## 4 Discussion
Additionally, when the line discharges, the current through the load is given by  
\[I_{load}=\frac{V_{c}}{2Z_{NLTL}}. \tag{3}\]  
Since the magnitude of this current translates to the transient magnetic field strength, NLTLs with lower impedance will have greater magnetic moment alignment during the initial pulse formation due to the higher transient magnetic field. This ultimately enhances RF formation on the subsequent reflected pulse through a more coherent precession of the magnetic moments as the pulse propagates back toward the load. This hypothesis also aids in understanding why the stronger oscillations observed on the output waveform follow the pulse. This behavior was also observed for other NLTLs used in this configuration [24] and was supported by LTSpice simulations [24]. While weaker modulations occur on the flat tops of these pulses, which is the common location for the RF burst to occur for gyromagnetic lines, much stronger oscillations form after the pulse. This succeeding RF burst is much higher in peak power compared to the oscillations on the top of the pulse. We hypothesize that it is necessary to achieve a threshold current, and a concomitant threshold transient magnetic field, to sufficiently align the magnetic moments for this setup. Thus, we suspect that stronger oscillations will occur for 50 \(\Omega\) and 25 \(\Omega\) NLTLs when magnetic field strengths become comparable to those generated in the 10 \(\Omega\) NLTL for the voltages used here. This threshold would theoretically differ for other ferrites/composites since the hysteresis behavior of the ferrite depends on numerous factors, such as composition, volume loading, and temperature. Although not explicitly discussed in this paper, the results presented here also suggest the importance of future material development. This study and our previous NLTL system studies [24; 29] have focused on various loadings of BST and NZF. However, other nonlinear materials could be used or developed to adjust nonlinear permittivity and permeability to better tune system impedance or output frequency by changing the conditions of the ensuing shockwave. Additionally, NLTLs used in this topology will ultimately be limited by the breakdown strength of the composite located between the inner and outer electrode. Previous studies have shown that a composite, such as the one presented here, has a DC breakdown strength of 401.20 \(\pm\) 150.73 kV/cm [21]. Thus, higher charging voltages are feasible if flashover can be prevented. The present setup has been limited by flashover between the high voltage side of the spark gap housing and the load. Future studies may address this issue by altering spark gap geometry and/or completely redesigning the switch to achieve higher charging voltages. Alternatively, the setup also provides the ability to explore other switching technologies. While spark gaps offer ease of manufacturing and simplicity, using them comes at the cost of repetition rate, which causes concern for achievable average output powers. As such, solid state switches are an appealing replacement for the spark gap in our system. Due to the voltage standoff requirements of the system, insulated-gate bipolar transistors (IGBTs) and power MOSFETs are an attractive alternative. Combinations of IGBTs in series and parallel configurations have successfully been used in modulators with voltage levels ranging from 1-150 kV with peak current amplitudes ranging from 0-5000 A and pulse repetition frequencies greater than 40 kHz [30; 31]. While such systems have been realized, ensuring that the load is shared equally among the switch configuration is paramount for ensuring device survivability [31]. Compared to closing switches, semiconductor opening switches (SOS) make the inductance in the circuit an active, rather than a passive (or stray) component [32]. Thus, using an opening circuit results in transferring energy to the load in a shorter time and with greater voltage amplitude compared to the closing circuit [32].