Single-cavity Frequency Calculating Method for Standing Wave Accelerating Structure Based on Neural Network

The standing wave accelerating structure, which usually consists of a series of resonant cavity chains, is the core component of electron linear accelerators. For these cavities in the accelerating structure, the frequency detuning is an ineluctable concern due to manufacturing errors including thermal deformation and machining tolerances. And precise measurement and correction of such frequency detuning constitute the critical objective in the tuning processes to achieve the designed single-cavity frequency. Traditional cavity detuning diagnostic method is implemented by inserting two inflexible conductive probes into the accelerating structure and measuring the resonant frequencies of each cavity one by one, which has a great risk of damage the cavity inner surface. Especially in complex application scenarios, such as fully enclosed accelerating structures and side-coupling structures, the traditional method has great limitations in applicability and diagnostic accuracy. With the development of intelligent optimization algorithm, neural networks and trust region optimization algorithms are gradually applied in the design and tuning of accelerating structures. Neural networks demonstrate superior feature extraction capabilities while trust region optimization algorithms provide high-precision search mechanisms, and their combination is an effective solution for complex system parameter optimization. In this paper, the relationship between reflection coefficients and single-cavity frequency based on equivalent circuit theory were established and a cavity frequency calculation method combining neural network and trust region optimization algorithm was proposed for the standing wave accelerating structures. After measuring the reflection coefficients of the accelerating structure from the input waveguide, the frequency of each cavity can be estimated with this method. Therefore, the risks and limitations of the traditional method can be avoided. In the tuning process, the coarse estimation of the cavity frequency was obtained by the neural network model at first. And then the cavity frequency could be accurately calculated by the trust region algorithm. By minimizing the deviation between the measured reflection results and the reflection coefficients calculated by the estimated cavity frequencies, the frequency of each single-cavity could be obtained. After modeling and training the neural network, three accelerating structures in S-band and C-band were analyzed. The comparation between the simulated cavity frequencies and the calculated results obtained by this method using the simulated reflection coefficients confirmed the feasibility of this method. Then, two real S-band accelerating structures were tested by this method and the traditional way. The results show that this method can reveal the trend of frequency deviation when single-cavity frequency exhibit significant deviations from design value, and the most deviations between this method and the traditional way are small in general situations. Therefore, this method can be used to guide the tuning of the standing wave accelerating structure and serve as a good supplement to the traditional method in the tuning of fully enclosed accelerating structures and side-coupling structures.