Introduction

Radiofrequency (RF) cavities are widely utilized for delivering power to the beam, accelerating the charged particles, and compensating for synchrotron radiation losses in different accelerator facilities, such as synchrotron radiation sources [1-5] and colliders [6-10]. The Super Tau-Charm Facility (STCF) is an electron-positron collider that has been proposed and studied by the Chinese particle physics community [10, 11]. It is designed to operate in a center-of-mass energy range from 2 to 7 GeV with a peak luminosity of 0.5 × 10³⁵ cm⁻²·s⁻¹ or higher. The STCF project is currently under development with an extensive R&D program, including the RF system. To meet the requirements of collider ring physics, the RF system must provide an accelerating voltage of 6 MV and a beam power of 3 MW for each ring. A TM₀₂₀-mode normal-conducting (NC) cavity was selected as a candidate for the RF system of the collider ring because such a cavity has a low R/Q [12].

The TM₀₂₀-mode RF cavities operating at TM₀₂₀-mode were initially proposed by researchers at KEK and RIKEN and successfully commissioned for the storage ring of NanoTerasu [13]. Compared to conventional TM₀₁₀-mode cavities, the TM₀₂₀-mode cavity exhibits a higher unloaded quality factor and a lower [4, 14]. This characteristic helps reduce the required detuning frequency, significantly suppressing the coupled bunch instabilities (CBIs) driven by the accelerating mode [15].

The distinctive symmetrical electromagnetic field distribution of the TM₀₂₀-mode enables the ferrites to be directly embedded into coaxial slots inside the cavity, as illustrated in Fig. 1 instead of using special waveguides or pipes. This damping scheme not only heavily suppresses all harmful parasitic modes without affecting the accelerating TM₀₂₀-mode, but also reduces the longitudinal spaces, making the cavity extremely compact. However, the introduction of a high-power input coupler and other components may disrupt the symmetry of the electromagnetic field, leading to leakage power of the accelerating mode into the coaxial slots and absorption by ferrites. Additionally, machining errors in the position of the coaxial slots may result in a large leakage power of the accelerating mode. The leakage power causes a reduction in the unloaded quality factor of the accelerating mode and a heating issue for the ferrites, significantly limiting the RF performance of the TM₀₂₀-mode cavity [16].

Fig. 1Full-screen View

(Color online) Magnetic field distribution of TM₀₂₀-mode in TM₀₂₀-mode RF cavity

To address the leakage issue, Li et al. [5] proposed a method to compensate for electromagnetic field distortion by introducing a geometrically optimized tab structure at the coaxial coupling port, thereby reducing the leakage rate to below 1%. The leakage rate is defined as the ratio of the power loss of the accelerating mode absorbed by the ferrites to the power dissipated on the cavity wall. Similarly, Yamaguchi et al. [16] developed a novel loop-type coupler to mitigate the perturbation of the electromagnetic field, achieving a leakage rate of less than 1%. These approaches effectively resolve the leakage issues associated with coaxial couplers. However, when a waveguide coupler is employed in a TM₀₂₀-mode cavity, leakage power remains an issue.

This study proposes a solution to resolve the power leakage issue in a TM₀₂₀-mode cavity with a waveguide input coupler. By employing an elliptical choke, the leakage of the accelerating mode was significantly reduced, and the mechanical structure was simplified. Section 2 introduces the theory of the choke. Section 3 analyzes the issues related to leakage power and provides the elliptical choke design in detail. Section 4 describes the design of the frequency tuners. Section 5 presents the suppression of the harmful parasitic modes. Section 6 presents the multipacting analysis. Section 7 presents the thermomechanical analysis of the cavity. Section 8 concludes the paper.

Theory of choke

The choke-mode accelerating geometry was initially proposed by Shintake et al. [17]. The principle is that the choke reflects the accelerating mode, whereas the harmful parasitic modes pass through the choke and are absorbed by the load. Based on this concept, Zha et al. proposed an improved X-band choke-mode damped structure for the main linac of the Compact Linear Collider (CLIC) [18], achieving nearly complete dipole damping and significantly reducing the total transverse kicks. Inspired by these developments, a choke can be introduced into the TM₀₂₀-mode cavity with a waveguide input coupler to address the issue of leakage power.

