Magnetic Alloy Core Loaded 2nd harmonic cavity design and testing for CSNS-II RCS

In this report, we present our recent progress in the design and high-power testing of the 2nd harmonic cavity for the China Spallation Neutron Source upgrade project. To achieve optimal performance, high-performance magnetic alloy (MA) cores with dimensions of Φ850mm × Φ316mm × 25mm were meticulously developed and fabricated to serve as the load material for the radio-frequency (RF) cavity. Through rigorous testing, we were able to achieve a remarkable cavity accelerating gradient of over 40 kV/m under 15% duty cycle. To ensure optimal cooling efficiency, we conducted a comprehensive fluid dynamics simulation analysis and verified our results through experiments. Finally, to assess the long-term stability and performance of the cavity, we conducted a series of extended operation tests. These experiments successfully confirmed the high-performance capabilities and exceptional stability of the 2nd harmonic cavity.


Introduction
The China Spallation Neutron Source (CSNS) is a multidisciplinary research facility dedicated to the advancement of neutron science.It includes an 80 MeV linac, a 1.6 GeV rapid cycling synchrotron (RCS), a target station and several instruments [1].
As part of the ongoing CSNS-II upgrade project, the beam intensity will be significantly increased from 1.56 × 10 13 to 7.80 × 10 13 protons per pulse (ppp) to achieve a higher beam power of 500 kW.However, this heightened beam intensity creates a significant space charge effect during the early stages of acceleration, which is a crucial issue for longitudinal beam dynamics [2].To address this challenge, a large second harmonic voltage superimposed on the fundamental must be adopted to alleviate the space charge effect, as illustrated in Fig. 1.The plot depicts the variation of the fundamental and second harmonic amplitude over the time required for beam capture and acceleration, based on the beam dynamics design.The horizontal axis represents the working time of the RCS at a repetition frequency of 25 Hz and 50% duty cycle, while the vertical axis denotes the total radiofrequency (RF) voltage.The ferrite loaded cavity provides the fundamental harmonic with a peak voltage of about 175 kV, while higher gradient cavities are necessary to achieve the second harmonic with a peak voltage of approximately 100 kV.Unfortunately, the limited tunnel space precludes the continuous use of the ferrite loaded cavity due to its low saturation flux density.

Figure 1.
The dual harmonic voltage operation curves..The use of magnetic alloy (MA) cores as loading material for RF cavities is widespread due to their high saturation flux density, contributing to achieving high gradient [3].Additionally, the low Q-product property of MA cores allows for a wideband property, enabling the establishment of a simpler RF system without tuning loops.Unfortunately, export regulations hinder the procurement of these MA cores, necessitating the development of a high-performance MA core.We have developed a MA core measuring 850 mm (outer diameter) ×316 mm (inner diameter) ×25 mm (thickness) by winding nanocrystalline soft magnetic alloy ribbon, with a thickness of approximately 18 μm and a width of 25 mm [4].The model of the MA ribbon, 1k107B, has the composition of Fe 84 Cu 1 Nb 5.5 Si 8.2 B 1.3 (at %) and is manufactured through a single roll rapid solidification method.The MA ribbon's surface is uniformly coated with about 2 μm of SiO2 insulation to reduce eddy current loss and prevent adjacent-ribbon breakdown in high electric fields.The MA core's inner and outer layers are shaped by high-strength Fiber Reinforced Polymer (FRP) tubes.Fig. 2 shows the cured layer, with few air bubbles visible after glass fiber cloth and high-concentration epoxy curing in a high-temperature and vacuum environment.The μQf product is an essential parameter for RF cavities, independent of loading material geometric dimensions, and proportional to the cavity shunt impedance, which determines the cavity accelerating voltage.Fig. 3 demonstrates the performance of 42 MA cores produced in our mass production.The average μQf products are 7 GHz, 9 GHz, and 11 GHz with a deviation of ±10% at the frequency point of 1 MHz, 3 MHz, and 5 MHz, respectively.The performance of the magnetic alloy cores is critical to the RF properties of the cavity, which are highly de-pendent on adequate cooling to manage high power loss.In this paper, we focus on the design of the MA-loaded cavity, including both the RF and cooling structures, and present a detailed fluid thermodynamic study of the cavity to verify its cooling efficiency.We also conduct high-power tests to assess the stability and performance of the cavity under actual operating conditions.

