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

1997.A NEW TYPE OF RF CAVITY
FOR IDGH INTEN SITY PROT ON SYNC HROT RON
Y. Mori,E.Ezura,M.Fuzieda,K. Koba* ,S.Machida,H. Nakayama,C.Ohmori,
K. Saito**,S.Sawada,A.Takagi,Y. Tanabe***,M.Toda, M.Yamamoto,M. Yoshii,T. Uesugi*

High Energy Accelerator Research Organization
3-2-1, Midori-cho, Tanashi-shi,Tokyo 188-0002, JAPAN(*also Miyazaki Univ.,**also Hitachi Co.,***also Toshiba Co.,****also U.Tokyo)***Abstract
A new type of RF accelerating cavity using high permeability magnetic alloy (MA) is proposed for high intensity proton synchrotron. Because of its hlrge accelerating efficiency compared with the conventional ferriteloaded cavity, total length of the cavity can be reduced
dramatically and stable operation under heavy beam loading becomes possible.

1. Introduc tion
In the intermediate energy proton synchrotron, the resonant frequenc y of the RF accelerating cavity has to betuned with the particle velocity. Using high penneability materials such as ferrite, the resonant frequency canbe varied by applying the static magnetic fi~ld. Performance of this type of cavity , therefore, depends largelyon the characteristics of the high permeability materials.
In evaluating the RF cavity performance, it is necessary
to consider the following two things: (I) acceleration efficiency and (2) beam induced effects.
The acceleration efficiency is defined as an effective field. gradient (=accelerating voltage per cavity length). In ordinary normal conducting RF cavity, the acceleration efficiency is limited by electric breakdown and cooling. For
the electric breakdown limit, the Kilpatrick's criterion has
been widely used. In the case of using a cooper cavity,
the maximum power density cooled by water is approximately severallOOW/cm3 •In the RF cavity using a high permeability ~aterial, the·effective field gradient relates the material characteristics itself. It is rather complicated compared with an ordinary normal conducting RF cavity.

When the toroidal shape of the core is used, this J.LQfproduct corresponds the shunt impedance per unit length
as follows.

R,fl =JL

Qf(l+ ~ )~~o xm(:.).

(1)
Here, R, is the core shunt impedance, l the core length, .Uothe vacuum penneability, r0 and r; the outer and inner radius of the core, respectively.
If Q> > 1, then, R /l is proportional to .uQf. The .uQfproduct depends largely on the RF characteristics of thematerial,· therefore, so many investigations on the .uQfproduct for the various comPQsite of the ferrite cores havebeen carried out so far.[ I]As described above, the effective field gradient is limited by the electric breakdown and the cooling efficiency.
There is no problem for the electric breakdow n in thistype of cavity because its maximum RF voltage is relatively low. The question is a cooling limit. In order toevaluate the cooling limit of the magnetic cores, the RFpower density in the core is important.
The RF power dissipated in the magnetic core is givenby,,

w. _muL-Q.

(2)Here, U is the stored RF energy in the cavity and co theRF angular frequency. The stored energy U is describedby,-J

1 B,/dv. .(J)U = /lJ.lo JH,/dv = 2 v
2/lJ.lo v
Here, B11 is the RF magnetic field strength in the core.
Thus; the average power density for a toroidal core is givenby,

2. Power Density
In order to evaluate the performance of the RF cavity
using a high permeability magnetic core, the product of
the relative permeability(p) and the quality factor ( Q) of
the material, so-called the .uQf-product, has been used.

- .... ~-1vif2

P- V - 41!JlJloQJ (ro2- 'i2) x 12 x In(~) .(4)2'iThe effective RF field gradient.is related to the power-224-

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

density as given by the following equation.

CJ)'

Power Density vs. Effctlve Gr.

Ii=A·JlQJ·/5,~ :

(5)

:::

---- Ferrite .

Mag~etlc Alloy(FINEMEl)i: ::::::::::I:::::::l[:::J::::::::::::;::::::::.::::r·::::·::····l:·::::··::·::r::·:·:::::.

where

A=:

. . ('f....... - -7 -···

21CJ.I.(r~- r,')m(;,}(6)
3

The power density p is proportional to (V,flY if .uQfproduct is constant. In the case of ferrite material, the.uQf-product is not constant and decreases when the RF
magnetic field strength, Bif is increased. In Fig. 1, closed
squares show the dependence of the typical .uQf-producton Brffor the Ni-Zn type offerrite which has been widelyused in the proton synchrotrons.. According to eq. (5),the power density is calculated for this type of ferrite andthe results is presented by a solid line of Fig. 2.

2.00E+10~

1.00E+10O.OOE+OO
1101001000

10000·Brf (Gaus:Fig.1 ,uQt-values vs. Brf.

