THE DESIGN OPTIMIZATION OF THE DIELECTRIC ASSISTACCELERATING STRUCTURE FOR BETTER HEAT AND GAS
TRANSFER
Shingo Mori∗ , Mitsuhiro Yoshida† , KEK, Tsukuba, Japan
Daisuke Satoh‡ , National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan
Abstract

Dielectric

The dielectric-assist accelerating (DAA) structure is adielectric-inserted normal-conducting cavity, which provides high Q value at room temperature. This acceleratingstructure is composed of dielectric disks and a dielectric
cylindrical layer inserted in a copper cavity. For the realistic
operation, the removal of heat from the dielectric cells andthe vacuum evacuation of gas inside the cylindrical layers
have not considered yet. In order to solve the problems, wepropose the optimized design of the DAA structure, where
the extended part of the dielectric disk is embedded in thecopper cavity and the choke structure is applied. We show
the result of the electromagnetic-field simulation of the extended DAA structure and the thermal simulation to clarify
the relation between a duty factor and maximum temperatureof the dielectric cells.

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DielectricDisk

Figure 1: The original design of the test cavity with theDAA structure. (left) The definition of the parameters to
distinguish the different choke structures. (right)

EXTENTION OF THE DAA STRUCTURE
INTRODUCTION
A dielectric-assist accelerating (DAA) structure [1, 2] ispromising in power efficiency and can be a new candidateof accelerating cavity for high duty operation because it
provides high efficiency Q ∼ O(105 ) at room temperature,and higher Q value at low temperature. Although the DAA
structure in the left figure of Fig. 1 has an advantage inefficiency, there are several problems required to consider
before use of DAA cavity as an accelerator.
First, the thermal contact between the dielectric cell andthe copper cavity is poor, because the dielectric cells andthe copper cavity are not welded together. Since the volume
heating of the dielectric cell is proportional to the square of
the magnitude of the electric field inside the dielectric cell,poor thermal contact causes an overheating of the cells. A
dielectric strength is known to be gradually decreasing at
higher temperature. [3] Then the overheating of the dielectric
cells may cause a breakdown at lower accelerating voltage.
Secondly, the pumping of gas from the inside of the DAA
cavity is difficult in the original design. This is becausesome region in the left figure of Fig. 1 are enclosed between
the dielectric cylinder and the copper cavity.
This paper is organized as follows. In Sec.2, we introduce
optimized designs of the DAA cavity. In Sec.3, we will
discuss the removal of heat from the dielectric disk. InSec.5, we will conclude our results.
∗ smori@post.kek.jp† mitsuhiro.yoshida@kek.jp‡ dai-satou@aist.go.jp

An Extended Dielectric Disk and a Choke Structure
In order to remove heat from the cells, we consider enlarging the diameter of the dielectric disk so that the extended
part of the disk is embedded in the copper cavity. Assuming
good thermal contact, the larger contact area can mitigate
overheating of the dielectric cells. In order to enhance heat
conduction between them, we will apply metalization on thedielectrics and welding them together.
Since a radial transmission line has no cutoff frequency,
all eigenmodes can leak via the extended disk. A solution
with axial symmetry is to add a choke structure to the radialtransmission line. [4, 5]Comparison of Three Types of Extensions
In the application of the choke structure to the DAA structure, there are several ways. The first configuration shownin the left figure of Fig. 2 fills the choke structure with thedielectrics. The second one shown in the second figure fromthe left of Fig. 2 does not fill the choke structure with thedielectrics. The third one shown in the third figure fromthe left of Fig. 2 does not fill the choke structure with thedielectrics and has a vacuum region between the dielectric
disk and the copper cylinder. The vacuum region enables
the cavity to evacuate from the flank beside the beam holes.
The advantage of the first design named as type-1 is thata multipaction cannot happen in the choke structure. But it
requires high accuracy of the machining of the dielectrics.
Moreover, we need to care about the difference in the coeffi-

Type-1

Type-2Type-3Type-1g

and the copper cylinder, i.e.
∫ c+r1+r2+g2
Irad =
dr H|z=(L+D)/2−0 .