As shown in Fig. 2a, the choke geometry can be regarded as a set of coaxial transmission lines strategically positioned at the magnetic field node of the TM₀₂₀-mode inside the cavity, instead of being arranged along the radial direction of the outer wall. This particular placement takes advantage of the electromagnetic field distribution of the TM₀₂₀-mode, allowing the choke to selectively reflect the accelerating mode while allowing the harmful parasitic modes to be absorbed. Through optimization of the choke, the leakage power of the accelerating mode can be significantly reduced, and the harmful parasitic modes can be effectively suppressed.

Fig. 2Full-screen View

A TM₀₂₀-mode cavity with choke (a), and the equivalent model of transmission lines (b), where L, W, D, and d represent the length, width, outer radius, and inner radius of the choke geometry; , , represent the characteristic impedances of each of the transmission lines, and , , represent the reflection coefficients at different planes

The choke can be equivalently modeled as a series combination of two uniform, lossless coaxial transmission lines, each characterized by its own characteristic impedance, as shown in Fig. 2b (1)where and represent the outer and inner radii of the coaxial section. Using the dimensions of the choke geometry, we obtained the characteristic impedances and . represents the characteristic impedance at the slot position inside the cavity, and it can be calculated as follows.

As shown in Fig. 2(b), the end of the coaxial transmission line was terminated with ferrites. This can be modeled as a perfectly matched load with a normalized characteristic impedance of 1. The transmission line, with two different characteristic impedances at each end, is connected in series at plane A. Consequently, the reflection coefficient at plane A is calculated using the following equation: (2)The RF wave propagates from plane A to plane B, and a phase shift is obtained, where is the free space wavelength. Thus, the reflection coefficient at plane B is expressed as: (3)where is the initial phase of the wave.

Similar to the reflection coefficient , the reflection coefficient at plane B is calculated as: (4)By substituting into Eq. (4), the characteristic impedance can be obtained. is determined by the ratio of reflected power and input power at plane B: (5)The input power can be divided into reflected power and power dissipated in the load: (6)Then we have: (7)where is the power absorbed by the load, is the input power to the choke, and is the reflection coefficient at plane B. The absorbed power is related to the quality factor of the resonant cavity as follows: (8) (9)where and are the quality factors without and with a matched load, respectively; is the angular frequency; U is the stored energy in the cavity; and is the power loss on the cavity surface.

Then we have: (10)By varying the choke length L to change the phase shift , can be directly simulated from ANSYS HFSS [19] as a function of L, with a fixed choke width mm, as shown in Fig. 3 (denoted by the dotted black curve). Two arbitrary points and are selected for Eqs. (7) and (10). The corresponding reflection coefficients and satisfy the following relationship: (11)Combining Eqs. (4) and (11), the value of is obtained. This is then substituted back into Eq. (4) to calculate the reflection coefficient as a function of the choke length L, as shown in Fig. 3 (denoted as the dotted red curve). It can be observed that there is a good agreement between the calculated and simulated , validating the proposed transmission line model. The reflection coefficient reaches its maximum at (12)with a fixed choke width W=25 mm. At these points, the TM₀₂₀-mode is strongly reflected back into the cavity, effectively reducing the leakage power.

Fig. 3Full-screen View

(Color online) Simulated and calculated as a function of choke length L

To reduce the leakage power of the accelerating mode while suppressing harmful parasitic modes, the influence of the choke width W is evaluated. By sweeping different choke widths W, calculations are performed with the aim to minimize the absorption rate for the TM₀₂₀-mode and minimize for other harmful modes including TM₀₁₀-mode, TM₀₂₁-mode, TM₀₃₀-mode, TM₀₃₁-mode, and TM₀₄₀-mode. As shown in Fig. 4, the absorption rate for the accelerating TM₀₂₀-mode gradually increases when the choke width W rises. In contrast, the reflection coefficients for the harmful parasitic modes show a significant reduction, particularly in the range of W=20~30 mm. A choke width in this range represents a compromise between the strong suppression of harmful parasitic modes and the minimum leakage rate for the accelerating mode. This provides a theoretical basis for the geometric design of the elliptical choke in the following sections.