RF cavity design
In accordance with the beam dynamics design, the total RF voltage required for the MA loaded cavity is 100 kV.However, with only three cavity installation locations provided in the RCS tunnel, each cavity must generate around 33.3 kV RF voltage, leaving little engineering allowance.To address this challenge, we designed a MA loaded cavity with three ceramic accelerating gaps to prevent gap flashover under high RF voltage.The cavity has a distinctive appearance, as shown in Fig. 4(a), and a schematic diagram of the structure is displayed in Fig. 4(b).It comprises three accelerating cells, with each cell consisting of a vacuum pipe, a ceramic gap, and two tanks equipped with a λ/4 coaxial structure.Each tank has three MA cores loaded in it and is immersed in deionized water for cooling.A water inlet and outlet are pre-sent on each tank and can be adjusted independently.The inner and outer conductors of the tanks are composed of 304 stainless steel, with inner and outer diameters of 298 mm and 946 mm, respectively.As a result of the high electric field in the tank's inner area, a 3 mm-thick FRP insulation cylinder is mounted on the inner conductor's surface.Two temperature probes (PT100 with an accuracy of 0.1 ℃) are installed at the entrance and exit of each tank to monitor the temperature rise.Two high power tetrode tubes in push-pull mode are used as the RF power source.Each tetrode works alternately for half a cycle in AB1 class mode, which the even harmonics introduced by nonlinearity of the dynamic-tube characteristics are eliminated and helps to achieve a high voltage gradient required for the particle accelerator [5].However, the high dielectric constant of deionized water used for cooling the MA cores causes the resonant frequency of the cavity to be lower than desired, which reduces the working efficiency of the tetrode tube in the range of dual harmonic working frequency.To address this issue, two air inductors are connected in parallel at the RF busbar end of the cavity to adjust the resonant frequency and Q value of the cavity.The impedance of the MA loaded cavity is significantly improved after the installation of the air conductor, and the resonant point is shifted to 2.07 MHz with a Q value of about 1.24, as shown in Fig. 2. The optimization methods used for the air inductor can be found in Ref [6].The main parameters of the MA loaded cavity are list in Table 1.

Fluid thermodynamics simulation
The Q value of the MA core being less than 1 results in the concentration of almost all RF power loss of the cavity in the MA cores.When operating the MA loaded cavity under high duty cycle, the average power loss in the MA cores becomes substantial, posing a challenge for the cavity cooling.To address this, a direct water-cooling method, known for its efficiency, was considered [7].In view of the large size of the MA core, ANSYS CFX was employed to carefully examine the fluid distribution inside the tank to prevent fluid back-flow and localized hyperthermia near the MA core surface.The main physical parameters of the materials for fluid thermodynamics simulation in ANSYS CFX have been presented in Table 2. Notably, the thermal conductivity of the MA core is anisotropic and is defined in a cylindrical axis system due to the higher thermal resistance of the core along the radius direction than that along the circumference and width direction, owing to a 2 μm SiO 2 layer between the adjacent MA ribbons.These thermal conductivity parameters were obtained from Ref. [8].The heat loading in the MA core is another critical parameter for simulations.The RF power loss density P d (r) of the MA core is proportional to the square of the magnetic flux density B rf as demonstrated in Eq. ( 1), where C denotes the normalization factor.Further calculations, as shown in Eq. ( 2), reveal that the RF power loss P is the volume fraction of the power loss density.For simulation, we used 12 kW/tank (4 kW/core) to normalize the power density distribution.
() =   () 2 •  (1) 7.1(Z) W/m/K 7.1(Ф) W/m/K 0.2(r) W/m/K The temperature of the interface between the MA core and curing layer has become a subject of heightened interest, as the MA core curing layer's maximum working temperature is limited.To distinguish between the two interfaces, we have labeled the MA core surface attached to the curing layer as interface A, and the curing layer face attached to the water as interface B. Fig. 6 displays the temperature of interface A when the tank inlet flow rate is 40 l/min.According to ANSYS CFX, the temperature rise in the tank outlet is 4.28 ℃, which closely aligns with the theoretical calculation of 4.31 ℃ by Eq. (3).
where the water flow rate, denoted as L, the water density ρ is set at 997 kg/m3 at 30 ℃, and the specific heat capacity of water, represented by C, which is set at 4181.7 J/kg/K at 30 ℃.At interface A, the highest temperature observed is approximately 73 ℃, which falls well below the 100 ℃ limit for the curing layer's operating temperature.Figure 6.The interface temperature distribution of three MA cores.Fig. 7 illustrates the trajectory of fluid inside the tank, with an upper limit for flow velocity set at 0.2 m/s for greater accuracy.Most areas on the surface of the MA core exhibit a laminar flow state, with flow velocities around 0.1 m/s.In the inlet buffer, the fluid first impinges on the tank wall, forming a large vortex before flowing up into the MA core area.The fluid then moves along the circumference direction, with minimal backflow observed in the MA core area.However, when water flows from the tank's bottom towards the outlet direction, a static water flow zone forms in region D, which is located near the core's inner diameter and is indicated by a dotted box in Fig. 4. The high-power density in this area leads to serious heating of the MA core.To address this issue, we designed a gap with a width of approximately 7 mm between the inner diameter of the MA core and the cavity inner conductor, as shown in Fig. 8.This gap allows water from the tank entrance to flow directly to region D, eliminating the static water flow zone.As shown in Fig. 5, the temperature region D is significantly lower than that in regions A and B, confirming the rationality of this design.IOP Publishing doi:10.1088/1742-6596/2687/8/0820037 losses and rising maximum temperatures of the MA cores, with an increment of 3 kW between 9 kW to 15 kW.Our analysis predicts that a tank with a power loss of 18 kW may push the maximum temperature of the curing layer to 97.7 ℃, which is perilously close to its upper operating limit of 100 ℃.Based on this, we maintaining an average power loss below 18 kW.
In Fig. 8(b), we present the maximum temperatures of the MA cores and curing layers at various flow rates, keeping the power loss of the tank constant at 12 kW.Our observations suggest that increasing the flow rate decreases the temperature of the MA core, but beyond a flow rate of 25 l/min, the temperature reduction drops to about 1 ℃ for every 5 l/min increase.This indicates that further increasing the flow rate is unlikely to significantly enhance the cooling efficiency of the cavity.We attribute this to the laminar flow state of the fluid inside the tank, wherein cooling efficacy primarily hinges on the characteristic size of the fluid structure.

