JAERI-Conf 95-021

2p2-4
Study on Tuning-Free Network for RF Accelerating Cavity
M.Yamamoto 1 , T.Rizawa 2 , T.Saitol, H.Tamural, M.Uraki 1 , Y.Morii 2 , K.Hosono 1 ,K.Hatanaka1 , T.Itahashi 1 , K.Takahisa 1 , K.Tamura 1 , I.Miura 1 , and K.Sato 1
1 Research Center for Nuclear Physics, Osaka Univ., 10-1, Mihogaoka, Ibaraki-shi, Osaka 567, Japan
2 Toshiba Corporation, Heavy Apparatus Engineering Lab.
2-4, Suehiro-cho, Tsurumi-ku, Yokohama-shi, Kanagawa 230, Japan

abstract
Applying a bridged-T type all-pass network to a resonator described as a parallel circuit, the output voltage of the resonator shows a band-pass feature over acertain frequency range, while the input impedanceis always constant against frequency. This feature
is considered to realize the ferrite-loaded tuning-free
RF accelerating cavity. It has several merits such asa simple cavity structure without bias windings, aneasy operation without feedback control of the bias
current, applying new ferrite with favorable RF characteristics and so on.
1. Introduction

A ferrite-loaded RF cavity for an RF system of a synchrotron produces, in general, the accelerating voltage
at its resonance frequency, which is synchronized withthe revolution frequency by bias field. On the otherhand, applying a bridged-T type all-pass network toa cavity regarded as a parallel resonance circuit, accelerating voltage shows a band-pass feature withoutbias field.
The accelerating cavity as above can be energized
by a commercial transistor RF power amplifier because the input impedance of the network with a ter-v

Figure 1: A bridged-T type all-pass network with aterminating resistor R.
In general, a lumped constant circuit of an accelerating cavity is shown as a parallel resonance circuitwith a self-inductance, a capacitance and a resistancecaused by RF power loss offerrite. However, an equivalent circuit of a cavity is approximately equal to aparallel circuit that Z 1 consists of L 1 and C 1 as shownin fig.2, because the RF power loss of new ferrite is
far less than the former one, as discussed in the next
section, and also because the terminating resistor exists.

minating resistor is always equal to one of the resistor,

i.e. always constant against frequency.
A rough estimation of behaviors of the all-pass cavity circuit has performed, based on RF characteristicsof new ferrite material under development. It showsthat an RF accelerating voltage of 630 V6ver the frequency range from 1 MHz to 8 MHz can be achievedin a 60 em long cavity by a 1 kW RF power amplifier. This type of accelerating cavity is applicable toa proton-synchrotron for radio therapy and a coolersynchrotron in multi-GeV region.
2. A bridged-T type all-pass network
As shown in fig.l, a bridged-T type circuit consists ofthree impedances, zl, z2 and z3, and is terminatedin a resistor R. In this circuit, the all-pass conditions
that the input impedance is always constant value Rare,(1)vR

Figure 2: A bridged-T type circuit regarding an accelerating cavity as a parallel resonance circuit.
From the all-pass conditions of eq.(1), z2 should bea series circuit of L2 and C2, Z 3 should be a parallel
circuit of L3 and C3. They should satisfy the following
conditions respectively in any resonance frequency;

When these conditions are satisfied, the ratio of theinput voltage V to the input current I is constantas R against frequency, that is, an all-pass featureappears. As for the voltage VR between both endsof the terminating resistor, /VR/V/ = 1 is satisfied-242-JAERI-Conf 95-021

at all frequencies. Then the voltage V1 that appears
between ends of the parallel resonant circuit of L1 andcl has band-pass characteristics, as shown in fig.3.
IVdVI = 1 is satisfied at frequencies wz and Wu, andvl exceeds the input voltage between them, which
satisfy(3)where w0 is a resonance frequency. The purpose ofthis study is to apply the band-pass characteristics
like fig.3 to an accelerating cavity.

'ii '0 ![(:'I,I, 'I! ''''i'
:

l':'

\iA

i.-/

::

1\v!'lilii\;:',II"'':!

Frequency (NfHz)

Figure 3: The frequency dependence of !Vr/VI. The
voltage V1 between both ends of a parallel resonant
circuit of L 1 and C 1 has band-pass characteristics.
Let N be the ratio wu/wz, then N is given as theexpression with the terminating resistor R and thecharacteristic impedance of the resonant circuit.

