Determination of plasma pinch time and effective current radius of double planar wire array implosions from current measurements on a 1-MA linear transformer driver

Abstract

Implosions of planar wire arrays were performed on the Michigan Accelerator for Inductive Z-pinch Experiments, a linear transformer driver (LTD) at the University of Michigan. These experiments were characterized by lower than expected peak currents and significantly longer risetimes compared to studies performed on higher impedance machines. A circuit analysis showed that the load inductance has a significant impact on the current output due to the comparatively low impedance of the driver; the long risetimes were also attributed to high variability in LTD switch closing times. A circuit model accounting for these effects was employed to measure changes in load inductance as a function of time to determine plasma pinch timing and calculate a minimum effective current-carrying radius. These calculations showed good agreement with available shadowgraphy and x-ray diode measurements.

MA-class linear transformer driver for Z -pinch research

“…The trigger circuit is a fundamental component of LTD generators, since accurate control (and monitoring) of the closing time for each switch in an LTD is essential to deliver the desired current pulse to the load [25]. For example, triggering the switches in a predetermined sequence allows tailoring of the current pulse [26], while, in order to have the fastest rise time and maximum peak current from a single LTD cavity, the switches should fire simultaneously [27]. The switches used in the CESZAR LTD have two 6.4 mm gaps symmetric around a trigger midplane.…”

A Primer on Pulsed Power and Linear Transformer Drivers for High Energy Density Physics Applications

“…However, all of the bricks in an LTD cavity are combined in parallel, thus L equiv = L brick /N bricks and R equiv = R brick /N bricks . For MAIZE, N bricks = 40, L brick ≈ 240 nH, and R brick ≈ 660 mΩ; therefore, L equiv ≈ 6 nH and R equiv ≈ 16.5 mΩ [110]. This means that about half of the overall ≈ 20-nH LTD cavity inductance on MAIZE is from the bricks and the outer regions of the power feed, while the remaining half comes from the inner power feed and the load.…”

“…This means that about half of the overall ≈ 20-nH LTD cavity inductance on MAIZE is from the bricks and the outer regions of the power feed, while the remaining half comes from the inner power feed and the load. Note that the outer ≈ 10-nH inductance on MAIZE is essentially fixed, while the inductance of the inner power feed and load can vary significantly from one experimental configuration to the next-e.g., from 8 nH to 23 nH for some of the configurations tested on MAIZE so far [110]. Also note that the L/R time on MAIZE is τ L/R = L/R ≈ 1.2 µs τ peak (meaning the voltage is primarily an inductive voltage: V ≈ Lİ + IL IR) while the RC time constant is τ RC = RC ≈ 26 ns τ peak (meaning the capacitors can discharge and recharge fast enough to support resonant oscillations).…”

“…It is also important to note that associated with the cores are resistive-like energy losses due to the hysteresis curve and Eddy currents [33]; these losses can be modeled using a resistor element R core (t) in the circuit modeling of an LTD (see, for example, Refs. [32], [33], [110]).…”

“…(2) the development of diagnostic instruments and techniques that can be transferred to Z and NIF; (3) a collaboration with the University of Nevada, Reno to study wire-array z-pinches for x-ray source development [109], [110]; (4) the study of power flow within LTDs and the coupling of LTDs to HED matter in general; (5) the study of magnetized plasma flows for laboratory astrophysics; and (6) an effort to create and study pulsed fusion neutron sources (e.g., deuterium gas-puff z-pinches and/or dense plasma focuses) as well as pulsed x-ray sources (e.g., gas-puff z-pinches with noble gases).…”