The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

THERMAL AND STRUCTURAL DESIGN OF AN RF CAVITY
FOR A CW MICROTRON
Y. Makita, Y. Pu, T. H. Kim, H. Tanaka, T. Nakanishi and S. Nakamura
Mitsubishi Electric Corporation,
8-1-1 Tsukaguchi-honmachi Amagasaki-shi, Hyogo, 661-8661, Japan

Abstract
Thermal and structural analysis of an rf cavity for a CW
microtron has been carried out. The cavity employs slot
coupled 2-cell structure. The resonant frequency and thewall loss of the cavity are 500 MHz and 20 kW per cell,respectively. The frequency shift caused by the thermal
deformation is expected to be -129 kHz through theanalysis, which can be corrected by movable tuners. Thefrequency shift caused by room and cooling watertemperature changes are also determined. The maximum
Von Mises stress is expected to be 31 MPa, which is low
enough compared with the yielding stress of copper.

deformation and the stress distribution. The optimisationof the cooling system has been performed as well. For all
analyses, SUPERFISH and the commercially available
finite element method code ANSYS were used in thisanalysis. This paper describes the results of analyses andthe design of the cavity. The designs were mainly donewith the parameters of the accelerated energy of 5 MeV.

1 INTRODUCTION
High power electron beams are necessary for industrial
application: X-rays irradiation and electron irradiation forthe processes such as sterilization for medical equipments,
SOx and NOx treatments systems of flue gas and food
pasteurisation and defect analysis in semiconductors witha slow positron beam. Required energies for theapplications are about 5 MeV, 10MeV and higher than 15MeV, respectively. The required beam power is several
tens of kW. Development of accelerators operated in acontinuous wave (CW) mode is a key issue for theapplications because the accelerators require compactness,
low cost and stable operation.
A CW microtron, with a racetrack beam trajectory anda high beam current, is proposed for these fields [1 ]. New
shaped bending magnets are proposed to adjust the beam
orbit of each turn and acceleration phases. A 500 MHz
normal conducting rf cavity is installed in the straightsection.
The rf system of the CW microtron is a core part fromthe point of view of the power efficiency. The cavity has
to be controlled precisely to compensate the change ofparameters during the operation. Therefore, the resonant
frequency and the frequency shift of the cavity has to be
estimated precisely, consequently the thermal deformationof the cavity needs a precise estimate, as well. Highpower operation may damage the cavity, such as theplastic deformation, crack and so on, due to fatigue ofcopper. Thus, it is essential to perform an optimum designof the cavity, with suitable values of all parameters basedon the detailed analysis using a numerical analysis and soon.
The thermal structural analysis based on a 2D finite
element model has been done to estimate the temperaturerise of the cavity, rf frequency shift due to thermal

Figure.1 Cross sectional view of the rf cavity

2 DESCRIPTION OF THE CAVITY
Figure 1 shows the cross sectional view of the rf cavity.
For simplicity, other parameters such as a vacuum port, acoupler port, and other ports are not shown. The cavity
consists of slot-coupled c~vities with two cells. The
selected resonance ftequency of 500 MHz is mainly basedon the consideration of input rf power and the total size ofthe accelerator.
The cavity is designed to operate in the n-mode. Nose
cones and rounded shape of the cavity design is applied tomake the shunt impedance higher. The material of thecavity is class-1 oxygen free copper so that high electricaland thermal conductivity and low out-gassing rate can beobtained. The design parameters of the cavity are shownin Table 1.
Table 1: General arameters of the cavit
295mm
Beam power
30 kW
Cell length
Wall loss
40 kW
Outer dia.
500mm
65mm
Radio freq.
500 MHz Bore dia.
Number of cells
2Ga volt. /cell 0.5MV

3THERMALANDSTRUCTURALANALYSIS
3.1 RF analysis
A power density distribution of the inner surface of thecavity was calculated by using SUPERFISH with a 2D-244-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

cylindrical model. Three-dimensional structures such as
coupling slots, a vacuum port, a coupler port and otherports were not taken into account in the calculation.
Under the calculation, the input power was normalized tosatisfy the required gap voltage of 0.5 MV, so that all
results of the calculation give an actual value for thecavity design. According to the results, the total rf power
dissipation of inner surface of the cavity was about 20 kW,
where correction factor due to the fabrication was added,
per cell. Figure 2 shows the distribution of the power
density obtained from the calculation in which wasviewed with ANSYS mesh generation module. The
lengths of arrays describe the distribution. The highest
loss was about 8 W/cm2 where is around the nose cone.
This power density distribution was applied to the thermaland structural analysis. The shunt impedance Rsh and Qvalue of the cavity were also calculated. The results were
Rsh=17 MOhrn/cell and 0=41000, respectively.

sss

Figure 2 Heat flux distribution of inner surface of thecavity (viewed by ANSYS mesh generator)

deformation was also estimated with the frequency
sensitivity calculated by SUPERFISH. The equivalentstress, Von-Mises stress, distribution was also calculated.
The heat transfer coefficient of each cooling channel
obtained from the spreadsheet calculation describedabove was used. The power density distribution obtained
from the rf analysis by SUPERFISH was used. Water
temperature in each channel was given by averaging thetemperature rise derived from the total temperature rise ofwater.
To find the optimum values for the cavity design,attention was paid to indexes such as the maximum
temperature and the equivalent stress loaded on copper. In
this design, we adopted temPt:rature of 70 °C andequivalent stress of 34 MPa where is the 50 % value ofthe yielding stress of copper, as the maximum acceptablevalues. ·Several models with different channel location weregenerated and calculated. The model was based on a halfcell model to save the memory consuming, calculation
times and so on. A symmetric boundary condition wasapplied along the line marked with "s" in Figure 2. Twogroups of water channels, C4 and C1-C2-C3, were taken
into account since we designed that water of each channel
flows in parallel. Cl is the inlet and C3 is the outlet. The
average temperature in each channel was added as aninitial condition. The result of optimisation showed thatthe cooling channel nearest to the nose cones was themost sensitive. Results of the various models having
different Cl locations were compared and the optimum
channel location was chosen. The summary of theoptimisation is described in the end of this chapter.
Figure 3 shows the temperature distribution of themodel with optimum channel location.
C4:31.6 oc