From eq.(4), a wider frequency range can be realized
by increasing a characteristic impedance or decreasinga terminating resistor R.

in this circuit and the ferrite containing Co can beused. Accordingly RF power loss can be reduced.
Now, Such material of the ferrite, which RF power
loss has minimum value around 4 MHz, has been developed, supposed that this cavity is used over thefrequency range 1-8 MHz. From the preliminary data
until now, the frequency dependence for J.LQf product of the ferrite recently developed is shown in fig.4.
From this data, it is shown that J.LQf product of developing ferrite is up to several decade times as large
as conventional ones, and finally, RF power loss isstrongly reduced. In fig.4, J.LQf product is largest
around 8 MHz, but the ferrite material for a lower
frequency is being developed.
An equivalent lumped circuit of an accelerating cavity is approximately equal to a parallel circuit of a selfinductance and a capacitance because the RF power
loss of the new ferrite is much smaller and terminating
resistor exists in this circuit. It is also a merit thatthe accelerating cavity can be used for large amplitude. Thus Q-loss effect caused by the excitation of
the exchange spin wave associated with the bias field
is much less, because the ferrite without bias field isalways used in the initial state.
An inner diameter of a ferrite ring cannot be verysmall because of the bias windings in a conventional
cavity[1). However the inner diameter of the ferrite
is a little larger than the outer diameter of the flangeof the vacuum duct in a new cavity, because the bias
windings are not necessary. Thus the occupation of
the ferrite is higher, and the self-inductance turns tobe larger. From this point, a length of an accelerating
cavity can be shortened. And a high characteristic
impedance cavity is realized, if a capacitance of anaccelerating gap can be made small.
4. Design and estimation of performance foraccelerating cavity

3. Development of new ferrite

Frequency (NfHz)

Figure 4: A frequency dependence example for J.LQf
product of new ferrite developed.
Since there is no bias field on ferrite of a cavity inthis circuit, new type ferrite material can be applied.
NiZn has been used for the cavity because of quick
response to the bias field. However, it is not necessary

Assuming a diameter of a beam duct is 200mm, its
conflat flange cannot be smaller than ICF253. Thus
ferrite toroidal core with inner diameter 255 mm isused, and the space between the vacuum duct and theflange is used for the installation space of the baking
heater and for insulation. The outer diameter of thecommercially available ferrite is 500 mm and its thickness is 25 mm. Since RF power loss of the new ferrite
is small, a cooling system for the ferrite RF power loss
becomes simpler. The structure of the system is that
1 mm thickness copper plates, whose edges are silver brazed with the copper cooling pipes, are inserted
between the 25 mm thickness ferrite alternately.
The relative permeability of the ferrite is determined to be 200 because it is necessary for the ferritethat its permeability is not much changed in a available frequency range below Snoek's limit. Using 20
ferrite cores, the self-inductance is 13.5 J.lH, and theresonance frequency is 3 MHz, if a capacitance of an-243-

JAERI-Confaccelerating gap is 200 pF. And the terminating resistor is 200 n, because a characteristic impedance is250 n. From the rough estimation as above, 630 v
of an accelerating voltage is achieved, in case a 60 em
accelerating cavity is energized by a 1 kW RF power
amplifier.
''IH\If"~ IIi..

i.

.

I::1/i;'/ I I: I i! !

II I

1\\i!: \i¥' 'I ij

95-021

as a parallel resonant circuit, and measured the performance. The model is shown in fig.6, and the figureof its equivalent lumped circuit is shown in fig.7. Thesize of the model is 25 em x 20 em . x 25 em. The
main body is made of a copper plate, capacitances areceramic condensers, the inductor of 56.8 J.tH in fig.7
is ferrite loaded coil, and other inductors are plastic
loaded coil. The voltage V1 in fig. 7 is shown in fig.8.
It is obvious that the same characteristics as fig.3 andfig.5 appears in fig.8.

iI/\:f--.-- i-rr

i\'\'.

Frequency (114Hz)

Figure 5: Frequency dependence of IV!/VI including
RF power loss of ferrite.
Fig.5. shows an analysis result for the output voltage of the cavity including the ferrite RF power loss
and the frequency dependence of the ferrite complex permeability. From fig.5, the available frequency
range, where Vi exceeds V, does not change so much.

'\\\Frequency (114Hz)

Figure 8: Frequency dependence of the output voltage
IV!/ VI of the model.
6. Discussion

5. Measurement of the performance in an
equivalent lumped circuit

In the next stage, the authors will construct a realcavity with a bridged-T type circuit, and will investigate whether the all-pass characteristics are achieved.
With developing the ferrite, design of a real cavity isproceeding.
Since the frequency range can be tuned arbitrarily
from eq.(4), this cavity can be applied in various syn~chrotrons. Furthermore, this cavity is also applicable
to a rapid cycle synchrotron due to no bias windings.
For a high energy synchrotron, a larger amplitude
circuit must be developed.
If an accelerating frequency range is higher thana resonance frequency of a cavity, the influence ofthe beam loading is avoided. However the case thatan accelerating frequency range includes a resonancefrequency is under investigation now. And in thebridged-T type circuit, when the cavity is excited by
the beam energy, the current taken by the beam isconsidered to have a band-pass characteristic as theinput current. It also must be investigated in the nextstep.

Figure 6: An equivalent lumped circuit model.

Acknowledgementsv

The authors wish to thank Mr.
S.Watabe andK.Takamura of TDK for their developing new ferrite.
Reference

Figure 7: The equivalent lumped circuit model.
The authors fabricated a simple model of an equivalent lumped circuit, regarding an accelerating cavity[1] M.Kanazawa et al.,"RF High Power System of theHIMAC Synchrotron", Proc. of 8th Symp. on Accelerator Science and Technology(1991),p. 161.

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