As can be clearly seen from this figure, when the effective field gradient is more than -20kV/m, the power density increases enormously. In other words, the ferrite hasa limitation on the effective field gradient, which is lessthan 20kV/m. Since the stacking factor in fabricating the20021o'

41o'

6 1o'81o'

1 1o'

1.21o'

Vjl [Yirn)

Fig.2:Variations of the power density as a function ofthe effective field gradient.
just proportional to (V,flY . Even when the field gradient is so high as V,fl=100kV/m, the power density is stillless than 2.5 W/cm3• The practical field gradient will be
70kV/m if the sacking factor of the cores is assumed to be
0. 7. This power density is marginal for cooling if propercooling medium such as oil or even purified water can beused. Thus, the field gradient achieved by the MA coreis more than 5 times higher than that of the ferrite core.
This means that a total number of cores required for generating the same RF voltage is 5 times less and the total
cavity length becomes also smaller by a factor of about 5.
This is a big advantage in the RF system of the high intensity rapid cycling synchrotron. Of course, the required
RF power increases. However, in high intensity synchrotron, the beam power is also huge. Therefore, the netincrease of the total RF power becomes not so large. Moreover, the electric consumption power in the RF system ismuch less than that required by the ring magnets. The
total impedance of the cavity seen from the beam becomesalso small, which is good for stable acceleration.

practical cavity is about -0.7, the practical effective field
gradient becomes -14-15kV/m at maximum for the ferrite core .
. On the other hand, the amorphous type of the magnetic
alloy(MA), which becomes available recently, does nothave such behavior on the .uQf-product because the saturation magnetic field strength of the MA is almost oneorder magnitude larger than that of ferrite and the hysteresis loss of MA is negligible small. A typical .uQf-product of the MA (FINEMET) for different Brf is also shownwith closed triangles and open squares in Fig. 1. The,uQf-product is fairly constant even at large Brf of morethan 1kG. 'ForMA, the power density as a function ofthe effective field gradient is calculated and the result isshown in Fig.2 with a broken line. The power density is

1.41o'The

f=3.25MHz

WA1ER

Fig.3: Schematic layout of the test cavity.

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The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997.. .! • • • 1· • • •:J•~ . 'L o+·' oto oo·io··~·~ ototal cavity cost is, of course, reduced a lot..

!

.• •

3. High Gradient Cavity with Water Cooling
40As a cooling medium for the core, various candidates
such as insulating oils, some organic medium such as Fluorinate, some gases like SF6 , and purified water, are considered. Looking at an environmental condition in thering, purified water seems to be one of the best. The
problem of using water is that it has a large dielectric constant ( e=80.36@20°C). The capacitance contributed bywater has to be included into the total capacitance of theresonator. Fortunately, the Q-value of the MA-loaded
cavity is normally low (1-2), therefore, the control of thecapacitance is not so difficult.
In order to estimate the water contributed capacitance,
we have made an experiment using a small test cavity
which is shown in Fig.3. The size of the MA(FINEMET)
core is as follows: the inner radius is 50mm, the outerradius 170mm, and the width 25mm, respectively. The·water was purified and its volume resistivity w~s morethan 10MQ.cm.The variations of the resonating frequency
as a function of the purified water level from the bottomof the cavity were measured. The results are shown inFig. 4 with closed circles, Once the water level exceeded
the upper surface of the core, the resonating frequency
decreased gradually. The water capacitance contribution to the resonant capacitance appeared when the electric field leaking from the gap saw the water. We havealso made Superfish calculation to compare with the experiment. The calculated resonant frequency changes
as a function of the water level are also shown with theclosed squares in Fig. 4. Calculations agrees with themeasurements nicely. From these results, it is found that
we can estimate the capacitance contributed from the pu-••:'je0• i0• ; cP..... !!...... J.. o[] ________ j_ _____________ _(__ ____________ j_____________

3 5

•'0;

:o
6/i''

J ___________ _j············jl,_~_:_~~-~e-MrET_J..

j·D•

0' ' io:·········t·····

i +·········:··············[::20

3 02 00

1 0405060time rminute 1Fig.5:Variations oft water and core temperatures as a·function of time.
rified water by Superfish calculation.
We have also measured the effective heat transferring
coefficient of the MA core by using the same test cavity.
The MA core is made from thin MA tapes, whose thickness is -20f..Lm, winding around a spool. It is important toknow the effective heat transferring coefficient of the corefor making a cooling design properly. The RF power ofabout lkW was fed into the cavity and measured the coreand water temperature. The flowing rate of the purified
water was 0.51/min. Figure 5 shows the temperature configurations for both core and water as a function of timeafter the RF power is introduced.
From this measurement, we obtain that the effective heat transferring coefficient is 20-30 W/m.K, which is a little larger than that ofstainless steel. There seems to be no problem for cooling of the MA cores when the consumption RF power
density is even more than 10W/cm3•

4.Summary
A new type of RF cavity using a magnetic alloy for highintensity proton synchrotron is proposed. The effective
accelerating field gradient of more than 70kV/m will bepossible if it is properly cooled. The purified water cooling seems to be the most simple iif careful design for water dielectric effect is accomplished.
REFERENCE[1] T.Uesugi et al; JHP Report, JHP-31,1997.
-1 00102030405060

Water Level (mm)Fig.4 :Resonating frequecy vs. water level.

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