also Toshiba Co. Ltd.
'I Also Institute for Chemical Research, Kyoto Univ.
II On leave from The Bureau of Basic Sciences of Academic
China.

(2)

N(N = 1, 2, 3, · · ·)Then, an accelerating voltage Vacc is,(3)
where Vg is the voltage of an rf power amplifier.

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Using Vacc, the synchrotron motion is presented asfollowing equations,= qVacc(iP)- qVg(l/>s)(15if>)turn = -27rh1] fl.p,p(15~)turn

(4)
(5)

The following parameters are used in this simulation.
Ring circumference
Amp. generating voltage Vg
Harmonic number
Initial revolution frequency
Initial energy
Initial tl.pfp
Initial bunch length
Bunch shape
Synchronous phase
Momentum compaction factor a:p
Number of particle per bunch

1445 m280 kV
17201.5 kHz
3 GeV± 0.4 %
120 ns_ec.
parabolla
0 Deg.
-0.0011.25 x 1013

Figure 3: Beam emittance in a phase space after 1000turns under the beam loading.

The Figure 3 shows a beam emittance in a phasespace(dE/ E-¢> plain) after 1000 turns(4.47 msec.). Even
under the beam loading all particles ·still remain in therf bucket, but the beam emittance is slightly collapsed
for the lower quality factor.

Induced Voltage and Gap Voltage

Table 1: JHF 50 GeV main ring parameters.
The number of the macro particle in the simulation
was 5000 per bunch.

100~--~'
100

200300

400

500

600

700

800

0

100

200

300

400

500

600

100

200

300

400

500

600

SIMI

600

700

800

900

Time(nsec.)

100200

300

400

500

6011

700

800

900

400

500

600

700

800

900

Time(nsec.)

900

700

800

0

700

800

100

200300Time(nsec.)

Figure 4: The Compensating voltage for the beam induced voltage.

900

Time(nsec.)

~-~~~
0400

Time(nsec.)t-~·
0300t-~·Induced Voltage and Gap Voltage

0200900Time(nsec.)

Figure 2: Accelerating voltage shift caused by the beam
induced voltage.
The Figure 2 shows how the beam induced voltage(dot line) affects the gap voltage(thin solid line), andthe phase of the gap voltage is shifted. As shown in Fig.
2, the beam induced voltage reachs 220 kV, 200 kV and180 kV in case of Q = 0.7, Q = 1 and Q = 2, respectively. The larger quality factor brings the smaller beam
induced voltage.

The thick dot lines in Fig. 4-are the compensatingvoltages. The compensating voltage is obtained fromthe Fourier analyzed amplitudes and phases of the beam
induced voltages -by integrating up to some higher harmonics. In Fig. 4, the compensating voltage is consistsof the fundamental and the 2nd harmonic component.
As can be clearly seen from Fig. 4, the distortion of
the accelerating voltage( thick solid line) is compensated.
Applying the accelerating voltage after compensation, the beam emittance in the phase space after 1000
turns are simulated and the results are shown in Fig. 5.
Different from the Fig. 3, the beam shape is mostly notcollapsed in all cases.

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The lith Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

References[1] Y. Mori et al., The Japanese Hadron Facility, Proceedings of 1997 Particle Accelerator Conference,
Vancouver, B.C., Canada 1997.

Figure 5: Beam emittance in a phase space after 1000
turns with beam loading compensation.
The particles are stably holded in the rf bucket even
without the compensation, however more stable acceleration is achieved by the above mentioned harmoniccompensation for the beam induced voltage.
3The Measurement of Beam Loading

The beam loading measurement is under preparation.
Electron beam generated by electron-gun is injected into
the proto-type ofMA loaded rf cavity. A schematic setup
is shown in Fig. 6, and the parameters are shown inTable 2.

Electron Energy
Peak current
Pulse width[2] C. Ohmori et al., A Broad Band RF Cavity for JHF
Synchrotrons, Proceedings of 1997 Particle Accelerator Conference, Vancouver, B.C., Canada 1997.
[3] M. Fujieda et al., A Broad Band RF Cavity for JH~
Synchrotrons, in this symposium, SPringS 1997.
[4] Tom. Uesugi et al., New Magnetic Material f9r Proton Synchrotron RF Cavity, in this symposium,
SPringS 1997.
[5] Tom. Uesugi et al., Longitudinal Coupled Bunch Instability in the JHF 50 GeV Main Ring, Proceedingsof 1997 Particle Accelerator Conference, Vancouver,B.C., Canada 1997.

rv200 keV
rv7A
50 "' SO nsec.

Table 2: The parameters of the electron-gun.

Accelerating

GapSolenoidCT~----~'-------=!

DD

RF Amplifier

Figure 6: Schematic view of the beam loading measurement setup.
Using electron beams, the compensation scheme
mentioned above will be tried.
4Summary

The beam loading effects for the MA loaded rf cavityare investigated by the simulation. In order to suppress
the beam loading effects, the compensation of the beam
induced voltage up to 2nd higher harmonic on the rf
frequency is fairly effective.

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