The 9th Symposium on Accelerator Science and Technology, Tsukuba, Japan 1993

A Ferrite Loaded Untuned Cavity for a Compact Proton Synchrotron
J.l. Hirota, T. Norimine, K. Hiramoto and M. Nishi
Energy Research Laboratory, Hitachi, Ltd.
2-1, Omika-cho, 7-chome, Hitachi-shi, lbaraki-ken,
319-12,JapanAbstract
A ferrite Joaded untuned type RF cavity and its operation
scheme for a compact proton synchrotron to be applied to
medical use are presented. To produce a high accelerating voltage
over a wide frequency range, Ni-Zn ferrite with a highly complexpermeability is chosen for the cavity. Two types of mechanicalstructures, quarter wavelength and half wavelength resonators,
are compared for their ability to provide a high impedance. To
realize smooth synchrotron control from injection to extraction,an accelerating pattern for the accelerating voltage of the cavity
is proposed.

I. INTRODUCTION
A ferrite loaded untuned cavity in an ion synchrotron
was first used forty years ago at Cosmotron [1]. In the 1980's,
it was adopted in a proton synchrotron dedicated to cancer
therapy at Lorna Linda University Medical Center[2]. In aproton synchrotron for medical use, a beam energy of70-250MeV
is smaller than that of physical experiments. This beam energy
results in a decrease of accelerating voltage in the cavity.
Then, a ferrite loaded untuned cavity in which resonant frequency
tuning is unnecessary is a suitable choice for a compact medical
proton synchrotron of the future.
A 250MeV proton synchrotron with a low emittance
extraction scheme using transverse RF noise has been presented
by other workers at the Energy Research Laboratory Hitachi
Ltd. in another paper in these proceedings[3]. To realize its RF
accelerating system, permeability of ferrite and mechanicalstructure of the untuned cavity were studied by resonant analysis.
For medical use, a simple operation not only for extraction
but also for acceleration is required because when installed in a
hospital, the system is used daily by a small number of
nonprofessionals. Then an acceleration pattern to achieve smooth
control of the cavity from injection to extraction of theaccelerating voltage is proposed.

II. ACCELERATING PARAMETERS
The parameters of the synchrotron for RF acceleration
are given in Table 1.
A proton beam of 10MeV is injected from a linac tothe synchrotron with combined function lattice and accelerated
up to the energy of 250MeV by the accelerating system. After
acceleration, the proton beam is extracted slowly. This operation

Table 1
Parameters of RF acceleration system
Machine Parameters
combined function
Lattice composition
27[m]Circumference
10-250[MeV]
Range of Energy
Radius of Curvature of Bending 1.62[m)0.28-1.5[T]Field Strength of Bending
1
Harmonic Number
Momentum Spread of Injection 0.3[%]
RF Accelerating Parameters1.608-6.813[MHz]Revolution Frequency
0-145[eV]
Energy Gain per Turn
162-430[V]
Accelerating Voltage
0-22[deg]
Synchronous Phase Angle<l[m]Cavity Length
is conducted with a repetition rate of 0.5Hz.

III. CAVITY STRUCTURE
Two types of structures, a quarter wavelength resonatorand a half wavelength resonator, were considered. The outerand inner diameters of the cavity are 600 and 200mm,respectively, for each structure. The accelerating gap length is
20mm so as to increase the accelerating voltage allowing
capture of a wide range of the momentum spread at injection.
The cavity length is 800mm, and total length is lOOOmm.
At first, the required complex permeability f.l(real,imaginary) and volume of ferrite relative to the cavity volume
A V were estimated by a calculation ·using the quarter wavelength
resonator. The results of the real part are shown in Fig.l. The
imaginary part was estimated by a perturbation method. The
electric field distribution is shown in Fig.2. From these results,f.l>(900, 20) and AV>2% were needed to get a center resonant
frequency of about 4.5MHz and a frequency range of 5MHz.
Materials corresponding to these conditions are Mn-Zn andNi-Zn ferrite. Since it is difficult to manufacture a large toroidusing Mn-Zn ferrite, Ni-Zn ferrite was chosen. From theseinvestigations, a model cavity was made and tested. The
dimensions of the ferrite toroid installed in the cavity are
500mm outer diameter, 280mm inner diameter, and 12.7mm
thickness, with a complex permeability of (1000, 100) at
SMHz. With an extra shunt resistor of S()Q across the acclerating-154-

1000I

0 AV=0.8%
0 AV=1.6%
0 AV=2.4%-- n~156Q over the operation frequency range.
It is necessary to capture a wider range of the momentum
atspread injection and to accelerate firster to increase theextraction current. Then the half wavelength resonator shownin Fig.4 was examined under an unloaded condition by anumerical calculation to increase accelerating voltage. The
electric field strength at the accelerating gap is about 2 times
higher than that of quarter wavelength cavity although theresonance characteristics of this resonator with 2.4% ferrite
volume are the same as quarter wavelength resonator's. Thiswas resulted by the cavity shape near accelerating gap which00ig.

