## 3 Results
### Adaptation of the Damping Resistor \(R_{\mathrm{D}}\)  
With a damping resistor of almost no resistance, damping is poor, and an accumulation of magnetic energy in the cores of the current-compensated chokes can be expected. Figure 8 shows the simulated common-mode currents in the charging path for the first five pulses. The common-mode current rises stepwise from pulse to pulse. As a consequence, the cores of the current-compensated chokes will be driven into saturation. Figure 8: Simulated common-mode currents in the charging path (I\({}_{\mathrm{L,C}}\)) for the first five pulses with R\({}_{\mathrm{D}}\) almost 0 Ohm. Thereby, I\({}_{\mathrm{L,C}}\) is the superposition of the almost equal common-mode currents in all current-compensated chokes. V\({}_{\mathrm{Ch}}\) is the charging voltage at the input terminal for charging the Marx generator. Figure 7: Energy stored in the core of two current-compensated chokes (W\({}_{\mathrm{Cone}}\)) and common-mode current I\({}_{\mathrm{CM}}\) through the chokes (Simulation for current-compensated chokes comprising L1, L2 and L3, L4 according to Figure 3, R\({}_{\mathrm{D}}\): open circuit, t\({}_{\mathrm{on}}\) = 22 \(\mu\)s). In order to achieve a considerable amount of damping, a value of 20 Ohm has been selected. This choice has been made based on simulations. Figure 9 shows the voltages across the stage capacitors for the case of R\({}_{\rm D}\) equal to 20 Ohm. The results are similar to the corresponding results achieved without R\({}_{\rm D}\), as shown in Figure 4. Again, the charging process of the capacitor of the leftmost stage (C1) continues after the charging process of the other stage capacitors has already ended. Figure 10 shows the simulation results of the charging voltage V\({}_{\rm Ch}\) and the charging current I\({}_{\rm Ch}\), both derived from the charging input terminal of the generator, the voltage V\({}_{\rm iso}\) across D20, and the voltage V\({}_{\rm D}\) across the damping resistor R\({}_{\rm D}\) (=R3). The voltage V\({}_{\rm D}\) does not decay to zero between two pulses. However, the magnetic energy in the current-compensated chokes is sufficiently low in order to prevent the core from saturation. The simulation shows that the pulse generator operates under steady-state conditions. Thereby, the voltage V\({}_{\rm iso}\) across D20 is much lower than in the case without a damping resistor, as shown in Figure 4 (V\({}_{\rm 19,G}\)). However, some energy stored in the current-compensated chokes dissipates in R\({}_{\rm D}\) instead of being re-used for additional charging of the leftmost stage. Figure 11 shows the power and the current at R\({}_{\rm D}\). The average power is 50.3 W. Figure 12 shows the energy stored in the cores of the leftmost and its neighbouring current-compensated choke and the common-mode currents through both. When a part of the energy stored in the chokes is dissipated by R\({}_{\rm D}\), in the considered case, the reduction of the stored energy is 15.8 mJ per choke, so the average power delivered by one choke into R\({}_{\rm D}\) when operating at a pulse repetition rate of 500 Hz is 7.85 W. Summing up over all seven current-compensated chokes of the circuit results in a total average power of 55.0 W, which fits well to the average power at R\({}_{\rm D}\). The remaining losses of approximately 5 W are distributed among the other components of the circuit. Figure 9: Simulated voltages across the stage capacitors C1, C4, C7, C10, C13, C16, C19, and C22 according to Figure 3, together with the generator’s charging current I\({}_{\rm ch}\) (R\({}_{\rm D}\) = 20 Ohm). Figure 11: Losses at the damping resistor R\({}_{\rm D}\) (R3 in Figure 3): Power P\({}_{\rm RD}\) and current through R\({}_{\rm D}\) (I\({}_{\rm RD}\)).