Nanocrystalline soft magnetic alloy (MA) cores are essential magnetic loading components in proton/heavy-ion synchrotron rf cavities. While conventional MA cores fabricated from 16 μm ribbons offer reliable performance, further enhancing their shunt impedance and thermal stability to meet the demands of next-generation high-power synchrotrons presents significant challenges. Although the use of thinner ribbons (e.g., 13 μm) can improve high-frequency magnetic properties, their widespread application is hindered by manufacturing difficulties and reduced packing factor consistency. To address this, we propose an embedded MA core design that strategically integrates 13 μm ribbons in specific radial regions alongside normal 16 μm ribbons. This approach not only increases shunt impedance but also optimizes the electromagnetic field distribution, thereby reducing peak surface temperature and improving thermal stability. This paper first elucidates the physical mechanism through which the embedded structure improves temperature uniformity. Additionally, a two-dimensional heat transfer numerical model is developed and experimentally validated to assess the thermal performance of the embedded MA core under actual operating conditions. Experiments are conducted and the results demonstrate the embedded core’s peak surface temperature is reduced by 2.5 °C compared to a normal MA core. Finally, parameter optimization of the embedded structure is conducted, demonstrating that optimizing the radial position, volume ratio, and thickness of thinner ribbons can achieve a temperature reduction of approximately 6 °C and a 12% impedance increase. The findings of this study provide a theoretical foundation for the performance optimization of MA cores in high-power synchrotrons.

In many engineering applications, multi-objective optimization problems can be reformulated as single-objective problems with multiple constraints to improve computational efficiency. This paper discusses the characteristics and challenges of RF accelerating structure optimizations and proposes an enhanced single-objective optimization strategy based on progressive exploration method to find the global optimal solution within a large solution space characterized by a continuous and confined distribution of feasible solutions. It begins from an arbitrary feasible solution and progressively slides and expands the solution space fragment along the distribution path of feasible solutions to rapidly explore the entire space. By incorporating a re-initialization mechanism to enhance swarm diversity and introducing penalty factors in place of constraints to increase the number of feasible solutions, the algorithm significantly improves its ability to escape local optima traps. The proposed algorithm is applied to optimize a DAA structure, yielding satisfactory results and convergence speed. These results highlight the method’s effectiveness and its potential applicability to other complex constrained optimization problems.

Developing multifrequency acceleration systems is crucial for optimizing beam dynamics in high-brightness particle beams, particularly for minimizing energy spread, manipulating bunch length, and facilitating beam bunching. This paper introduces a novel bimodal radio frequency (rf) cavity design that integrates both fundamental and harmonic modes within a single structure, offering enhanced spatial efficiency and improved operational flexibility for multifrequency rf systems. Unlike traditional designs, our cavity enables independent and simultaneous operation of each mode, along with effective suppression of higher-order modes (HOMs), which is critical for high-current beam stability. This breakthrough addresses significant challenges in bimodal cavity technology, such as intermode tuning coupling, rf-driving coupling, and effective HOM damping, providing essential solutions for high-current beam applications. Our work opens new research avenues in advanced rf cavity design, with significant implications for the future of high-brightness beam technologies, including advanced accelerator designs and improved beam quality.

Radiofrequency cavities are crucial components in synchrotron light sources, providing beam energy replenishment and accelerating voltage. TM020 mode cavities offer superior performance compared to conventional TM010 cavities, exhibiting a higher quality factor and accelerating gradient. Their unique electromagnetic field distribution enables effective suppression of both higher and lower order modes via strategically placed dampers at the radial magnetic or electric field wave nodes. However, the sensitivity to misalignment is heightened near these nodes, where the magnetic or electric field gradient is maximized. Consequently, even minor deviations in coupling slot or wave node positioning can induce substantial electromagnetic field leakage, limiting the achievable accelerating voltage due to finite damper power handling. We present a novel leakage suppression scheme employing a Sector waveguide for precise control of coupling slot placement and a waveguide-to-coaxial input coupler to minimize azimuthal perturbations, thus stabilizing the field wave node. This approach drastically reduces accelerating field leakage, enabling stable operation of TM020 damped cavities at high accelerating gradients. Simulations of a 500 MHz TM020 cavity demonstrate leakage reduction to below 1% under operational conditions.

