Comparison of Nonuniform Transmission Lines With Gaussian and Exponential Impedance Profiles for $Z$-Pinch

The circuit simulation of nonuniform transmission lines that were under consideration for the next generation of petawatt-class
$Z$
-pinch drivers was performed. It was confirmed that the power-transport efficiency of the designed radial transformer with an exponential impedance profile is higher than that with Gaussian profiles. Based on Fourier's theorem and the principle of superposition, it was found that there are considerable low-frequency components for the input voltage of a half-sine wave with an angular frequency of 14 Mrad/s. Compared with the exponential transformer, the Gaussian transformers amplify the low-frequency components to a lower extent, which makes the difference in power efficiency between the two types of transformers. The radial transformer also serves as a passive high-pass filter, and the Gaussian transformer may give better performance than the exponential transformer does if the signal transport rather than the power transport is concerned.