Fig. 4Full-screen View

(Color online) Calculated for the accelerating TM₀₂₀-mode and selected harmful parasitic modes (TM₀₁₀-mode, TM₀₂₁-mode, TM₀₃₀-mode, TM₀₃₁-mode, and TM₀₄₀-mode) and the absorption rate for the accelerating TM₀₂₀-mode as a function of choke width W

Design and analysis

Owing to the distinctive symmetrical electromagnetic field distribution of the TM₀₂₀-mode, the coaxial slots must be positioned at the radial node of the magnetic field so that all harmful parasitic modes are strongly damped without affecting the accelerating mode. However, the introduction of an input coupler and frequency tuners may induce localized perturbations to the TM₀₂₀-mode, thereby disrupting the symmetry of the field distribution. In this situation, some partial power of the accelerating mode leak into the coaxial slots and are absorbed by the ferrites. This reduces the unloaded quality factor of the accelerating mode and increases the heating load on the ferrites. The frequency tuner effect can be solved by using multiple structures for symmetrical distribution. This is described in Sect. 4.

To investigate the asymmetrical electromagnetic field distribution of the TM₀₂₀-mode caused by the introduction of the coupler, cavities with and without a waveguide input coupler were simulated using ANSYS HFSS [19], as shown in Fig. 5.

Fig. 5Full-screen View

(Color online) Geometry of two TM₀₂₀-mode cavity models: (a) without an input coupler; (b) with a waveguide input coupler

As shown in Fig. 6(a), the node of magnetic field for the TM₀₂₀-mode is a symmetrical circle inside a cavity without an input coupler. The introduction of a waveguide input coupler distorts the node from a circle into an approximate ellipse, as shown in Fig. 6(b). The center of the ellipse is offset toward the coupler.

Fig. 6Full-screen View

(Color online) Magnetic field distribution of the TM₀₂₀-mode (a), and deformation of the TM₀₂₀-mode magnetic field node (b). The white dashed line represents the simulated shape of the TM₀₂₀-mode magnetic field node without an input coupler, while the red dashed line represents the node with a waveguide input coupler

This distortion is analyzed in detail in Fig. 7, where is the magnetic field normalized to the peak magnetic field inside the cavity, and RR is the distance to the beam axis. After introducing a waveguide input coupler into the cavity, the magnetic field distribution of the TM₀₂₀-mode underwent an obvious transformation. As shown in Figs. 7(a2) and 7(a3), the node of the magnetic field shrinks toward the beam axis by 0.5 mm along the X-axis. Meanwhile, Figs. 7(b2) and 7(b3) illustrate that the node of the magnetic field along the Y-axis shifts toward the coupling port, with the entire distribution moving upward by approximately 1 mm. This change was attributed to the interaction between the coupler and cavity, which broke the rotational symmetry of the magnetic field distribution. When the coaxial slots remain rotationally symmetrical, the asymmetrical magnetic field distribution for the TM₀₂₀-mode may lead to leakage power into these slots, where the leaked power is ultimately absorbed by the ferrites. However, the absorption capacity of ferrites is limited by overheating issues. In a 500 MHz TM₀₂₀-mode RF cavity, assuming that the ferrites can handle up to 10 kW of power and the leakage rate is 10%, the maximum allowable input power is limited to 100 kW. By reducing the leakage rate to 2%, the maximum input power could be increased to 300 kW, based solely on the thermal capacity of the ferrites [20].