A dual-harmonic acceleration system is utilized to mitigate the space-charge effect in the rapid-cycling synchrotron of the China Spallation Neutron Source upgrade project (CSNS-II). A magnetic alloy (MA)-loaded cavity with a high accelerating gradient is developed to satisfy the requirements of dual-harmonic acceleration and provide the necessary second-harmonic cavity voltage. However, the MA-loaded cavity exhibits a wideband frequency response, resulting in numerous higher harmonics in the radio-frequency (RF) voltage. These higher harmonics are caused by both the beam-loading effect and distorted amplifier current, which distort the RF bucket, increase the power dissipation in the cavity, and lower the gradient. To address these issues, a multiharmonic independent feedback-control approach is implemented to compensate for higher harmonics. The effectiveness of this control strategy is validated experimentally. This study provides details regarding the feedback-control design and presents the commissioning results.

Radiofrequency cavities play a crucial role in synchrotron light sources by replenishing beam energy and providing sufficient accelerating voltage. Compared to traditional TM010 cavities, TM020 cavities offer advantages such as higher quality factor, higher accelerating voltage, and lower characteristic impedance. Additionally, their unique field distribution allows strategic placement of dampers at radial nodes, effectively suppressing higher-order modes within a compact structure. However, the radiofrequency performance of cavity is highly sensitive to the placement of the higher-order modes coupling slot and the Electromagnetic(EM) field symmetry. These factors can easily lead to leakage of the accelerating mode, with the leaked energy absorbed by the absorber, whose power handling capacity is limited. Consequently, the leakage rate of the TM020 mode damping cavity becomes critical in limiting the achievable accelerating cavity voltage. This paper proposes a novel extraction scheme utilizing a circular waveguide structure and a waveguide-coaxial input coupler to significantly reduce accelerating field leakage, thereby achieving a high-fidelity TM020 cavity. A detailed design of a 500 MHz TM020 HOM-damped cavity is presented. Simulation results demonstrate that the energy leakage of the accelerating mode can be suppressed below 1% during operation.

The second phase of the China Spallation Neutron Source (CSNS-II) will employ a dual-harmonic RF system to mitigate the significant space charge effects associated with 500 kW beam power. To address this, three magnetic alloy loaded cavities, characterized by their wideband and high-gradient properties, will be integrated as multi-harmonic cavities in the upgrade project. Additionally, the current LLRF control system hardware, based on the CPCI platform, is encountering issues related to discontinuation and performance limitations. This paper presents the testing and verification of hardware upgrades and multi-harmonic control system algorithms for the magnetic alloy loaded cavity LLRF control system, ensuring the effective implementation of the multi-harmonic control algorithm within the new hardware framework.

Here, we report our recent progress in the design, fluid thermodynamics simulation, and high-power test of the2nd harmonic cavity for the China Spallation Neutron Source Phase II. A high-performance and large-size magnetic alloy (MA) core was developed as the load material for the radiofrequency cavity to achieve a high gradient of 40 kV/m. The water-cooling structure and cooling efficiency were studied and improved through numerical analysis and thermal experiments. The long-term stability of the cavity, especially the waterproofness of the MA cores with high heat load, was verified by high power tests.

The application of high-power solid state amplifiers (SSAs) in accelerator facilities is increasing, and equipment failure caused by reflected power is the main risk to their long-term operation. High-power SSAs often comprise multiple power amplifier modules. Full power reflection is more likely to damage the modules in SSAs if the amplitudes of the modules are unequal. Optimization of the power combiners is an effective means for improving the stability of SSAs under high power reflection. This study analyzes the mechanisms and conditions of reflected power generation using the scattering parameters of the combiner and proposes an optimization scheme for the combiner. The simulation and experimental results show that some modules may receive reflected power as high as nearly four times the rated power of one module when the SSA meets certain conditions, which could damage the modules. The maximum reflected power can be effectively reduced and the anti-reflection ability of SSAs can be improved by optimizing the combiner parameters to suppress the maximum reflected power.

