## 1 Introduction
Thereby, the effective capacitance \(C\) is formed by the series configuration of the stage capacitors \(C_{stage}\) as given in Equation (1) and depends on the number of stages \(n\). \[C=\frac{C_{stage}}{n} \tag{1}\]  
The treatment chamber comprises an electrode system for the pulsed electric field applied to the processed material. It can be modelled as an ohmic resistance \(R\). The inductance \(L\) can either be formed by the stray inductance of the pulse circuit only or augmented by a coil added to the pulse circuit. The resistance of the treatment chamber may vary with the electric conductivity of the processed material, which depends, among other parameters, on the temperature and the filling factor. As a consequence, the pulse shape may vary. The solution of the differential Equation (2)  
\[v_{\text{C}}(t)+RC\cdot\dot{v}_{\text{C}}(t)+LC\cdot\ddot{v}_{\text{C}}(t)=0\] (  
Critically damped case (\(Q\) = 0.5):  
\[v_{R}(t)=R\frac{V_{0}}{L}\cdot t\cdot e^{-\frac{R}{L}\cdot t} \tag{4}\]  
Damped periodic case (\(Q\) > 0.5):  
\[v_{R}(t)=R\frac{V_{0}}{L\sqrt{\frac{1}{LC}-\frac{R^{2}}{4L^{2}}}}e^{-\frac{R}{2 }\cdot t}\sin\left(\sqrt{\frac{1}{LC}-\frac{R^{2}}{4L^{2}}}\cdot t\right) \tag{5}\]  
with  
\[Q=\frac{1}{R}\cdot\sqrt{\frac{L}{C}} \tag{6}\]  
with the voltage across the resistance R of the treatment chamber, \(v_{R}(t)\), the pulse current \(i_{p}(t)\) can be calculated according to Equation (7). \[i_{p}(t)=\frac{1}{R}\cdot v_{R}(t) \tag{7}\]  
For the pulsed electric field treatment of biological material, a pulse shape similar to the aperiodically damped case or the strongly damped periodic case of an RLC circuit is already in use in industrial-scale electroporation devices equipped with Marx generators [2]. Therefore, for the new generator design, a Marx-type generator with solid-state switches and an RLC pulse circuit serving as a conventional pulse-forming circuit has been chosen. However, the free-wheeling diodes as part of the pulse generator topology prevent the stage capacitors from being charged in reverse polarity in the case of an oscillatory waveform of the pulse. In this case, as soon as the stage capacitors are discharged, the current driven by the circuit inductance commutates into the free-wheeling diodes and from that moment on, the pulse current decays exponentially, governed by the time constant \(\tau\) of the resulting LR circuit. \[\tau=\frac{L}{R} \tag{8}\]  
Figure 1 shows the simulated pulse voltage V\({}_{\rm P}\) and pulse current I\({}_{\rm P}\) at the output terminal of an 8-stage Marx generator with free-wheeling diodes. After the discharge of the stage capacitors, the pulse current commutates to the free-wheeling diodes (I\({}_{\rm D}\)). Figure 1: Simulated pulse voltage V\({}_{\rm P}\) and pulse current I\({}_{\rm P}\) at the output terminal of an 8-stage Marx generator with free-wheeling diodes. After the discharge of the stage capacitors, the pulse current commutates to the free-wheeling diodes (I\({}_{\rm D}\)). For such a design, a conventional charging circuit equipped with charging coils can be used. However, when operating such a pulse generator at a higher pulse repetition rate and as a consequence, the product of pulse length and pulse repetition rate becomes larger, using current-compensated chokes instead of the charging coils is advantageous for enabling fast charging [2]. Current-compensated chokes feature a low inductivity during charging, as they are operated in differential mode. During pulse generation, their high inductivity under common-mode conditions serves well for transient stage insulation. The design based on current-compensated chokes in the charging path can be combined with a power supply having the characteristic of a voltage source and an additional inductance between the power supply and the Marx generator to enable resonant charging of the generator [10]. Figure 2 shows a simplified circuit for basic studies on resonant charging. The voltage source \(V_{0}\) supplies energy to the circuit.