Fig. 7Full-screen View

(Color online) Magnetic field distributions of TM₀₂₀-mode along (a) X-axis and (b) Y-axis

Two models were employed for comparison to evaluate the RF performance. One model includes a TM₀₂₀-mode cavity with an elliptical choke (see Fig. 8a), while the other model is a TM₀₂₀-mode cavity with a circular slot (see Fig. 8b). The TM₀₂₀-mode cavity operates at the same frequency in both models. The elliptical choke (Fig. 8a) includes an elliptical slot with its center exactly positioned at the node of the magnetic field. The dimensions of the elliptical slot are shown in Fig. 6(b). Based on the theoretical analysis presented in Sect. 2, a choke length of L=50 mm was used to maximize the reflection of the TM₀₂₀-mode, thereby minimizing the leakage of the accelerating TM₀₂₀-mode. The theoretical analysis in Section II also indicates that a choke width of W=20-30 mm balances the strong suppression of parasitic modes and preservation of the accelerating mode. Through optimizations, W=25.7 mm was selected as a compromise between minimizing the leakage of the accelerating mode and deeply suppressing the parasitic modes.

Fig. 8Full-screen View

Geometry of two models: (a) elliptical slot with choke; (b) circular slot without choke

The simulated RF performances of both models are summarized in Table 1. It can be observed that the cavity with a circular slot has a leakage rate of 12.1% for the accelerating TM₀₂₀-mode. After adding an elliptical choke to the cavity, the leakage rate was significantly reduced to 1.5%. Therefore, the elliptical choke can effectively address the leakage issue of the TM₀₂₀-mode cavity.

A tolerance analysis was performed by introducing an offset ΔR in the slot center position. Figure 9 shows the variation of the unloaded quality factor Q₀ and leakage rate as a function of the offset ΔR in both cavities. The cavity with an elliptical choke (see Fig. 8a) maintains a higher Q₀ and lower leakage rate across the entire ±3 mm offset range, compared to the cavity without the elliptical choke (see Fig. 8b). These results show that the elliptical choke not only addresses the leakage issue but also exhibits a higher tolerance to the positional offset caused by fabrication errors. To maintain a leakage rate P_f/P_c < 5%, the offset ΔR must be within the range of ± 0.3 mm for the proposed cavity with elliptical choke, as shown in Fig. 9b.

Fig. 9Full-screen View

(Color online) Unloaded quality factor (a) and the leakage rate (b) as a function of the slot center position offset , where P_f and P_c represent the power loss of the accelerating mode absorbed by the ferrites and the power dissipated on the cavity wall, respectively

Frequency tuners

Frequency tuners are typically employed as metallic plungers to adjust the frequency of the cavity. The introduction of frequency tuners can perturb the electromagnetic field distribution of the TM₀₂₀-mode so that some partial power of the accelerating mode leaks into the coaxial slots and is absorbed by the ferrites [16]. When inserted into the cavity, the tuner causes radial displacement of the magnetic field node, as shown in Fig. 10. This displacement results in leakage power into the coaxial slots, thereby reducing the unloaded quality factor of the accelerating mode. Consequently, this effect increases the thermal load on the ferrite, potentially causing overheating issues.

Fig. 10Full-screen View

Schematics of magnetic field node deformation of the TM₀₂₀-mode caused by the introduction of: (a) the input coupler; (b) one tuner; (c) two tuners; and (d) three tuners

To minimize the leakage power and ensure the required frequency tuning range, simulations were performed using one tuner, two tuners, and three tuners, respectively. The simulation results are presented in Fig. 11. The adjustable resonant frequency range was set to ±200 kHz to meet the physics requirements. When a single frequency tuner is introduced (see Fig. 10(b)), the node of magnetic field is further shifted along the Y-axis. To achieve a tuning range of ±200 kHz, the maximum leakage rate was calculated to be 26%, as shown in Fig. 11. This may increase the thermal load on the ferrite, potentially causing overheating issues. When two tuners are placed symmetrically (see Fig. 10(c)), the node of magnetic field shrinks along X-axis. It can be seen from Fig. 11 that the maximum leakage rate is simulated to be 15%. When three tuners are arranged at 120° intervals (see Fig. 10(d)), the node of magnetic field stays unchanged. This setup minimizes the magnetic field distortion and significantly reduces the power leakage. As shown in Fig. 11, a minimum leakage rate of 1.5% can be achieved when using three symmetrically placed tuners. Throughout the tuning range of ±200 kHz, the frequency f increases linearly with the tuner insertion length, whereas Q₀ remains above 63,000 and remains below 5%, as shown in Fig. 12. Therefore, three tuners with 120° rotational symmetry were selected for effective frequency tuning while minimizing the leakage rate.