(1)

c+r1

Figure 2: The choke application for the extended DAA structure. The horizontal line denotes the beam axis. We assume
the axial symmetry of the structure and the field configuration. The red curves denote the real part of the electric forceline and the green curves denote the imaginary part of that.
The radius of the red circle denotes the magnitude of theaxial component of the magnetic field.

We choose an optimized point from the data set generated
above in the following steps. We select a dataset with higher
Q-value of top 10%, then within them, we choose one data
point which minimizes the value of Irad .
As at the junction of the radial transmission line and thechoke structure the wall current vanishes, the accelerating
mode does not transmit. Thus the simple design strategy is tominimize the wall current at the junction. In the right figureof Fig. 1 we show the definition of the dimension parameters
used in the optimization process. The gray region denotes
the dielectric cell and the white regions denote the vacuum.
For the calculation of type-1, the length of choke structure,λ/4−δck , is modified as λ/(4n)−δck , where n is the refractive
index of the dielectric material.
Table 1: Parameter List of Each Design

cient of thermal expansion between the dielectrics and thecopper. The temperature rises during the welding changes
the radius of the choke part of the copper cavity and thedielectrics, which might crack the dielectrics if the bending
strength of the dielectrics is low.
The second design named as type-2 has also high Q-value.
The vacuum region in the choke structure requires a further
considering of the multipaction and tests about a vacuum
sealing between the dielectric disk and the copper cylinder.
In the third design named as type-3, we can enhance a
pumping conductance by pumping from the end of the radialtransmission line as well as the beam holes. But, in theradial transmission line and the choke structure, the vacuum
region would cause the multipaction. Then the conditioningof the cavity would take longer hours than the previous twodesigns.

Optimization Using the Eigenmode Calculation
Tab. 1 shows the rf parameters and dimensions of the threedesigns shown in Fig. 2. In the right figure of Fig. 1, we show
the definitions of the dimension parameters. In the obtained
parameters listed in Tab. 1 and the eigenmode calculation
described below, we use the parameter of polycrystallinemagnesia applied in our previous paper [2]; the relative
permitivity ϵr = 9.64 and the loss tangent tan δ = 6.0×10−6
near 10 GHz.
We calculate the eigenmode of the accelerating mode
for a single cell with a periodic-boundary condition throughSuperFish. In the lattice of a parameter region of r1 , g2 , andδck with number of the lattice points from 300 to 1000, wecalculate the field configuration and the rf parameters suchas Q-value and the shunt impedance. Using the obtained
field configurations, we calculate the line integral of themagnetic field near the boundary between the dielectric diskName
f0 [MHz]Q [105 ]Zsh [MV/m]
Irad [A]r1 [mm]r2 [mm]g1 [mm]g2 [mm]g3 [mm]δck [mm]
g [mm]

type-15711.2
1.44
883
2.26
5.0
30
–
6.0
–
-1.0
–

type-25711.5
1.44
948
0.490
1230
–
10
3.0
5.0
–

type-35711.4
1.09
708
92.9
1230
1.0
6.0
2.0
3.0
–

type-1g
5711.2
1.21
757
0.175
9.0
30
–
8.0
–
-4.0
1.0

As we choose the larger gap between the dielectric diskand the copper cavity, g1 , the Q-value of the type-3 design,Q3 , decreases. From the calculation with SuperFish we
obtain a relation Q3 (g1 ) = Q0,3 (1 − αg1 ), where α is thedimensionful parameter to quantify the reduction of the Qvalue of type-3 design per 1[mm] of the gap, g1 . We obtained
α = 0.20.

