An Iterative Method to Determine the Vacuum Impedance of Magnetically Insulated Transmission Line System

Abstract

In this article, the dimensionless ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E/{\textit{cB}}$ </tex-math></inline-formula> at the starting point of constant-gap section of the magnetically insulated transmission line (MITL) at the time of peak MITL voltage was used as a figure of merit of a disk MITL. Taking a 15-MA driver as an example, the equivalent circuit model and the impedance iterative method are established by means of the TL-code circuit simulations. The vacuum impedance of the four-level outer-MITLs is determined. In particular, when the target ratio ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E/{\textit{cB}})_{i}$ </tex-math></inline-formula> is set to 0.25 (the ratio of flow current to anode current <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{f}/I_{a}$ </tex-math></inline-formula> is 3.12%), the impedance of the four-level MITLs is 1.70, 2.12, 2.88, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.16~\Omega $ </tex-math></inline-formula> . When ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E/{\textit{cB}})_{i}$ </tex-math></inline-formula> of the four-level MITLs is set to 0.15, 0.18, 0.20, and 0.22 (the ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{f}/I_{a}$ </tex-math></inline-formula> is 1.23%), the impedances are 2.68, 2.89, 3.06, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.02~\Omega $ </tex-math></inline-formula> , respectively.