Fig. 11Full-screen View

(Color online) Simulated leakage rate as a function of the frequency f

Fig. 12Full-screen View

(Color online) Frequency f, unloaded quality factor , and leakage rate as a function of frequency tuner insertion length for three tuners

HOMs for TM₀₂₀-mode cavity with elliptical choke

When an electron beam traverses an accelerating RF cavity, harmful parasitic modes, including higher-order modes (HOMs) and TM₀₁₀-mode, are excited. These harmful parasitic modes can potentially degrade the beam quality by inducing longitudinal and transverse coupled-bunch instabilities (CBIs). Therefore, it is particularly important to strongly dampen these harmful parasitic modes and reduce their impedances below critical thresholds to prevent CBIs. In previous studies, we achieved a high unloaded quality factor Q₀ and a low , reducing the required detuning frequency and significantly suppressing CBIs driven by the accelerating mode [15]. In this section, a TM₀₂₀-mode cavity with an elliptical choke is further optimized to ensure that all harmful parasitic modes are deeply suppressed for STCF collider rings with a beam current of up to 2 A.

The parameters of the STCF collider rings impose stringent requirements for the deep suppression of harmful parasitic modes. The longitudinal and transverse impedance thresholds can be calculated using the well-established equations with the parameters listed in Table 2 [21]: (13) (14)where and are the total longitudinal and transverse impedance thresholds, is the frequency of the longitudinal harmful parasitic modes; is the beam energy; is the beam current; is the synchrotron tune; is the momentum compaction factor; is the longitudinal damping time; is the revolution frequency; are the transverse damping times; and are the beta functions at the cavity location.

As shown in Fig. 13, a TM₀₂₀-mode cavity incorporates the elliptical choke with a slot width of W=25.7 mm along with three frequency tuners. The diameter of the beam pipes was chosen to be 50 mm, so the corresponding cut-off frequencies of the TE₁₁ and TM₀₁ modes in the beam pipes were 1.75 GHz and 2.30 GHz, respectively. The optimized RF parameters of the TM₀₂₀-mode are listed in Table 3.

Fig. 13Full-screen View

(Color online) Simulation model of a TM₀₂₀-mode RF cavity with an elliptical choke geometry, three frequency tuners, a waveguide input coupler, and two ring ferrites

Through optimization, the magnetic field nodes of the harmful parasitic modes were separated from those of the accelerating mode within the cavity, as shown in Fig. 14. This spatial separation allows the harmful parasitic modes to propagate through the elliptical choke and be effectively damped by the ferrites.

Fig. 14Full-screen View

(Color online) Magnetic field distributions of the TM₀₂₀-mode and harmful parasitic modes in the cavity with elliptical choke

For the longitudinal impedance and transverse impedance , the following definitions are used: (15) (16) (17)where is the wave number, is the angular frequency, c is the speed of light, r is the radial offset from the cavity axis, is the cavity voltage, and U is the stored energy in the cavity.

As shown in Fig. 15, the longitudinal and transverse impedances of the harmful parasitic modes in the TM₀₂₀-mode cavity are calculated using CST Particle Studio and Microwave Studio [22]. Almost all impedances were below the threshold. This indicates that all harmful parasitic modes were deeply suppressed, meeting the requirements of the STCF collider rings with a beam current of up to 2 A.