3.2 Design of cooling channels.ANB'iB 5. 6

Heat transfer calculations using spreadsheet have been
done to determine the optimum cooling channel.
Attention was paid to indexes such as the fluid velocity
and the maximum pressure drop of the cooling system.
Several cases of calculations have been done with varying
parameters in cooling channels such as heat exchangearea, fluid velocity, and temperature rise of the water
through the cavity. The total flow rate of water per cell
was selected to be 50 Vmin. Consequently, the mean fluid
velocity is 2.0 rn/s. The maximum water pressure drop
was expected to be 2.6 kg/m2• The surface heat transfer
coefficient was calculated 8323 W/cm2K. Under thepower dissipation of 20 kW per cell of cavity, the watertemperature rise through the cavity was expected to beabout 6 °C.
3.3 Finite element analysis

The thermal and structural analysis has been performed
to estimate cavity thermal deformation by using ANSYS
code. The cavity frequency shift caused by thisliOV 1.1 2000

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111!115Z.421-.'19.7?.7;~:=~=Figure 3 Cavity temperature distributions
The water temperature at the water inlets was set to30 °C. A heat flux to the atmosphere from the cavity wasalso taken into account. According to the table, the heat
flux of 281 W/m2 [2] was estimated in this case.
Under these conditions, the maximum copper
temperature was calculated to be 60 °C at nose cones. The
average temperature at the outer surface of the cavity was-245-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

about 41 °C. The maximum thermal deformation of r-axisand z-axis per cell was 70 !!ill and 140 !!ill, respectively.
The cavity deformation in each coordinate due to thevacuum condition were 0.5 !!ill for r-axis and 5 !!ill for zaxis, where the surface pressure of 1 kg/cm 2 was loaded.
Figure 4 shows the thermal deformation distribution andthe order of the cavity segmentation.

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Figure 4 Distribution of cavity thermal ri .. J'rwrn<>ti'M;
Thus, with the results above and frequency sensitivity
calculated by SUPERFISH, the cavity frequency shifted
is estimated to be -129kHz. This value can be correctedby movable tuners.
To determine the frequency shift due to temperaturechange of atmosphere, the sensitivity analysis was carriedout by varying the room temperature in the range of 5 to
30 oc and the water temperature at inlets of coolingchannels in the range of 20 to 42 oc. Figure 5 shows thesensitivity curve obtained by the analysis. It wasdetermined that the sensitivities of cavity frequency shift
in terms of the room temperature change and the watertemperature change are 0.8 kHz;oC and 7 kHz;oC,respectively.

3.4 Summary

As described above, the thermal and structural design
was carried out. The design parameters of the cavity aresummarized in Table 2.
Table 2 Summary of the cavity parameters
r:70!!m, z: 140 !!illMax. thermal deformation per cell-129 kHz
Cavity Frequency shift
0.8 kHz;oC
Sensitivity rf freq. of the room temp.
7 kHz;oc
Sensitivity rf freq. of the water temp.
31 MPaMax. equivalent stress
60 °C
Max. copper temp.
Average copper temp. at the outer surface 41 °C
2.6 kg/m2
Pressure drop of water through the cav.
At the cavity optimisation, the maximum yielding
stress, frequency shift and maximum copper temperatureof the cavity of each model were compared. Table 3
summarizes the results of the calculation. It was pointed
out that as decreasing the yielding stress, the cavity
frequency shift increases. It is more important to decrease
the yielding stress low enough than to keep the frequency
shift lower, because the frequency shifts are all smallenough compared with the frequency range whichmovable tuners can cover. Therefore, the model having
the lowest maximum stress was chosen to be the optimum
design.
· · fon. l resu ts of coo rmg channe ~tlmtsa
Table 3 Ttyptca
1Max.CuFreq.
Max.
Model finnermosttemp.
shiftstress#cooling chan.
(OC)(MPa) (kHz)(mm)
62-121#1
38
45-124
60
35
#250
59.7
-129
31
#355

4 CONCLUSIONS

-250

-150

'N'.::The thermal and structural design of the rf cavity of theCW microtron was performed. The optimum design of thecavity was obtained. All calculated results werereasonable for the fabrication of the cavity and thecontinuous operation of the cavity.

§;ACKNOWLEDGEMENTS():r:: -148-200~.

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The authors would like to thank Messrs. T. Hirano, K.
Hanakawa, M. Yamada, Dr. N. Nakamura, and manymembers of our company for helpful discussions.

~0Temperature (C)Figure 5 Sensitivity of cavity frequency shift in terms ofthe room and the water temperature change
To determine the thermal stress, the equivalent stress(Von-Mises stress) was adopted. The maximum
equivalent stress was 31 MPa. This is low enoughcompared with the yielding stress of annealed copper, 69
MPa [3].

5 REFERENCES[1] H. Tanaka, et a!, "Beam Dynamics in a CW Microtron
for Industrial Applications," EPAC2000, 1005,2000[2] JMSE Heat Transfer Handbook, Japan Society ofMechanical Engineering, 1993
[3] http://www.matls.com/-246-