## 4 Discussion  
The NLTLs presented here utilize a combination of both ferroelectric and ferrimagnetic materials. As such, one naturally wonders the degree to which each nonlinear material is responsible for oscillation formation. The power spectrum density and the resulting frequencies of enhancement suggest that the ferrite in the line is primarily responsible for the observed oscillations because the low-GHz frequencies generated are similar to the frequencies generated by other gyromagnetic lines [26]. For ferrites, the damped gyromagnetic precession of the electrons' magnetic moment modulates the incident pulse; however, for ferroelectrics, the motion of the induced dipole moment induces the modulation [21]. The magnetic moments may precess at much faster rates compared to dipole moments, generating higher frequencies. In this setup, we hypothesize that the output oscillations are directly tied to the impedance of the line because a larger impedance correlates to a lower transient current, which correlates to a lower transient magnetic field. This, combined with the mechanism of pulse formation, results in a more effective gyration of the material's magnetic moments as the pulse propagates. The gyration of the material's magnetic moment modulates the pulse and forms oscillations through gyromagnetic precession. Lines that utilize ferroelectrics are typically limited to output frequencies of hundreds of MHz, making it unlikely that BST causes the low GHz lobes observed in the power spectrum of the 10 \(\Omega\) line [2]. Thus, while BST is crucial for tuning impedance, minimizing loss tangents, and preventing breakdown within the line [21], it does not necessarily provide additional nonlinearity under these conditions [25]. Additionally, the volume-averaged electric field suggests that BST is not in the nonlinear regime at these charging voltages [27; 28]. Thus, we conclude that the gyromagnetic precession of the ferrite's moments is most likely responsible for the RF formation at these charging voltages. Future efforts will assess higher charging voltages that will push BST into a more nonlinear region so that the BST and NZF can harmoniously aid in RF generation to enhance NLTL performance [25]. We hypothesize that if both the NZF and BST can harmoniously modulate the pulse, a broader power spectrum will result. We are currently working on preventing flashovers at the spark gap of our system to experimentally test this hypothesis. NLTLs that utilize ferrites frequently use an external magnetic field as an auxiliary system to allow for coherent precession of the magnetic moments; however, we do not require one here. We have hypothesized that the observed oscillations result from magnetic moment precession; however, our experimental setup does not use an external field to  
Figure 4: Measured output spectrum for 10, 25, and 50 \(\Omega\) NLTLs at 20 kV charging voltages given in (**a**) logarithmic and (**b**) linear power. allow for the moments to precess coherently. This provides the benefit of reduced system weight and complexity but warrants a discussion on how such a result is possible. We conjecture that this behavior arises due to the mechanism of PFL operation coupled with the absence of a biasing magnetic field. In this setup, all magnetic moments in the line are randomly oriented initially and the line is charged to a voltage \(V_{c}\). Once the spark gap triggers, a voltage of \(V_{c}/2\) is applied to the load and a voltage step travels down the line toward the power source. Upon reaching the source, the voltage step is reflected due to the high impedance, which in our case is \(5\,\mathrm{M}\Omega\), and propagates back up the line uninverted. This gives a pulse width of  
\[P_{w}=\frac{2L}{c_{m}} \tag{2}\]  
where \(L\) is the NLTL length and \(c_{m}\) is the speed of light in the NLTL medium.