## 2 Materials and Methods  
For the circuit simulation of an 8-stage Marx generator, a circuit model for circuit simulation using the software LTSpice [11] has been set up, which is shown in Figure 3. Based on the circuit topology and component values, LTSpice sets up a system of difference equations and solves them numerically for a sequence of adapted time steps considering the appropriate initial conditions. In between the time steps, linear interpolation is applied [11]. LTSpice has also been used for post-processing, i.e., the calculation of data, which has been derived from the original simulation data, such as, e.g., the integration over time or averaging of a curve. Each stage is represented by its stage capacitor having the capacitance C_ST = 6 \(\mu\)E, and the solid-state switch, which is modelled using a voltage-controlled switch and an anti-parallel diode representing the internal diode co-packed with many IGBT switches. Additionally, each stage features a bypass diode (D1, D5, D9, D13, D17, D21, D25, and D29 in Figure 3). The load is modelled as a combined resistive and inductive load (R1 + R2, L16 + L17). The charging path comprises the coupled inductor-pairs (L1, L2), (L3, L4)... (L13, L14), each representing one current-compensated choke. The capacitance between both windings is represented by the sum of the adjacent capacitors (C2 + C3)... (C20 + C21). Each winding has an inductance of \(L_{L}\) = 4.7 mH and resistance of \(L_{R}\) = 5 m\(\Omega\). With a coupling coefficient of KPLG = 0.999, very well magnetic coupling between both windings has been assumed. The common-mode current component through one current-compensated choke is obtained by calculating the difference of the currents through both windings. The stages are connected to the charging path via diodes (D3, D4), (D7, D8)... (D31, D32). These diodes prevent the stage capacitors from discharging via the charging path after resonant charging. The voltage source needed for the resonant charging circuit is modelled by the ideal voltage source V1. The voltage source V1 is paralleled with a capacitance C23 serving in a real setup as a DC-link capacitor. However, for the simulation, this capacitor is not required. The inductance L15 forms, together with the paralleled stage capacitors, the resonant circuit for resonant charging. Just after pulse generation, the stage capacitors are discharged completely. The bypass diodes of each stage prevent the stage capacitors from being charged at the opposite polarity and, hence, prevent the pulse circuit from oscillating. As soon as the voltage of the stage capacitors falls below the voltage of the power supply, the charging current starts to rise and recharges the stage capacitors in a parallel arrangement. Thereby, the voltage across the stage capacitors reaches approximately twice the voltage of the feeding voltage source. The values of the stage capacitors, the load, the current-compensated chokes, and the inductance L15 have been selected based on a design for a solid-state Marx generator with a stage voltage of 1 kV delivering pulses with an approximate pulse length \(t_{h}=10\)\(\upmu\)s at a pulse repetition rate of up to 500 Hz to the load. Thereby, the pulse length is measured at half amplitude, and the average power of one stage operating at 1 kV and 500 Hz is 1.5 kW [10; 12; 13]. In order to generate an output voltage, which is symmetric to ground potential, the pulse generator is grounded at its centre. This arrangement is of advantage for a later connection of a pulsed electric field treatment chamber [14]. The power supply for charging  
Figure 3: Circuit simulation model for an 8-stage Marx generator with resonant charging. the generator is isolated to ground potential. During the operation of the real circuit, a varistor may limit the voltage versus ground in case of an over-voltage event. During pulse generation, some amount of magnetic energy is stored in the chokes resulting in a common-mode current.