Conceptual design of the high-power electron beam irradiator using niobium-tin superconducting cavity

In recent years, there has been an increasing demand for high-intensity beams in the field of electron beam irradiation. This includes mass production of nuclear medicine examinations using 99Mo and high-efficiency production through material modification via material irradiation. Although superconducting cavities can achieve high-current beam acceleration, a compact accelerator is desirable for general-purpose irradiation beams. In this paper, we designed a practical 10 MeV, 50 mA high-current beam irradiator using a new Nb3Sn superconducting cavity.


Introduction
There is a wide-range applications for electron beam irradiation, including medical applications, sterilization, and material irradiation.The most popular compact electron accelerator for beam irradiation is the linear accelerator that uses normal-conducting cavities, especially for medical use, and can operate at various energy ranges from several MeV to a few tens MeV.However, generating a high-intensity electron beam with this type of accelerator is challenging due to the significant cavity wall loss.The Rhodotron accelerator is also used for sterilization applications, usually operating 7 MeV with several 10 mA [1].The energy of Rhodotron was fixed in commerce.For these irradiation applications, we constructed an irradiation beamline at the Compact ERL (cERL) in KEK [2], which is based on Nb-Superconducting (SC) cavity for acceleration, and can produce up to 20 MeV continuous wave (CW) electron beams.In this beamline, we have produced radioisotopes (RI) for medical applications [3], and have recently achieved the high-efficiency generation of nanocellulose, a new material made from wood, by electron beam irradiation of wooden samples [4].These results show the significant potential of high current CW beams with SC cavities for various irradiation applications.
Recently, a new superconducting (SC) material called niobium tin (Nb 3 Sn) has been developed as an alternative to Nb.This technology was developed at Cornell Universi-ty in the mid-2010s, and lowloss cavities have been achieved [5].Nb 3 Sn cavities can operate at 4.2 K with an accelerating gradient of about 17 MV/m.Compared to Nb operating at 1.3 GHz, the heat load in the Nb 3 Sn cavity at 4.2 K can be drastically reduced, making it possible to operate the beam using a simple small refrigerator instead of a conventional large He refrigerator.So recently, we started 1.3 GHz Nb 3 Sn cavity development in KEK [6].
These situations led us to consider the design of a com-pact high-current beam irradiator by using Nb 3 Sn SC cavities to meet the growing demand for irradiation applications.As a result, there has been great interests in accelerator design [7,8].
In this study, we have designed a general-purpose accelerator using Nb 3 Sn.Based on the basic research of high-efficiency nanocellulose production at cERL, we designed a 10 MeV, 50 mA highcurrent SC accelerator to meet the global demand for nanocellulose production.We estimated the potential compactness of the accelerator and the operating electrical power of cryogenic system by using the new Nb 3 Sn cavities, compared to the Nb cavities currently used at cERL in KEK.We have made significant efforts to minimize beam loss in the cryomodule during designing.

Conceptual design of accelerator using niobium-tin cavities
Figure 1 shows a schematic of the entire system, which includes an injector part with electron gun, a superconducting cryomodule, and an irradiation part.

Design of Injector Part
It is important that the injector part have been designed to the level of existing mature technologies for stable beam operation.Therefore, the electron gun was started to use thermionic gun and the injection part was based on the existing cERL injector [9].The layout of the injector section is shown in Figure 2. A thermionic gun was used because it can stably supply a large current of more than 10 mA with an acceleration voltage of 100 kV.The CW beam was generated by the hot cathode with a grid pulse.In the 1990s, a high-power thermionic electron gun synchronized to a 1 GHz RF was developed [10].This development provided the basis for high-power, high-repetition thermionic electron guns.For our design, we used gridded dispenser cathodes (Y-845) that are available from Communications & Power Indus-tries LLC [11] for our electron gun.Two solenoid coils are installed around the buncher cavity for transverse beam focusing.A collimator was introduced into the injector design to create a vacuum pressure step between the electron gun and the SC cavities.Another reason for the collimator is to control the beam size and suppress beam loss in the SC cavities.A profile monitor and a Faraday cup are used to check beam parameters.The results of the beam simulation will be presented in the last subsection.