The utilization of a low-frequency (<200 MHz) RF system in storage facilitates the attainment of ultra-low emittances in synchrotron light sources through on-axis injection. This paper focuses on the development of a low-frequency normal conducting (NC) cavity with higher-order mode (HOM) damping for fourth-generation synchrotron light sources. We propose a novel approach to achieve efficient HOM damping in a NC cavity by optimizing the lowest frequency HOM and implementing a beam-line absorber. Notably, unlike conventional NC cavities, the presence of a large beam tube for the beam-line absorber does not compromise the accelerating performance in a coaxial resonant cavity, enabling effective HOM damping while maintaining a high shunt impedance. Through simulations, the prototype design of a 166.6 MHz HOM-damped cavity demonstrates a fundamental mode impedance of ∼8 MΩ, with longitudinal and transverse HOM impedances below 2.0 and 50 kΩ/m, respectively.

Objective In the optimization design of optomechanical systems, polynomials can not only retain a significant amount of information but also provide a more compact representation of structural deformation and facilitate integration between mechanical structures and optical models. Zernike polynomials have been widely employed due to their orthogonality properties on a unit circle. However, the orthogonality of Zernike polynomials only applies to continuous data on a circular aperture, and it degrades for discrete interpolation and non- circular apertures. Non-orthogonality means that coupling exists among different terms of polynomials, and the number of polynomials cannot be arbitrarily increased or decreased, which can lead to accuracy and stability problems in surface approximation and optimization design. This study aims to propose a conformal orthogonal basis generated by the eigenmodes of the Laplace equation for utilization in the topology optimization of support structures for reflective mirrors, thus avoiding Zernike orthogonality loss. Additionally, due to the conformal properties of the Laplace eigenmodes in the domain, the obtained basis represents the deformed information along the surface normal. As the principal direction of deformation, the surface normal makes the eigenmodes a better fit for surface deformations. Methods The Laplace characteristic equation and Zernike polynomials both originate from the Sturm-Liouville problem. The solutions on the planar circular domain exhibit similarities with Zernike polynomials, and Trevino et. al. [10] have compared the characteristic modal functions (Bessel circle polynomials) and Zernike polynomials in eye surface fitting, which indicates that the former provides better fitting. This paper extends the planar domain to surfaces. The finite element solution of the Laplace equation and properties of the eigenvalue problem ensure the discrete orthogonality of the characteristic modal functions. The mathematical properties of this equation guarantee the completeness of analytical solutions of the characteristic modal functions, and the completeness is verified by combining function approximation theory and numerical experiments. In addition, a specific topology optimization example demonstrates that the characteristic modal functions not only yield similar results to Zernike polynomials on circular domains but also can be applied to non-circular apertures where Zernike polynomials are not suitable. Results and Discussions First, based on the Sturm-Liouville decomposition on compact Riemannian manifolds, the completeness of the eigenmodes under analytic conditions is demonstrated. Then, the feasibility of adopting eigenmodes to fit surface deformations is numerically validated by adopting function approximation theory as the basis (Figs. 4 and 5). Additionally, this paper applies the method of surface approximation using eigenmodes to topology optimization of circular mirror support structures and compares it with Zernike polynomial approximation. The comparative results indicate that the objective functions optimized through characteristic modal functions and Zernike polynomials are 4. 40% and 4. 43% of the original structure respectively. The root mean square (RMS) values are 4. 40% and 2. 55% of the original structure respectively, and the peak to valley (PV) values are 10. 51% and 8. 73% of the original structure respectively. Both methods prove comparable optimization effectiveness (Table 1). The curves of the objective and constraint values during the iteration show that both methods have consistent stability and can converge (Figs. 11 and 12). However, there are slight differences in the resulting structures (Figs. 9 and 10). After comparative experiments, this study applies the modal fitting method to a hexagonal mirror, thereby completing the topology optimization design of a hexagonal mirror support structure ( Fig. 14) and extending its applicability to non-circular apertures. Conclusions This paper proposes to adopt a conformal orthogonal basis, which is the Laplace eigenmodes, for approximating surface deformations, and applies it to topology optimization of optical structures. It also demonstrates analytically and numerically that the Laplace eigenmodes are not only completed on circular domains but also on other irregular shapes. Surface eigenmodes can be employed to approximate smooth mirror surface deformations and achieve topology optimization of optical single mirror support structures with specific modal coefficients being the optimization objectives. Two optimization examples show the applicability of the proposed basis on circular domains and its extensibility on non-circular domains. However, compared to Zernike polynomials, the Laplace eigenmodes studied in this paper only exist in piecewise discrete numerical solutions, which means that the eigenmodes do not have an analytical representation like Zernike polynomials. When solving for the normal of a deformed mirror surface, it is necessary to pay attention to the continuity of the normal vector at the element boundary, which is a field that deserves further exploration in future work.