Verification of cavity cooling efficiency
We employed a single-gap MA loaded test cavity to validate the accuracy of our simulation results.In each tank, only one MA core was present while the other cores were replaced with FRP material cores of identical size.The power losses of the two tanks were calculated using Eq. ( 3), based on the temperature increase measured at the tank outlet.To measure the temperature of the MA core curing layer surface, we affixed a thermal probe (PT100 with 0.1℃ accuracy) measuring 10mm (H) × 5mm (V) × 10mm (L) to the D region of each MA core within the tank.The thermal probe was coated with epoxy resin and a metal shell to make it waterproof.We installed the thermal probe at region D because the fluid trajectory in this area is almost parallel to the probe length direction, which has minimal impact on the fluid.As the D region experiences a high electric field, we limited the maximum cavity voltage to 4 kV to prevent the thermal probe from breaking down electrically.To minimize measurement errors, we adjusted the flow rate in each tank to be within the range of 15~25 l/min to increase the tank temperature rise.
Fig. 9(a) illustrates the temperature rise of the tanks after reaching thermal equilibrium when the flow rate is 15 l/min and the MA core power is 2 kW, 3 kW, and 4 kW, respectively.Fig. 9(b) depicts the surface temperature of the MA core curing layer in region D, as the flow rate increases from 10 l/min to 25 l/min at 5 l/min intervals.These experimental results show that simulation results agree with the data obtained within an error margin of approximately 5%, indicating that the fluid simulation approach for the MA loaded cavity design is trustworthy.