Design of Nb 3 Sn SC Cryomodule
There are three main factors that need to be considered during the design: the maximum power of the input coupler required for beam acceleration, the acceleration gradient, and the heat load of the SC cryomodule.We used the same frequency of 1.3 GHz for the Nb 3 Sn cavity.The maximum beam power is 10 MeV × 50 mA = 500 kW, which is supplied by RF power through the input coupler.Currently, input couplers at the 40 kW level have been developed for the cERL injector [12], and 60 kW input couplers have been developed at the Cornell ERL injector [13].The maximum power assumed for the input coupler is 60 kW to ensure safe operation.In our case, two couplers were used for one cavity in both cERL and Cornell ERL.Therefore, we used 5 cavities with 2 input couplers for our cryomodule, with one coupler supplying 50 kW of power, which is within our technology.The accelerating voltage (V c ) of one cavity is determined by the product of the accelerating gradient (E acc ) and the cavity length (L).In order to achieve a total acceleration of 10 MV across 5 cavities, Vc of 2 MV is required.The length of one cell of the cavity is 115 mm, which is half of the 1.3 GHz wavelength ().We selected that each cavity has two cells based on cERL injector cavity [14].The accelerating gradient is reduced to 8.7 MV/m, providing a sufficient margin of the existing Nb 3 Sn SC production level [5] .
The total heat load during cavity operation was calculated based on the accelerating voltage and the number of cavities mentioned above.The heat load (P c ) per cavity is derived from the formula Pc = (Vc) 2 /(R/Q)/Q 0 , where R/Q is the "shunt impedance" and Q 0 is the unloaded-Q of a 2-cell cavity.R/Q of 2-cell cavity of the cERL injector cavity is 205 ohms [14].The unique feature of Nb 3 Sn is that an unloaded-Q of 1 x 10 10 can be realized at 4 K.The heat load per cavity (Pc) is calculated to be 1.95 W, and the total heat load (at 4 K) of 5 cavities is 9.75 W.
On the basis of beam dynamics calculations, as shown later, two 1-cell Nb 3 Sn cavities with low-β (β = 0.8) were added before the 2-cell cavities because the initial beam of 100 kV is in the nonrelativistic region and sufficient accelerating voltage from 100 kV electron beam could not be obtained by the 2-cell cavity (β = 1).The design of the 1-cell cavity for β=0.8 is shown in the bottom-left figure of Fig. 3.The length of 1-cell cavity of β=0.8 is set to  to accelerate low energy beam of 100 kV.The voltage of the two 1-cell cavities in the first stage is about 0.5 MV by design, resulting in an accelerating voltage of 1/4 of 2 MV.The heat load of 1-cell cavity is approximately 0.1 W. Therefore, the total dynamic heat load of all cavities is about 10 W at 4 K.
Figure 3 illustrates the conceptual design of our Nb 3 Sn cryomodule (top).A single small cryocooler is attached to cool one 2 W heat-load cavity.The RDE-418ED4 4 K refrigerator manufactured by Sumitomo Heavy Industries, Ltd. is selected as the small cryocooler, as shown in the bottom-right figure of Figure 3 [15].This refrigerator has two cooling points, where cooling at the first stage of 40 K is available.The second stage at the tip goes down to 4 K, with a maximum 4 K cooling power of about 2 W, which equals the AC power consumption of 6-7 kW at room temperature [15].The second stage is used to cool each 2-cell cavity, while the first stage is used to cool the thermal shield.The heat load from the input coupler is another issue, as a total of 100 kW power enters the cavity through two input couplers.The heat load from one coupler is about 1 W per coupler at 4 K.The second stage of the cryocooler is independently used to cool the heat load of the coupler, and the first stage is also used to cool the thermal shield.We note that there is little heat load on the cavity body and the input coupler of the low- cavity, therefore, we apply only one cryocooler as shown in Figure 3.The top figure in Figure 3 shows a detailed drawing of the actual arrangement.Small refrigerators are placed side by side on the top plate of the module to cool the 2-cell cavities via a copper or aluminum thermal link for conduction cooling.The input couplers are also cooled via conduction cooling.The pink part in the top figure of Figure 3 represents the thermal shield, which is connected to the first-stage cryo-coolers.The magnetic shield is placed on the outside of the cryostat, and the inside of the cavity is kept under high vacuum.All components are suspended from the top plate of the cryomodule.
We have made a estimate of the AC power consumption between Nb cavities under normal cryogenic operation and Nb 3 Sn cavities in our design with small refrigerators.A cooling capacity of 10 W is used for 5 Nb 3 Sn cavities by using five small refrigerators.Therefore, the AC power required is 6-7 kW x 5 = 30-35 kW.Thus, an average of 33 kW of AC power is needed to cool the Nb 3 Sn cavity by cryo-coolers.In contrast, the same Q-value can be achieved at 2 K for Nb cavities, but it would require a larger helium refrigerator.For example, the typical Linde L70 refrigerator [16], which has 10 W cooling power (converted to latent heat of vaporization) at 4.2 K, is assumed to cool Nb cavities.The total required AC power for Nb cavities is roughly 60 kW [17].Considering that the ratio of the Coefficient of Performance (COP) between 4 K and 2 K is about 4 on average [17], it can be estimated that 240 kW of AC power is needed to absorb the heat load of the total 2 K Nb cavities.Therefore, the use of Nb 3 Sn cavity allows for a significant reduction in AC power consumption for refrigerators, down to about 33 kW / 240 kW = 14%.

