THE RF GUN ADOPTING THE DIELECTRIC ASSIST ACCELERATINGSTRUCTURE
Shingo Mori∗ , Mitsuhiro Yoshida† , KEK, Tsukuba, Japan

Daisuke Satoh‡ , National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan
Abstract
We apply the dielectric assist accelerating (DAA) structure to the RF gun, which is a candidate for a high average current and high brightness electron source. The DAA
structure consists of ultralow-loss dielectric cylinders anddisks which are periodically arranged in a metallic enclosure. Due to the high quality factor and the high shunt
impedance of the DAA cavity, the RF gun adopting the
DAA cavity can be a high-duty electron beam source atroom temperature. We provide design work for RF gun
adopting the DAA structure.

INTRODUCTION
The RF photoinjectors have been widely used as a sourceof high-quality beam. The electron beam of low emittanceand high beam current are now considered as the electron
sources for the x-ray free electron laser (FEL) which requires lower emittance to obtain shorter wavelengths andhigh peak current to obtain good gain, and linear colliders
to meet the requirement of a complex pulse structure and toprovide small emittance flat beam [1].
The first use of the RF photoinjector was done by Fraser
et al. [2] in 1985 at LANL for the application to the FEL.
The idea to combine a photocathode and a laser system withan RF cavity that supports a standing-wave field has many
advantages. First, the electron bunch length is determinedby the laser pulse without the following buncher section andprovides narrow energy spread. Second, the electron beam
is immediately accelerated up to relativistic energy by highRF field on the cathode within the first cell, which can decrease the space-charge growth of the emittance when theelectrons are non-relativistic. Third, the quite low emittance beams can be produced by decreasing the laser spot
size at the photocathode [3] which can reach as small emittance as 0.1 mm · mrad with relatively small bunch charge> 0.1 nC. The electron beam dynamics after generationfrom the cathode is well understood analytically [?, 5] andnumerically. The emittance of the beam produced by the RF
electron gun is determined by three contributions: the emittance as the bunch emerges from the cathode; the electromagnetic interaction among the non-relativistic electrons
called as the space charge eﬀect; nonlinear radial dependence of the transverse components of RF.
In most cases, the RF photoinjector operates at a low duty
factor and have relatively low average current. The first photoinjector with a duty factor of 25% was designed by Boe∗ smori@post.kek.jp† mitsuhiro.yoshida@kek.jp‡ dai-satou@aist.go.jp

ing in 1992 [6]. Currently, a collaboration between LANL
and AES is developing a normal conducting photoinjector,
which works in the CW mode. In the CW mode operationof a normal conducting photoinjector, the large amount of
RF power loss causes cooling problems and bounds the gradient, e.g. 7 MV/m in ref. [6], which becomes drawbacks
in the emittance. While superconducting RF photoinjectors
also provides CW mode operation with high average current, with low emittance O(1) mm · mrad due to the moderate gradient 20-50 MV/m.
A dielectric assist accelerating (DAA) structure [7, 8] ispromising in power eﬃciency and could be a new candidate of photoinjector with CW mode operation, because
it provides high eﬃciency Q ∼ O(105 ) at room temperature. Due to the structures of the dielectrics and the use of
the ultra-low-loss dielectric material [8], the five cell DAA
cavity provides the Q-value, Q = O(105 ), and the shunt
impedance Zsh ≃ 650 MΩ/m. We have constructed thetest stand for the DAA test cavity whose design frequency
is 5712 MHz. In the tentative high voltage test, we foundthe gradient can reach up to multi-MV/m. This test cavity isplanned to examine the main cavity to accelerate a relativistic electron beam which is generated from the RF photoinjector. In order to examine the possibility of the high-duty
operation of the DAA main cavity, it is reasonable to construct the RF photoinjector which applies the DAA structure
as well.
In order to investigate the possibility of the DAA structure as an RF photoinjector, we carry out the numerical calculation of the electromagnetic field in the cavity and thecoupler, and the dynamics of an electron bunch generated
by the photocathode.
This paper is organized as follows. In Sec.2, the dielectric
cell of the DAA structure is introduced and we discuss theboundary problem which appear when the beam hole opens.
In Sec.3, we introduce the novel structure of the end cell to
avoid the boundary problem. In Sec.4, we will show thenumerical result of the RF photoinjector based on the DAA
structure. In Sec.5, we will summarize our result.

THE DAA STRUCTURE AND THE
BOUNDARY PROBLEM
In this section, we will review the concept of the DAA
structure and its boundary eﬀect.
The basic structure of the DAA cavity is periodic, whichis composed of the cylindrical waveguide made of metal anda cell called regular cell. Figure 1 shows the distribution of
the electric force line calculated using SUPERFISH in the
pillbox cavity which contains a regular cell. We call thehorizontal axis and vertical axis as z and r direction, which
describe the beam axis and radial direction of the dielectric
cell. The dielectric cell is the combination of the disk-likestructure and the coaxial structure, which are shown as therectangular region around z ∈ (1, 1.5) cm and the horizontal region around r ∼ 2.5 cm, respectively. SUPERFISH
provides us the electromagnetic field distribution in the frequency domain in (z, r) coordinates assuming the rotational
symmetry about the beam axis. The red lines denote thereal part of the electric force line and the green lines shows
the imaginary part of them, which describe the magnitudeof the accelerating field Ez (z, r) has maximum value at thebeam axis.

