The development of Relativistic Klystron Amplifiers (RKAs) has long been hindered by prolonged design cycles, primarily due to the strong nonlinearity of beam-wave interactions, the high dimensionality of the parameter space, and the prohibitive computational cost of Particle-in-Cell (PIC) simulations. To address these challenges, this paper proposes a conditional inverse design framework that integrates surrogate modeling with physical constraints for the efficient generation of RKA structural parameters. First, using a PIC simulation model of an X-band single-beam seven-cavity RKA as a physical baseline, equivalent one-dimensional (1D) parameters of the resonant cavities are extracted and combined with electron beam characteristics to construct a 33-dimensional design parameter space with explicit physical constraints. Subsequently, a fast 1D large-signal simulation software KlyH is employed to generate approximately 1. 3 10^5 samples. These samples are used to train a forward surrogate model, enabling accurate characterization of the nonlinear mapping between design parameters and device efficiency. To satisfy the hard constraints prevalent in engineering design, a Split-Merge tandem neural network architecture is introduced. By directly embedding user-defined constraint parameters into the design vector, this architecture facilitates conditional inverse generation while guaranteeing strict satisfaction of the constraints at the network structure level. Comparative validation demonstrates that the generated designs achieve an average error of 3. 7% against the KlyH baseline. Furthermore, when verifying these designs in PIC simulations, the results show a maximum deviation of 8. 8% compared to the KlyH. The proposed framework significantly reduces the computational burden of inverse design while maintaining essential physical consistency, offering a practical solution for the rapid optimization and engineering design of RKAs.
Zhao et al. (Thu,) studied this question.