Fig. 15Full-screen View

Calculated longitudinal (a) and transverse (b) impedance with different frequency

Multipacting analysis

Multipacting is a phenomenon of resonant electron multiplication when an RF cavity with an input coupler is used for high-power conditioning. This occurs when RF fields sustain electrons on resonant trajectories, causing repeated wall impacts and secondary electron emissions that drive exponential electron multiplication. If the impact energy and material-dependent secondary electron yield (SEY) favor emission, exponential electron multiplication occurs, as described by the secondary electron effect in Eq. 18. When in Eq. 18, the number of particles increases exponentially over time, which is equivalent to the relationship in Eq. 19. A key parameter, SEY, is introduced, and its definition is provided in Eq. 20. When SEY > 1, secondary electron multiplication occurs [23]. (18) (19) (20)where is the initial number of particles, is a growth factor, is the number of electrons after m times of secondary electron emission, m is the times of secondary electron emission, SEY is the secondary emission yield, and are the secondary and primary electron numbers, respectively, and are the secondary and primary currents, respectively.

Multipacting simulations were performed using the CST Particle Studio [22]. As shown in Fig. 16, Region 1 corresponds to the coupling port area, whereas Region 2 and Region 3 represent the inner face of the optimized cavity. For the coupling port area, the input power was swept from 10 kW to 300 kW at a step of 10 kW, and the corresponding SEY are plotted in Fig. 17. As shown in Fig. 17, SEY remains below 1, indicating multiplicating doesn’t occur in the coupling port area. For the inner face of the cavity, the input power was swept from 5 kW to 60 kW at a step of 5 kW. As shown in Fig. 18, the simulated SEY in Region 2 is slightly above 1, which can be readily eliminated through high-power conditioning, while the ssimulated SEY of in Region 3 remains below 1, indicating multipacting doesn’t occur at all. Therefore, these simulations demonstrate that there is no risk of multipacting for the optimized cavity when it is used for high-power conditioning.

Fig. 16Full-screen View

(Color online) Modelling of the optimized cavity for multipacting simulations

Fig. 17Full-screen View

Simulated SEY as a function of the input power for the coupling port area

Fig. 18Full-screen View

Simulated SEY as a function of the input power for the inner face of the optimized cavity

Thermomechanical analysis

When tens of kW RF power is transmitted into the optimized TM₀₂₀-mode cavity, the cavity undergoes mechanical deformation, resulting in frequency shifts and degrading the RF performance of the accelerating mode. Therefore, thermomechanical analysis must be performed for this cavity.

7.2

Mechanical design

Using the optimum dimensions in Sects. 3 and 4, a mechanical TM₀₂₀-mode cavity was modeled. As shown in Fig. 19, the brown and gray regions represent components made of oxygen-free high-conductivity copper (OFHC) and stainless steel (SS), respectively. The cavity comprises two beam pipe flanges, twelve ferrite modules, two ferrite flanges, two end plate flanges, a main body, two nose cone plates, and structural supports. The main body was machined from OFHC and brazed to SS end plates, forming internal cooling water channels within the cavity (see Fig. 20a). Each nose cone plate consists of two OFHC components brazed together to create an internal water-cooling passage (see Fig. 20b), and subsequently brazed to an SS ferrite flange. Each ferrite flange features six openings to install six ferrite modules. Each ferrite module is composed of eighty ferrite blocks (16 mm × 16 mm × 2 mm), a copper base, and an SS flange, as shown in Fig. 20c). Vacuum sealing between the ferrite modules, ferrite flanges and end plate flanges was achieved using metal O-rings or gaskets.

