The Electrothermal Instability On Pulsed Power Ablations Of Thin Foils

The electrothermal instability (ETI) arises from the temperature dependence of electrical resistivity, $\eta (\mathrm {T})$, in current-carrying materials. When $\delta \eta / \delta \mathrm {T}>0$, as in condensed metals, ETI tends to cause exponentially growing temperature perturbations perpendicular to the direction of current. In pulsed power explosions of wires, foils, or liners, this causes sections of the target to ablate faster than the bulk material, creating an interface perturbation. This interface perturbation has been shown to be responsible for seeding the Magneto-Rayleigh-Taylor (MRT) instability and other MHD instabilities ¹ , which are significant impediments to stable implosions in magnetized liner implosion fusion experiments.An experimental study at the University of Michigan ² has demonstrated the exponential growth of ETI as a temperature perturbation on thin (100s of nm thickness) aluminum foils during atmospheric ablations. Additional experiments have been performed to evaluate material dependence of ETI and its coupling to later-time instabilities. Thin foils of varying materials are ablated using a 1-MA linear transformer driver; an ultrafast 12-frame camera with 5 ns temporal resolution and $70 \mu \mathrm {m}$ spatial resolution collects visible self-emission images. Some shots also add shadowgraphy using collinear, frequency-doubled Nd:Yag laser pulses (532 nm, 2 ns per pulse) synchronized with the framing camera. Preliminary results on exploding liners have shown that tantalum foils exhibit significantly reduced seeding of sausage, kink and MRT instabilities compared to aluminum in identical geometry. This agrees with existing ETI theory ³ , which holds that the most important parameter for determining the integral growth of ETI on a pulsed power ablation is the ratio of the target's critical temperature to its melting temperature; tantalum has one of the lowest such ratios of all pure metals. These results indicate that plasma instabilities may be substantially reduced by suppressing ETI seeding.