本文基于功率合成网络散射参数,理论分析反射功率形成的机理,研究极限反射功率存在的条件,并提出合成网络优化方案.仿真计算和实验结果表明,当输出端失配,且固态功率源中仅一路功放模块失效时,部分模块可能承受接近4倍模块额定输出的反射功率,模块存在损毁风险.合成路数一定的情况下,通过优化合成网络级间电长度等参数破坏极限反射功率条件,可有效降低极限反射功率.

This paper presents an optimized design and preliminary test result of a high-power input coupler. The design is motivated by five-cell Petra-type cavities operating in the Southern Advanced Photon Sources booster. We optimize the design of the high-power input coupler from the prototype, including the window geometry redesign and multipacting analysis to meet a 250 kW operation power upgrade plan. The cooling system of the coupler is redesigned to achieve a low temperature in high-power operation. Design results fulfill the five-cell cavity operation requirement. The corresponding waveguide and coaxial transition structures are developed and tested. We also describe the coupler's coupling coefficient tests and high-power test plans.

为提高CSNS/RCS高频系统的动态响应和减小对射频功率源的影响,构建了CSNS/RCS高频系统直接反馈控制子系统.该子系统采用两级并联电子四极管进行反馈闭环控制,实现了功率增益大、响应频带宽和抗冲击能力强的功能.试验结果表明,其能够有效地提高CSNS/RCS高频系统的稳定性和抑制束流负载效应.

This paper introduces the working principle of magnetic alloy (MA)-loaded cavity, and analyzes the main performance test requirements of the magnetic alloy loading experimental cavity. A detailed test scheme of the magnetic alloy single ring, magnetic alloy loaded cavity and the high power performance test is worked out. The μQf test of the magnetic alloy ring and the impedance characteristics, thermal distribution characteristics and thermal stability of the magnetic alloy loading experimental cavity were tested.

The rapid cycling synchrotron (RCS) RF control system of China Spallation Neutron Source (CSNS) is a distributed control system (DCS)based on Gigabit Ethernet used stand EPICS CA protocol.The system consists of five parts:low level RF(LLRF) controller based on CPCI bus,monitoring and control network of high power tetrode amplifier and bias supply,interlock protection system,mid server to center control room and operator interfaces (OPIs).This paper mainly presents the architecture of the CSNS RCS RF control system,and show the hardware and software implementation at the various components.

A high power,broadband and rapid frequency sweeping RF system was developed to satisfy the demand of China Spallation Neutron Source (CSNS)rapid cycling synchrotron (RCS).The RF system mainly includes a ferrite loaded resonant cavity,a RF power source,a bias supply and a low level RF system.The repetition frequency is 25 Hz and the sweeping frequency range is 1.022-2.444 MHz.One cavity with two gaps can provide a maximum accelerating voltage of 30 kV.The tuning control of two stages can successfully solve the detuning problem during rapid frequency sweep-ing.The beam feed-forward and direct feedback can compensate the heavy beam loading effect.