# Electromagnetic Particle Algorithm for Beam-Wave Interaction in Traveling Wave Tube of Symmetry
## 6 Case Simulation  
The code is mainly developed for beam-wave interaction analysis in cylindrical TWT with symmetrical structure using MATLAB software. Because the applicable structure of this algorithm is fixed, it does not have the simulation function for irregular TWT, and the fixed structure makes its simulation speed faster. Next, the electromagnetic solution algorithm in TWT is tested, and the electron beam with beam voltage of 20 kV and 50 kV and input power of 100 W is added to the cylindrical TWT with symmetrical structure and center frequency of 2 \(\times\) 10\({}^{11}\) Hz for simulation. The same input conditions are set and the relatively mature CHPIC electromagnetic simulation software for simulation analysis and comparison are used. As shown in Figure 8, when the beam voltage in the algorithm is 20 kV, the circuit electric field distribution diagram and CHPIC code results generated at different positions in the traveling wave tube are compared. However, if the beam voltage is increased to 50 kV, the electric field distribution law has changed greatly. As shown in Figure 9, when the beam voltage is 50 kV, the circuit electric field distribution diagram and CHPIC code results generated at different positions in the traveling wave tube are compared. When the beam voltage in the algorithm is 20 kV, Figure 10 show the electron tracking using the space charge field and circuit field. It can be seen intuitively that the track of 20 kV electrons with beam voltage changes with time compared with the CHPIC code results. Figure 11 also shows the electron tracking trajectory of space charge field and circuit field in the calculation example when the beam voltage is 50 kV, and the comparison effect with CHPIC code. Figure 12 shows the simulation results of output voltage changes with different positions in TWT when the beam voltage is 20 kV, and the results are compared with the simulation results of CHPIC code. Table 1 compares the algorithm test results and CHPIC code results in detail, the output voltage value generated at the TWT inlet, and the maximum and minimum output voltage values corresponding to different positions in the TWT. Figure 13 shows the simulation results of output voltage changes with different positions in TWT when the beam voltage is 50 kV, and the results are compared with the simulation results of CHPIC code. Table 2 compares the algorithm test results and CHPIC code results in detail, the output voltage value generated at the TWT inlet, and the maximum and minimum output voltage values corresponding to different positions in the TWT. Figure 8: Circuit electric field (blue part) and CHPIC code generation result (purple part) generated by 20 kV RF voltage simulation in an algorithm test. Figure 10: Electronic tracking (blue part) and CHPIC code generation results (purple part) generated by 20 kV RF voltage simulation in an algorithm test. Figure 9: Circuit electric field (blue part) and CHPIC code generation result (purple part) generated by 50 kV RF voltage simulation in an algorithm test. Figure 14 shows the simulation results that the output power caused by beam-wave action changes with different positions in the TWT when the beam voltage is 20 kV, and the results are compared with the CHPIC code simulation results. Table 3 compares the algorithm test results and CHPIC code results in detail, the output power value generated at the TWT inlet, and the maximum and minimum output power values corresponding to different positions in the TWT.