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.