A Gap Between the Cylindrical Layer
In the original DAA structure shown in the left figure ofFig. 1 and the design of type-1 and type-2 in Fig. 2, theevacuation is still difficult in the region enclosed by thedielectric cylinder and the copper cavity.
In the above designs, the copper cylinder fixes the positionof the dielectric disks. In the design of type-1 and type-2,
the copper cylinder sandwiches the extended part of thedielectric disk, and then fixes the position of the dielectricdisk. In type-3, the dielectric cylinder can be welded together
with the copper cylinder.
Thus, we can disconnect neighboring dielectric cells andgive a gap between the cells as shown in the right figure ofFig. 2 named as type-1g. The gap makes the entire vacuum
region connected, which provides an ability to evacuate

whole the vacuum region from the beam hole for the threedesign proposed above.
We numerically calculate a relation between the Q-valueof the type-1 design, Q0,1 and one of the type-1g with a gap
2g [mm] between two neighboring cells, Q1 (g) = Q0,1 (1 −α ′ g), where α ′ is the dimensionful fitted parameter. We
obtained α ′ = 0.16.

THE THERMAL TRANSFER FROM THE
DIELECTRIC CELLS TO THE COPPER

Figure 3: The maximum temperature of the dielectric cellfor various duty factors and accelerating voltages.
Fig. 3 shows the relation among the maximum temperature of the dielectric cell and the accelerating voltage andthe duty factor for the type-1 cavity, which is obtained as
explained below. The volume loss in the dielectric cell is
proportional to square of the accelerating voltage and linearly proportional to the duty factor and the maximum temperature. We determine the maximum temperature of thedielectric cell by the transient thermal solver of CST, where
we fix the circumference temperature of the cavity at 15◦ C.
Then we obtain a relation between the the maximum temperature of the dielectric cell, Tmax [◦ C], and the volume
loss corresponding to the maximum accelerating gradientEacc,max [MV/m] with duty factor as rduty [%],
Tmax = T0 + k

rduty 2E,
100 acc,max(2)where the ambient temperature T0 = 15.0 [◦ C] and the fitted
dimensionful parameter k = 0.0284.
In the above calculation, we assume the perfect thermal
contact between the copper and the dielectric cells of MgO.
As long as we can guarantee the perfect thermal contact, thesituation is not different in the other two types of designs.

DISCUSSION AND CONCLUSION
The DAA structure is a candidate for the high duty accelerator at room temperature. Still, the actual use of theDAA cavity as an accelerator component has several requirements. We propose three candidates of solutions to solve
the problems.
First, the thermal transfer from the dielectric cells to thecopper cavity is required to avoid the overheating of thecells. To solve the problem, we make the extended dielectric
disk embedded in the copper cavity, so that the contact areaincreases as shown in the four designs in Fig. 2. This prescription has a side effect, which enables the copper cavity
to fix the position of the dielectric cells without stacking thecells touching with each other as the type-1g.
Secondly, the original DAA structure has a closed region
which is between the copper cavity and the dielectric cell,
where we can not pump easily from those regions. The
designs of type-3 and type-1g can solve this problem. While
Type-3 requires both the side hole of the cavity and the beamhole to evacuate, type-1g can be evacuated only from thebeam hole. Moreover, for the same separation of the gap, g1
for type-3 and 2g for type-1g, type-1g has higher Q-value
than that of type-3.
As future works, we will consider the effects of the multipaction and the wakefield. In the design of type-2, type-3 andtype-1g, the narrow gaps and the high secondary-electron
yeild of the dielectrics will cause a multipactoring at some
input power depending on the dimension of the gaps. Thedumping of wakefields produced by the transverse beam
offset is also important for the high current accelerator.

ACKNOWLEDGEMENTS
This work is supported by JSPS KAKENHI Grant
No. 16H02134. The authors would like to thank N. Shigeoka from the Mitsubishi Heavy Industries Mechatronics
Systems Ltd. for their continued support of the development
of DAA structures.

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