High power tests
The MA loaded cavity with three gaps was subjected to a test to determine its highest acceleration gradient under the 2 nd harmonic sweeping mode.The voltage waveforms at the ends of an acceleration gap are labelled as 'upstream' and 'downstream', as shown in Fig. 10.This waveform depicts only three RF periods of the peak of the fundamental amplitude curve.The RF voltage waveform at both ends of the gap is equipped with the same amplitude but opposite phase under the push-pull operation mode of the RF source.The synthetic voltage is the voltage difference between the two ends of the gap, which also represents the accelerating voltage experienced by the beam as it traverses the gap of the vacuum pipe.The test yielded the highest synthesized voltage of 52 kVpp, without gap flashover.This corresponds to a gradient of approximately 43 kV/m, which significantly surpasses the accelerating gradient of the ferrite loaded cavity in CSNS RCS, and is adequate for CSNS-II RCS applications.The MA loaded cavity could not undergo further gradient enhancement as the screen grid overcurrent of the tetrode tube was observed.To overcome this issue, we intend to upgrade the anode power supply of the tetrode tube.It should be noted that differences in the outlet temperature of each tank exist as shown in Fig. 11, mainly because the MA core impedance of each tank is not exactly the same, and the reference temperature of each temperature probe is also different.However, the low-level control system aims to keep the power loss of each tank as consistent as possible.To further evaluate the stability of the cavity, we measured its impedance before and after long periods of operation.The results, shown in Tables 3 and 4, indicate that the cavity impedance is stable, with a maximum change rate of less than 3% at different frequency points.We designed a new type of ceramic accelerating structure on November 1, 2022, and replaced it in the cavity, resulting in a change in the cavity impedance due to the variation in gap distributed capacitance.As such, the cavity impedance was statistically analysed with two tables, respectively, for convenient comparison.We will continue to monitor the stability of the cavity over a longer period of time.

Conclusions
In this paper, we present a comprehensive account of our progress in developing a 2nd harmonic cavity for CSNS-II.This cavity is loaded with high-performance MA cores that were fabricated domestically.We designed and tested a MA loaded cavity with three accelerating gaps, which is capable of providing a peak 2nd harmonic accelerating gradient of over 40 kV/m.We studied the cooling efficiency of the cavity using ANSYS CFX and verified it by conducting tests on a single gap MA loaded cavity.Furthermore, we demonstrated the stability of the MA loaded cavity by conducting longterm operations with a beam in the RCS tunnel.

Figure 3 .
Figure 3.The μQf products of domestic MA cores.The performance of the magnetic alloy cores is critical to the RF properties of the cavity, which are highly de-pendent on adequate cooling to manage high power loss.In this paper, we focus on the design of the MA-loaded cavity, including both the RF and cooling structures, and present a detailed fluid thermodynamic study of the cavity to verify its cooling efficiency.We also conduct high-power tests to assess the stability and performance of the cavity under actual operating conditions.

Figure 4 .
Figure 4. (a) The appearance of the cavity.(b) The schematic diagram of the cavity structure.

Figure 5 .
Figure 5.The impedance of the MA loaded cavity before and after optimization.Table1.The main parameters of the MA loaded cavity for CSNS-II RCS

Figure 7 .
Figure 7.The fluid flow trajectory inside the tank.To explore the cooling capacity limit of a tank, we conducted simulations to measure the maximum temperature of the MA cores and curing layers at varying power losses, with a constant flow rate of 40 l/min.Our findings, presented in Fig.8(a), reveal a linear correlation between increasing tank power

Figure 8 .
Figure 8.(a) The maximum temperature of MA core inside and curing layer under the power loss of 9 kW/tank, 12 kW/tank and 15 kW/tank.(b) The maximum temperature of MA core and curing layer with the change of the flow rate under the power loss of 12 kW/tank.

8 Figure 9 .
Figure 9. (a) The temperature difference between the inlet and outlet of the cavity under different power at a flow rate of 15l/min.(b) The surface temperature of the MA core curing layer on D region.

Figure 10 .
Figure 10.The voltage waveform in the both sides of an accelerating gap.The synthesized waveform is obtained by subtracting these two waveforms.The long-term stability of the MA-loaded cavity was evaluated under the 2 nd harmonic ramping mode of the CSNS-II RCS by monitoring the outlet temperature of each tank.The flow rate for each tank was set at 40 l/min and the inlet water temperature was around 24.5 ℃.Fig. 11 shows the variation in water temperature at each tank outlet since the installation of the first MA-loaded cavity in the RCS tunnel on September 26, 2022.It is apparent that the outlet temperature of each tank stabilized after the stable

Figure 11 .
Figure 11.The outlet temperature of each tank.Table3.The impedance of the cavity at different frequency before the beam pipe replacement

Table 1 .
The main parameters of the MA loaded cavity for CSNS-II RCS

Table 2 .
The main parameters of the MA loaded cavity for CSNS-II RCS

Table 3 .
The impedance of the cavity at different frequency before the beam pipe replacement

Table 4 .
The impedance of the cavity at different frequency after the beam pipe replacement