In the large number of cells limits, the eﬀect of the beamhole to the cavity parameters is negligible. If the cavity contains Ncell regular cells, the boundary cells of the both ends
eﬀect by 2/Ncell in the figure of merit of the whole cavity.
However, in the test DAA cavity shown in Fig. 2, we apply
Ncell = 6 and boundary eﬀect is huge. In order to avoid
the reduction from the boundary eﬀect, we apply additional
cylinder in the end cell, which is shown in r ∈ [0.5, 1] andz ∈ [0.5, 2] in Fig. 2, so that most of the electric force lines
hit above the beam hole and electric field around beam holebecomes smaller. Applying the end-cell structure, we obtained Q = 1.2 × 105 and Zsh ∼ 600 MΩ/m.

Figure 2: The electric field configuration in the frequency
domain calculated by SUPERFISH. The ticks denotes thedimension in cm unit. This figure describes the field configuration of the design frequency of the test cavity, i.e.
5712 MHz. The red curves denotes the electric force line.
Figure 1: The electric field configuration in the frequency
domain calculated by SUPERFISH. The ticks denote the dimension in cm unit. This figure describes the field configuration of the design frequency of the test cavity, i.e.
5712 MHz. The red curves denotes the electric force line.

The above naive solution still causes a new problem thatthe symmetry of the field in terms of each disk is broken
by the boundary eﬀect. Moreover, the peaks of the field
across the surface of the dielectric cells which would cause
the discharge in the high voltage test.

In Fig. 1, the electric field is the standing wave along thez-direction and has periodic structure due to the metal walls
on the left and the right side. The whole field configuration inside the DAA cavity is similar to the TM02n modein the pillbox cavity, whose diﬀerence appears from the dielectric cells. The dimensions of the dielectric structure aredetermined so that the peaks of the electric field is confinedwithin the ceramics which has relatively high permittivity,ϵr ∼ 10 and can hold many electric force lines.
The structure of the DAA cavity has advantage of the highQ-value and the high shunt impedance as described below.
As for the Q-value, the coaxial dielectric layer partially confines the electromagnetic field in the cavity so that the surface magnetic field at the copper surface becomes relatively
small compared to one of the pillbox cavity. As for the shunt
impedance, it is known that the waveguides with dielectricdisks have a higher shunt impedance than all-metal waveguides [9]. Naively, this is because the dielectric disks makethe electric force line concentrated around the beam axis,
which is also applied in the DAA structure.
Due to the eﬃcient structure to keep the RF energy andconcentrate them to the beam axis, the result of the simulation shown in Fig. 1 is Q = 1.4×105 and Zsh ≃ 900 MΩ/m.
However, once the beam hole opens, the figures of merit
significantly decrease by around 80%.

THE NOVEL END CELL STRUCTURE OF
THE DAA CAVITY
We found a configuration shown in Fig. 3 which can confine the field in the dielectric cells approximately restoring the symmetry even the neighboring cell of the end cell,which can also optimize the figures of merit.

Figure 3: The electric field configuration in the frequency
domain calculated by SUPERFISH. The ticks denotes thedimension in cm unit. This figure describes the field configuration of the design frequency of the optimized end cell,i.e. 5712 MHz. The red curves denotes the electric forceline.
The class of field configurations like Fig. 3 can be reproduced by considering the interference condition along z di-rection. In Fig. 4, we show a schematic figure to explain theconcept of the end cell structure. The gray region denotes
the dielectrics and the white region denotes the vacuum.
The parameters a, b, c, δ, d, and D are numerically determined so that the field configuration in the regular cell is
optimized in terms of the Q-value and the shunt impedance.
Other three parameters, l1, l2, and l3 are determined as below. Compared with the regular cell shown in Fig. 1, here
we introduce an additional dielectric cylinder near the beamhole with a length of l1 and a vacuum region with a lengthof l2 . Considering the optical path length of the path1 andthe path2 which are shown in Fig. 4 as L1 and L2 , since therefractive index n of the dielectric cell is greater than one,apparently they should satisfy L1 < L2 . As the length of aregular cell corresponds to a half wavelength, it is natural
to consider the interference conditions, L1 = λ, L2 = 3λ/2,
which determine two parameters, l1 and l2 . We found thefield configuration calculated with the dimensions l1 and l2
obtained as above can improve both Q and Zsh . Then, wetune the third parameter l3 in order to confine the electricforce lines in the dielectrics and optimize the Q-value andthe shunt impedance, further.

Figure 4: The schematic picture of the new end cell structure.

Figure 5: The RF photoinjector and the coupler used in our
simulation.