J: 10:-0~9f=SMHz5~

has a smaller outer diameter.

11 ~1~o~~L~I~I~I~I
1 ~1 ~~~~~~~~~·~L~1 ~1 ~1 ~~

1000

500

0Re(J.t)

1500

Fig.1 The dependence ofpenneability on resonant frequencyof the cavity. IJI indicates ferrite volume ratio relative to thecavity volume.

ferrite toroid\\IIIIIIIIIII)RoolOO

unit: mmFig.4 Dimensions of the half wavelength resonator.

IV. OPERATION SCHEME
unit: mmFig.2 The electric field distribution of the cavity with ferrite
volume ratio 2.4%.

aCDIn the acceleration process, the accelerating voltage
and its phase are usually changed by keeping the area of theRF bucket constant without losing the captured proton beam.
In order to simplify the synchrotron control system, twoconditions are added. The first is a no phase jump at the startof acc;:leration. The second is that the synchronous phaseapproaches 0 degrees gradually at the end of acceleration.
Under these conditions, strength of the bending magnet B(t)and synchronous phase cjl(t) are described in the following
relation:(.)

r::~ 60CDa.

E

1

2

3

456w

(l- 1

so~~~~~~~~~~~y~7Frequency(MHz)=dB(t)

B(t)2p2c2+Eij +B(t)2p2c2
cjl(t) )2dt,~Of~P)2/ (a(Vsinsin cjl(t))

Fig. 3 Magnitude of impedance of the cavity withshunt resistor

sm .

2lrgap, the measured magnitude of the cavity impedance is shownin Fig.3. The magnitude of the impedance varies from 62 to(1)P

where y 1 is transition gamma, p is radius of bending, c is light
velocity, h is harmonic number, I is circumference, fl is-155-relativistic factor, ~pip is momentum spread and a(siojl(t)) isa compression factor of the separatrix[4]. Since it is difficuJtto solve this equation ana1ytica11y, a tria] function for B(t) is
assumed to extract the phase t(t). A ca1cu1ated accelerating
voltage pattern satisfying the above conditions is shown inFig.5. Accelerating vo1tage is sequentia11y increased at thestart of acceleration, and decreased to 0 at the end of it. This500

REFERENCES[1] J.P. Blewett eta]., "Radio-Frequency System. Part
IV-AcceJerating Unit", The Rev. of Scie. lost., voJ. 24,
pp. 795-800, Sep. 1953.
[2] "Conceptual Design of a Proton Therapy Synchrotron For
Lorna Linda University Medica] Center", FerrniJab, June
1986.
"Lorna Linda University Medica] Center Proton Therapy
FaciJity Engineering Design Report", FerrniJab, Feb.
1987.
[3] K. Hiramoto et aJ., in these proceedings.
[4) C. Bovet eta]., CERN/MPS-SI/Int. DU70/4.

014-------------,----------------Y
0.5
0.0

Accelerating Time
Fig.5 Accelerating voltage pattern during acceleration.
leads to a reduction. of the loop gain for the standard ~ t
feedback system at the start. At the end of acceleration, thecirculating beam become a coasting beam. Then favorable
conditions are formed for extraction. Further, the combinedfunction lattice has an advantage for operation because at thesimpler tracking between bending and quadrupole magnets.
This accelerating voltage may be done by automatic gain
control of the cavity feedback system in place of phase control

V. CONCLUSION
A ferrite loaded untuned cavity for a compact medica]
proton synchrotron was presented. Required characteristics ofthe ferrite were complex perrneabiJity larger than (900, 20) anda volume ratio larger than 2%. In order to increase accelerating
voltage, a half wavelength resonator which has a smaller outer
diameter near the accelerating gap was discussed. Fina11y, an
accelerating voltage pattern was proposed to give favorable
conditions for extraction and simpJified control of the accelerator
system.

ACKNOWLEDGEMENT
The authors wish to express their thanks to Dr. T.,
Iimura, Hitachi Metals Ltd. for helpful advice and selection ofsuitable ferrite toroid.

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