# Electromagnetic Particle Algorithm for Beam-Wave Interaction in Traveling Wave Tube of Symmetry
## 1 Introduction  
As the best combination of bandwidth and gain in microwave tube, the traveling wave tube (TWT) is still ahead of solid-state amplifier in bandwidth and efficiency. TWT has the advantages of high power, high efficiency, high gain, wide bandwidth, large dynamic range and low noise [1]. It is also widely used in radar, electronic countermeasures and satellite communication. In the era of the rapid development of computer technology, computer numerical simulation technology is also developing rapidly [2, 3]. In terms of the problem of scientific research and practical application being difficult to link, the computer numerical simulation method can conduct numerical modeling of the studied system and then simulate from a given initial state and obtain the whole simulation process and meaningful results, which is a good solution [4, 5, 6]. The numerical simulation results can also be compared with the theoretical calculation results and experimental results to study the essence of the problem. Particle simulation method is an excellent computer numerical simulation method, which can be used to study the interaction process of charged particles with electric field and magnetic field [7, 8, 9]. It plays an irreplaceable role in the application of electronic signal amplifier, space astrophysics, plasma and vacuum electronics and has important military application prospects [10, 11]. The particle simulation method can fully consider the various factors of particle motion, truly reflect the particle motion, and obtain better results than the experiment [12, 13, 14, 15]. At the same time, in the process of simulation calculation, all motiondata of each simulated particle will be recorded in the computer, and then detailed data information will be obtained for observation and analysis. The interaction between the magnetic field generated by the rapid movement of the electron beam in the aircraft and the electron beam body can accumulate enough energy to release, thus causing damage to the aircraft [16; 17; 18]. For example, the electrons moving to the space around the aircraft gather on the surface of the aircraft, which leads to surface electrification [19; 20]. This charge and related magnetic field will lead to surface arc discharge, electronic blowout, enhanced pollution and the movement of the electrical ground of the aircraft. The continuous flow of electric charges entering and exiting the aircraft surface constitutes a current, which may lead to electric leakage inside or outside the aircraft and become a potential safety hazard [21; 22; 23; 24; 25]. Therefore, it is of great significance to study the electromagnetic radiation generated during the launch and movement of the aircraft, analyze the electromagnetic characteristics of the aircraft surface potential change in time and frequency domain, and then effectively protect and shield its impact [26; 27; 28]. Because of the background of high current electron beam and electromagnetic static field, many physical problems are nonlinear, and there are strong coupling problems [29; 30]. It is difficult to obtain accurate results only by traditional analytical methods and linear analysis. The physical process must be simulated by the electromagnetic particle algorithm. Therefore, it is very necessary to design the electromagnetic particle algorithm for beam-wave interactions. In this algorithm, the finite difference method is used to simulate the field of the coupled slow-wave transmission line. The coupling between the beam and the transmission line is based on the finite difference equation proposed by [PERSON] (1949) [31; 32]. Based on the difference principle, it directly starts from [PERSON]'s curl equation, which summarizes the general law of electromagnetic field, converts it into difference equations and samples the data of the continuous electromagnetic field at a certain volume and a certain period of time. Therefore, it is the most basic, essential and complete numerical simulation of electromagnetic field problems and has the widest applicability.