Dispersion Relation of Stratified Electrothermal Instability in Warm, Dense, Tamped Aluminum-6061 with Current in a Skin Layer

The dispersion relation of the stratified electrothermal instability (ETI) has been measured on the surface of aluminum-6061 rods pulsed with rapidly rising lineal current density (
$3\times 10^{15}$
A m-1s-1 for 70 ns). The
$500-\mu \mathrm{m}$
rod radius was much larger than the electrical skin depth. A transparent,
$70-\mu \mathrm{m}$
. -thick, Parylene-N [poly(p-xylylene)
$({}_{8}\text{CH}_{8})_{n}$
] coating tamped the aluminum expansion and suppressed surface plasma. This enabled persistent observation, with time-resolved microscopy (
$3-\mu \mathrm{m}$
resolution, 2–13 ns gate), of discrete azimuthally-correlated stratified emission structures perpendicular to the current. Intensified CCD images of the surface were converted to temperature maps via radiometric calculations, assuming blackbody emission. Fourier analysis of these maps indicates the strata are comprised of temperature perturbations that grow exponentially at the rate \begin{equation*}\gamma(k)=0.06\text{ns}^{-1}-(0.4\text{ns}^{-1}\mu \mathrm{m}^{2}\text{rad}^{-2})k^{2},\end{equation*} where
$k < 0.4\mu \mathrm{m}/\text{rad}$
is the perturbation axial wavenumber. The aluminum was in the warm dense matter state, with density ~ 1 g/cm3 and temperature ~ 7,000 K.