3-D electromagnetic simulation of monolithic radial transmission lines for Z-pinch

In the design of future Z-pinch driver the monolithic radial transmission lines were used to combine the outputs of many pulse generators to Z-pinch load. An important aspect of the previous studies is that the researchers had dealt usually with the nonuniform lines by circuit simulation on the assumption that the voltage wave transmits in quasi-TEM mode. In order to test thoroughly the quasi-TEM mode approximation, we performed 3-D electromagnetic simulation of the monolithic water-insulated radial transmission lines with a code called CST microwave studio. In consideration of the pulse generator being huge in size, the total number of the pulse generators that can be put around the periphery of one monolithic radial transmission line is limited. The pulse generators were installed on 3 stacked levels that drive 6 stacked levels of the monolithic radial transmission lines. The parameters for each radial transmission line are Z_in=0.203 Ω at r₂=36.83 m and Z_out=2.16 Ω at r₁=3 m, which means a line length of 33.83 m and a one-way transit time of 1009 ns. The impedance profile of the nonuniform line is exponential or Gaussian. The input voltage is half-sine shape with an angular frequency of 14 Mrad/s, corresponding to pulse width (FWHM) of 150 ns, which is close to the pulse shape for Zpinch. In the simulation, the monolithic radial transmission line was considered as n fan-shaped radial transmission lines in parallel. Having an angle of 2π/n, each fan-shaped line connects a pulsed generator at the input end and a resistor of n·Z_out at the output end. In this case, parameter n, the total number of the fan-shaped lines is equal to the total number of the pulsed generators to drive the monolithic radial transmission line. From the electromagnetic simulation it was found that the transmitted power efficiency increases as n increases, but this increase shows a saturated value of about - 1% when n is larger than 160. The transmitted power efficiency for the exponential line is higher than that for the Gaussian lines, which is similar to that from the circuit simulation. However, all the transmitted power efficiencies obtained by the electromagnetic simulation are at least 10% lower than those obtained by the circuit simulation, indicating the existence of non-TEM modes during the transmission. If the pulse generator can be made much smaller in size, all the pulse generators may be put around the periphery of one monolithic radial transmission line. In this case, only one monolithic radial line is needed. Z_in and Z_out for this monolithic radial line should be changed from 0.203 Ω and 2.16 Ω to 0.203Ω/6 and 2.16Ω/6, respectively. The transmitted power efficiency increases to 89%.