Fig. 19Full-screen View

(Color online) Structural overview of the TM₀₂₀-mode cavity

Fig. 20Full-screen View

(Color online) Mechanical model of the cavity: the layout of cooling channels for the main body (a), each nose cone plate (b), and each ferrite module (c)

7.3

Thermal analysis

To assess the mechanical robustness of the cavity, a coupled thermal-structural analysis was conducted using ANSYS Mechanical [19]. A thermal load of P_c=55 kW (corresponding to an accelerating voltage of 500 kV) was utilized in the following analysis, as shown in Fig. 21. For the cooling system shown in Fig. 20, the flow rate of 10–15 L/min (corresponding to an average velocity of 3 m/s) and an inlet water temperature of 24 ℃ are assumed. The heat transfer coefficient on the cooling channel walls was estimated to be 1.5 W/(cm²·K). The steady-state temperature field obtained from the thermal analysis was subsequently used as an input for the structural stress analysis to assess the effects of thermal expansion. In addition, atmospheric pressure was applied as an external mechanical load.

Fig. 21Full-screen View

(Color online) The power density distribution for the cavity with a thermal load of P_c=55 kW

The simulated temperature distribution is presented in Fig. 22a, the von Mises stress distributions for different components are presented in Figs. 22b and c. The maximum temperature of 42.31 ℃ occurs on the inner surface of the end plate. The peak von Mises stress was 82.07 MPa in the SS region of the flange and 60.85 MPa in the main body with OFHC. Both values were within the acceptable limits for reliable operation. The maximum total deformation of 0.16 mm occurred on the flange, as shown in Fig. 22d. Using this deformation, the resonant frequency of the accelerating TM₀₂₀-mode was simulated to shift by less than -100 kHz under high-power testing. Such a frequency shift can be compensated back through three tuners inside the cavity. The thermal analysis showed that the mechanical design of the cavity was sufficiently robust.

Fig. 22Full-screen View

(Color online) The coupled thermal-structural analysis for the whole cavity: (a) temperature distribution, (b) von Mises stress distribution in the whole cavity, (c) von Mises stress distribution in the OFHC parts, and (d) total deformation in the whole cavity

A similar thermal analysis was also performed for a single ferrite module. The total power absorbed by the ferrites was calculated to be 9.35 kW; thus, a power of 12 kW was utilized for the maximum heat load of the ferrites, leaving 2.65 kW as a safety margin. In this situation, a power of 1 kW was applied to each ferrite module, resulting in a total of 12 kW across all twelve ferrite modules. When the field distributions at the slots for the accelerating mode are employed for the thermal analysis, the heat load is distributed unevenly on a single ferrite module, as shown in Fig. 23a.

Fig. 23Full-screen View

(Color online) The coupled thermal-structural analysis for a single ferrite module: (a) power density distribution and (b) temperature distribution in the ferrite blocks; (c) temperature distribution in the ferrite module flange, and (d) von Mises stress distribution in the ferrite blocks

The simulated temperature distributions of the ferrite module are shown in Figs. 23b and c, while the von Mises stress distribution is presented in Fig. 23d. The temperature of the ferrite blocks increases from 24 ℃ to a maximum of 64.7 ℃, resulting in a temperature rise of 40.7 ℃. Given the Curie temperature of 100 ℃ for ferrites, such a high temperature is acceptable. The peak von Mises stress was 35.7 MPa at the bonding interface between the ferrite blocks and copper base. Considering that the typical tensile strength of Ni-Zn ferrites is 50 MPa, the simulated von Mises stress remains approximately 70% of the tensile limit for ferrite blocks. Therefore, the mechanical design of the ferrite module exhibited good robustness through thermal analysis.

Summary

A 500 MHz TM₀₂₀-mode cavity with an elliptical choke was designed in detail in this study. By employing an elliptical choke, the leakage power of the accelerating mode caused by the waveguide coupler was significantly reduced to approximately 1.5%. Additionally, an analysis of the leakage power caused by the frequency tuners was conducted. All harmful parasitic modes can be strongly suppressed through optimizations of the inner shape of the cavity with a large beam pipe, meeting the requirements of the STCF collider rings with a beam current of up to 2 A. The mechanical design and thermal analysis of the TM₀₂₀-mode cavity were completed and presented, demonstrating the feasibility of the design. The fabrication of this cavity is currently underway. Benchmark measurements are expected to be performed with the results from simulations to further optimize the cavity by the end of 2025.