Total Design of Accelerator
Figure 4 shows the overall conceptual design of the 10 MeV, 50 mA irradiator using Nb 3 Sn cavities.The accelerator's total size can be reduced to approximately 8 m x 1 m x 2 m.In the irradiation part, two quadrupoles are located 1 m downstream of the cryomodule to adjust the beam size.The beam is then bent downward by the di-pole magnet, reaches the extraction window, and irradiates wooden materials.

Results of Beam Simulation
Our goal for beam transportation during irradiation is to reduce beam loss through the injector and cryomodule to almost zero.To estimate beam transportation, we per-formed particle tracking using the General Particle Tracer code (GPT) [18] with the inclusion of space charge effects.The initial parameters of the electron beam from the electron gun are as follows: bunch charge of 77 pC/bunch with a repetition rate of 650 MHz, equivalent to 50 mA.The cathode size is 5.73 mm in diameter, and the initial bunch length is 100 ps in r.m.s.(Gaussian ±4σ).
Beam simulation was done under the layout as shown in Figure 4.In reality, it was necessary to adjust the amplitudes and phases of the cavities, as well as the strengths of the solenoids, to find the optimum conditions for reaching the target energy of 10 MeV while keeping the energy width of the emitted beam narrow to avoid any beam loss during transportation.Once all the free parameters of the model were confirmed, the particle distribution was tracked through the transportation line, and the beam parameters were evaluated, as shown in Fig. 5. Initially, we used a 1.3 GHz buncher cavity identical to those at cERL, but it was difficult to compress the 100 ps bunch length.Therefore, we modified a buncher cavity based on 650 MHz to increase the RF phase range, which effectively compressed the bunch length.In addition, the 1-cell cavities helped minimize the energy spread.During the transportation simulation, the transverse beam size of 4σ was reduced to within a 70 mm diameter, which is equivalent to the iris and beam pipe diameter of the cavities.Finally, no beam loss was observed up to 10 MeV with 1,000,000 particles transmission, indicating that less than 0.5 W beam loss was achieved in this simulation.

Conclusion
Using Nb 3 Sn cavities, it is possible to achieve lossless acceleration of 10 MeV and 50 mA, and to design a compact irradiation accelerator with conduction cooling.The AC power consumption for refrigerators can be significantly reduced to 14% compared to conventional Nb cavities.

Figure 2 .
Figure 2. Layout of the injector part.

Figure 5 .
Figure 5. Beam parameter through the transportation line: rms bunch length (top left); rms transverse beam size (top right); energy and energy spread (bottom)