Analysis of electron flow current in the vacuum magnetically-insulated-transmission-line for a 15 MA Z-pinch driver

The 15 MA driver is powered by 24 linear-transformer-driver (LTD) modules connected electrically in parallel. The stack-MITL system of the 15 MA driver adopts a four-level design. It is expected that the primary sources deliver more than 15 MA to a physics load. The typical 1D steady-state pressure-balance model is adopted to calculate the electron flow current of the outer magnetically-insulated transmission lines (MITLs) of the 15 MA driver after the magnetic insulation is established. The cathode plasma expansion and the collisional flow electrons are considered on the basis of that model. Multiple designs with different characteristic parameters of the MITL system are designed including the vacuum impedance of the constant-impedance segment of the outer-MITL, the minimum gap of the outer-MITL, and the location of the Post-hole convolute (PHC). The flow current of these designs are calculated in three typical times (1/3 peak load current time, peak load current time and 5 ns before the z-pinch stagnation) by establishing the equivalent circuit model of the 15 MA driver. The influence of these characteristic parameters on the electrical pulse transmission and convergence of the 15 MA driver is obtained. The calculation results show that the electron flow current at the end of MITL is greatly affected by the impedance of the end of MITL after entering the steady state magnetic insulation. The flow current decreases from 184.7 kA to 106.9 kA, while the load current decreased by 0.5 MA, as the vacuum impedance increases from 0.42 Ω to 0.84 Ω. This is mainly because that the central inductance increases by about 1.43 nH (from 9.94 nH to 11.37 nH). In the time of 5 ns before load stagnation, the flow current decreases from 181.9 kA to 85.1 kA as the minimum gap of the outer-MITL increases from 7.10 mm to 14.00 mm, and the peak load current only drops by about 0.1 MA. The flow current and load current decrease slowly as the location radius of the PHC decreases until the radius decreases to 7.65 mm. The research in this paper is helpful to guide the structure optimization for the central converging region of future Z-pinch drivers.