## 3 Numerical Simulation of EMP Propagation
Figure 2: Input, reflected, and transmitted signals with EMP generators connected to the coaxial line, which were found by the numerical simulation: (**a**) unipolar pulse with duration of 600 ps FWHM and an amplitude of 50 kV, and (**b**) bipolar pulse with a duration of 1.4 ns FWHM and the same amplitude. forward and backward and forming a long trail of low-level signals after the main pulse. Therefore, for a pulse 200 ps long, the calculated level of the reflected signal increased significantly (by 28%, in terms of the voltage), the amplitude of the transmitted signal decreased noticeably (to 63% in terms of the voltage), and the FWHM pulse duration increased by about 50% (see Figure 5). The increase of the EMP duration up to several (2-5) ns did not lead to a decrease in the transformation coefficient at the tapered transitions. The effect of EMP front distortion at the line input became less significant, and the relative waveform distortion of the transmitted pulse also decreased. The widths of the plates of the outer conductor and the gaps between them were chosen based on the performed numerical simulations. In this process, the limitations of the minimal gap value determined by the possibility of inserting diagnostic tools and antennas, which are used to produce background ionization, were taken into account. Figure 6 presents the instantaneous electric field map in an optimized line that consists of plates and gaps having widths of 7.5 cm and 5 cm, respectively, in the process of the propagation of a test EMP with duration of 200 ps. The fields outside of the internal volume of the line are the boundary fields of the plates, and do not lead to noticeable radiation of  
Figure 4: Numerically simulated pattern of the distributions of the modulus of the electric field for the case where a unipolar EMP with duration of 200 ps FWHM is excited in the coaxial line, at three sequential time instants. Figure 5: Numerically simulated input, reflected, and transmitted signals with an EMP with a duration of 200 ps FWHM. the energy through the gaps. Specifically, in the line comprised by plates with gaps, the reflected and transmitted signals are not visibly different from the signals calculated for the line with a solid outer conductor. The influence of the plasma on the EMP characteristics at a low (linear) power level, in the case of propagation in the coaxial line, was modeled by the finite-difference time-domain (FDTD) method [28]. Within the framework of this method, the system of the Maxwell equations for the pulsed process was solved in combination with the linearized equations of hydrodynamics, where the electron response was taken into account in the form of polarization and conductivity currents. The solved system of equations is written in the SGS system in the following form:  
\[rot\overset{\rightarrow}{E}=-\frac{1}{c}\frac{\partial}{\partial t}\overset{ \rightarrow}{E}+\frac{4\pi}{c}\left(\overset{\rightarrow}{j}+\overset{ \rightarrow}{j}_{ext}\right) \tag{1}\] \[\overset{\rightarrow}{\partial t}\overset{\rightarrow}{j}= \frac{e^{2}n_{e}}{m}\overset{\rightarrow}{E}-\
u_{e}\overset{ \rightarrow}{j}\]  
where \(\overset{\rightarrow}{E}\) and \(\overset{\rightarrow}{B}\) are the AC electric field and the AC magnetic field intensity, respectively, \(\overset{\rightarrow}{j}\) is the density of the electron current in the plasma, \(\overset{\rightarrow}{j}_{ext}\) is the density of the extrinsic current in the region of the EMP source (antenna), \(n_{e}\) is the plasma density, \(\
u_{e}\) is the electron collision frequency, \(e\) and \(m\) are the electron charge modulus and the electron mass, respectively, and c is the speed of light in vacuum. The calculation was performed in a cylindrical system of coordinates. To cut down the computation time, the problem was reduced to a cylindrically symmetric problem with the electromagnetic-field components depending only on two coordinates (_r_,_z_).