## 3 Numerical Simulation of EMP Propagation  
The geometry of the line, including the design of the tapered transitions, was optimized by numerical simulation performed using the commercial software CST Microwave Studio [27] and ANSYS Electromagnetics Suite 2019 R3 software (Customer Number 280108). The transmission and reflection coefficients of signals in the nanosecond and subnanosecond duration ranges were analyzed, as well as the structure of the electromagnetic field in the line at different time instants and distortions of the EMP waveform. When simulating, the coaxial line was assumed to be perfectly conducting, and the contacts at the joints of the line elements ideal. Most of the simulations and the optimization of the line parameters were performed with the solid outer conductor, and the final simulations were made with the slit-type design of the outer conductor. The simulation was performed on highly non-uniform grids, refined until the simulation result stabilized. The maximum grid step used on the segment of the cylindrical working section was several mm for 600 ps EMPs, and decreased proportionally for shorter EMPs. Figure 2 presents the results of the simulation for unipolar and bipolar EMPs (with durations of 600 ps and 1.4 ns, respectively) in a line fed by a generator with an output voltage amplitude of 50 kV. For the unipolar EMPs, the amplitude of the signal transmitted through the line was 47.5 kV (95% of the input amplitude), and the level of the reflected signal amplitude did not exceed 1 kV. Distortions in the shape of the transmitted unipolar EMP were insignificant, and the pulse widening at the full width at half maximum (FWHM) level did not exceed 5%. For the bipolar EMP, the shape distortions and the amplitude losses were insignificant and did not exceed several percent for a coaxial line with a solid outer conductor. The waveforms of the electric field in the coaxial line, which were obtained at a distance of 30 cm from the axis of the line in various cross-sections of the three-meter-long uniform section, are shown in Figure 3 for the unipolar and bipolar EMPs. To specify the pattern of the distortions introduced by the coaxial line to the EMP waveform, we simulated the propagation of a pulse with the duration reduced to 200 ps FWHM. Pulse shortening imposes stricter requirements for the matching of the tapered transitions with connectors and feeding cables, as well as with the uniform cylindrical section. That was the reason for using the 200 ps pulse to optimize the geometric parameters of the input section and determine the width of the plates of the outer conductor, and the admissible width of the gaps between the plates. The snapshots of the electric field in the process of propagation of a short EMP in the line, which are shown in Figure 4, visibly demonstrate the nature of the arising distortions. The spatial length (or \"thickness\") of the pulse is only about 6 cm. The coaxial line having a distance between inner and outer conductors of 60 cm proves to be significantly oversized. Therefore, one can clearly see in the line both the curvature of the front of the propagating EMP, and additional waves with circular (in the plane of projection) fronts, which are scattered at the line irregularities, especially at the joint of outer conductors of the tapered transition and the uniform section. As a result, it was not possible to excite a \"pure\" TEM mode in the line: part of the EMP power was scattered in other modes propagating both  
Figure 3: Radial component of the EMP electric field calculated at the following distances z from the start of the uniform section of the line: 0 m, 1 m, 2 m, and 3 m. The distance from the axis of the line is r = 30 cm. (**a**) Unipolar pulse and (**b**) bipolar pulse.