Figure 5 shows the picture of the DAA applied RF photoinjector. We introduce a coupler between the waveguideand the cavity as four coaxial holes which are on the periphery of the cavity, so that the iris of the beam hole canbe minimized keeping the coupling large. Due to the parity
symmetry of the system in terms of the x-z plane and they-z plane, we apply the symmetry condition to reduce thecalculation cost as Ht = 0 on the both planes.
In Fig. 6, we show the distribution of the electric field inunit of V/m in the (z, r) plane calculated by CST. In Fig. ??,we show the magnetic field in unit of A/m in the (z, r) plane
calculated by CST.

Figure 6: The contour plot of the tangential component of
the electric field calculated using CST.

THE APPLICATION OF THE DAA CELL
TO THE RF PHOTO INJECTOR
In this section, we show the numerical result of theparticle-in-cell simulation using CST MICROWAVE STUDIO (CST) in the RF photoinjector applying the DAA structure. In the following calculation, we adopt the end cellshown in Fig. 3. Since the high power test of the DAA
cavity has not been completed and tens of MV/m region
has not been established yet, we assume the moderate value
for the accelerating gradient, i.e. 20 MV/m. Although the
DAA test cavity is designed to work with the frequency of
5712 MHz, the RF frequency of 5712 MHz is too high,in the gradient assumed here, to accelerate non-relativistic
electrons bunches generated at the cathode up to relativisticenergy within the first half cell. Thus, we adopt a frequencyof 2856 MHz as the design frequency, which enlarges all thedimensions of the cavity in Fig. 3 by a factor of two.

Figure 7: The contour plot of the normal component of themagnetic field calculated using CST.
In Fig. 8, we show the distribution of the gradient on the
beam axis normalized by the maximum magnitude of it,
Ez (z, r = 0)/Ez (z = 0, r = 0), and the phase, Arg(Ez (z, r =0)), calculated by CST as blue dots and orange dots, respectively. The plot shows the field configuration when the amplitude of the electric field is maximum. As expected fromthe coupler structure, the gradient outside the cavity is suppressed well.

2

Ez(r=0)/Ezmax
1

ϕ[rad]

50

100

150

200

z[mm]

RF frequency [MHz]2856
field on cathode [MV/m]
20
RF phase at cathode for laser pulse 3π/2
thermal loss [kW]290
laser spot [σ in mm]
2.0
laser pulse width [σ in ps]
10
charge in bunch [nC]0.1
ϵz at exit [mm · mrad]
1.5
ϵT at exit [mm · mrad]
1.3
beam energy spread at exit [%]4.0
bunch length at exit [σ in mm]
1.5
bunch radius at exit [σ in mm]
1.5
Table 1: The parameters related to the RF and the emittance.

-1

Figure 8: The accelerating field Ez (z, r = 0) calculated bynumerical simulation.
The thermal loss contains two contributions from the surface of the cavity and the dielectric loss, whose power dissipation is 245 kW and 45 kW, respectively. The thermal
conductivity of the ceramics we adopt is about ten times
smaller than one of the pure copper, while the heating power
generated at the dielectrics is around ten times smaller than
one of the pure copper. Then, the diﬀerence of the thermal
conductivity is canceled by the diﬀerence of the power loss.

CONCLUSION

Figure 9: The z dependence, namely time dependence, ofthe β distribution and the energy distribution of a bunch
calculated by CST.
The upper and lower figures in Fig. 9 show the β-z distribution and the Energy-z distribution in a bunch for eachtime step with a step size of 52 ps, respectively. Apparently,
the electrons become relativistic at the exit of the RF cavity.
In Table 1, we show the parameters used in our calculation and beam parameters measured at the outside of thecavity. In our analysis, we synchronize the laser pulse andthe RF phase so that emitted electron bunches are maximally accelerated in the first half cell. We numerically estimate the thermal loss in the cavity to support the gradient of 20 MV/m, which is about 290 kW in our simulation. At present, the water cooling can remove the power
deposited as the surface temperature, whose typical capacity is 100 kW, which corresponds to the duty factor about
34 %. In contrast, if we want to operate the system withthe duty factor of 1 %, the cooling power required is about
2.9 kW.

The DAA structure is a candidate for the highly eﬃcient
accelerator which could realize the continuous-wave-mode
operation at room temperature with a relatively larger current. We investigate the application of the DAA structure to
the RF electron gun, which could provide the high-quality
beam with high peak current.
In our analysis, the structure of the end cell appears to beimportant since the RF photoinjector is constructed from asmall number of cells. First, we try to optimize the eﬀectof opening the beam hole by introducing the vacuum region between the end cell and the wall, which weakens thestrength of the field at the beam hole satisfying the interference conditions along z direction.
We apply the optimized structure to the DAA applied RF
photoinjector and numerically investigate the behavior of aelectron bunch generated at the cathode, which shows thata bunch with the normalized emittance of O(1)mm · mrad
can be generated by the DAA adopted photoinjector. The
duty factor of 1 % is possible with the cooling power of
2.9 kW. Considering the water cooling capacity of 100 kW
the possible duty factor is 34 %.

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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